ETABS Composite Floor Frame Design Manual

Computers and Structures, Inc.Berkeley, California, USA

Version 8January 2002

ETABS®

Integrated Building Design Software

Composite Floor Frame Design Manual

Copyright Computers and Structures, Inc., 1978-2002.The CSI Logo is a trademark of Computers and Structures, Inc.

ETABS is a trademark of Computers and Structures, Inc.Windows is a registered trademark of Microsoft Corporation.

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Copyright

The computer program ETABS and all associated documentation are proprietary andcopyrighted products. Worldwide rights of ownership rest with Computers andStructures, Inc. Unlicensed use of the program or reproduction of the documentation inany form, without prior written authorization from Computers and Structures, Inc., isexplicitly prohibited.

Further information and copies of this documentation may be obtained from:

Computers and Structures, Inc.1995 University Avenue

Berkeley, California 94704 USA

Phone: (510) 845-2177FAX: (510) 845-4096

e-mail: [email protected] (for general questions)e-mail: [email protected] (for technical support questions)

web: www.csiberkeley.com

DISCLAIMER

CONSIDERABLE TIME, EFFORT AND EXPENSE HAVE GONE INTO THEDEVELOPMENT AND DOCUMENTATION OF ETABS. THE PROGRAM HASBEEN THOROUGHLY TESTED AND USED. IN USING THE PROGRAM,HOWEVER, THE USER ACCEPTS AND UNDERSTANDS THAT NO WARRANTYIS EXPRESSED OR IMPLIED BY THE DEVELOPERS OR THE DISTRIBUTORSON THE ACCURACY OR THE RELIABILITY OF THE PROGRAM.

THIS PROGRAM IS A VERY PRACTICAL TOOL FOR THE DESIGN/CHECK OFSTEEL STRUCTURES. HOWEVER, THE USER MUST THOROUGHLY READ THEMANUAL AND CLEARLY RECOGNIZE THE ASPECTS OF COMPOSITE DESIGNTHAT THE PROGRAM ALGORITHMS DO NOT ADDRESS.

THE USER MUST EXPLICITLY UNDERSTAND THE ASSUMPTIONS OF THEPROGRAM AND MUST INDEPENDENTLY VERIFY THE RESULTS.

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©COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001

COMPOSITE BEAM DESIGN

Contents

General Composite Beam Design Information

1 General Design InformationDesign Codes 1-1Units 1-1Beams Designed as Composite Beams 1-1

Material Property Requirements for Com-posite Beams 1-2

Other Requirements for CompositeBeams 1-2

Frame Elements Designed by Default asComposite Beams 1-3

Overwriting the Frame Design Procedurefor a Composite Beam 1-3

How the Program Optimizes Design Groups 1-5Using Price to Select Optimum Beam

Sections 1-6Design Load Combinations 1-8Analysis Sections and Design Sections 1-8Output Stations 1-10

2 Composite Beam Design ProcessDesign Process for a New Building 2-1Check Process for an Existing Building 2-4

3 Interactive Composite Beam DesignMember Identification 3-1Section Information 3-2Acceptable Sections List 3-3ReDefine 3-4

Composite Beam Design Manual

ii

Temporary 3-5Show Details 3-5

4 Output Data Plotted Directly on the ModelOverview 4-1Labels Displayed on the Model 4-2Design Data 4-3Stress Ratios 4-4Deflection Ratios 4-5

5 Input DataGeneral 5-1Using the Print Composite Beam Design

Tables Form 5-1Material Properties Input Data 5-2Section Properties Input Data 5-3Deck Properties Input Data 5-4Design Preferences Input Data 5-6Beam Overwrites Input Data 5-8

6 Output DataOverview 6-1Using the Print Composite Beam Design

Tables Form 6-1Summary of Composite Beam Output 6-2

7 Composite Beam PropertiesBeam Properties 7-1Metal Deck and Slab Properties 7-3Shear Stud Properties 7-5Cover Plates 7-5

8 Effective Width of Concrete SlabLocation Where Effective Slab Width is

Checked 8-1Multiple Deck Types or Directions Along the

Beam Length 8-2Effect of Diagonal Beams on Effective Slab

Width 8-6

Contents

iii

Effect of Openings on Effective SlabWidth 8-8

Effective Slab Width and TransformedSection Properties 8-9

9 Beam Unbraced LengthOverview 9-1Determination of the Braced Points of a

Beam 9-2User-Defined Unbraced Length of a Beam

Overview 9-3User-Specified Uniform and Point

Bracing 9-4Design Check Locations 9-7

10 Design Load CombinationsOverview 10-1Special Live Load Patterning for

Cantilever Back Spans 10-2Special Live Load Patterning for

Continuous Spans 10-4

11 Beam Deflection and CamberDeflection 11-1Camber 11-4

12 Beam VibrationOverview 12-1Vibration Frequency 12-1Murray's Minimum Damping Requirement 12-4

Initial Displacement Amplitude 12-4Effective Number of Beams Resisting

Heel Drop Impact 12-6References 12-7

13 Distribution of Shear Studs on a CompositeBeamOverview 13-1Composite Beam Segments 13-1


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Physical End of the Beam Top Flange 13-2Distribution of Shear Studs Within a

Composite Beam Segment 13-5How the Program Distributes Shear Studs

on a Beam 13-5Equations Used When the Program

Works from Left to Right 13-8Equations Used When the Program

Works from Right to Left 13-9Minimum and Maximum Number of

Shear Studs in a Composite BeamSegment 13-11

A Note About Multiple Design LoadCombinations 13-11

14 The Number of Shear Studs that Fit in aComposite Beam SegmentGeneral 14-1Solid Slab or Deck Ribs Oriented Parallel to

Beam Span 14-2Deck Ribs Oriented Perpendicular to Beam

Span 14-6Different Deck Type or Orientation on Beam

Sides 14-8

15 User-Defined Shear Stud PatternsSpecifying a User-Defined Shear Connector

Pattern 15-1Uniformly Spaced Shear Studs Over the

Length of the Beam 15-2Additional Shear Studs in Specified Sections

of Beam 15-4Defining Additional Beam Sections 15-4Example of a User-Defined Shear Stud

Pattern 15-8How the Program Checks a Beam with User-

Defined Shear Studs 15-9

Contents

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Composite Beam Design Specific to AISC-ASD89

16 General and NotationIntroduction to the AISC-ASD89 Series of

Technical Notes 16-1Notation 16-2

17 PreferencesGeneral 17-1Using the Preferences Form 17-1Preferences 17-2Factors Tab 17-3Beam Tab 17-3Deflection Tab 17-4Vibration Tab 17-5Price Tab 17-6

18 OverwritesGeneral 18-1Using the Composite Beam Overwrites

Form 18-2Overwrites 18-3Beam Tab 18-4Bracing (C) Tab and Bracing Tab 18-6Deck Tab 18-9Shear Studs Tab 18-10Deflection Tab 18-13Vibration Tab 18-14Miscellaneous Tab 18-14EQ Factor 18-15

19 Width-to-Thickness ChecksOverview 19-1Limiting Width-to-Thickness Ratios for

Flanges 19-2Compact Section Limits for Flanges 19-2Noncompact Section Limits for

Flanges 19-2


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Limiting Width-to-Thickness Ratiosfor Webs 19-3Compact Section Limits for Webs 19-3Noncompact Section Limits for Webs 19-3

Limiting Width-to-Thickness Ratios forCover Plates 19-4Compact Section Limits for Cover

Plates 19-5Noncompact Section Limits for Cover

Plates 19-5

20 Transformed Section Moment of InertiaBackground 20-2Properties of Steel Beam (Plus Cover

Plate) Alone 20-4Properties of the Composite Section

General Calculation Method 20-7Equivalent Hand Calculation Method to

Calculate the Distance ye 20-10Background Equations 20-11

Hand Calculation Process for ye 20-17Equivalent Hand Calculation Method to

Calculate the Composite Properties 20-18

21 Elastic Stresses with Partial CompositeConnectionEffective Moment of Inertia for Partial

Composite Connection 21-1Effective Section Modulus Referred

to the Extreme Tension Fiber 21-2Location of the ENA for Partial

Composite Connection 21-3Steel Section Stresses for Partial

Composite Connection 21-5Concrete Slab Stresses for Partial

Composite Connection 21-6

22 Allowable Bending StressesGeneral 22-1

Contents

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Allowable Bending Stress for Steel BeamAlone 22-2

Allowable Bending Stresses for PositiveBending in the Composite Beam 22-6

23 Bending Stress ChecksBending Stress Checks Without

Composite Action 23-1Positive Moment in a Composite Beam 23-2Important Notes Regarding Unshored

Composite Beams 23-5Steel Stress Checks 23-5Concrete Stress Checks 23-6

24 Beam Shear ChecksShear Stress Check 24-1

Typical Case 24-1Slender Web 24-2

Copes 24-3Shear Rupture Check 24-4Limitations of Shear Check 24-7

25 Shear StudsOverview 25-1Shear Stud Connectors 25-1

Reduction Factor when Metal Deck isPerpendicular to Beam 25-2

Reduction Factor when Metal Deck isParallel to Beam 25-3

Horizontal Shear for Full CompositeConnection 25-4

Number of Shear Studs 25-5Between the Output Station with

Maximum Moment and thePoint of Zero Moment 25-6

Between Other Output Stations andPoints of Zero Moment 25-6


viii

26 Calculation of the Number of Shear StudsBasic Equations 26-1Shear Stud Distribution Example 1 26-4Shear Stud Distribution Example 2 26-8Shear Stud Distribution Example 3 26-13

Detailed Calculations 26-15

27 Input DataBeam Overwrites Input Data 27-1

28 Output DetailsShort Form Output Details 28-1

Composite Beam Design Specific to AISC-LRFD93

29 General and NotationAISC-LRFD93 Design Methodology 29-1Notation 29-7

30 PreferencesGeneral 30-1Using the Preferences Form 30-1Preferences 30-2Factors Tab 30-3Beam Tab 30-4Deflection Tab 30-5Vibration Tab 30-5Price Tab 30-6

31 OverwritesGeneral 31-1Using the Composite Beam Overwrites

Form 31-2Resetting Composite Beam

Overwrites to Default Values 31-3Overwrites 31-3Beam Tab 31-4Brace (C) Tab and Bracing Tab 31-6

Contents

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Deck Tab 31-9Shear Studs Tab 31-10Deflection Tab 31-12Vibration Tab 31-13Miscellaneous Tab 31-14

32 Design Load CombinationsStrength Check for Construction Loads 32-1Strength Check for Final Loads 32-2Deflection Check for Final Loads 32-2Reference 32-3

33 Compact and Noncompact RequirementsOverview 33-1Limiting Width-to-Thickness Ratios for

Flanges 33-2Compact Section Limits for Flanges 33-2Noncompact Section Limits for

Flanges 33-2Limiting Width-to-Thickness Ratios for

Webs 33-3Compact Section Limits for Webs 33-3Noncompact Section Limits for Webs 33-4

Limiting Width-to-Thickness Ratios forCover Plates 33-5Compact Section Limits for Cover

Plates 33-5Noncompact Section Limits for Cover

Plates 33-6

34 Composite Plastic Moment Capacity forPositive BendingOverview 34-1Location of the Plastic Neutral Axis 34-2

PNA in the Concrete Slab Abovethe Steel Beam 34-5

PNA within the Beam Top Flange 34-8PNA within the Beam Top Fillet 34-9PNA within the Beam Web 34-10


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PNA within the Beam Bottom Fillet 34-11PNA within the Beam Bottom Flange 34-12PNA within the Cover Plate 34-13Calculating the PNA Location 34-15

Plastic Moment Capacity for PositiveBending 34-16

35 Composite Section Elastic MomentCapacityPositive Moment Capacity with an Elastic Stress

Distribution 35-1

36 Moment Capacity for Steel Section AloneOverview 36-1Steel Beam Properties 36-1Moment Capacity for a Doubly Symmetric Beam

or a Channel Section 36-2Lateral Unbraced Length Checks 36-3Yielding Criteria in AISC-LRFD93 Section

F1.1 36-5Lateral Torsional Buckling Criteria in

AISC-LRFD93 Section F1.2a 36-5AISC-LFRD Appendix F1(b) Equation

A-F1-3 46-5Moment Capacity for a Singly Symmetric

Beam with a Compact Web 36-7AISC-LFRD93 Equation A-F1-1 for

WLB 36-8AISC-FLRD93 Equation A-F1-1 for

FLB 36-8AISC-FLRD93 Equation A-F1-3 for

FLB 36-9AISC-FLRD93 Equation A-F1-1 for

LTB 36-9AISC-FLRD93 Equation A-F1-2 for

LTB 36-10Moment Capacity for a Singly Symmetric

Beam with a Noncompact Web 36-11

Contents

xi

AISC-LFRD93 Equation A-F1-3 forWLB 36-12

37 Partial Composite Connection with a Plas-tic Stress DistributionEstimating the Required Percent Composite

Connection 37-1Calculating MPFconc 37-2Location of PNA 37-3

Determining the Effective Portion ofthe Concrete Slab 37-4

Moment Capacity of a Partially CompositeBeam with a Plastic StressDistribution 37-6

38 Bending and Deflection ChecksBending Check Locations 38-1Bending Check 38-1Deflection Check 38-2

39 Shear ConnectorsShear Stud Connectors 39-1Horizontal Shear for Full Composite

Connection 39-1Number of Shear Connectors 39-2

Between Maximum Moment andPoint of Zero Moment 39-2

Between Point Load and Point ofZero Moment 39-3

40 Beam Shear CapacityShear Capacity 40-1Checking the Beam Shear 40-2Limitations of Beam Shear Check 40-2

41 Input DataBeam Overwrites Input 41-1


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42 Output DetailsShort Form Output Details 42-1Long Form Output Details 42-8

Design Codes Technical Note 1 - 1



Technical Note 1General Design Information

This Technical Note presents some basic information and concepts that areuseful when performing composite beam design using this program.

Design CodesThe design code is set using the Options menu > Preferences > Compos-ite Beam Design command. You can choose to design for any one designcode in any one design run. You cannot design some beams for one code andothers for a different code in the same design run. You can however performdifferent design runs using different design codes without rerunning theanalysis.

UnitsFor composite beam design in this program, any set of consistent units can beused for input. Typically, design codes are based on one specific set of units.The documentation in the Composite Beam Design series of Technical Notes ispresented in kip-inch-seconds units unless otherwise noted.

Again, any system of units can be used to define and design a building in theprogram. You can change the system of units at any time using the pull-downmenu on the Status Bar or pull-down menu on individual forms where avail-able.

Note:

You can use any set of units in composite beam design and you can change the units "onthe fly."

Beams Designed as Composite BeamsSection Requirements for Composite BeamsOnly I-shaped and channel-shaped beams can be designed as compositebeams. The I-shaped and channel-shaped beams can be selected from the

General Design Information Composite Beam Design

Technical Note 1 - 2 Beams Designed as Composite Beams

built-in program section database, or they can be user defined. The user-defined sections can be specified using the Define menu > Frame Sectionscommand and clicking either the Add I/Wide Flange or the Add Channel op-tion.

Note that beam sections that are defined in Section Designer are alwaystreated as general sections. Thus, if you define an I-type or channel-typesection in Section Designer, the program will consider it as a general section,not an I-shaped or channel-shaped section, and will not allow it to be de-signed as a composite beam.

Note:

Beam sections defined in the section designer utility cannot be designed as compositebeams.

Material Property Requirement for Composite BeamsIf a beam is to be designed as a composite beam, the Type of Design associ-ated with the Material Property Data assigned to the beam must be Steel. Usethe Define menu > Material Properties > Modify/Show Materials com-mand to check your beams.

Other Requirements for Composite BeamsThe line type associated with the line object that represents a compositebeam must be "Beam." In other words, the beam element must lie in a hori-zontal plane. Right click on a line object to bring up the Line Information formto check the Line Type.

For composite beams, the beam local 2-axis must be vertical. The Local axis 2Angle is displayed on the Assignments tab of the Line Information form.

Note:

The line object representing a composite beam should span from support to support.Composite beams should not be modeled using multiple, adjacent line objects betweensupports for a single composite beam.

The line object representing a composite beam should span from support tosupport. In the case of a cantilever beam overhang, the line object shouldspan from the overhang support to the end of the beam. The cantilever beamback span should be modeled using a separate line object. If you do notmodel cantilever beams in this way, the analysis results for moments and

Composite Beam Design General Design Information

Beams Designed as Composite Beams Technical Note 1 - 3

shears will still be correct but the design performed by the Composite BeamDesign processor probably will not be correct.

Frame Elements Designed by Default as Composite BeamsThe program will design certain frame elements using the design proceduresdocumented in these Technical Notes by default. Those elements must meetthe following restrictions:

The beam must meet the section requirements described in the subsectionentitled "Section Requirements for Composite Beams" in this TechnicalNote.

The beam must meet the material property requirement described in thesubsection entitled "Material Property Requirement for Composite Beams"in this Technical Note.

The beam must meet the two other requirements described in the subsec-tion entitled "Other Requirements for Composite Beams" in this TechnicalNote.

At least one side of the beam must support deck that is specified as aDeck section (not a Slab or Wall section). The deck section can be filled,unfilled or a solid slab. When the deck is unfilled, the beam will still gothrough the Composite Beam Design postprocessor and will simply be de-signed as a noncomposite beam.

The beam must not frame continuously into a column or a brace. Bothends of the beam must be pinned for major axis bending (bending aboutthe local 3-axis).

Overwriting the Frame Design Procedure for a Composite BeamThe three procedures possible for steel beam design are:

Composite beam design

Steel frame design

No design

By default, steel sections are designed using either the composite beam de-sign procedure or the steel frame design procedure. All steel sections that


Technical Note 1 - 4 Beams Designed as Composite Beams

meet the requirements described in the previous subsection entitled "FrameElements Designed by Default as Composite Beams" are by default designedusing the composite beam design procedures. All other steel frame elementsare by default designed using the steel frame design procedures.

Change the default design procedure used for a beam(s) by selecting thebeam(s) and clicking Design menu > Overwrite Frame Design Proce-dure. This change is only successful if the design procedure assigned to anelement is valid for that element. For example, if you select two steel beams,one an I-section and the other a tube section, and attempt to change the de-sign procedure to Composite Beam Design, the change will be executed forthe I-section, but not for the tube section because it is not a valid section forthe composite beam design procedure. A section is valid for the compositebeam design procedure if it meets the requirements specified in the subsec-tions entitled "Section Requirements for Composite Beams," "Material Prop-erty Requirement for Composite Beams" and "Other Requirements for Com-posite Beams" earlier in this Technical Note.

Note that the procedures documented for composite beam design allow fordesigning a beam noncompositely. One of the overwrites available for com-posite beam design is to specify that selected beams are either designed ascomposite, noncomposite but still with a minimum number of shear studsspecified, or noncomposite with no shear studs. These overwrites do not af-fect the design procedure. Changing the overwrite to one of the noncompositedesigns does not change the design procedure from Composite Beam Designto Steel Frame Design. The noncomposite design in this case is still performedfrom within the Composite Beam Design postprocessor.

Using the composite beam design procedure, out-of-plane bending is not con-sidered and slender sections are not designed. This is different from the SteelFrame Design postprocessor. Thus, the design results obtained for certainbeams may be different, depending on the design procedure used.

Finally, note that you can specify that the composite beam design proceduresare to be used for a beam even if that beam does not support any deck, or forthat matter, even if no slab is specified. In these cases, the beam will be de-signed as a noncomposite beam by the Composite Beam Design postproces-sor.


How the Program Optimizes Design Groups Technical Note 1 - 5

How the Program Optimizes Design GroupsThis section describes the process the program uses to select the optimumsection for a design group. In this description, note the distinction betweenthe term section, which refers to a beam section in an auto select sectionlist, and the term beam, which refers to a specific element in the designgroup.

When considering design groups, the program first discards any beam in thedesign group that is not assigned an auto select section list.

Next, the program looks at the auto select section list assigned to each beamin the design group and creates a new list that contains the sections that arecommon to all of the auto select section lists in the design group. The pro-gram sorts this new common section list in ascending order, from smallestsection to largest section based on section weight (area).

Note:

When designing with design groups, the program attempts to quickly eliminate inade-quate beams.

The program then finds the beam with the largest positive design moment inthe design group, or the "pseudo-critical beam." The program then checks thedesign of the pseudo-critical beam for all sections in the common section list.Any sections in the common section list that are not adequate for the pseudo-critical beam are discarded from the common section list, making the listshorter. This new list is the shorter common section list. The shorter commonsection list is still in ascending order based on section weight (area).

Now the program checks all beams in the design group for the first section(smallest by weight [area]) in the shorter common section list. If the optimi-zation is being performed on the basis of beam weight and the section is ade-quate for all beams in the design group, the optimum section has been iden-tified. If the section is not adequate for a beam, the next higher section in theshorter common section list is tried until a section is found that is adequatefor all beams in the design group.

If the optimization is based on price instead of weight, the program finds thefirst section in the shorter common section list (i.e., the one with the lowestweight) that is adequate for all beams. Next it calculates the cost of this first


Technical Note 1 - 6 Using Price to Select Optimum Beam Sections

adequate section and then determines the theoretical heaviest section thatcould still have a cost equal to the adequate section by dividing the total priceof the beam with the adequate section (steel plus camber plus shear connec-tors) by the unit price of the steel. This assumes that when the cost of thesteel section alone is equal to or greater than the total cost of the adequatesection, the section could not have a total cost less than the adequate sec-tion. The program then checks any other sections in the shorter common sec-tion list that have a weight less than or equal to the calculated maximumweight. If any of the other sections are also adequate, a cost is calculated forthem. Finally, the section with the lowest associated cost is selected as theoptimum section for the design group.

Regardless of whether the optimization is based on weight or cost, if all sec-tions in the shorter common section list are tried and none of them are ade-quate for all of the beams in the design group, the program proceeds to de-sign each beam in the design group individually based on its own auto sectionlist and ignores the rest of the design group. If for a particular beam none ofthe sections in the auto select section list are adequate, the program displaysresults for the section in the auto select list with the smallest controlling ratioin a red font. Note that the controlling ratio may be based on stress or deflec-tion.

Note:

By default, the program selects the optimum composite beam size based on weight, notprice.

Using Price to Select Optimum Beam SectionsBy default, when auto select section lists are assigned to beams, the programcompares alternate acceptable composite beam designs based on the weightof the steel beam (not including the cover plate, if it exists) to determine theoptimum section. The beam with the least weight is considered the optimumsection. The choice of optimum section does not consider the number of shearconnectors required or if beam camber is required.


Using Price to Select Optimum Beam Sections Technical Note 1 - 7

You can request that the program use price to determine the optimum sectionby clicking the Options menu > Preferences > Composite Beam Designcommand, selecting the Price tab and setting the "Optimize for Price" item toYes. If you request a price analysis, the program compares alternate accept-able beam designs based on their price and selects the one with the least costas the optimum section.

For the cost comparison, specify costs for steel, shear studs and beam cam-ber. The steel cost is specified as a part of the steel material property usingthe Define menu > Material Properties command. The shear stud andbeam camber costs are specified in the composite beam preferences.

The costs for steel and cambering are specified on a unit weight of the beambasis; for example, a cost per pound of the beam. The shear connector cost isspecified on a cost per connector. By assigning different prices for steel, shear

Important Note about Optimizing Beams by Weight and Price

When a beam is optimized by weight, the program internally optimizes thebeam based on area of steel (excluding the cover plate, if it exists). Thus,the weight density specified for the steel is irrelevant in such a case.

When a beam is optimized by price, the program determines the price as-sociated with the steel by multiplying the volume of the beam (includingthe cover plate, if it exists) by the weight density of the beam by the priceper unit weight specified in the material properties for the steel. The priceassociated with camber is determined by multiplying the volume of thebeam (including the cover plate, if it exists) by the weight density of thebeam by the specified price per unit weight for camber defined in the com-posite beam preferences. The price for shear connectors is determined bymultiplying the total number of shear connectors by the price per connec-tor specified in the composite beam preferences. The total price for thebeam is determined by summing the prices for the steel, camber andshear connectors. Thus, when a beam is optimized by price, the weightdensity for the steel is important and must be correctly specified for theprice to be correctly calculated.

Note that the volume of the beam is calculated by multiplying the area ofthe steel beam (plus the area of the cover plate, if used) by the length ofthe beam from center-of-support to center-of-support


Technical Note 1 - 8 Design Load Combinations

connectors and camber, you can influence the choice of optimum section. Thecost of the cover plate is not included in the comparison (but it would be thesame for all beam sections if it were included).

See the previous "Important Note about Optimizing Beams by Weight andPrice" for additional information.

Design Load CombinationsUsing the Composite Beam Design postprocessor, three separate types ofload combinations are considered. They are:

Construction load strength design load combinations

Final condition strength design load combinations

Final condition deflection design load combinations

You can specify as many load combinations as you want for each of thesetypes. In addition, the program creates special live load patterns for cantile-ver beams. See Composite Beam Design Technical Note 20 Design Load Com-binations for additional information on design load combinations for the Com-posite Beam Design postprocessor.

Analysis Sections and Design SectionsAnalysis sections are those section properties used to analyze the modelwhen you click the Analyze menu > Run Analysis command. The designsection is whatever section has most currently been designed and thus desig-nated the current design section.

Tip:

It is important to understand the difference between analysis sections and design sec-tions.

It is possible for the last used analysis section and the current design sectionto be different. For example, you may have run your analysis using a W18X35beam and then found in the design that a W16X31 beam worked. In thatcase, the last used analysis section is the W18X35 and the current designsection is the W16X31. Before you complete the design process, verify thatthe last used analysis section and the current design section are the same.


Analysis Sections and Design Sections Technical Note 1 - 9

The Design menu > Composite Beam Design > Verify Analysis vs De-sign Section command is useful for this task.

The program keeps track of the analysis section and the design sectionseparately. Note the following about analysis and design sections:

Assigning a beam a frame section property using the Assign menu >Frame/Line > Frame Section command assigns the section as both theanalysis section and the design section.

Running an analysis using the Analyze menu > Run Analysis command(or its associated toolbar button) always sets the analysis section to bethe same as the current design section.

Assigning an auto select list to a frame section using the Assign menu >Frame/Line > Frame Section command initially sets the design sectionto be the beam with the median weight in the auto select list.

Unlocking a model deletes the design results, but it does not delete orchange the design section.

Using the Design menu > Composite Beam Design > Select DesignCombo command to change a design load combination deletes the designresults, but it does not delete or change the design section.

Using the Define menu > Load Combinations command to change adesign load combination deletes the design results, but it does not deleteor change the design section.

Using the Options menu > Preferences > Composite Beam Designcommand to change any of the composite beam design preferences de-letes the design results, but it does not delete or change the design sec-tion.

Deleting the static nonlinear analysis results also deletes the design re-sults for any load combination that includes static nonlinear forces. Typi-cally, static nonlinear analysis and design results are deleted when one ofthe following actions is taken:

Use the Define menu > Frame Nonlinear Hinge Properties com-mand to redefine existing or define new hinges.


Technical Note 1 - 10 Output Stations

Use the Define menu > Static Nonlinear/Pushover Cases com-mand to redefine existing or define new static nonlinear load cases.

Use the Assign menu > Frame/Line > Frame Nonlinear Hingescommand to add or delete hinges.

Again, note that these actions delete only results for load combinations thatinclude static nonlinear forces.

Output StationsFrame output stations are designated locations along a frame element. Theyare used as locations to report output forces and to perform design, and asplotting points used for graphic display of force diagrams. When force dia-grams are plotted, exact forces are plotted at each output station and thenthose points are connected by straight lines. Output stations occur at user-specified locations and at point load locations along a beam. Designate theoutput stations for a frame element using the Assign menu.

Note:

Access the display of frame element output stations using the View menu.

For composite beam design, the program checks the moments, shears anddeflections at each output station along the beam. No checks are made at anypoints along the beam that are not output stations.

Design Process for a New Building Technical Note 2 - 1



Technical Note 2Composite Beam Design Process

This Technical Notes describes a basic composite beam design process usingthis program. Although the exact steps you follow may vary, the basic designprocess should be similar to that described herein. Separate processes aredescribed for design of a new building and check of an existing building. OtherTechnical Notes in the Composite Beam Design General series provide addi-tional information.

Design Process for a New BuildingThe following sequence describes a typical composite beam design process fora new building. Note that although the sequence of steps you follow mayvary, the basic process probably will be essentially the same.

1. Use the Options menu > Preferences > Composite Beam Designcommand to choose the composite beam design code and to review othercomposite beam design preferences and revise them if necessary. Notethat default values are provided for all composite beam design prefer-ences, so it is unnecessary to define any preferences unless you want tochange some of the default values. See AISC-ASD89 Composite Beam De-sign Technical Note 17 Preferences and AISC-LRFD93 Composite BeamDesign Technical Note 30 Preferences for more information about prefer-ences.

2. Create the building model, as described in Volumes 1 and 2.

3. Run the building analysis using the Analyze menu > Run Analysiscommand.

4. Assign composite beam overwrites, if needed, using the Design menu >Composite Beam Design > View/Revise Overwrites command. Notethat you must select beams before using this command. Also note thatdefault values are provided for all composite beam design overwrites so itis unnecessary to define overwrites unless you want to change some of

Composite Beam Design Process Composite Beam Design

Technical Note 2 - 2 Design Process for a New Building

the default values. Note that the overwrites can be assigned before or af-ter the analysis is run. See AISC-ASD89 Composite Beam Design Techni-cal Note 18 Overwrites and See AISC-LRFD93 Composite Beam DesignTechnical Note 31 Overwrites.

5. Designate design groups, if desired, using the Design menu > Compos-ite Beam Design > Select Design Group command. Note that youmust have already created some groups by selecting objects and clickingthe Assign menu > Group Names command.

6. To use design load combinations other than the defaults created by theprogram for composite beam design, click the Design menu > Compos-ite Beam Design > Select Design Combo command. Note that youmust have already created your own design combos by clicking the De-fine menu > Load Combinations command.

Note that for composite beam design, you specify separate design loadcombinations for construction loading, final loading considering strength,and final loading considering deflection. Design load combinations for eachof these three conditions are specified using the Design menu > Com-posite Beam Design > Select Design Combo command. See Compos-ite Beam Design Technical Note 10 Design Load Combinations.

7. Click the Design menu > Composite Beam Design > Start De-sign/Check of Structure command to run the composite beam design.

8. Review the composite beam design results by doing one of the following:

a. Click the Design menu > Composite Beam Design > Display De-sign Info command to display design input and output information onthe model. See Composite Beam Design Technical Note 4 Data PlottedDirectly on the Model.

b. Right click on a beam while the design results are displayed on it toenter the interactive design mode and interactively design the beam.Note that while you are in this mode, you can also view diagrams(load, moment, shear and deflection) and view design details on thescreen. See Composite Beam Design Technical Note 3 InteractiveComposite Beam Design for more information.

Composite Beam Design Composite Beam Design Process

Design Process for a New Building Technical Note 2 - 3

If design results are not currently displayed (and the design has beenrun), click the Design menu > Composite Beam Design > Inter-active Composite Beam Design command and then right click abeam to enter the interactive design mode for that beam.

c. Use the File menu > Print Tables > Composite Beam Designcommand to print composite beam design data. If you select beamsbefore using this command, data is printed only for the selectedbeams. See AISC-ASD89 Composite Beam Design Technical Note 27Input Data, AISC-LRFD93 Composite Beam Design Technical Note 41Input Data, AISC-ASD89 Composite Beam Design Technical Note 28Output Details, and AISC-LRFD93 Composite Beam Design TechnicalNote 42 Output Details for more information.

d. Use the Design menu > Composite Beam Design > Verify allMembers Passed command to verify that no members are over-stressed or otherwise unacceptable.

9. Use the Design menu > Composite Beam Design > Change DesignSection command to change the beam design section properties for se-lected beams.

10. Click the Design menu > Composite Beam Design > Start De-sign/Check of Structure command to rerun the composite beam designwith the new section properties. Review the results using the proceduresdescribed in Step 8.

11. Rerun the building analysis using the Analyze menu > Run Analysiscommand. Note that the beam section properties used for the analysis arethe last specified design section properties.

12. Click the Design menu > Composite Beam Design > Start De-sign/Check of Structure command to rerun the composite beam designwith the new analysis results and new section properties. Review the re-sults using the procedures described in Step 8.

13. Again use the Design menu > Composite Beam Design > ChangeDesign Section command to change the beam design section propertiesfor selected beams, if necessary.


Technical Note 2 - 4 Check Process for an Existing Building

14. Repeat Steps 11, 12 and 13 as many times as necessary.

Note:

Composite beam design in the program is an iterative process. Typically, the analysisand design will be rerun multiple times to complete a design.

15. Select all beams and click the Design menu > Composite Beam Design> Make Auto Select Section Null command. This removes any auto se-lect section list assignments from the selected beams.

16. Rerun the building analysis using the Analyze menu > Run Analysiscommand. Note that the beam section properties used for the analysis arethe last specified design section properties.

17. Click the Design menu > Composite Beam Design > Start De-sign/Check of Structure command to rerun the composite beam designwith the new section properties. Review the results using the proceduresdescribed above.

18. Click the Design menu > Composite Beam Design > Verify Analysisvs Design Section command to verify that all of the final design sectionsare the same as the last used analysis sections.

19. Use the File menu > Print Tables > Composite Beam Design com-mand to print selected composite beam design results if desired. SeeAISC-ASD89 Composite Beam Design Technical Note 28 Output Detailsand AISC-LRFD93 Composite Beam Design Technical Note 42 Output De-tails

It is important to note that design is an iterative process. The sections used inthe original analysis are not typically the same as those obtained at the endof the design process. Always run the building analysis using the final beamsection sizes and then run a design check using the forces obtained from thatanalysis. Use the Design menu > Composite Beam Design > VerifyAnalysis vs Design Section command to verify that the design sections arethe same as the analysis sections.

Check Process for an Existing BuildingThe following sequence is a typical composite beam check process for an ex-isting building. In general, the check process is easier than the design process

Composite Beam Design Composite Beam Design Process

Check Process for an Existing Building Technical Note 2 - 5

for a new building because iteration is not required. Note that although thesequence of steps you follow may vary, the basic process probably will be es-sentially the same.

Tip:

You can define your own shear stud patterns on the Shear Studs tab in the compositebeam overwrites. This allows you to model existing structures with composite floor fram-ing.

1. Use the Options menu > Preferences > Composite Beam Designcommand to choose the composite beam design code and to review othercomposite beam design preferences and revise them if necessary. Notethat default values are provided for all composite beam design prefer-ences so it is unnecessary to define preferences unless you want tochange some of the default preference values. See AISC-ASD89 Compos-ite Beam Design Technical Note 17 Preferences and AISC-LRFD93 Com-posite Beam Design Technical Note 30 Preferences for more informationabout preferences.

2. Create the building model, as explained in Volumes 1 and 2.

3. Run the building analysis using the Analyze menu > Run Analysiscommand.

4. Assign composite beam overwrites, including the user-defined shear studpatterns, using the Design menu > Composite Beam Design >View/Revise Overwrites command. Note that you must select beamsfirst before using this command. See AISC-ASD89 Composite Beam De-sign Technical Note 18 Overwrites and See AISC-LRFD93 Composite BeamDesign Technical Note 31 Overwrites.

5. Click the Design menu > Composite Beam Design > Start De-sign/Check of Structure command to run the composite beam design.

6. Review the composite beam design results by doing do one of the follow-ing:

a. Click the Design menu > Composite Beam Design > Display De-sign Info command to display design input and output information onthe model. See Composite Beam Design Technical Note 4 Data PlottedDirectly on the Model.


Technical Note 2 - 6 Check Process for an Existing Building

b. Right click on a beam while the design results are displayed on it toenter the interactive design and review mode and review the beam de-sign. Note that while you are in this mode you can also view diagrams(load, moment, shear and deflection) and view design details on thescreen. See Composite Beam Design Technical Note 3 InteractiveComposite Beam Design for more information.

If design results are not currently displayed (and the design has beenrun), click the Design menu > Composite Beam Design > Inter-active Composite Beam Design command and then right click abeam to enter the interactive design mode for that beam.

c. Use the File menu > Print Tables > Composite Beam Designcommand to print composite beam design data. If you select beamsbefore using this command, data is printed only for the selectedbeams.

d. Use the Design menu > Composite Beam Design > Verify allMembers Passed command to verify that no members are over-stressed or otherwise unacceptable. See AISC-ASD89 Composite BeamDesign Technical Note 27 Input Data, AISC-LRFD93 Composite BeamDesign Technical Note 41 Input Data, AISC-ASD89 Composite BeamDesign Technical Note 28 Output Details, and AISC-LRFD93 CompositeBeam Design Technical Note 42 Output Details for more information.

Member Identification Technical Note 3 - 1



Technical Note 3Interactive Composite Beam Design

Interactive composite beam design is a powerful feature that allows the userto review the design results for any composite beam and interactively revisethe design assumptions and immediately review the revised results.

Note that a design must have been run for the interactive design mode to beavailable.

To enter the interactive design mode and interactively design the beam, rightclick on a beam while the design results are displayed in the active window. Ifdesign results are not displayed (and the design has been run), click the De-sign menu > Composite Beam Design > Interactive Composite BeamDesign command and then right click a beam.

The following sections describe the features that are included in the Interac-tive Composite Beam Design and Review form.

Member IdentificationStory IDThis is the story level ID associated with the composite beam.

Beam LabelThis is the label associated with the composite beam.

Design GroupThis list box displays the name of the design group that the beam is assignedto if that design group was considered in the design of the beam. If the beamis part of a design group but the design group was not considered in the de-sign, N/A is displayed. If the beam is not assigned to any design group,"NONE" is displayed.

If a beam is redesigned as a result of a change made in the Interactive Com-posite Beam Design and Review form, the design group is ignored and onlythe single beam is considered. Thus, as soon as you design a beam in the

Interactive Composite Beam Design Composite Beam Design

Technical Note 3 - 2 Section Information

Interactive Composite Beam Design and Review form, the Design Group boxeither displays N/A or None.

You cannot directly edit the contents of this list box.

Section InformationAuto Select ListThis drop-down box displays the name of the auto select section list assignedto the beam. If no auto select list has been assigned to the beam, NONE isdisplayed. You can change this item to another auto select list or to NONEwhile in the form and the design results will be updated immediately. If youchange this item to NONE, the design is performed for the Current De-sign/Next Analysis section property.

OptimalIf an auto select section list is assigned to the beam, this list box displays theoptimal section as determined by beam weight or price, depending on whathas been specified in the composite beam preferences. If no auto select list isassigned to the beam, N/A is displayed for this item.


Last AnalysisThis list box displays the name of the section that was used for this beam inthe last analysis. Thus, the beam forces are based on a beam of this sectionproperty. For the final design iteration, the Current Design/Next Analysis sec-tion property and the Last Analysis section property should be the same.


Current Design/Next AnalysisThis list box displays the name of the current design section property. If thebeam is assigned an auto select list, the section displayed in this form initiallydefaults to the optimal section.

Tip:

The section property displayed for the Current Design/Next Analysis item is used by theprogram as the section property for the next analysis run.

Composite Beam Design Interactive Composite Beam Design

Acceptable Sections List Technical Note 3 - 3

If no auto select list has been assigned to the beam, the beam design is per-formed for the section property specified in this edit box.

It is important to note that subsequent analyses use the section propertyspecified in this list box for the next analysis section for the beam. Thus, theforces and moments obtained in the next analysis are based on this beamsize.

The Current Design/Next Analysis section property can be changed by clickingthe Sections button that is described later in this Technical Note.

Important note: Changes made to the Current Design/Next Analysis sectionproperty are permanently saved (until you revise them again) if you click theOK button to exit the Interactive Composite Beam Design and Review form. Ifyou exit the form by clicking the Cancel button, these changes are consid-ered temporary and are not permanently saved.

Acceptable Sections ListThe Acceptable Sections List includes the following information for each beamsection that is acceptable for all considered design load combinations.

Section name

Steel yield stress, Fy

Connector layout

Camber

Ratio

Tip:

A single beam displayed in a red font in the Acceptable Sections List means that none ofthe sections considered were acceptable.

Typically, the ratio displayed is the largest ratio obtained considering thestress ratios for positive moment, negative moment and shear for both con-struction loads and final loads, as well as the stud ratio(s), deflection ratios,and if they are specified to be considered when determining if a beam sectionis acceptable, the vibration ratios.


Technical Note 3 - 4 ReDefine

If the beam is assigned an auto select list, many beam sections may be listedin the Acceptable Sections List. If necessary, use the scroll bar to scrollthrough the acceptable sections. The optimal section is initially highlighted inthe list.

If the beam is not assigned an auto select list, only one beam section will belisted in the Acceptable Sections List. It is the same section as specified in theCurrent Design/Next Analysis edit box.

At least one beam will always be shown in the Acceptable Sections List, evenif none of the beams considered are acceptable. When no beams are accept-able, the program displays the section with the smallest maximum ratio in ared font. Thus, a single beam displayed in a red font in the Acceptable Sec-tions List means that none of the sections considered were acceptable.

ReDefineSections ButtonUse the Sections button to change the Current Design/Next Analysis sectionproperty. This button can designate a new section property whether the sec-tion property is or is not displayed in the Acceptable Sections List.

When you click on the Sections button, the Select Sections form appears.Assign any frame section property to the beam by clicking on the desiredproperty and clicking OK. Note that if an auto select list is assigned to thebeam, using the Sections button sets the auto select list assignment toNONE.

Overwrites ButtonClick the overwrites button to access and make revisions to the compositebeam overwrites and then immediately see the new design results. Modifyingsome overwrites in this mode and exiting both the Composite Beam Over-writes form and the Interactive Composite Beam Design and Review form byclicking their respective OK buttons permanently saves changes made to theoverwrites.

Exiting the Composite Beam Overwrites form by clicking the OK button tem-porarily saves changes. Subsequently exiting the Interactive Composite BeamDesign and Review form by clicking the Cancel button cancels the changesmade. Permanent saving of the overwrites does not occur until the OK but-


Temporary Technical Note 3 - 5

tons in both the Composite Beam Overwrites form and the Interactive Com-posite Beam Design and Review form have been clicked.

TemporaryCombos ButtonClick this button to access and make temporary revisions to the design loadcombinations considered for the beam. This is useful for reviewing the resultsfor one particular load combination, for example. You can temporarily changethe considered design load combinations to be just the one you are interestedin and review the results.

The changes made to the considered design load combinations using thecombos button are temporary. They are not saved when you exit the Interac-tive Composite Beam Design and Review form, whether you click OK or Can-cel to exit it.

Show DetailsDiagrams ButtonClicking the Diagrams button displays a form with the following four types ofdiagrams for the beam.

Applied loads

Shear

Moment

Deflection

The diagrams are plotted for specific design load combinations specified in theform by the user.

Details ButtonClicking the Details button displays design details for the beam. The infor-mation displayed is similar to the short form output that can be printed usingthe File menu > Print Tables > Composite Beam Design command. TheTechnical Notes describe short form output.


Technical Note 3 - 6 Show Details

Note:

Stud Details Information is available using the Details button, but is not included in theshort form output printed using File Menu > Print Tables> Composite Beam Design.

Stud details information is one item included in the interactive design detailsthat is not included in the short form output details (and thus not described inAISC-ASD89 Composite Beam Design Technical Note 28 Output Details orAISC-LRFD93 Composite Beam Design Technical Note 42 Output Details). Thisinformation is provided in a table with six columns on the Stud Details tab.The definitions of the column headings in this table are given in the followingbullet items.

Location: This is either Max Moment or Point Load. If it is Max Moment,the information on the associated row applies to the maximum momentlocation for the specified design load combination. If it is Point Load, theinformation on the associated row applies to the point load location for thespecified design load combination.

Distance: The distance of the Max Moment or Point Load location meas-ured from the center of the support at the left end (I-end) of the beam.

Combo: The final strength design load combination considered for the as-sociated row of the table.

L1 left: The dimension L1 left associated with the specified location. See"How the Program Distributes Shear Studs on a Beam" in CompositeBeam Design Technical Note 13 Distribution of Shear Studs on a Beam formore information.

Recall that L1 left is the distance from an output station to an adjacent pointof zero moment or physical end of the beam top flange, or physical end ofthe concrete slab, measured toward the left end (I-end) of the beam.

L1 right: The dimension L1 right associated with the specified location. See"How the Program Distributes Shear Studs on a Beam" in CompositeBeam Design Technical Note 13 Distribution of Shear Studs on a Beam formore information.

Recall that L1 right is the distance from an output station to an adjacentpoint of zero moment or physical end of the beam top flange, or physical


Show Details Technical Note 3 - 7

end of the concrete slab, measured toward the right end (J-end) of thebeam

Studs: The number of shear studs required between the specified locationand adjacent points of zero moment, the end of the concrete slab, or theend of the beam top flange.

The Stud Details table reports information at each maximum moment locationand each point load location (if any) for each final strength design load com-bination.

The Stud Detail information allows you to report your shear studs in compos-ite beam segments that are different from the default composite beam seg-ments used by the program. See "Composite Beam Segments" in CompositeBeam Design Technical Note 13 Distribution of Shear Studs on a Beam for adefinition of composite beam segments. It is very important that you un-derstand how the program defines composite beam segments, be-cause in the composite beam output, the program reports the re-quired number of shear studs in each composite beam segment. See"How the Program Distributes Shear Studs on a Beam" in Composite BeamDesign Technical Note 13 Distribution of Shear Studs on a Beam for discus-sion of how the program distributes shear studs along a beam.

Overview Technical Note 4 - 1



Technical Note 4Data Plotted Directly on the Model

This Technical Note describes the input and output data that can be plotteddirectly on the model.

OverviewUse the Design menu > Composite Beam Design > Display Design Infocommand to display on-screen output plotted directly on the model. If de-sired, the screen graphics can then be printed using the File menu > PrintGraphics command.

The on-screen display data is organized into four data groups, as follows.

Labels

Design Data

Stress Ratios

Deflection Ratios

Each of these data groups is described in more detail later in this TechnicalNote. It is important to note that items from different data groups cannot bedisplayed simultaneously.

Tip:

The colors related to the beam ratios can be modified by clicking the Options menu >Colors > Output command.

When design information is displayed directly on the model, the frame ele-ments are displayed in a color that indicates the value of their controlling ra-tio. (Note that this controlling ratio may be a stress ratio or a deflection ra-tio.) The colors associated with various ranges of ratios are specified in theSteel Ratios area of the Assign Output Colors form, which is accessed usingthe Options menu > Colors > Output command.

Data Plotted Directly on the Model Composite Beam Design

Technical Note 4 - 2 Labels Displayed on the Model

Labels Displayed on the ModelBeam labels and associated beam design group labels can be displayed on themodel. A beam label is the label that is assigned to the line object that repre-sents the composite beam.

Tip:

Long labels may not display or print properly (fully).

If a beam has been assigned to a group that has been designated as a com-posite beam design group, the group name for the beam will be displayedwhen requested. If a beam is not part of a composite beam design group, nogroup name will be displayed for that beam. Note that you can assign beamdesign groups by clicking the Design menu > Composite Beam Design >Select Design Group command.

As shown in Figure 1, beam labels (B7, B8, etc.) are plotted above or to theleft of the beam, and beam design groups (Group01, Group07, etc.) are dis-played below or to the right of the beam.

Figure 1: Example of Beam and Design Group Labels

Floor Plan

B7

B8Group01

B9Group01

B24

Gro

up07B2

3G

roup

08

Composite Beam Design Data Plotted Directly on the Model

Design Data Technical Note 4 - 3

Tip:

The design data and ratios output that is plotted directly on the model is also available intext form in the short and long form printed output, which are described in AISC-ASD89Composite Beam Design Technical Note 28 Output Details and AISC-LRFD93 Compos-ite Beam Design Technical Note 42 Output Details.

Design DataThe following design data can be displayed on the model:

Beam section (e.g., W18X35)

Beam yield stress, Fy

Shear stud layout

Beam camber

Beam end reactions

One or more of these items can be displayed at the same time. Figure 2shows an example where all five of these items are displayed. The beam sec-tion size (e.g., W18X35) is apparent and needs no further explanation.

The beam yield stress is displayed just after the beam section size.

The shear stud layout pattern is displayed in parenthesis just after the beamyield stress. The number of equally spaced shear studs is reported for eachcomposite beam segment. See “Composite Beam Segments” in CompositeBeam Design Technical Note 13 Distribution of Shear Studs on a CompositeBeam for more information on composite beam segments.

Important note: It is very important that you fully understand the conceptof composite beam segments. This is necessary to properly interpret the out-put results for shear studs.

The beam camber is displayed below or to the right of the beam. All otherdata is displayed above or to the left of the beam.

The end reactions are displayed at each end of the beam. They are displayedbelow or to the right of the beam. The end reactions displayed are the maxi-mum end reactions obtained from all design load combinations. Note that the


Technical Note 4 - 4 Stress Ratios

left end reaction and the right end reaction displayed may be from two differ-ent design load combinations.

Note that cover plate information is not displayed on the model. This infor-mation is available in the printed output (short form or long form; see AISC-ASD89 Composite Beam Design Technical Note 28 Output Details and AISC-LRFD93Composite Beam Design Technical Note 42 Output Details) and in the overwrites.

Tip:

The length of the composite beam segments associated with the shear stud layout isdocumented in the short and long form printed output, which are described in AISC-ASD89 Composite Beam Design Technical Note 28 Output Details and AISC-LRFD93Composite Beam Design Technical Note 42 Output Details.

Stress RatiosThe following design data can be displayed on the model:

Construction load bending and shear ratios

Final load bending and shear ratios

Floor Plan

W16X26 Fy=36.00 (14)

W18X35 Fy=36 (22)

W24

X55

Fy=5

0 (1

6,16

)C

=0.7

5

W24

X55

Fy=5

0 (1

6,16

)C=

1.00

W18X35 Fy=36 (48)C=1.25

16.2 16.2

20.7 20.7

25.2 25.2

23.7

23.7

18.4

18.4 Right reaction

Shear stud layout inparenthesis

Camber

Beam section

Left reaction

Yield stress

Figure 2: Example of Design Data that Can be Displayed on the Model

Composite Beam Design Data Plotted Directly on the Model

Deflecti

You can display the construction load ratios, the final load ratios, or both.Bending ratios are always displayed above or to the left of the beam. Shearratios are always displayed below or to the right of the beam.

When both construction and final stress ratios are displayed, the constructionload ratios are displayed first, followed by the final load ratios. See Figure 3for an example.

DeflWhenthe fo

Thlo

Thal

Whenlowed

0.678, 0.961

Figur

on Ratios Technical Note 4 - 5

ection Ratios the Deflection Ratios option is chosen, the program plots one or both ofllowing two ratios.

e maximum live load deflection ratio (live load deflection divided by al-wable live load deflection) for deflection loads.

e maximum total load deflection ratio (total load deflection divided bylowable total load deflection) for deflection loads.

both ratios are plotted, the live load deflection ratio is plotted first, fol- by the total load deflection ratio, as shown in Figure 4.

Floor Plan

0.678, 0.9610.121, 0.245

0.882, 0.9780.134, 0.222

0.765, 0.9940.179, 0.311

0.46

7, 0

.968

0.13

5, 0

.224

0.56

1, 0

.983

0.21

3, 0

.293 Construction

load bendingratio

Final loadbending ratio

Constructionload shearratio

Final loadshear ratio

0.121, 0.245

Legend

e 3: Example of Stress Ratios That Are Displayed on the Model


Technical Note 4 - 6 Deflection Ratios

Floor Plan

0.521, 0.426

0.612, 0.433

0.445, 0.409

0.41

9, 0

.326

0.39

2, 0

.372

Live loaddeflection ratio

Total loaddeflection ratio

0.521, 0.426

Legend

Figure 4: Example of Deflection Ratios That AreDisplayed on the Model

General Technical Note 5 - 1



Technical Note 5Input Data

GeneralThis Technical Note describes the composite beam input data that can beprinted to a printer or to a text file when you click the File menu > PrintTables > Composite Beam Design command. You can print any combina-tion of five data categories.

Using the Print Composite Beam Design Tables FormTo print composite beam design input data directly to a printer, use the Filemenu > Print Tables > Composite Beam Design command and click thecheck box on the Print Composite Beam Design Tables form next to the de-sired type(s) of input data. Click the OK button to send the print to yourprinter. Click the Cancel button rather than the OK button to cancel theprint.

Use the File menu > Print Setup command and the Setup>> button tochange printers, if necessary.

To print composite beam design input data to a file, use the File menu >Print Tables > Composite Beam Design command and click the Print toFile check box on the Print Composite Beam Design Tables form. Click theFilename>> button to change the path or filename. Use the appropriate fileextension for the desired format (e.g., .txt, .xls, .doc). Click the OK buttonson the Open File for Printing Tables form and the Print Composite Beam De-sign Tables form to complete the request.

Note:

The File menu > Display Input/Output Text Files command is useful for displaying out-put that is printed to a text file.

The Append check box allows you to add data to an existing file. The path andfilename of the current file is displayed in the box near the bottom of the Print

Input Data Composite Beam Design

Technical Note 5 - 2 Material Properties Input Data

Composite Beam Design Tables form. Data will be added to this file. Or usethe Filename>> button to locate another file, and when the Open File forPrinting Tables caution box appears, click Yes to replace the existing file.

If you select a specific composite beam(s) before using the File menu >Print Tables > Composite Beam Design command, the Selection Onlycheck box will be checked. The print will be for the selected beam(s) only. Ifyou uncheck the Selection Only check box, the print will be for all compositebeams.

Material Properties Input DataThe Material Properties input data item prints the concrete and steel materialproperties assigned to all frame sections that are the current design sectionfor a selected composite beam. If no objects are selected, it prints the con-crete and steel material properties assigned to all frame sections that are thecurrent design section for any composite beam.

The material properties printed in this output are those that are used in thecomposite beam design. For example, mass per unit volume is not used in thecomposite beam design so it is not printed in these tables. Table 1 lists thecolumn headings in the material property tables and provides a brief descrip-tion of what is in the columns.

Table 1 Material Properties Input Data

COLUMN HEADING DESCRIPTIONConcrete Material PropertiesMaterial Label Label (name) of the concrete material property.

Modulus of Elasticity Modulus of elasticity, Ec, of the concrete material. Note that thisis the modulus of elasticity used for deflection calculations, butnot necessarily for stress calculations. See "Effective SlabWidth and Transformed Section Properties" in Compos-ite Beam Design Technical Note 8 Effective Width of theConcrete Slab for more information.

Unit Weight Weight per unit volume of the concrete.

Concrete f'c Compressive strength of the concrete.

Composite Beam Design Input Data

Section Properties Input Data Technical Note 5 - 3

Table 1 Material Properties Input Data

COLUMN HEADING DESCRIPTIONSteel Material PropertiesMaterial Label Label (name) of the steel material property.

Modulus of Elasticity Modulus of elasticity, Es, of the steel material.

Unit Weight Weight per unit volume of the steel.

Steel Fy Yield stress of the steel.

Steel Fu Minimum tensile strength of the steel.

Steel Price Price per unit weight (e.g., $/pound) of the steel.

Section Properties Input DataThe section properties input data is provided in two tables, labeled FrameSection Property Data (Table 1) and Frame Section Property Data (Table 2).This data is provided in two tables because it would not all fit onto one line ina single table. Table 2 herein lists the column headings in the section propertytables and provides a brief description of what is in the columns.

Table 2 Section Properties Input Data

COLUMN HEADING DESCRIPTION

Frame Section Property Data (Table 1)Section Label Label (name) of the steel frame section.

Material Label Label (name) of the steel material property that is assigned tothe steel frame section.

bf Top Width of beam top flange.

tf Top Thickness of beam top flange.

d Depth Depth of beam measured from the top of the beam top flange tothe bottom of the beam bottom flange.

tw Web Thick Thickness of beam web.

bf Bottom Width of beam bottom flange.

tf Bottom Thickness of beam bottom flange.


Technical Note 5 - 4 Deck Properties Input Data

Table 2 Section Properties Input Data

COLUMN HEADING DESCRIPTIONFrame Section Property Data (Table 2)Section Label Label (name) of the steel frame section.

Material Label Label (name) of the steel material property that is assigned tothe steel frame section.

k In a rolled beam section, the distance from the outside face ofthe flange to the web toe of the fillet.

I33 Major Moment of inertia about the local 3-axis of the beam section.

S33 Major Section modulus about the local 3-axis of the beam section. Ifthe section moduli for the top and bottom of the beam are dif-ferent, the minimum value is printed.

Z33 Major Plastic modulus about the local 3-axis of the beam section. Ifthe plastic moduli for the top and bottom of the beam are differ-ent, the minimum value is printed.

Deck Properties Input DataThe deck properties input data is provided in three tables, labeled Deck Sec-tion Property Data (Geometry), Deck Section Property Data (Material Proper-ties), and Deck Section Property Data (Shear Studs). Table 3 lists the columnheadings in the deck property tables and provides a brief description of whatis in the columns.

Table 3 Deck Properties Input Data


Deck Section Property Data (Geometry)

Section Label Label (name) of the deck section.

Solid Slab This item is Yes if the deck section represents a solid slab withno metal deck. Otherwise it is No.

Slab Cover The depth of the concrete slab above the metal deck, tc. If thedeck section represents a solid slab with no metal deck, this isthe thickness of the solid slab.

Deck Depth The height of the metal deck ribs, hr. This item is specified asN/A if the deck section represents a solid slab.


Deck Properties Input Data Technical Note 5 - 5

Table 3 Deck Properties Input Data


Rib Width The average width of the metal deck ribs, wr. This item is speci-fied as N/A if the deck section represents a solid slab.

Rib Spacing The center-to-center spacing of the metal deck ribs, Sr. Thisitem is specified as N/A if the deck section represents a solidslab.

Deck Section Property Data (Material Properties)Section Label Label (name) of the deck section.

Deck Type This item is either Filled, Unfilled or Solid. Filled means that thedeck section is a metal deck filled with concrete. Unfilled meansit is a bare metal deck. Solid means it is a solid slab with nometal deck.

Slab Material This is the concrete material property associated with the con-crete slab defined by the deck section. If the Deck type is Un-filled, this item is specified as N/A.

Deck Material This is the steel material property associated with the metaldeck. This item is only specified when the Deck Type is Un-filled. If the Deck type is not Unfilled, this item is specified asN/A.

Deck Shear Thickness This is the shear thickness of the metal deck. This item is onlyspecified when the Deck Type is Unfilled. It is used for calcu-lating the shear (in-plane, membrane) stiffness of the deck. Ifthe Deck type is not Unfilled, this item is specified as N/A.

Deck Unit Weight This is the weight per unit area of the metal deck, wd. See"Metal Deck and Slab Properties" in Composite BeamDesign Technical Note 7 Composite Beam Properties formore information.

Deck Section Property Data (Shear Studs)Section Label Label (name) of the deck section.

Stud Diameter Diameter of the shear studs associated with the deck section,ds.

Stud Height Height after welding of the shear studs associated with the decksection, Hs.

Stud Fu Minimum specified tensile strength of the shear studs associ-ated with the deck section, Fu.


Technical Note 5 - 6 Design Preferences Input Data

Design Preferences Input DataThe output for the composite beam design preferences is provided in a seriesof tables. The tables correspond to the tabs in the Preferences form. You canclick the Options menu > Preferences > Composite Beam Design com-mand to access the composite beam preferences.

Note:

The composite beam preferences are described in AISC-ASD89 Composite Beam De-sign Technical Note 17 Preferences and AISC-LRFD93 Composite Beam Design Tech-nical Note 30 Preferences.

Recall that the composite beam preferences apply to all beams designed us-ing the Composite Beam Design postprocessor. A few of the preference itemscan be overwritten on a beam-by-beam basis in the composite beam over-writes. Those preferences items that can be overwritten are mentioned in thisdocumentation. You can select one or more beams and then click the Designmenu > Composite Beam Design > View/Revise Overwrites commandto access the composite beam overwrites.

The preference input data is provided in tabular format. Table lists the columnheadings in the preference table and provides a brief description of what is inthe columns.

Table 4 Preferences Input Data


FactorsThe input data related to factors is described in AISC-ASD89 Composite Beam DesignTechnical Note 17 Preferences and AISC-LRFD93 Composite Beam Design TechnicalNote 30 Preferences.

Beam PropertiesShored Floor This item is Yes if the composite beam preferences designate

that the composite beams are to be shored. Otherwise, it is No.Note that this item can be modified on a beam-by-beam basisin the composite beam overwrites.


Design Preferences Input Data Technical Note 5 - 7



Middle Range Length in the middle of the beam over which the programchecks the effective width on each side of the beam, expressedas a percentage of the total beam length. See "Location WhereEffective Slab Width is Checked" in Composite Beam DesignTechnical Note 8 Effective Width of the Concrete Slab for moreinformation.

Pattern LL Factor Factor applied to live load for special pattern live load check forcantilever back spans and continuous spans. See "Special LiveLoad Patterning for Cantilever Back Spans" and "Special LiveLoad Patterning for Continuous Spans" in Composite BeamDesign Technical Note 10 Design Load Combinations for moreinformation.

Deflection and CamberNote:

Deflection and camber are described in Composite Beam Design TechnicalNote 11 Beam Deflection and Camber.

Live Load Limit Live load deflection limitation. The term L represents the lengthof the beam. Note that this item can be modified on a beam-by-beam basis in the composite beam overwrites.

Total Load Limit Total load deflection limitation. The term L represents the lengthof the beam. Note that this item can be modified on a beam-by-beam basis in the composite beam overwrites.

Camber DL Percent Percentage of dead load (not including superimposed deadload) on which the program camber calculations are based.See "Camber" in Composite Beam Design Technical Note 11Beam Deflection and Camber for more information.

VibrationNote:

Vibration is described in Composite Beam Design Technical Note 12 BeamVibration.

Percent Live Load Percentage of live load plus reduced live load considered (inaddition to full dead load) when computing weight supported bythe beam for use in calculating the first natural frequency of thebeam.


Technical Note 5 - 8 Beam Overwrites Input Data



Consider Frequency If this item is Yes, the specified minimum acceptable frequencyis considered when selecting the optimum beam section froman auto select section list. If this item is No, frequency is notconsidered when selecting the optimum beam section.

Minimum Frequency The minimum acceptable first natural frequency for a floorbeam. This item is used when the Consider Frequency item isset to Yes.

Murray Damping If this item is Yes, the Murray's minimum damping requirementis considered when selecting the optimum beam section froman auto select section list. If this item is No, Murray's minimumdamping requirement is not considered when selecting the op-timum beam section. See "Murray's Minimum DampingRequirement" in Composite Beam Design Technical Note 12Beam Vibration for more information.

Inherent Damping Percentage critical damping that is inherent in the floor system.This item is used when the Murray Damping item is set to Yes.

PriceConsider Price If this item is Yes, the section price rather than steel weight is

considered when selecting the optimum beam section from anauto select section list. If this item is No, section price is notconsidered when selecting the optimum beam section. Thesection price is based on specified prices for steel, shear studs,and camber.

Stud Price Installed price for a single shear stud.

Camber Price Camber price per unit weight of steel beam (including coverplate, if it exists).

Beam Overwrites Input DataBeam Overwrites Input Data is described in AISC-ASD89 Composite BeamDesign Technical Note 18 Overwrites and AISC-LRFD93 Composite Beam De-sign Technical Note 31 Overwrites.




Technical Note 6Output Details

OverviewThis Technical Note describes the composite beam output summary that canbe printed to a printer or to a text file. Additionally, both short form and longform of the output details can be printed. See AISC-ASD89 Composite BeamDesign Technical Note 28 Output Details and AISC-LRFD93 Composite BeamDesign Technical Note 42 Output Details for more information about theshort- and long-form outputs.

Using the Print Composite Beam Design Tables FormTo print composite beam design output data directly to a printer, use the Filemenu > Print Tables > Composite Beam Design command and click theSummary check box on the Print Composite Beam Design Tables form. Alsoselect the form, or detail, of the print by selecting None, Short Form, or LongForm. Click the OK button to send the print to your printer. Click the Cancelbutton rather than the OK button to cancel the print. Use the File menu >Print Setup command and the Setup>> button to change printers, if neces-sary.

Note:

A design must be run before output data can be generated.

To print summary output data to a file, use the File menu > Print Tables >Composite Beam Design command and click the Print to File check box onthe Print Composite Beam Design Tables form. Click the Filename>> buttonto change the path or filename. Use the appropriate file extension for the de-sired format (e.g., .txt, .xls, .doc). Click the OK buttons on the Open File forPrinting Tables form and the Print Composite Beam Design Tables form tocomplete the request.

Output Details Composite Beam Design

Technical Note 6 - 2 Summary of Composite Beam Output

Note:

The File menu > Display Input/Output Text Files command is useful for displaying out-put that is printed to a text file.

The Append check box allows you to add data to an existing file. The path andfilename of the current file is displayed in the box near the bottom of the PrintComposite Beam Design Tables form. Data will be added to this file. Or usethe Filename button to locate another file, and when the Open File for Print-ing Tables caution box appears, click Yes to replace the existing file.

If you select a specific composite beam(s) before using the File menu >Print Tables > Composite Beam Design command, the Selection Onlycheck box will be checked. The print will be for the selected beam(s) only. Ifyou uncheck the Selection Only check box, the print will be for all compositebeams.

Summary of Composite Beam OutputThe summary of composite beam output prints a concise summary of thecomposite beam results in a tabular form. One row of the output table is de-voted to each composite beam.

If you have selected some composite beams before printing the summarydata, only summary data for the selected beams is printed. If you have notselected any composite beams before printing the summary data, summarydata for all composite beams is printed.

Table 1 lists the column headings in the Summary of Composite Beam Outputtable and provides a brief description of what is in the columns.

Table 1 Composite Beam Output Table


Story Level Story level associated with the beam.

Beam Label Label associated with the line object that represents the beam.A typical beam label example is "B23." Do not confuse this withthe Section Label, which may be identified as "W18X35."

Section Name The current design section for the beam.

Beam Fy Yield stress of the beam, Fy.

Composite Beam Design Output Details

Summary of Composite Beam Output Technical Note 6 - 3

Table 1 Composite Beam Output Table


Stud Diameter Diameter of shear studs, ds.

Stud Layout Number of studs in each composite beam segment separatedby commas. They are listed starting with the composite beamsegment at the I-end of the beam and working toward the J-endof the beam.

Beam Shored This item is Yes if the beam is shored and No if it is unshored.

Beam Camber The camber for the beam. This item may be calculated by theprogram, or it may be user-specified.

Beam Properties Technical Note 7 - 1



Technical Note 7Composite Beam Properties

This Technical Note provides an overview of composite beam properties.Items described include beam properties, metal deck and concrete slab prop-erties, shear connector properties, user-defined shear connector patterns,cover plate properties, effective slab width and beam unbraced length.

The many properties associated with composite beams are defined using vari-ous menus in the program. The steel beam itself is defined using the Definemenu > Frame Sections command. The cover plate, if it exists, is defined inthe composite beam overwrites for the beam. The metal deck, concrete slaband shear connectors are defined together as part of the Deck section prop-erties using the Define menu > Wall/Slab/Deck Sections command.Other items related to the beam properties are specified in the compositebeam preferences or overwrites.

Beam PropertiesFigure 1 shows a typical composite beam for reference. The beam shown is arolled beam section from the built-in section database.

Tip:

The Composite Beam Design postprocessor only designs beams that are I-shaped sec-tions and channel sections.

Basic steel beam properties are defined using the Define menu > FrameSections command. Use this command to define the basic geometry of thesteel section, except for the cover plate, if it exists. Define the cover plate onthe Beam tab in the composite beam overwrites. When defining a beam, amaterial property that includes the yield stress for that beam is also assigned.That yield stress is assumed to apply to the beam and the cover plate unlessit is revised in the beam overwrites. The steel Material Property also includesthe price or cost-per-unit-weight that is assigned to the beam.

Composite Beam Properties Composite Beam Design

Technical Note 7 - 2 Beam Properties

The beam section for a composite beam can be any I-shaped section, or achannel. The I-shaped section can be defined by selecting a W, M, S or HPshape from the built-in program steel section database, or by defining yourown I-shaped section using the Define menu > Frame Sections commandand selecting the Add I/Wide Flange option from the drop-down list on theDefine Frame Properties form. It is not necessary that the top and bottomflanges have the same dimensions in user-defined I-shaped sections used ascomposite beams. A channel section used as a composite beam can also be asection taken from the built-in program steel section database or user-defined, using the Define menu > Frame Sections command and selectingthe Add Channel option from the drop-down list on the Define Frame Proper-ties form.

Note:

See the section entitled “Cover Plates” later in this Technical Note for more information.

Figure 1: Illustration of Composite Beam

��

bcp

h rt c

dt cp

Concrete slab

Metal deck

Shear stud

Steel beam

Cover plate

wr

Sr

Hs

Composite Beam Design Composite Beam Properties

Metal Deck and Slab Properties Technical Note 7 - 3

Beam sections defined using Section Designer are considered as general sec-tions, not I-shaped or channel-shaped sections (even if they really are I-shaped or channel-shaped), and cannot be designed using the CompositeBeam Design postprocessor.

If you define a beam section by selecting it from the built-in section database,the program assumes that it is a rolled section and applies the design equa-tions accordingly. If you create your own user-defined section, the programassumes it is a welded section and revises the design equations as necessary.The program does not check or design any of the welding for these weldedbeams.

Metal Deck and Slab PropertiesBasic metal deck and concrete slab properties are defined using the Definemenu > Wall/Slab/Deck Sections command. This command specifies thegeometry and the associated material properties of the metal deck, concreteslab and shear connectors.

Tip:

A beam designed using the Composite Beam Design postprocessor can only have com-posite behavior if it supports a deck section (not a slab or wall section).

Important note: You must specify the concrete slab over metal deck as adeck section property (not a slab section property) if you want the beam tohave composite behavior. If you specify the slab using a slab section propertyinstead of a deck section property, the Composite Beam Design postprocessordesigns the beams supporting that slab as noncomposite beams.

Using the Define menu > Wall\Slab\Deck Sections command, select adeck-type section and click the Modify/Show>> button to bring up the DeckSection form. This box allows you to specify that the deck section is a FilledDeck (metal deck filled with concrete), an Unfilled Deck, or a Solid Slab (solidconcrete slab with no metal deck). Alternatively, you can select "Add NewDeck" from the drop-down list in the "Click to:" area of the form to add a newdeck and specify its section type.

In the Geometry area of the Deck Section form, the specified metal deck ge-ometry includes:


Technical Note 7 - 4 Metal Deck and Slab Properties

Slab Depth: The depth of concrete fill above the metal deck. This item islabeled tc in Figure 1.

Deck Depth: The height of the metal deck ribs. This item is labeled hr inFigure 1.

Rib Width: The average width of the metal deck ribs. This item is labeledwr in Figure 1.

Rib Spacing: The center-to-center spacing of the metal deck ribs. Thisitem is labeled Sr in Figure 1.

In the Composite Deck Studs area of the Deck Section form, the followingitems are specified:

Diameter: The diameter of the shear stud.

Height: The height of the shear stud. This item is labeled Hs in Figure 1.

Tensile Strength, Fu: The specified tensile strength of the shear stud.

In the Material area of the Deck Section form, if the Deck type is Filled Deckor Solid Slab (not Unfilled Deck), specify a Slab Material for the concrete. Thisshould be a previously specified concrete material property. This concretematerial property is used to specify all material properties of the concrete,except in some code-specific cases. See "Effective Slab Width and Trans-formed Section Properties" in Composite Beam Design Technical Note 8 Effec-tive Width of the Concrete Slab for additional information.

If the Deck type is Unfilled Deck, specify a steel material property for thedeck material and an equivalent shear thickness for the deck. These twoitems are used by the program to determine the membrane shear stiffness ofthe deck.

Note:

Deck section properties can be specified as a metal deck filled with concrete, unfilledmetal deck, or a solid slab with no metal deck.

In the Metal Deck Unit Weight area of the Deck Section form, specify theweight-per-unit-area of the deck, wd.

Composite Beam Design Composite Beam Properties

Shear Stud Properties Technical Note 7 - 5

The self-weight of the deck element representing the concrete slab over metaldeck is calculated using the weight-per-unit-area shown in Equation 1. In theequation, wc is the weight-per-unit-volume of concrete. The first term is theweight-per-unit-area of the concrete and the second term is the weight-per-unit-area of the metal deck.

Weight-per-Unit-Area = dcr

rrc wt

Shw

w +

+ Eqn. 1

Note that the program does not check the design of the metal deck itself.

Shear Stud PropertiesAs described in the previous section, shear studs are defined along with thedeck properties using the Define menu > Wall/Slab/Deck Sections com-mand. The properties specified for shear studs are the diameter, dsc, theheight, Hs, and the specified tensile strength of the shear stud, Fu.

Tip:

In this program, you can define your own shear connector patterns.

The program automatically calculates the strength of a single shear connectorbased on the shear stud and concrete slab properties. Revise this value usingthe composite beam overwrites, if desired.

For additional information about shear studs, see AISC-ASD89 CompositeBeam Design Technical Note 22 Allowable Bending Stresses, AISC-ASD89Composite Beam Design Technical Note 23 Bending Stress Checks, and AISC-ASD89 Composite Beam Design Technical Note 24 Beam Shear Checks.

Cover PlatesIn this program, full-length cover plates can be specified on the bottom flangeof a composite beam. Cover plates are not defined as part of the beam prop-erties. They can only be specified on the Beam tab of the composite beamoverwrites. Thus, to specify a beam with a cover plate, define the beam asyou normally would without the cover plate and then add the cover plate inthe overwrites by selecting a composite beam(s) and using the Design Menu> Composite Beam Design > View/Revise Overwrites command.


Technical Note 7 - 6 Cover Plates

One consequence of this process is that the cover plate is not included foroverall analysis of the building. However, the cover plate is considered bothfor resisting moments and deflections for design of the composite beamwithin the program's Composite Beam Design postprocessor.

Tip:

Cover plates are specified in the composite beam overwrites.

The properties specified for a cover plate on the Beam tab of the CompositeBeam Overwrites form are the width, bcp, the thickness, tcp, and a yieldstress, Fycp. The width and thickness dimensions are illustrated in Figure 1.The program does not check or design any of the welding between the coverplate and the beam bottom flange. It also does not determine cutoff locationsfor the full length cover plate.

Location Where Effective Slab Width is Checked Technical Note 8 - 1



Technical Note 8Effective Width of the Concrete Slab

This Technical Note explains how the program considers the effective width ofthe concrete slab separately on each side of the composite beam. This sepa-ration is carried through in all of the calculations. It allows you to have differ-ent deck properties on the two sides of the beam.

You can redefine the effective slab width on either side of the beam in theoverwrites. In the composite beam overwrites on the Beam tab (display usingthe Design menu > Composite Beam Design > View/Revise Over-writes command), the effective widths are specified on the left and rightsides of the beam. As illustrated in Figure 1, if you stand at the I-end of thebeam looking toward the J-end of the beam, the program assumes the rightside of the beam to be on your right side.

Location Where Effective Slab Width is CheckedBy default, the program checks the effective width of the beam over the en-tire middle 70% of the beam and uses the smallest value found as the effec-tive width of the beam, beff, everywhere in the calculations for that beam. The70% number is derived based on two assumptions:

The capacity of the composite beam is approximately twice that of thesteel beam alone.

The steel beam alone is capable of resisting the entire moment in thecomposite beam for the last 15% of the beam length at each end of thebeam. Note that for a uniformly loaded beam, the moment drops off tohalf of the maximum moment or less in the last 15% of the beam.

Redefine this default “middle range” of 70% in the composite beam designpreferences, if desired. In the preferences, the Middle Range item is on theBeam tab (display using the Options > Preferences > Composite BeamDesign command).

Effective Width of the Concrete Slab Composite Beam Design

Technical Note 8 - 2 Multiple Deck Types or Directions Along the Beam Length

Multiple Deck Types or Directions Along the BeamLengthFor the design calculations, the program assumes one deck type and deckdirection on each side of the beam along the entire length of the beam, re-gardless of the actual number of types and directions of deck that may exist.The program allows different deck types and deck directions on the two sidesof the beam in the calculations. Figure 2 shows examples of different decktypes and different deck directions on the two sides of the beam.

Note:

The program allows a different deck type and deck orientation on each side of the beam.

The program checks the deck types and deck directions on each side of thecomposite beam within the specified middle range (see the previous subsec-

i-end of beam

2

1

3

j-end of beam

Right side of beamLeft side of beam

Figure 1: Example of How the Program Defines the Left and RightSides of the Beam

Composite Beam Design Effective Width of the Concrete Slab

Multiple Deck Types or Directions Along the Beam Length Technical Note 8 - 3

tion). When multiple deck types or deck directions occur on the same side ofa composite beam, the program decides which single deck section and direc-tion to use on that side of the beam.

The program goes through these steps in this order to choose the deck sec-tion.

1. The program calculates the product of tc * 'cf for each deck where tc is

the depth of the concrete above the metal deck and 'cf is the concrete

slab compressive strength. It uses the deck section that has the small-

est value of tc * 'cf in the calculations for the beam.

2. If two or more deck sections have the same value of tc * 'cf but the

deck spans in different directions, the program uses the deck sectionthat spans perpendicular to the beam.

Important note about deck orientation: In this program's compos-ite beam design, the deck is assumed either parallel or perpendicularto the span of the beam. If the deck span is exactly parallel to thebeam span or within 15 degrees of parallel to the beam span, the deckspan is assumed to be parallel to the beam span. Otherwise, the deckspan is assumed to be perpendicular to the beam span.

��

��

Deck Direction Different on Two Sides of Beam

Deck Type Different on Two Sides of Beam

Figure 2: Different Deck Types and Different Deck Directions on the TwoSides of the Beam


Techn

3. If two or more deck sections span in the same direction and have the

same value of tc * 'cf , the program uses the deck section with the

smaller tc value.

4. If two or more deck sections span in the same direction and have the

same values of tc and 'cf , the program use the first defined deck sec-

tion.

Tip:

You can change the assumed deck type and deck direction on each side of the beam onthe Deck tab in the composite beam overwrites.

Refer to the floor plan shown in Figure 3. The typical floor in this plan consistsof 2-1/2" normal weight concrete over 3" metal deck that is designated DeckType A. However, the upper left-hand quadrant of the floor consists of 4-1/2"normal weight concrete over 3" metal deck that is designated Deck Type B.Assume that the concrete compressive strength is 3,500 psi for both decktypes.Now consider the beam labeled “Girder F” in the figure. Deck Type A existsalong the entire length of the right-hand side of this beam. Thus, the program

��

Figu

ical Note 8 - 4 Multiple Deck Types or Directions Along the Beam Length

Edge of deck

��

��

Gird

er F

Deck Type A: 2-1/2"normal weight concreteover 3" metal deck

Deck Type B: 4-1/2"normal weight concreteover 3" metal deck

Step in floor slab

Floor Plan

re 3: Example of Different Deck Types on the Left and Right Sides ofa Beam


Multiple Deck Types or Directions Along the Beam Length Technical Note 8 - 5

uses Deck Type A on the right side of the beam in the calculations. Both DeckType A and Deck Type B exist along the left-hand side of the beam. The pro-gram uses the following method to determine which of these deck types touse on the left side of the beam in the calculations:

1. Determine the product of tc * 'cf for each deck type.

a. For Deck Type A: tc * 'cf = 2.5 * 3,500 = 8,750 lbs/in.

b. For Deck Type B: tc * 'cf = 4.5 * 3,500 = 15,750 lbs/in.

2. Use Deck Type A on the left side of the girder in the composite beam

calculations because it has the smaller value of tc * 'cf .

Note that the loads applied to the beam are still based on the actual decktypes. Thus, the load applied to the upper half of Girder F in Figure 3 wouldinclude the contribution from Deck Type B even though Deck Type B mightnot be used in calculating the composite beam properties.

A second example is shown in Figure 4. In this example, the deck type is thesame throughout the floor, but the direction of the deck changes in the upperleft-hand quadrant of the floor.

Now consider the beam labeled “Girder G” in the figure. The deck ribs areoriented parallel to the span of Girder G along the entire length of the right-hand side of this beam. Thus, the program uses Deck Type A oriented parallelto the span of Girder G on the right side of the beam in the calculations.

Deck ribs oriented both perpendicular and parallel to the span of Girder Gexist along the left-hand side of the beam. Because only the deck direction isdifferent along the left side of the beam, not the deck type (and thus tc and

'cf do not change), the program uses the deck that spans perpendicular to

Girder G on the left side of the beam.


Technical Note 8 - 6 Effect of Diagonal Beams on Effective Slab Width

Effect of Diagonal Beams on Effective Slab WidthConsider the example shown in Plan A of Figure 5. In Plan A, the length ofBeam A is LA. Assume that the effective width of this beam is controlled bythe distance to the centerline of the adjacent beam. Also assume that theprogram checks the effective width of the slab over the default middle range(70%) of Beam A. If the variable labeled xA in the figure is less than or equalto 0.15, the effective width of the concrete slab on the upper side of Beam A(i.e., the side between Beam A and Beam X) is controlled by the distancebetween Beam A and Beam X. On the other hand, if xA is greater than 0.15,the effective width of the concrete slab on the upper side of Beam A is con-trolled by the distance between Beam A and Girder Y, at a location of 0.15LA

from the left end of Beam A. This distance is measured along a line that isperpendicular to Beam A.

Edge of deck

��

��

Gird

er G



Floor Plan

Figure 4: Example of Different Deck Orientations on Left and Right Sidesof the Beam


Effect of Diagonal Beams on Effective Slab Width Technical Note 8 - 7

Now consider the example shown in Plan B of Figure 5. Assume that the ef-fective width of Beam B is controlled by the distance to the centerline of theadjacent beam. When considering the perpendicular distance from Beam B tothe adjacent beam on the upper side of Beam B, the program considers thediagonal beam labeled Beam Z when the angle θ is less than 45 degrees. Ifthe angle θ is greater than or equal to 45 degrees, Beam Z is ignored whencalculating the effective slab width on the upper side of Beam B.

Plan C in Figure 5 shows a special case where two diagonal beams frame intoBeam C at the same point. In this special case, the program assumes that theeffective width of the slab on the side of the beam where the two diagonalsexist is zero. You can, of course, change this in the overwrites. The programassumes the zero effective width because although it is checking the effective

Plan A Plan B

Beam BBeam A

LA

xA * LA

Beam X

Gird

er Y

θ

Beam

ZPlan C

Beam C

θ1

Beam

Z1

θ2

Beam Z2

Figure 5: Examples for the Effect of Diagonal Beams on Composite BeamEffective Width


Technical Note 8 - 8 Effect of Openings on Effective Slab Width

width for Beam C, it is unable to determine whether a slab is actually betweenthe two diagonal beams.

Effect of Openings on Effective Slab WidthNow consider Plan D shown in Figure 6. In this case, there is an opening onboth sides of the slab at the left end of Beam D. Assume again that the effec-tive width of this beam is controlled by the distance to the centerline of theadjacent beam, and also assume that the program checks the effective widthof the slab over the default center 70% of the Beam D length. If the width ofthe opening, xD * LD is less than 0.15LD, the program bases the effectivewidth of the concrete slab on the distance to the adjacent beams. On theother hand, if xD * LD exceeds 0.15LD, the program assumes the effectiveconcrete slab width for Beam D to be zero; that is, it assumes a noncompo-site beam.

Figure 6: Example of the Effect of Openings on Composite BeamEffective Width

Plan D

Beam D

LV

xD * LD


Effective Slab Width and Transformed Section Properties Technical Note 8 - 9

Effective Slab Width and Transformed SectionPropertiesWhen the program calculates the transformed section properties, the concreteis transformed to steel by multiplying beff by the ratio Ec / Es. This ratio maybe different on the two sides of the beam. For AISC-ASD89 composite beamdesign, Ec may be different for stress and deflection calculations. See AISC-ASD89 Composite Beam Design Technical Note 20 Transformed Section Mo-ment of Inertia for more information.




Technical Note 9Beam Unbraced Length and Design Check Locations

OverviewThe program considers the unbraced length for construction loading sepa-rately from that for final loads. For both types of loading, the unbraced lengthof the beam associated with buckling about the local 2-axis (minor) of thebeam is used to determine the flexural capacity of the noncomposite beam.The local 2-axis is illustrated in Figure 1.

By default, the program automatically determines the locations where thebeam is braced for buckling about the local 2-axis. This information is thenused to determine the unbraced length associated with any point on thebeam. Instead of using the program calculated bracing points, you can specifyin the overwrites your own brace points for any beam.

i-end of beam

2

1

3

Figure 1: Local 2-Axis of Beam

Beam Unbraced Length and Design Check Locations Composite Beam Design

Technical Note 9 - 2 Determination of the Braced Points of a Beam

Tip:

The program considers the unbraced length for construction loading separately from thatfor final loads.

For buckling about the local 2-axis, the program differentiates between brac-ing of the top flange of the beam and bracing of the bottom flange of thebeam. The program automatically recognizes which flange of the beam is thecompression flange at any point along the beam for any design load combina-tion. With this ability and the program-determined or user-specified bracingpoint locations, the program can automatically determine the unbraced lengthof any segment along the beam and can apply appropriate code-specifiedmodification factors (e.g., Cb factor for flexure) to the flexural strength of thebeam.

Note:

The program can automatically determine the unbraced length of any beam segmentbased on the assumed or specified bracing points.

Determination of the Braced Points of a BeamThe program considers the lateral bracing for the top and bottom flangesseparately. In the Composite Beam Design postprocessor, the program as-sumes that beams can be braced by the deck section (or slab section) thatthey support and by other beams framing into the beam being considered.The program automatically determines the braced points of a beam for buck-ling about the local 2-axis as follows:

The top flange is assumed to be continuously laterally supported (un-braced length of zero) anywhere there is metal deck section with concretefill framing into one or both sides of the beam or there is a slab sectionframing into both sides of the beam.

Note:

In the Composite Beam Design postprocessor, either deck or slab sections can brace thetop flange of a beam.

Tip:

You can choose to accept the program default bracing points for a beam. Alternatively,you can enter the composite beam overwrites and specify the actual bracing points for abeam or specify a maximum unbraced length.

Composite Beam Design Beam Unbraced Length and Design Check Locations

User-Defined Unbraced Length of a Beam Technical Note 9 - 3

Beam

Con

side

red

Bracing Beam

θ > 30°

Metal deck sections with no concrete fill are assumed to continuouslybrace the top flange if the deck ribs are specified as oriented perpendicu-lar to the beam span. If the deck ribs are specified as oriented parallel tothe beam span, the deck is assumed to not brace the top flange.

The top and bottom flange are assumed to be braced atany point where another beam frames into the beambeing considered at an angle greater than 30 degrees,as shown in the sketch to the right. It is up to you toprovide appropriate detailing at this point to assure thatthe bottom flange is adequately braced. If appropriatedetailing is not provided, you should redefine the bracepoints using one of the methods described in the nextsection.

When the bracing is program calculated or brace points are user specified,the program always assumes that each end of the beam is braced at boththe top and the bottom flange. If the unbraced length of a beam is longerthan the actual beam, specify a user-defined unbraced length, not user-defined brace points.

User-Defined Unbraced Length of a BeamOverviewTo use unbraced lengths other than those determined by the program,change the assumed unbraced length for any beam in the composite beamoverwrites. This is true for both the construction loading unbraced lengthsand the final loading unbraced lengths. Select a beam and click the Designmenu > Composite Beam Design > View/Revise Overwrites commandto access the overwrites. The construction loading bracing is specified on theBracing (C) tab. The final condition bracing is specified on the Bracing tab.

For buckling about the local 2-axis, you can specify specific bracing pointsalong the beam that apply to the top flange, bottom flange, or both, or youcan specify one maximum unbraced length that applies over the entire lengthof the beam to both the top and bottom flanges.


Technical Note 9 - 4 User-Defined Unbraced Length of a Beam

Important Note: As soon as you specify any user-defined bracing points orunbraced lengths for a beam, all of the program-determined lateral bracinginformation on that beam is ignored. Thus, if you specify any bracingpoints for a beam, you should specify all of the bracing points for thatbeam.

User-Specified Uniform and Point BracingIf you specify your own bracing along the beam for buckling about the local 2-axis, you can specify continuous bracing along a beam flange, bracing at spe-cific points along a beam flange, or both.

Point BracesTo define point braces, specify a distance along the beam that locates thebrace point, and then indicate whether the top, bottom, or both flanges arebraced at this location. Specify the distance as an actual distance or as arelative distance, both measured from the I-end of the beam. All distancesare measured from the center of the support, not the physical end of thebeam. The distances may be specified as either absolute (actual) distances oras relative distances. A relative distance to a point is the absolute distance tothat point divided by the length of the beam measured from the center-of-support to center-of-support.

Tip:

You can change the default bracing assumed for a beam in the composite beam over-writes. The bracing specified can be different for construction loading and final loading.

Use the following procedure in the composite beam overwrites (display usingthe Design menu > Composite Beam Design > View/Revise Over-writes command) on the Bracing (C) or Bracing tab to specify point braces:

1. Check the box next to the Bracing Condition overwrite item and thenselect Bracing Specified from the drop-down box to the right of theBracing Condition title.

2. Check the box next to the No. Point Braces title and then click in thecell to the right of the title.

3. The Point Braces form appears. In this form:


User-Defined Unbraced Length of a Beam Technical Note 9 - 5

a. Indicate whether the specified distances will be relative or absolutefrom the I-end of the beam by selecting the appropriate optionnear the bottom of the form.

b. In the Define Point Braces area, input a distance from end-I in theLocation box and choose a brace type in the Type box. In the Typebox, Top means only the top flange is braced; Bottom means onlythe bottom flange is braced; and All means both flanges are bracedat that point.

c. Click the Add button to add the brace point.

4. Repeat step 3 as many times as required.

5. To modify an existing point brace specification, do the following:

a. Highlight the item to be modified in the Define Point Braces area.Note that the highlighted distance and type appear in the editboxes at the top of the area.

b. Modify the distance and type in the edit box as desired.

c. Click the Modify button to modify the brace point.

Note:

You can specify uniform bracing, point braces, or a combination of both for a compositebeam.

6. To delete an existing point brace specification, do the following:

a. Highlight the item to be deleted in the Define Point Braces area.Note that the highlighted distance and type appear in the editboxes at the top of the area.

b. Click the Delete button to delete the brace point.

7. Click the OK button to return to the Composite Beam Overwrites form.Note that the No. Point Braces item is automatically updated by theprogram to reflect the point braces specified.


Technical Note 9 - 6 User-Defined Unbraced Length of a Beam

Uniform BracesTo define uniform or continuous bracing, specify a distance along the beamthat locates the starting point of the continuous bracing, specify a second(longer) distance along the beam that locates the ending point of the continu-ous bracing, and then indicate whether the top, bottom, or both flanges arecontinuously braced over this length. You can specify the distances as abso-lute (actual) distances or as relative distances, both measured from the I-endof the beam. A relative distance to a point is the absolute distance to thatpoint divided by the length of the beam measured from the center-of-supportto center-of-support.

Use the following procedure in the composite beam overwrites on the Bracing(C) or Bracing tab to specify point braces:

1. Check the box next to the Bracing Condition overwrite item and thenselect Bracing Specified from the drop-down box to the right of theBracing Condition title.

2. Check the box next to the No. Uniform Braces title and then click inthe cell to the right of the title.

3. The Uniform Braces form appears. In this form:


b. In the Define Uniform Braces area, input distances from end-I inthe Start and End boxes and choose a brace type in the Type box.The distance in the End box must be larger than that in the Startbox. In the Type box, Top means only the top flange is braced;Bottom means only the bottom flange is braced; and All meansboth flanges are braced at that point.

Note:

You can specify whether a bracing point braces the top flange, bottom flange or bothflanges of a beam.

c. Click the Add button to add the brace point.

4. Repeat step 3 as many times as required.


Design Check Locations Technical Note 9 - 7

5. To modify an existing uniform brace specification, do the following:

a. Highlight the item to be modified in the Define Uniform Bracesarea. Note that the highlighted distances and type appear in theedit boxes at the top of the area.

b. Modify the distances and type in the edit boxes as desired.

c. Click the Modify button to modify the uniform brace.

6. To delete an existing uniform brace specification, do the following:

a. Highlight the item to be deleted in the Define Uniform Braces area.Note that the highlighted distances and type appear in the editboxes at the top of the area.

b. Click the Delete button to delete the uniform brace.

7. Click the OK button to return to the Composite Beam Overwrites form.Note that the No. Uniform Braces item is automatically updated by theprogram to reflect the uniform braces specified.

Design Check LocationsOne of the first tasks the program performs when designing or checking acomposite beam is to determine the design check locations for the designload combinations used for checking the strength of the beam to carry thefinal design loads. There may be many design check locations along a beam.The design check locations are determined as follows:

The point of maximum positive moment for each design load combinationused for checking the strength of the beam to carry the final design loadsis a design check location. Note that there may be more than one of thesedesign load combinations and thus there may be more than one point ofmaximum moment to consider.

The point of maximum negative moment (if negative moment exists) foreach design load combination used for checking the strength of the beamto carry the final design loads is a design check location.


Technical Note 9 - 8 Design Check Locations

A point load or point moment location for any design load combinationused for checking the strength of the beam to carry the final design loadsis a design check location.

The ends of a cover plate, if one is specified, are design check locations.

The end or edge of the deck. This occurs, for example, at locations wherethe beam spans through an opening in the deck.

At each design check location the program checks the moment capacity of thecomposite beam and determines the number of shear connectors requiredbetween that location and the nearest point of zero moment (or in some spe-cial cases, the end of the slab).

Note:

The program determines one set of design check locations that applies to all design loadcombinations.

Consider, for example, a composite beam with two design load combinationsused for checking the strength of the beam to carry the final design loads.Assume one of those load combinations is a uniform load over the full lengthof the beam and the other is a point loads at the third points of the beam.Also assume there is positive moment only in the beam and no cover plate. Inthis example, the program considers the following design check locations:

The point of maximum positive moment for the design load combinationwith uniform load only.

The point of maximum positive moment for the design load combinationwith point loads at the third points.

The locations of the point loads, that is, the third points of the beam.

The program checks the moment capacity and the number of shear connec-tors required between each of these four locations and the nearest point ofzero moment for both of the design load combinations. Thus, for the designload combination with uniform load only, the program still checks how manyshear studs are required between the location of the point load in the otherdesign load combination and the nearest point of zero moment. This ensuresthat there is always a sufficient number of shear connectors in the appropri-ate location on the beam.




Technical Note 10Design Load Combinations

OverviewThis Technical Note described the three types of design load combinations forcomposite beam design in the program:

Strength Check for Construction Loads: Design load combinations forchecking the strength of the beam to carry construction loads. Note thatthis design load combination is only considered if the beam is specified tobe unshored.

You can specify on the Beam tab in the composite beam preferences thatall beams considered by the Composite Beam Design postprocessor areshored. Access these preferences using the Options menu > Prefer-ences > Composite Beam Design command. Modify the shoring prefer-ence for selected beams on the Beam tab in the composite beam over-writes. Access the overwrites by selecting a beam and then clicking theDesign menu > Composite Beam Design > View/Revise Overwritescommand.

Strength Check for Final Loads: Design load combinations for checkingthe strength of the beam to carry the final design loads.

Deflection Check for Final Loads: Design load combinations for check-ing the deflection of the beam under final design loads.

Note:

This program automatically creates code-specific design load combinations for compositebeam design.

Tip:

None of the program default load combinations include the effect of lateral loads. If lateralloads need to be considered, you should specify your own design load combinations.

Design Load Combinations Composite Beam Design

Technical Note 10 - 2 Special Live Load Patterning for Cantilever Back Spans

The design load combinations are defined separately for each of these threeconditions. The program automatically creates code-specific composite beamdesign load combinations for each of the three types of design load combina-tions based on the specified dead, superimposed dead, live and reducible liveload cases. You can add additional design load combinations and modify ordelete the program-created load combinations. Use the Design menu >Composite Beam Design > Select Design Combo command to review ormodify design load combinations. Note that the Design Load CombinationsSelection form that appears when you use this command has three separatetabs. There is one tab for each of the three types of load combinations.

Special Live Load Patterning for Cantilever Back SpansFor strength design of cantilever back spans, the program performs speciallive load patterning. The live load patterning used for cantilever back spans isslightly different from what you might expect, so you should read this sectioncarefully to understand what the program does.

Each composite beam design load combination for a cantilever has a deadload (DL), superimposed dead load (SDL) and a live load plus reduced liveload (LL + RLL) component. There may also be other types of load compo-nents as well. The nature of the other types of load components is not im-portant. The DL, SDL, (LL + RLL) and other components are shown in Figure1a.

The program internally creates a simply supported model of the cantileverback span. It applies a load to this simply supported span that is equal to afactor times the LL + RLL applied to the span. The factor used is specified onthe Beam tab in the composite beam design preferences as the Pattern LiveLoad Factor. (Access the preferences using the Options menu > Prefer-ences > Composite Beam Design command.) This internally created modeland loading is illustrated in Figure 1b. In the figure, PLLF is short for PatternLive Load Factor.

Finally for strength design (final loads only) of cantilever back spans, the pro-gram considers the following two conditions for each design load combination:

Composite Beam Design Design Load Combinations

Special Live Load P

DL + SDLover the fu

DL + SDL span plus by the Paspan.

These two con

Note that the sign for final checks for def

DL SDL

Figure 1: CoSp

atterning for Cantilever Back Spans Technical Note 10 - 3

+ LL + RLL (+ any other type of load if it exists) as specifiedll length (back span plus overhang) of the cantilever beam.

(+ any other type of load if it exists) over the full length (backoverhang) of the cantilever beam plus the (LL + RLL) multipliedttern Live Load Factor applied to the simply supported back

ditions are shown in Figure 1c.

conditions described herein are only considered for strength de-loads. The program does not do any special pattern loadinglection design or for construction loading design.

a) Components of a Design Load Combination

LL + RLL

b) Simply Supported Back Span with Factored LL + RLL Loading

PLLF * (LL + RLL)

c) Two Conditions Considered for Each Design Load Combination

DL + SDL + LL + RLL + Other

DL + SDL + Other PLLF * (LL + RLL)

1.

2. +

Other

Note: PLLF = The Pattern Live Load Factor asspecified on the Beam tab in thecomposite beam preferences.

nditions Considered for Strength Design of a Cantilever Backan


Technical Note 10 - 4 Special Live Load Patterning for Continuous Spans

Note:

The live load patterning used for continuous spans is slightly different from what youmight expect, so you should read this section carefully to understand what the programdoes.

If load patterning different from that provided by the program is needed, youshould create your own design load combination. When creating your own liveload patterning, it typically works best if you give the specially defined pat-tern live load cases an “Other” design type instead of a “Live Load” designtype. That way, the special pattern live load cases are not included in theautomatically created default design load combinations, avoiding possibledouble counting of some live loads in those load combinations.

Special Live Load Patterning for Continuous SpansFor strength design of spans that are continuous at one or both ends, theprogram performs special live load patterning similar to that described in theprevious section for back spans of cantilevers. The live load patterning usedfor continuous spans is slightly different from what you might expect, so youshould read this section carefully to understand what the program does.

Each composite beam design load combination for a continuous span has aDL, SDL and (LL + RLL) component. There may also be other types of loadcomponents as well. The nature of the other types of load components is notimportant. The DL, SDL, (LL + RLL) and other components are shown in Fig-ure 2a.

The program internally creates a simply supported model of the continuousspan. It applies a load to this simply supported span that is equal to a factortimes the LL + RLL applied to the span. The factor used is specified on theBeam tab in the composite beam design preferences as the Pattern Live LoadFactor. (You can access the preferences using the Options menu > Prefer-ences > Composite Beam Design command.) This internally created modeland loading is illustrated in Figure 2b. In the figure, PLLF is short for PatternLive Load Factor.

Finally for strength design (final loads only) of continuous spans, the programconsiders the following two conditions for each design load combination:

Composite Beam Design Design Load Combinations

Special L

DLwit

DLconapp

These

Figure

DL SDL

ive Load Patterning for Continuous Spans Technical Note 10 - 5

+ SDL + LL + RLL (+ any other type of load if it exists) as specifiedh actual continuity.

+ SDL (+ any other type of load if it exists) as specified with actualtinuity plus the (LL + RLL) multiplied by the Pattern Live Load Factorlied to the simply supported beam.

two conditions are shown in Figure 2c.

2: Conditions Considered for Strength Design of a Continuous Span

a) Components of a Design Load Combination

b) Simply Supported Span with Factored LL + RLL Loading

c) Two Conditions Considered for Each Design Load Combination

PLLF * (LL + RLL)

1.

2. +

LL + RLL

DL + SDL + LL + RLL + Other

DL + SDL + Other

Other

PLLF * (LL + RLL) Note: PLLF = The Pattern Live Load Factor asspecified on the Beam tab in thecomposite beam preferences.


Technical Note 10 - 6 Special Live Load Patterning for Continuous Spans

Note that the conditions described herein are only considered for strength de-sign for final loads. The program does not do any special pattern loadingchecks for deflection design or for construction loading design.

If load patterning different from that provided by the program is needed, youshould create your own design load combination. When creating your own liveload patterning, it typically works best if you give the specially defined pat-tern live load cases an “Other” design type instead of a “Live Load” designtype. That way, the special pattern live load cases are not included in theautomatically created default design load combinations, avoiding possibledouble counting of some live loads in those load combinations.

Deflection Technical Note 11 - 1



Technical Note 11Beam Deflection and Camber

This Technical Note describes how the program calculates beam deflectionsand how it considers beam camber.

DeflectionIn the Composite Beam Design postprocessor, when a beam is shored, thedeflection is calculated using (a) the transformed moment of inertia, Itr, ifthere is full (100%) composite connection, (b) the effective moment of iner-tia, Ieff, if there is partial composite connection, or (c) the moment of inertiaof the steel beam alone, Ibare, if the beam is designed noncompositely orfound to be a cantilever overhang.

Note:

The program checks the deflection of composite beams against default or user-specifieddeflection limits.

Itr is calculated as follows:

( ) 2trO

21trtr yAIyAI ∑∑∑ −+= Eqn. 1

where,

Atr = Area of an element of the composite beam section, in2.

yl = Distance from the bottom of the bottom flange of the steelbeam section to the centroid of an element of the beam sec-tion, in.

IO = Moment of inertia of an element of a steel beam section takenabout its own elastic neutral axis, in4.

y = Distance from the bottom of the bottom flange of the steelbeam section to the elastic neutral axis of the fully compositebeam, in.

Beam Deflection and Camber Composite Beam Design

Technical Note 11 - 2 Deflection

Ieff is calculated as follows:

( )baretrbareeff IIPCCII −+= Eqn. 2

where,

PCC = Percent composite connection, unitless. The percentage variesbetween 25% and 100% inclusive.

Ibare = Moment of inertia of the steel beam alone plus cover plate, if itexists, in4.

Ieff = Effective moment of inertia of a partially composite beam, in4.

Itr = Transformed section moment of inertia about elastic neutralaxis of the composite beam calculated as described in Equation1, in4.

Ibare is calculated as follows:

( ) ( ) 2bareO

21bare yAIAyI ∑∑∑ −+= Eqn. 3

where,

∑(Ay12) = Sum of the product A times y1

2 for all of the elements of thesteel beam section (including the cover plate, if it exists), in4.

∑Io = Sum of the moments of inertia of each element of the beamsection taken about the center of gravity of the element, in4.

∑A = Sum of the areas of all of the elements of the steel beamsections (including the cover plate, if it exists), in2.

ybare = Distance from the bottom of the bottom flange of the steelsection of the elastic neutral axis of the steel beam (pluscover plate, if it exists), in.

If a composite beam is unshored, the dead load deflection is always based onthe moment of inertia of the steel section alone (plus cover plate, if it exists),Ibare. The deflection for all other loads is calculated using (a) the transformedmoment of inertia, Itr, if there is full (100%) composite connection, (b) the

Composite Beam Design Beam Deflection and Camber

Original position of beam

Deflection Technical Note 11 - 3

effective moment of inertia, Ieff, if there is partial composite connection, or (c)the moment of inertia of the steel beam alone, Ibare, if the beam is designednoncompositely or found to be a cantilever overhang.

When deflection is used as a criterion for selecting the optimum beam size,the program checks that the total load deflection minus the camber does notexceed the specified total load deflection limit. It also checks that the live loaddeflection does not exceed the specified live load deflection limit.

The program calculates composite beam deflections using a moment-areatechnique. An M/EI diagram is constructed by calculating M/EI values at eachoutput station along the length of the beam and then connecting the M/EIvalues at those stations with straight-line segments. The program assumesthat the moment of inertia does not vary along the length of the beam (lineobject).

Deflections for the beam are calculated at each output station. The overalldeflected shape of the beam is drawn by connecting the computed values ofdeflection at each output station with straight-line segments. Thus, the pro-gram assumes a linear variation of M/EI between output stations.

In this program's composite beam design, the reported deflection is the verti-cal displacement relative to a line drawn between the deflected position ofthe ends of the beam. For example, refer to the beam shown in Figure 1. Fig-ure 1a shows the original undeformed beam and also shows an arbitrary point

AA

Line betweenposition of beamshown

Deflection reported byComposite Beampostprocess

b) Deflected Shape ofa)

Figure 1: Deflection Results Reported by the Composite Beam DesignPostprocessor

Beam Deflection and Camber Composite Beam Design

Technical Note 11 - 4 Camber

along the beam labeled A. Figure 1b shows the beam in its deformed positionand illustrates the deflection that the Composite Beam Design postprocessorreports for the beam at point A.

Deflection Reported for Cantilever OverhangsFor cantilever overhangs, the program's Composite Beam Design postproces-sor reports the displacement of the beam relative to the deformed position ofthe supported end. This displacement is calculated by the design postproces-sor assuming that the supported end of the cantilever overhang is fixedagainst rotation.

If you use the Display menu > Show Deformed Shape command to reviewthe displacement at the end of the cantilever, the displacement is reportedrelative to the undeformed position of the end of the cantilever. In that case,the rotation at the supported end of the cantilever overhang is correctly takeninto account. However, the displacements displayed are all based on theanalysis section properties (noncomposite moment of inertias).

CamberWhen beam camber is calculated, the amount of camber is based on a per-centage of the dead load (not including superimposed dead load) deflection.By default, this percentage is 100%, but you can modify this value on theDeflection tab of the composite beam design preferences. The name of theitem to modify is "Camber DL (%)." Use the Options menu > Preferences> Composite Beam Design command to access the composite beam designpreferences.

The minimum camber that the program specifies (other than zero) is ¾ inch.The maximum camber the program specifies is 4 inches. The program speci-fies the camber in ¼ inch increments. Table 1 shows how the program as-signs camber to a beam based on the specified percentage of dead load de-flection.

Composite Beam Design Beam Deflection and Camber

Camber Technical Note 11 - 5

Table 1: How the Program Specifies Camber

CP * ∆∆∆∆DL

(inches)

CamberSpecified by the

Program(inches)

CP * ∆∆∆∆DL

(inches)

CamberSpecified bythe Program

(inches)

≥ < ≥ <

N.A. 0.5 0 2.375 2.625 2.5

0.5 0.875 0.75 2.625 2.875 2.75

0.875 1.125 1 2.875 3.125 3

1.125 1.375 1.25 3.125 3.375 3.25

1.375 1.625 1.5 3.375 3.625 3.5

1.625 1.875 1.75 3.625 3.875 3.75

1.875 2.125 2 3.875 N.A. 4

2.125 2.375 2.25

In the table, CP is the specified percentage of dead load deflection upon whichthe camber is based. The CP * ∆DL column is broken into two subcolumns la-beled “≥” and “<”. These two subcolumns specify the range of CP * ∆DL forwhich the program specifies a particular camber.

The program specifies camber for those beams for which you request it tospecify camber, regardless of the beam depth or length. Review the beamcambers calculated by the program together with beam camber informationrelated to your design code and any other information provided by your steelfabricator to make any necessary adjustments.




Technical Note 12Beam Vibration

OverviewBy default the program calculates the first natural vibration frequency foreach beam and reports it in the output, but it does not by default use this in-formation to determine the adequacy of a composite beam section. You canchange this on the Preferences tab in the composite beam design preferences.You can also indicate that a beam section must satisfy the Murray minimumdamping requirement to be considered acceptable.

Vibration FrequencyThe program calculates the first natural vibration frequency of a beam usingEquation 1.

3trs

fLW

IEgKf = Eqn. 1

where,

f = First natural frequency of the beam in cycles per second.

Kf = A unitless coefficient typically equal to 1.57 unless the beam is theoverhanging portion of a cantilever with a back span, in which case Kf

is as defined in Figure 1 and digitized in Table 1, or the beam is acantilever that is fully fixed at one end and free at the other end, inwhich case Kf is 0.56. Note that Figure 1 is based on a similar figurein Murray and Hendrick (1977).

g = Acceleration of gravity, in/sec2.

Es = Steel modulus of elasticity, ksi.

Itr = Transformed section moment of inertia for the composite beam cal-culated assuming full (100%) composite connection, regardless of the

Beam Vibration Composite Beam Design

T

actual percent composite connection, in4. Itr is calculated using Equa-tion 1 of Composite Beam Design Technical Note 11 Beam Deflectionand Camber. If there is no deck supported by the beam, Ibare is usedfor this item. Ibare is calculated using Equation 3 of Composite BeamDesign Technical Note 11 Beam Deflection and Camber.

W = Total load supported by the beam, kips. This is calculated by the pro-gram as the sum of all of the dead load and superimposed dead loadsupported by the beam, plus a percentage of all of the live load andreducible live load supported by the beam. The percentage of liveload is specified in the composite beam preferences. The percentageis intended to be an estimate of the sustained portion of the live load(about 10% to 25% of the total design live load). See Naeim (1991).Also see the Important Note About W.

L = Center-of-support to center-of-support length of the beam, in.

Note:

For vibration calculations, the program calculates the moment of inertia assuming full(100%) composite connection, regardless of the actual percent composite connection.

Important Note About W, the Weight Used in the Frequency Calculation

The weight, W, used in the frequency calculations is determined by theprogram as the sum of all dead loads, plus the sum of all superimposeddead loads, plus some percentage of the sum of all live loads and reducedlive loads on the beam, regardless of whether those loads are included in adesign load combination. The program determines the type of load (dead,live, etc.) based on the type of load specified in the load case definition.You define a load case using the Define menu > Static Load Casescommand.

Thus, for the program to correctly calculate the weight supported by thebeam, and thus correctly calculate the frequency, you must be sure to tagall of your load types correctly when you define your static load cases. Becareful not to define the same load twice (i.e., in two different load cases)as a Dead, Superimposed dead, Live or Reducible Live load type. If youwant or need to define the same load twice, you may want to tag the loadas an Other-type load in the second case. Doing this keeps the programfrom double counting the load when calculating the weight, W.

echnical Note 12 - 2 Vibration Frequency

Composite Beam Design Beam Vibration

Vibration Frequency Technical Note 12 - 3

Table 1:Table 1 Digitization of Figure 1 as used by the Program

Point H/L Kf Point H/L Kf Point H/L Kf

1 0 1.57 11 0.6 0.8 21 1.6 0.15

2 0.05 1.57 12 0.7 0.64 22 1.7 0.14

3 0.1 1.56 13 0.8 0.52 23 1.8 0.13

4 0.15 1.55 14 0.9 0.43 24 1.9 0.12

5 0.2 1.53 15 1 0.37 25 2 0.11

6 0.25 1.5 16 1.1 0.31 26 2.1 0.1

7 0.3 1.44 17 1.2 0.27 27 2.2 0.09

8 0.35 1.35 18 1.3 0.22 28 2.3 0.08

9 0.4 1.25 19 1.4 0.2 29 2.4 0.07

10 0.5 1.03 20 1.5 0.17 30 2.5 0.06

Figure 1: Kf Coefficient for an Overhanging Beam for use in Equation 1.See the definition of Kf on page 1 of this Technical Note.

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Freq

uenc

y Co

effic

ient

, Kf

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.40

Cantilever / Backspan Ratio, H / L

L H

3tr

f LW

IEgKf =


Technical Note 12 - 4 Murray’s Minimum Damping Requirement

Murray’s Minimum Damping RequirementIn his paper entitled “Acceptability Criterion for Occupant-Induced Floor Vi-brations,” Thomas M. Murray (Murray 1981) proposed that a criterion for ac-ceptable steel beam-concrete slab floor systems subject to human walkingvibrations is as shown in Equation 2:

2.5fNA

35Deff

sb +≥ Eqn. 2

where,

D = Damping ratio, percent critical damping inherent in the floorsystem, unitless. This item is specified on the Vibration tab inthe composite beam preferences.

Asb = Initial displacement amplitude of a single beam resulting from aheel drop impact, in.

Neff = The effective number of beams resisting the heel drop impact,unitless.

f = First natural frequency of the beam in cycles per second as cal-culated from Equation 1.

If the damping ratio, D, is greater than the right side of Equation 2, the beamis considered acceptable. Approximate damping ratio values for typical build-ing configurations are published in the literature (see, for example, Allen1974; Allen and Rainer 1976; Allen, Rainer and Pernica 1979; Murray 1975;and Murray 1991). The derivation of the initial displacement amplitude is de-scribed herein.

Initial Displacement AmplitudeTo calculate the initial displacement amplitude of a single beam, Asb, first cal-culate the time to the maximum initial displacement, tO, in seconds. This timeis calculated using Equation 3.

f)(0.1πtanfπ

1t 1-O = Eqn. 3


Murray’s Minimum Damping Requirement Technical Note 12 - 5

where f is the first natural vibration frequency as determined from Equation 1and tan-1(0.1πf) is evaluated in radians. After the value of tO has been deter-mined, the value of Asb is calculated from either Equation 4a or 4b, dependingon the value of tO.

sec 0.05 t if ,)t(0.1I2.4E

LPA OO

trs

3O

sb ≤−= Eqn. 4a

sec 0.05 t if ,VF*f2

1*

I2.4ELP

A Otrs

3O

sb >π

= Eqn. 4b

where,

( ) ( )[ ] ( )2f1.0f1.0cosf0.1sinf0.1-12VF π+π−ππ= Eqn. 4c

In Equation 4c, the terms sin(0.1πf) and cos(0.1πf) are evaluated in radians.

In Equations 4a through 4c,

Asb = Initial displacement amplitude of a single beam resulting from aheel drop impact, in.

PO = Heel drop force, kips. This force is taken as 0.6 kips.


Es = Steel modulus of elasticity, ksi.

Itr = Transformed section moment of inertia for the composite beamcalculated assuming full (100%) composite connection, re-gardless of the actual percent composite connection, in4. Itr iscalculated using Equation 1 of Composite Beam Design Techni-cal Note 11 Beam Deflection and Camber. If there is no decksupported by the beam, Ibare is used for this item. Ibare is calcu-lated using Equation 3 of Composite Beam Design TechnicalNote 11 Beam Deflection and Camber.

f = First natural frequency of the beam in cycles per second, ascalculated from Equation 1 of this Technical Note.


Technical Note 12 - 6 Murray’s Minimum Damping Requirement

Effective Number of Beams Resisting Heel Drop ImpactThe program defaults to using an Neff value of 1. Alternatively, specify a valueof Neff on the Vibration tab in the composite beam overwrites, if desired, orspecify that the program calculate Neff using Equation 5 of this Technical Note.

Note:

The program defaults to using an Neff value of 1. You can specify your own value of Neff inthe composite beam overwrites, if desired, or you can specify that the program calculateNeff based on a user-specified beam spacing using Equation 5.

Note the following about the program's implementation of Equation 5:

• When calculating Neff using Equation 5, the program does not check orconsider the number of parallel, equally spaced identical beams.

• The beam spacing used in Equation 5 is user input in the composite beamoverwrites.

• If the beam considered is a cantilever overhang, the program calculatedvalue of Neff is always set to 1.0.

• If the beam considered has deck on one side, or less, the program calcu-lated value of Neff is always set to 1.0.

3

btr

48

avg

beff

sL

0.00010IL

10*2.556

ds

0.057762.967N

+

+

−=

−

Eqn. 5

where,

Neff = Effective number of beams resisting heel drop impact, unitless.

sb = Beam spacing as input by the user in the composite beamoverwrites, in.

davg = Average depth of concrete slab including the concrete in themetal deck ribs, in.



References Technical Note 12 - 7

Itr = Transformed section moment of inertia for the composite beamcalculated assuming full (100%) composite connection regard-less of the actual percent composite connection, in4. Itr is cal-culated using Equation 1 of Composite Beam Design TechnicalNote 11 Beam Deflection and Camber. If there is no deck sup-ported by the beam, Ibare is used for this item. Ibare is calculatedusing Equation 3 of Composite Beam Design Technical Note 11Beam Deflection and Camber.

The depth davg is calculated as:

rightefflefteff

righteffrightcrightr

rightrrightr

lefteffleftcleftr

leftrleftr

avg bb

btS

hw

btS

hw

d+

+

+

+

= Eqn. 6

where,

wr = Average width of metal deck ribs, in.

hr = Height of metal deck ribs, in.

Sr = Center-to-center spacing of metal deck ribs, in.

tc = Depth of concrete slab above metal deck ribs or depth of solidconcrete slab, in.

beff = Effective slab width for composite design, in.

Each of the above quantities may be different on the left and right sides ofthe beam.

ReferencesAllen, D.L. 1974. Vibrational Behavior of Long Span Floor Slabs. Canadian

Journal of Civil Engineering. Vol. 1, No. 1. September.


Technical Note 12 - 8 References

Allen, D. E., and J.H. Rainer. 1976. Vibration Criteria for Long Span Floors.Canadian Journal of Civil Engineering. Vol. 3, No.2. June.

Allen, D.E., J.H. Rainer, and G. Pernica. 1979. Vibration Criteria for Long SpanConcrete Floors. Vibrations of Concrete Structures. Publication SP-60.American Concrete Institute. Detroit, MI.

Murray, T.H. 1975. Design to Prevent Floor Vibration. Engineering Journal.American Institute of Steel Construction, Inc. Vol. 12, No. 3.

Murray, T.H. 1981. Acceptability Criterion for Occupant-Induced Floor Vibra-tions. Engineering Journal. American Institute of Steel Construction,Inc. Vol. 18, No. 2.

Murray, T.M. 1991. Building Floor Vibrations. Engineering Journal. AmericanInstitute of Steel Construction, Inc. Vol. 28, No. 3.

Murray, T.M. and W.E. Hendrick. 1977. Floor Vibrations and CantileveredConstruction. Engineering Journal. American Steel Institute of SteelConstruction, Inc. Vol. 14, No. 3.

Naeim, F. 1991. Design Practice to Prevent Floor Vibration. Steel Tips, Techni-cal Information & Product Service. Structural Steel Educational Coun-cil. September.


COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001


Technical Note 13Distribution of Shear Studs on a Composite Beam

OverviewThis Technical Note describes how the program calculates and reports thedistribution of shear studs on a composite beam. It begins by introducing theterm “composite beam segments.” Next it describes how the program calcu-lates the shear stud distribution for a beam.

Composite Beam SegmentsFor the purposes of reporting the number of shear studs required on eachcomposite beam, the program divides the top flange of each composite beaminto segments. The segments extend along the length of the beam. Eachcomposite beam consists of one or more composite beam segments.

Note:

When the program designs a composite beam, it reports the required number ofshear studs in each composite beam segment. Therefore, it is very important that youunderstand the explanation in this Technical Note describing how composite beam seg-ments are defined.

A composite beam segment may span between any two of the following threeitems provided that there is concrete on the beam and the beam top flange isavailable over the full length of the segment:

1. The physical end of the beam top flange.

2. Another beam in the program model that frames into the beam beingconsidered.

3. The physical end of the concrete slab on top of the beam considered.

A composite beam segment cannot exist in locations where concrete is notover the beam or where the beam top flange has been coped. Figure 1 shows

Distribution of Shear Studs on a Composite Beam Composite Beam Design

Technical Note 13 - 2 Composite Beam Segments

some examples of composite beam segments. The figure uses the followingnotation:

L = Length of composite beam measured from center-of-support tocenter-of-support, in.

LCBS = Length of a composite beam segment, in.

Note that a composite beam can have more than one composite beamsegment, as shown in Figure 1c.

Physical End of the Beam Top FlangeWhen one or both ends of a composite beam segment lie at the end of acomposite beam, the program must assume the exact location of the end(s)of the beam top flange to calculate a length, LCBS, for the composite beamsegment.

When determining the location of the ends of the beam top flange, the pro-gram begins by assuming that the top flange extends from the center of theleft support to the center of the right support. It then subtracts a supportdistance, S, from each end of the beam and a gap distance, G, from each endof the beam. The gap distance, G, is always 1/2". The support distance variesdepending on the type of support and the angle at which the beam framesinto the support.

If the end of the beam is supported by a wall or a point support, the supportdistance, S, is assumed to be zero. If the end of the beam is supported byanother beam, support distance S is determined as illustrated in Cases 1 and2 in Figure 2, which show the beam supported by an I-shaped beam. A simi-lar method is used in the unusual case of other types of support beams.

If the end of the beam is supported by a column, S is determined as illus-trated in Cases 3, 4 and 5 in Figure 1, which show the beam supported by anI-shaped column. A similar method is used for box columns and in the veryunusual case of some other column shape.

Composite Beam Design Distribution of Shear Studs on a Composite Beam

Composite Beam Segments

Figure 1:

Examples of CompositeBeam Segments, LCBS.

Technical Note 13 - 3

��

c) LCBS when Beams Frame into Considered Beam

L

LCBS

a) LCBS for Beam Between Two Columns

L

LCBS

b) LCBS for Beam Between Two Girders

L

LCBS LCBSLCBS

d) LCBS when Slab Ends in Beam Span

L

LCBS

End ofslab


Techni

Figur

Column

cal Note 13 - 4 Composite Beam Segments

e 2: Examples of Support Distance, S, and Gap Distance, G.

GS

Case 3

GS

G = 0.5"

Case 4

Case 1 Case 2

Case 5

G

S

GS

G

S

θ

θ

d2S =

G = 0.5"

S = bf

2G = 0.5"

S = bf

2G = 0.5"

S = bf

2sinθ

S is the support distance.

G is the gap distance.

If a beam is supported by a wall or a point support, the program assumes that thedimension S is 0".

The dimension bf in Cases1 and 2 is the top flange width of the supporting girder.

The dimension bf in Cases 3 and 5 is the flange width of the supporting column(dimension parallel to the local 3-axis). If the two flanges have different widths, thelarger flange width is used.

The dimension d in Cases 4 and 5 is the depth of the supporting column(dimension parallel to the local 2-axis).

1.

2.

3.

4.

5.

6.

Notes:

Beam

Beam

Beam

Beam

Beam

Gird

er

Gird

er

Column

Column

G = 0.5"

S = , θ ≤ 90° bfsinθ + dcosθ

2


How the Program Distributes Shear Studs on a Beam Technical Note 13 - 5

In the unusual case of some other column shape, the program draws abounding rectangle around the shape. The sides of the rectangle are parallelto the local 2- and 3-axes of the shape. The beam is assumed to connect tothe center of the bounding rectangle. The dimensions of the edges of therectangle are assumed to be bf and d, where bf is the dimension parallel tothe local 3-axis and d is the dimension parallel to the local 2-axis.

Distribution of Shear Studs Within a Composite Beam SegmentThe program always assumes a uniform intensity of shear studs within acomposite beam segment. This is a convenient assumption that in some casesmay lead to a slightly conservative number of shear studs.

How the Program Distributes Shear Studs on a BeamThis section describes how the program calculates the shear stud distributionon a beam.

When determining the distribution of shear studs on a composite beam, theprogram considers the following output stations:

1. The output station with the maximum positive moment.

2. Any output station with a positive moment greater than 0.999 timesthe maximum positive moment.

3. Any output station that has a point load applied to it for any load casedefined in the program. Even if the load case with the point load is notused in the design load combinations for composite beam design, theprogram will still consider the output station associated with the pointload when it determines the shear stud distribution. It will not, how-ever, in any way explicitly consider the loads in that unused load casewhen determining the shear stud distribution.

At each considered output station, the program begins by determining thedistances L1 left and L1 right. These are illustrated in Figure 3 for a typical com-posite beam with positive moment only and with a concrete slab over metaldeck along its entire length. The following notation is used in the figure:


Technical Note 13 - 6 How the Program Distributes Shear Studs on a Beam

L = Length of composite beam measured from center-of-supportto center-of-support, in.

L1 left = Distance from the output station considered to the closestpoint of zero moment or physical end of the beam top flange,or physical end of the concrete slab on the left side of theoutput station considered, in.

L1 right = Distance from the output station considered to the closestpoint of zero moment or physical end of the beam top flange,or physical end of the concrete slab on the right side of theoutput station considered, in.

Next, the program calculates the number of shear studs, N, required withinthe lengths L1 left and L1 right. This is a code-specific calculation and is describedin AISC-ASD89 Composite Beam Design Technical Note 26 Calculation of theNumber of Shear Studs and AISC-LRFD93 Composite Beam Design TechnicalNote 39 Shear Connectors.

The program works along the beam from left to right, making calculations ateach considered output station along the way. These calculations are de-scribed later in this Technical Note. When there is more than one composite

S = = = 5.00 in9.9902

bf

2G = 0.5 in

S = = = 3.50 in7.0052

bf

2G = 0.5 in

4.00 in 5.50 inL1 right = 234.50 inW27X94W24X55

W18X40

L = 30 ft = 360 in

L1 left = 116.00 in

Output station located10 feet from the leftend of the beam

Figure 3: Illustration of L1 left and L1 right



beam segment along the beam, the program must also work back along thebeam from right to left, again making calculations at each considered outputstation along the way, after finishing the pass from left to right.

When the program completes the necessary calculations at each consideredoutput station, it has determined the required uniformly spaced shear studs ineach composite beam segment along the beam based on strength considera-tions. If the calculated number of studs is then found to be less than theminimum required number of studs on the beam, the program increases thenumber of studs on the beam accordingly. This check is described later in thesubsection entitled "Minimum and Maximum Number of Shear Studs in aComposite Beam Segment."

The program also checks if the number of shear studs required based onstrength considerations or minimum stud requirements actually fit on thebeam. This check is described in Composite Beam Design Technical Note 14The Number of Shear Studs that Fit in a Composite Beam Segment. If the re-quired number of studs does not fit on the beam, the program considers thebeam to be inadequate.

In the following description of the calculations the program performs as itsteps along the beam and then back again, the terms LCBSn and NCBSn areused. LCBS is the length of a composite beam segment and NCBS is the numberof uniformly spaced shear studs required in a composite beam segment. Then is the composite beam segment number. The leftmost composite beamsegment is always LCBS1 and the numbering of composite beam segments thenproceeds in order toward the right end of the beam.

The values we are ultimately interested in are the NCBSn values. Note that thefinal NCBSn values calculated are the values of interest. All other NCBSn valuesare intermediate values.

Also in the equations used (Equations 1 through 4d) note that NCBSx Prev is thevalue of NCBSx calculated at the previously considered output station. Finallythe term Roundup used in Equations 1 through 5 means to calculate the indi-cated quantity and round it up to the next integer.



Equations Used When the Program Works from Left to RightWhen the program is working from left to right along the beam, the equationused to calculate NCBSn depends on the location of the output station consid-ered.

Output Station in Composite Beam Segment 1When working along the beam from left to right and the output station con-sidered falls in composite beam segment 1, or at the right end of compositebeam segment 1, Equation 1 is used to determine the value of NCBS1. Notethat when there is only one composite beam segment along the beam, Equa-tion 1 is the equation that is used at each considered output station.

PrevCBS1CBS1right1left1

CBS1

NL*L

N,

LN

MaxRoundup

N

≥

=

Eqn. 1

Values of NCBSn where n > 1 (i.e., values of NCBS for composite beam seg-ments 2, 3, etc.) are not applicable and thus not calculated at these stationswhen working along the beam from left to right.

Note:

In the term NCBS1, the "1" denotes composite beam segment 1.

Output Station in Composite Beam Segment n, n > 1The equations in this subsection are used when the output station consideredfalls in composite beam segment n, where n > 1, and the program is workingfrom left to right along the beam. Note that if the output station consideredcoincides with the right end of composite beam segment n, the output stationis assumed to be in composite beam segment n (when you are working alongthe beam from left to right).

Equation 2a applies for composite beam segments i, where i is an integer lessthan n.

PrevCBSiCBSileft1

CBSi NL*L

NRoundupN ≥

= Eqn. 2a



Equations 2b and 2c apply for composite beam segment n.

If ∑∑−

=

−

=

<1n

1iCBSi

1n

1iCBSi

left1NL*

LN

, use Equation 2b to calculate NCBSn. Otherwise

use Equation 2c to calculate NCBSn.

PrevCBSnCBSn1n

1iCBSileft1

1n

1iCBSi

CBSn

NL*

LL

N-N

Roundup

N

≥

−

=

∑

∑−

=

−

= Eqn. 2b

PrevCBSnCBSnleft1

CBSn NL*L

NRoundupN ≥

= Eqn. 2c

When i > n, values of NCBSi are not applicable and thus are not calculated atthose stations when working along the beam from left to right.

Equations Used When the Program Works from Right to LeftRecall that it is only necessary for the program to work back along the beamfrom right to left if there is more than one composite beam segment alongthe length of the beam. When the program is working back along the beamfrom right to left, the equation used to calculate NCBSn again depends on thelocation of the output station considered.

Output Station in Rightmost Composite Beam SegmentThe equations in this subsection are used when working back along the beamfrom right to left and the output station considered falls in the right-mostcomposite beam segment, or at the left end of the right-most compositebeam segment. For the right-most composite beam segment:

prevrightmostCBSrightmost CBS

rightmostCBSright1left1

rightmost CBS

NN

,L*L

N,

LN

MaxRoundup

N

≥

=

Eqn. 3a



For other composite beam segments that are not the right-most compositebeam segment, Equation 3b applies. In Equation 3b, i represents the com-posite beam segment number.

PrevCBSiCBSi NN = Eqn. 3b

Output Station Not in Rightmost Composite Beam SegmentThe equations in this subsection apply when you are working back along thebeam from right to left. (Note that this implies that there is more than onecomposite beam segment along the beam.) In this section, assume that theoutput station considered falls within (or at the left end of) composite beamsegment n.

Equation 4a applies for composite beam segments i, where i is an integergreater than n. For example, if the output station considered falls in compos-ite beam segment 2, Equation 4a applies to composite beam segments 3, 4,etc.

PrevCBSiCBSiright1

CBSi NL*L

NRoundupN ≥

= Eqn. 4a

Equations 4b and 4c apply for composite beam segment n. For example, if theoutput station considered falls in composite beam segment 2, Equations 4band 4c apply to composite beam segment 2 only.

If ∑∑+=+=

<rightmost

1niCBSi

rightmost

1niCBSi

right1

NL*L

Nuse Equation 4b to calculate NCBSn. Otherwise,

use Equation 4c to calculate NCBSn.

PrevCBSnCBSnrightmost

1niCBSiright1

rightmost

1niCBSi

CBSn

NL*

LL

N-N

Roundup

N

≥

−

=

∑

∑

+=

+= Eqn. 4b

PrevCBSnCBSnright1

CBSn NL*L

NRoundupN ≥

= Eqn. 4c


A Note About Multiple Design Load Combinations Technical Note 13 - 11

Equation 4d applies for composite beam segments i, where i is an integer lessthan n. For example, if the output station considered falls in composite beamsegment 2, Equation 4d applies to composite beam segment 1.

PrevCBSiCBSi NN = Eqn. 4d

Minimum and Maximum Number of Shear Studs in a Composite Beam SegmentAfter the number of shear studs required in a composite beam segment hasbeen calculated using the procedure described in the previous section, theprogram checks that the number of studs is not less than the required mini-mum. This required minimum, MSCBS, is calculated based on the maximumlongitudinal spacing of shear studs along the length of the beam, MaxLS,which is specified on the Shear Studs tab in the composite beam overwrites.This calculations is shown in Equation 5.

=

MaxLSL

RoundupMS CBSCBS Eqn. 5

The program also checks that the number of studs required in a compositebeam segment does not exceed the number that can actually fit in the seg-ment. Composite Beam Design Technical Note 14 The Number of Shear Studsthat Fit in a Composite Beam Segment describes how the program determinesthe maximum number of shear studs that can fit into a composite beam seg-ment.

Note:

The minimum number of shear studs required in a composite beam segment is calcu-lated based on the maximum longitudinal spacing of shear studs specified on the ShearStuds tab in the overwrites.

A Note About Multiple Design Load CombinationsWhen there are multiple design load combinations on a composite beam, theprogram determines the stud distribution separately for each design loadcombination and then uses an intelligent algorithm to determine the final studdistribution that satisfies all design load combinations.

As an example, consider a beam with four composite beam segments (CBS1through CBS4) and two separate design load combinations (1 and 2). Figure4a shows the stud distribution obtained for the first design load combination


Technical N

and Figure 4b shows the stud distribution obtained for the second design loadcombination. Note that the term NCBS in the figure denotes the number ofshear studs in the corresponding composite beam segment.

Figure 4c shows the final stud distribution that reports for this beam. Notethat the intelligent algorithm allows the program to shift one of the five shearstuds required in composite beam segment 2 for design load combination 1out into composite segment 1.

Figure 4

ote 13 - 12 A Note About Multiple Design Load Combinations

: Example for Shear Stud Distribution When Multiple Design LoadCombinations Are Considered.

CBS1 CBS2 CBS3 CBS4

NCBS = 5 NCBS = 5 NCBS = 5 NCBS = 5

a) Shear Stud Distribution for Design Load Combination 1

CBS1 CBS2 CBS3 CBS4


b) Shear Stud Distribution for Design Load Combination 2

CBS1 CBS2 CBS3 CBS4


c) Final Shear Stud Distribution Reported by the Program




Technical Note 14Number of Shear Studs that Fit in a

Composite Beam Segment

GeneralComposite beam segments are defined in "Composite Beam Segments" ofComposite Beam Design Technical Note 13 Distribution of Shear Studs on aComposite Beam. In short, a composite beam segment spans between any ofthe following: (1) physical end of the beam top flange, (2) another beamframing into the beam being considered, (3) physical end of the concrete slabon top of the beam. When the program designs a composite beam, it reportsthe required number of uniformly spaced shear studs in each composite beamsegment.

Tip:

It is very important that you understand how the program defines composite beam seg-ments. See "Composite Beam Segments" of Composite Beam Design Technical Note 13Distribution of Shear Studs on a Composite Beam for more information.

For a beam section to be adequate in the program Composite Beam Designpostprocessor, the stresses and deflections for the beam must be less thanthe allowable stresses and deflections, and the number of shear studs re-quired in each composite beam segment must be less than or equal to themaximum number of shear studs that can fit in the composite beam segment.This Technical Note describes how the program calculates the maximumnumber of shear studs that fit in a composite beam segment.

The program uses the same process to determine the number of shear con-nectors that can fit on a composite beam when there is a solid slab with nometal deck and when the deck ribs span parallel to the beam span. The pro-gram uses a different process when the deck ribs span perpendicular to thebeam. These conditions are described in the next two sections.

Number of Shear Studs that Fit in a Composite Beam Segment Composite Beam Design

Technical Note 14 - 2 Solid Slab or Deck Ribs Oriented Parallel to Beam Span

Solid Slab or Deck Ribs Oriented Parallel to Beam SpanWhen there is a solid slab with no metal deck, or when there is metal deckand the metal deck ribs are assumed to be oriented parallel to the beamspan, the program uses the following process to determine the number ofshear studs that can be placed within a composite beam segment. See "Com-posite Beam Segments" of Composite Beam Design Technical Note 13 Distribution ofShear Studs on a Composite Beam for a definition of a composite beam segment.

Note:

The number of shear studs that can fit in a row across the beam top flange may be lim-ited by the width of the beam top flange, by the width of the deck ribs, or by the MaxStuds per Row item specified on the Shear Studs tab in the composite beam overwrites.

1. The program determines the number of shear studs that can fit in a singlerow across the width of the top flange of the beam. When there is a solidslab (no metal deck), the number of shear studs is limited by the width orthickness of the beam flange (item 1a below), or by the "Max Studs perRow" item specified on the Shear Studs tab in the composite beam over-writes. When the deck spans parallel to the beam, the number of shearstuds may be limited by the width or thickness of the beam flange (item1a below), the width of the metal deck rib (item 1b below), or by the "MaxStuds per Row" item specified on the Shear Studs tab in the compositebeam overwrites. Following is a description of each of these limits:

a. When checking the number of shear studs that fitacross the width of the beam flange, the program as-sumes that the studs are centered about the center-line (web) of the beam and that the center of a shearstud can be no closer than ds or 1 inch, whichever islarger, to the edge of the beam flange. This is illus-trated in the sketch to the right.

In the preceding paragraph and the sketch (above right), ds is the di-ameter of the shear stud. The clearance requirement means that theminimum clear distance from the face of a shear stud to the edge ofthe beam flange is equal to one-half of a shear stud diameter. Forshear studs less than 1" in diameter (typically they are 3/4" in diame-ter), the program clearance is slightly more than one-half of a shear

≥ ds & ≥ 1"

Composite Beam Design Number of Shear Studs that Fit in a Composite Beam Segment

Solid Slab or Deck Ribs Oriented Parallel to Beam Span Technical Note 14 - 3

stud diameter. This clear distance is provided by the program to allowfor adequate welding of the shear stud.

b. When checking the number of shear studsthat fit within a metal deck rib, the programassumes that the studs and deck rib arecentered about the centerline (web) of thebeam and that the center of a shear studcan be no closer than ds + hr/4 to the edgeof the beam flange. This is illustrated in thesketch to the right.

In the preceding paragraph and the sketch, ds is the diameter of theshear stud and hr is the height of the metal deck ribs. The wr dimen-sion in the sketch is the average width of the deck ribs. The spacingbetween the shear studs is the “Min Tran. Spacing” item specified onthe Shear Studs tab in the composite beam design overwrites. Thedefault value for this shear stud spacing is 4ds.

The dimension ds + hr/4 is derived by assuming that the slope of thesides of the metal deck ribs is 2 to 1 and that the clear distance fromthe face of the shear stud to the point where the edge of the deck ribstarts to rise is equal to one-half of a shear stud diameter. This cleardistance is provided by the program to allow for adequate welding ofthe shear stud.

Regardless of the number of studs calculated to fit across the width ofthe beam flange in items 1a or 1b above, the program does not use anumber of studs larger than the “Max Studs per Row” item specifiedon the Shear Studs tab in the composite beam design overwrites.

2. The program determines the number of rows of shear studs that can fitbetween the two considered points on the beam top flange. This numberof rows is controlled by the “Min Long Spacing” item specified on theShear Studs tab in the composite beam design overwrites.

3. The program multiplies the maximum number of shear studs in a singlerow, determined in item 1, by the number of rows of studs that can fit in acomposite beam segment, determined in item 2, to calculate the maxi-mum number of studs that can fit in the composite beam segment.

≥ (ds + hr/4)

wr

≥ (ds + hr/4)

h r


Technical Note 14 - 4 Solid Slab or Deck Ribs Oriented Parallel to Beam Span

Tip:

Modify the default minimum transverse and longitudinal shear stud spacingusing the composite beam overwrites.

Figure 1 is a flowchart that illustrates the details of how the program calcu-lates the maximum number of shear studs that fit in a composite beam seg-ment when there is a solid slab or when the span of the metal deck is parallelto the beam span.

The term "Int" in the flowchart means to calculate the indicated quantity andround the result down to the nearest integer. The definitions of the variablesused in the flowchart are:

tf-top = Thickness of beam top flange, in.

ds = Diameter of a shear stud connector, in.

SPRmax = Maximum number of shear studs that can fit in one rowacross the top flange of a composite beam, unitless.

Temp = Temporary variable equal to the minimum of the 2 or 3 itemsspecified in the parenthesis, in. The items specified are sepa-rated by commas.

bf-top = Width of beam top flange, in.

wr = Average width of metal deck rib, in.

hr = Height of the metal deck rib, in.

MTS = Minimum transverse spacing of shear studs across the beamtop flange as specified on the Shear Studs tab in the compos-ite beam overwrites, in.

MSPR = Maximum shear studs per row across the beam top flange asspecified on the Shear Studs tab in the composite beamoverwrites, unitless.


Solid Slab or Deck Ribs Oriented Parallel to Beam Span Technical Note 14 - 5

RSmax = Maximum number of rows of shear studs that can fit in acomposite beam segment, unitless.

LCBS = Length of a composite beam segment, in.

MLS = Minimum longitudinal spacing of shear studs along the lengthof the beam as specified on the Shear Studs tab in the com-posite beam overwrites, in.

NSmax = Maximum number of shear studs that fit in a composite beamsegment, unitless.

Note that in the flowchart formulation, the studs located closest to the ends ofthe composite beam segment are located no closer than MLS/2 to the ends ofthe composite beam segment. This helps prevent possible double-counting ofshear studs in adjacent composite beam segments.

Figure 1: Flowchart of the Method Used to Determine Maximum Numberof Shear Studs that Can Fit within a Composite Beam SegmentWhen There is a Solid Slab or the Metal Deck Ribs Are OrientedParallel to the Beam SpanThe term "Int" in the flowchart means to calculate the indicated quantityand round the result down to the nearest integer.

MSPR1MTS

TempIntSPR max ≤

+=

?2.5

dtIs s

topf <−

No

SPRmax = 1Yes

=

+−=

MLS

LInt1

MLS

MLSLIntRS CBSCBS

max

NSmax = SPRmax * RSmax

StartHere

Is this a solid slab (i.e., nometal deck)?

No

Temp = Minimum of (bf-top -2ds, bf-top -2)Yes

Temp = Minimum of (bf-top -2ds, wr - 2ds - 0.5hr, bf-top -2)


Technical Note 14 - 6 Deck Ribs Oriented Perpendicular to Beam Span

Deck Ribs Oriented Perpendicular to Beam SpanWhen the deck ribs are oriented perpendicular to the beam span, the programlimits the number of rows of shear studs across the width of the beam flangein each metal deck rib to one. For a typical case with 3/4" diameter shearstuds and an average width of the deck rib equal to 6 inches, it is difficult tofit more than one row of shear studs in a deck rib and still have adequateedge clearances. To have more than one row of shear studs in a single deckrib, specify a user-defined shear connector pattern for the beam.

The process used to determine the number of shear studs that can fit in acomposite beam segment when the metal deck is assumed to span perpen-dicular to the beam span is described as follows.

1. The program determines the number of shear studs that can fit in a singlerow across the width of the top flange of the beam. This number of shearstuds is limited by either the width or thickness of the beam flange, or bythe "Max Studs per Row" item specified on the Shear Studs tab in thecomposite beam overwrites.

When checking the number of shear studs that fitacross the width of the beam flange, the program as-sumes that the studs are centered about the centerline(web) of the beam and that the center of a shear studcan be no closer than either ds or 1 inch, whichever islarger, to the edge of the beam flange. This is illus-trated in the sketch to the right.

In the preceding paragraph and the sketch, ds is the diameter of the shearstud. The clearance requirement means that the minimum clear distancefrom the face of a shear stud to the edge of the beam flange is equal toone-half of a shear stud diameter. For shear studs less than 1" in diame-ter (typically they are 3/4" in diameter), the program clearance is slightlymore than one-half of a shear stud diameter. This clear distance is pro-vided by the program to allow for adequate welding of the shear stud.

≥ ds & ≥ 1"


Deck Ribs Oriented Perpendicular to Beam Span Technical Note 14 - 7

Note:

If the diameter of the shear studs exceeds 2.5 times the thickness of the beam top flange,the shear studs can only be placed directly over the beam web.

Some codes require that if the thickness of the beam flange is less thanthe diameter of the stud divided by 2.5, the shear studs must be locatedon top of the beam web. This means that only one stud can fit across thewidth of the beam flange if tf < ds/2.5. The program checks the top flangethickness for this requirement when determining the number of studs thatfit across the width of the beam flange.

2. The program determines how many deck ribs are available to receiveshear studs within the length of the composite beam segment. To deter-mine this, the program makes several assumptions, which are describedas follows:

a. The midheight of a side of the metal deck rib is assumed to align withone end of the composite beam segment, as shown in Figure 2. Inother words, one end of the composite beam segment is always as-sumed to start with an "up" flute.

b. If one-half or more of the width of a metal deck rib down flute is withinthe length of the composite beam segment, the program assumes that

Figure 2: Illustration of Some of the ETABS Assumptions Used toDetermine the Number of Available Deck Ribs

Length of composite beam segment

Sr - wr

Sr

≥ 0.5 wr for shear stud tobe assumed to fit in thedown fluteMidheight of metal deck rib

is assumed to align withone end of the compositebeam segment as shown.

wr


Technical Note 14 - 8 Different Deck Type or Orientation on Beam Sides

the deck rib is available to receive shear studs. This is illustrated inFigure 2.

c. The minimum longitudinal spacing of shear studs along the length ofthe beam as specified on the Shear Studs tab in the composite beamoverwrites is assumed to apply when the deck ribs run perpendicularto the beam span. In some cases, this could cause deck ribs that arewithin the length of the composite beam segment to be unavailable toreceive shear studs.

3. The program multiplies the maximum number of shear studs in a singlerow across the beam flange, determined as described in item 1, by thenumber of deck ribs within the length of the composite beam segmentthat are available to receive shear studs, determined as described in item2, to calculate the maximum number of studs that can fit in the compositebeam segment.

Figure 3 is a flowchart that illustrates the details of how the program calcu-lates the maximum number of shear studs that fit in a composite beam seg-ment when the span of the metal deck is perpendicular to the beam span.

The term "Int" in the flowchart means to calculate the indicated quantity andround the result down to the nearest integer. The definitions of the variablesused in the flowchart are the same as those used in the Figure 1 flowchart,with the following additions:

Sr = Center-to-center spacing of metal deck ribs, in.

NR = Available number of metal deck ribs within the composite beamsegment that are available to receive shear studs, unitless.

Different Deck Type or Orientation on Beam SidesWhen a different type or orientation of the metal deck exists on the two sidesof the beam, the program determines the maximum number of shear studsthat fits in the composite beam segment for each of the two decktypes/orientations. The smaller maximum value obtained is used as themaximum number of shear studs that fit within the composite beam segment.


Different Deck Type or Orientation on Beam Sides Technical Note 14 - 9

Figure 3: Flowchart of the Method to Determine the MaximumNumber of Shear Studs that Can Fit Within a CompositeBeam Segment When the Metal Deck Ribs Are OrientedPerpendicular to the Beam SpanThe term "Int" in the flowchart means to calculate the indicatedquantity and round the result down to the nearest integer.

Is ds ≤ 1" ?

?2.5

dtIs s

topf <−

No

Yes

SPRmax = 1Yes

+

+

+−= 1

S1S

MLSInt

0.5wSLIntNR

rr

rrCBS

NSmax = SPRmax * NR

No

StartHere

MSPR1MTS

2dbIntSPR stopf

max ≤

+

−= −

MSPR1MTS

2bIntSPR topf

max ≤

+

−= −

Specifying a User-Defined Shear Connector Pattern Technical Note 15 - 1



Technical Note 15User-Defined Shear Stud Patterns

This Technical Note explains how to specify the shear stud pattern yourselfrather than having the program determine the distribution of shear studs foryou. This can be useful if you are checking an existing building or if there is acertain shear stud pattern that you want; for example, one shear stud perfoot of beam length.

Specifying a User-Defined Shear Connector PatternUser-defined shear connector patterns are specified on the Shear Studs tab inthe composite beam overwrites. See AISC-ASD89 Composite Beam DesignTechnical Note 18 Overwrites or AISC-LRFD93 Composite Beam Design Tech-nical Note 31 Overwrites for more information.

Tip:

You can use user-defined shear connector patterns to specify shear connectors in exist-ing construction.

The composite beam overwrites option enable you to specify a uniform spac-ing of shear studs located on top of the beam web and centered along thelength of the beam top flange, or to specify a starting and ending point for abeam section and the number of studs that are uniformly spaced within thebeam section. Use one of these options or use the two options together todefine the studs on a beam.

Important note: The term beam section is purposely used here to differen-tiate it from a composite beam segment. Do not confuse composite beamsections and composite beam segments. They are two entirely different items.Composite beam segments are described in "Composite Beam Segments" ofComposite Beam Design Technical Note 13 Distribution of Shear Studs on aComposite Beam. Beam sections are simply an arbitrary length of the beam,defined by a starting and ending location over which you specify a certainnumber of uniformly spaced shear studs.

User-Defined Shear Stud Patterns Composite Beam Design

Technical Note 15 - 2 Uniformly Spaced Shear Studs Over the Length of the Beam

The following two sections describe the two methods of specifying user-defined shear studs.

Uniformly Spaced Shear Studs Over the Length of theBeamWhen you specify uniformly spaced user-defined shear studs over the lengthof the beam, the program treats the shear studs as if they were all in a singleline along the beam web and disregards any checks for minimum longitudinalspacing requirements.

Figure 1 illustrates uniformly spaced user-defined shear studs over the lengthof the beam. These shear studs are specified by inputting the spacing for theUniform Spacing item on the Shear Studs tab in the composite beam over-writes. Note the following about these shear studs:

1. The shear studs are assumed to occur over the length of the top flangeof the beam. In most cases, this is shorter than the center-of-supportto center-of-support length of the beam.

2. There is assumed to be one shear stud per row. To use this option tospecify 2 studs every 12 inches, specify a spacing of 6 inches. The 6-inch spacing gives you the closest equivalent to two studs every 12inches.

Tip:

Modify the default minimum longitudinal shear stud spacing in the compositebeam overwrites.

3. The program determines the exact distance from the end of the beamtop flange (or end of the concrete slab) to the first shear stud, asshown in Equation 1. In Equation 1 the term "Int" means to calculatethe indicated quantity and round the result down to the nearest inte-ger, and the term "Specified Spacing" is the spacing input in the com-posite beam overwrites for the Uniform Spacing item.

2

SpacingSpecified*SpacingSpecifiedMLS-TFL

Int-TFLED

= Eqn. 1

Composite Beam Design User-Defined Shear Stud Patterns

Uniformly Spaced Shear Studs Over the Length of the Beam Technical Note 15 - 3

where,

ED = Distance from the end of the beam top flange (or end ofthe concrete slab) to the first shear stud, in.

TFL = The length of the beam top flange available to receiveshear studs, in. This length is typically determined bysubtracting the support distance and the gap distance ateach end of the beam from the center-of-support to cen-ter-of-support length of the beam. In special cases, youmay subtract an additional distance if the slab does notexist over some portion of the beam.

MLS = Minimum longitudinal spacing of shear studs along thelength of the beam, as specified on the Shear Studs tab inthe composite beam overwrites, in.

Greater than or equal toMLS / 2 and less than one-half the specified uniformshear connector spacingplus MLS / 2

Specified uniformshear connectorspacing

Elevation

Plan View of Top Flange

Shear studs are centeredalong the length of thebeam top flange

Shear studs at specified uniform spacing centered along length of beam top flange End distanceis the sameat each end

End distanceis the sameat each end

Figure 1: Uniformly Spaced User-Defined Shear Connectors Over theLength of the Beam Specified Using the Uniform Spacing Item onthe Shear Studs Tab in the Composite Beam Overwrites


Technical Note 15 - 4 Additional Shear Studs in Specified Sections of Beam

After the shear studs at the end of the beam top flange (or end of theconcrete slab) have been located using Equation 1, the program knowsthe exact location of each uniformly spaced shear stud along the length ofthe beam.

In Equation 1, the studs at the ends of the beam are assumed to be nocloser than MLS/2 from the end of the beam top flange. The studs at theends of the beam are also assumed to be no farther than (MLS + Speci-fied Spacing)/2 from the end of the beam top flange. Finally, the distancefrom the studs at the ends of the beam to the end of the beam top flangeis assumed to be the same at each end of the beam.

Similar to the preceding, if the concrete slab stops before the end of thebeam, the first shear stud at that end of the beam is assumed to occur ata distance not less than MLS/2 from the end of the slab and not morethan (MLS + the specified uniform spacing)/2 from the end of the slab.

Additional Shear Studs in Specified Sections of BeamWhen you specify the starting and ending points of a beam section and thenumber of uniformly spaced shear studs in the section, the program treatsthe shear connectors as if they were all in a single line and disregards anychecks for minimum longitudinal spacing requirements.

Defining Additional Beam SectionsTo define your own additional beam sections for specifying shear studs, sim-ply specify a distance along the beam that locates the starting point of thebeam section, specify a second (longer) distance along the beam that locatesthe ending point of the beam section, and then specify the total number ofuniformly spaced shear studs that fall within the specified beam section.

Distances can be specified as absolute (actual) distances or relative distances,both measured from the I-end of the beam. A relative distance to a point isthe absolute distance to that point divided by the length of the beam meas-ured from the center-of- support to center-of-support.


Additional Shear Studs in Specified Sections of Beam Technical Note 15 - 5

Tip:

Do not confuse beam sections with composite beam segments. See the section entitled"Specifying a User-Defined Shear Connector Pattern" earlier in this Technical Note formore information.

Use the following procedure in the composite beam overwrites on the ShearStuds tab (display using Design menu > Composite Beam Design >View/Revise Overwrites command) to define shear studs in additionalbeam sections:

1. Check the box next to the "User Pattern?" overwrite item, then click inthe cell to the right and select Yes from the drop-down box.

2. Check the box next to "No. Additional Sections" and then click in thecell to the right.

3. The Additional Sections form appears. In this form:


b. In the Define Additional Beam Sections area, input distances fromend-I in the Start and End boxes and input a total number of uni-

Right end ofbeam section

Left end ofbeam section

Beam section length = 110"

10 spaces @ 10" = 100"5" 5"

Figure 2: Assumed Spacing of User-Defined Shear Studs


Technical Note 15 - 6 Additional Shear Studs in Specified Sections of Beam

formly spaced studs in the No. Studs box. The distance in the Endbox must be larger than that in the Start box.

c. Click the Add button to add the additional beam section.

4. Repeat step 3 as many times as required to define additional beamsections.

5. To modify an existing additional beam section specification, do thefollowing:

a. Highlight the item to be modified in the Define Additional BeamSections area. Note that the highlighted distances and number ofstuds appear in the edit boxes at the top of the area.

b. Modify the distances and number of studs in the edit boxes as de-sired.

c. Click the Modify button to modify the additional beam section.

6. To delete an existing additional beam section specification, do the fol-lowing:

a. Highlight the item to be deleted in the Define Additional Beam Sec-tions area. Note that the highlighted distances and number of studsappear in the edit boxes at the top of the area.

b. Click the Delete button to delete the additional beam section.

7. Click the OK button and you return to the Composite Beam Overwritesform. Note that the No. Additional Sections item is automatically up-dated by the program to reflect the beam sections modifications thatyou specified.

Note the following about the shear studs specified for additional beam sec-tions:

The program assumes that the specified shear studs occur in a single linealong the beam web within the specified length of the beam section. Itfurther assumes that the end shear studs in the beam section are locatedone-half of the equal space from ends of the specified beam section.These assumptions mean that the spacing of shear studs in a beam sec-


Additional Shear Studs in Specified Sections of Beam Technical Note 15 - 7

tion is equal to the length of the beam top flange available to receiveshear studs in the beam section divided by the specified number of shearstuds. See Figure 2 for an example.

The figure shows a beam section that is 110 inches long. Assume that 11shear studs have been specified for this beam section. The spacing ofshear studs in the beam section is equal to the beam section length di-vided by the number of studs, that is, 110"/11 studs = 10"/stud. The endstuds are located one-half of a space, that is, 10"/2 = 5", from each endof the beam section.

Note:

The program does not check shear stud spacing requirements for user-defined shearstud patterns.

Assume you specify a beam section at the end of a beam and the beamtop flange does not exist over a portion of that beam section length. Thiscan often happen because, as described “Physical End of the Beam TopFlange” of Composite Beam Design Technical Note 13 Distribution ofShear Studs on a Composite Beam, the program subtracts a support dis-tance and a gap distance from the end of the beam when computing thelength of the beam top flange.

In that case, the program places all of the specified shear studs on theportion of the top flange that does exist. See Figure 3 for an illustration.

The figure shows a beam section at the end of the beam that is 120inches long. The end of the beam top flange starts 10 inches from thespecified left end of the beam section. Thus, the actual length of topflange available for shear studs is 110 inches. Assume that 11 shear studshave been specified for this beam section.

As previously mentioned, the spacing of shear studs in a beam section isequal to the length of the beam top flange available to receive shear studsin the beam section divided by the specified number of shear studs. Inthis case, 110"/11 studs = 10"/stud. The end studs are located one-half ofa space, that is 10"/2 = 5", from each end of the beam top flange withinthe beam section.


Technical Note 15 -

If the beamfied beam for that bea

Example of a UsRefer to the exlayout shown how each of th

Table 1: Spec

Beam Sectio

1

2

3

Figure 3: ExSp

Beam section length = 120"

8 Additional Shear Studs in Specified Sections of Beam

top flange does not exist over the entire length of the speci-section, the program ignores the shear studs that are specifiedm section.

er-Defined Shear Stud Patternample shown in Figure 4. To specify the actual shear connectorin Figure 4a, you specify three beam sections. Table 1 showse three beam sections should be specified.

ification of Beam Sections in the Example Shown in Figure 4

n Starting Point Ending Point Number of Studs

0' 3.5' 6

3.5' 7.5' 4

7.5' 11' 6

ample Showing No Beam Top Flange Over a Portion of theecified Beam Section Length

Right end ofbeam section

Left end ofbeam section

Available length of beam top flange = 110"

10 spaces @ 10" = 100"5" 5"

10"


How the Program Checks a Beam with User-Defined Shear Studs Technical Note 15 - 9

Figure 4b illustrates how the program interprets the stud pattern as specifiedin Table 1. The location and spacing of shear studs is as described in thebulleted items in the previous subsection entitled “Defining Additional BeamSections.”

How the Program Checks a Beam with User-DefinedShear StudsWhen you define the number and location of shear studs on a beam, the pro-gram performs flexural design somewhat differently from how it is describedelsewhere in this manual. For flexural design with user-defined shear studs,the program calculates the percent composite connection (PCC) at each de-sign output station based on your specified shear stud layout. The programthen calculates the beam section properties for this PCC and derives a flexuralstress ratio (actual stress divided by allowable stress).

Figure 4: Example of a User-Defined shear Stud Pattern

b) Program Assumed Shear Connector Layout

a) Actual Shear Connector Layout

4' 3.5'3.5'

0.8'

0.8'6 shear studs 6 shear studs4 shear studs

5 spaces @ 0.45'

0.8'

0.225' 0.225'

0.5' 0.5'3 spaces @ 1.00' 0.8'5 spaces @ 0.45'

0.225' 0.225'

General and Notation Technical Note 16 - 1


COMPOSITE BEAM DESIGN AISC-ASD89

Technical Note 16General and Notation

Introduction to the AISC-ASD89 Series of TechnicalNotesThe AISC-ASD89 Composite Beam Design series of Technical Notes describesin detail the various aspects of the composite beam design procedure that isused by the program when the user selects the AISC-ASD89 Design Code.The various notations used in this series are listed herein.

The design is based on loading combinations specified by the user. To facili-tate the design process, the program provides a set of default load combina-tions that should satisfy requirements for the design of most building typestructures. See Composite Beam Design Technical Note 10 Design Load Com-binations for more information.

The program also performs the following check, calculation, or analysis pro-cedures in accordance with AISC-LRFD93 requirements:

Checks the width-to-thickness ratios of the beam flanges and web, and, if itexists, the cover plate as specified for compact and noncompact sections inAISC-ASD89 Specification Chapter B, Table B5.1; see Composite Beam De-sign AISC-LRFD93 Technical Note 19 Width to Thickness Checks.

Calculates the transformed moment of inertia for a composite section, Itr;see Composite Beam Design AICS-ASD89 Technical Note 20 TransformedSection Moment of Inertia.

Calculates elastic stresses for positive bending in the steel section and theconcrete slab when there is partial composite connection; see CompositeBeam Design AISC-ASD89 Technical Note 21 Elastic Stresses with PartialComposite Connection.

General and Notation Composite Beam Design AISC-ASD89

Technical Note 16 - 2 General and Notation

Determines the allowable bending stresses using the AISC-ASD89 specifi-cation for composite beams; see Composite Beam Design AISC-ASD89Technical Note 22 Allowable Bending Stresses.

Checks the bending stress for AISC-ASD89 design for cases with and with-out composite action; see Composite Beam Design AISC-ASD89 TechnicalNote 23 Bending Stress Checks.

Check the beam and reaction for shear for AISC-ASD89 composite beamdesign; see Composite Beam Design AISC-ASD89 Technical Note 24 BeamShear.

Defines the program fault allowable shear stud horizontal loads for AISC-ASD89 composite beam design and provides basic equations used to de-termine the number of shear studs on the beam; see Composite Beam De-sign AISC-ASD89 Technical Note 25 Shear Studs.

Determines the placement of shear studs on a composite beam, includingthree example problems; see Composite Beam Design AISC-LRFD93 Tech-nical Note 26 Calculations for Number of Shear Studs . Also see CompositeBeam Design Technical Note 13 Distribution of Shear Studs on a CompositeBeam, Technical Note 14 The Number of Shear Studs that Fit in a Compos-ite Beam Segment Composite Beam Design, and Technical Note 15 User-Defined Shear Stud Patterns Composite Beam Design for more informationabout shear stud distribution.

The program also provides input and output data summaries, which are de-scribed in Composite Beam Design AISC-LRFD93 Technical Note 27 InputData and Technical Note 28 Output Details Composite Beam Design AISC-LRFD93.

NotationAbare Area of steel beam (plus cover plate if one exists), in2. This

area does not include any contribution from the concreteslab.

Ac Area of the concrete slab, in2. When the deck span is per-pendicular to the beam span, this is the area of concrete inthe slab above the metal deck that is above the elastic

Composite Beam Design AISC-ASD89 General and Notation


neutral axis (ENA) of the fully composite beam. When thedeck span is parallel to the beam span, this is the area ofconcrete in the slab, including the concrete in the metaldeck ribs, that is above the ENA of the fully compositebeam. This item may be different on the left and rightsides of the beam.

Aelement Area of an element in the composite section, ignoring anyarea of concrete that is in tension and ignoring any con-crete in the metal deck ribs when the metal deck span isperpendicular to the beam span, in2.

Af Area of compression flange (not including the cover plate,even if it exists), in2

Agt Gross area along the tension plane of a bolted connection,in2.

Ans Net area along the shear plane of a bolted connection, in2.

As Area of rolled steel section alone (without the cover plate,even it one exists), in2

Asb Initial displacement amplitude of a single beam resultingfrom a heel drop impact, in.

Asc Cross-sectional area of a shear stud, in2.

Atr Area of an element of the composite beam section, in2.

Cb Bending coefficient dependent on moment gradient,unitless.

Cbot Cope depth at bottom of beam, in. This item is internallycalculated by the program and it may be different at eachend of the beam. It is used in the shear calculations.

Ctop Cope depth at top of beam, in. This item is internally cal-culated by the program and it may be different at each endof the beam. It is used in the shear calculations.



D Damping ratio, percent critical damping inherent in thefloor system, unitless. This item is used in checking theMurray damping requirement.

DL Acronym for deal load.

Ec Modulus of elasticity of concrete slab, ksi. Note that thiscould be different on the left and right sides of the beam.Also note that this may be different for stress calculationsand deflection calculations. For stress calculations in AISC-ASD89 design Ec is always based on Equation 1 of Com-posite Beam Design Technical Note 20 Transformed Section

Moment of Inertia using the 'cf value specified in the material

properties for the concrete and assuming that the concreteweighs 150 pcf regardless of its actual unit weight. This isconsistent with Section I2.2 of the AISC-ASD89 Specifica-tion.

Es Modulus of elasticity of steel, ksi

ENA Acronym for elastic neutral axis

Fb Allowable bending stress in steel beam, ksi

Fb-bbf Allowable bending stress at the bottom of the beam bot-tom flange, ksi

Fu Minimum specified tensile strength of the steel beam andthe shear studs, ksi

Fv Allowable shear stress in steel beam, ksi

Fy Minimum specified yield stress of structural steel, ksi

Fycp Minimum specified yield stress of cover plate, ksi.

G Gap distance between face of support and end of topflange of steel beam, in. The program always takes thisdistance as 1/2 inch.

Hs Length of shear stud connector after welding, in.



Ibare Moment of inertia for a steel beam (plus cover plate, if itexists), in4.

Ieff Effective moment of inertia for a beam about the ENA of acomposite beam with partial composite connection, in4.

I0 Moment of inertia of an element of a steel beam sectiontaken about its own ENA, in4.

Is Moment of inertia of the steel beam along (not includingcover plate, even if it exists), in4.

Itr Transformed section moment of inertia about ENA of acomposite beam with full (100%) composite connection,in4.

Kf A unitless coefficient typically equal to 1.57 unless thebeam is the overhanging portion of a cantilever with abackspan, in which case, Kf is as defined in Figure 1 ofComposite Beam Design Technical Note 12 Beam Vibration,or the beam is a cantilever that is fully fixed at one endand free at the other end, in which case Kf is 0.56.

L Center-of-support to center-of-support length of the beam,in.

Lc Limiting unbraced length for determining allowable bendingstress, in.

LCBS Length of a composite beam segment, in. A compositebeam segment spans between any of the following: (1)physical end of the beam top flange, (2) another beamframing into the beam being considered, (3) physical endof concrete slab. Figure 1 of Composite Beam DesignTechnical Note 13 Distribution of Shear Studs on a Com-posite Beam illustrates some typical cases for LCBS.



L1left Distance from an output station to an adjacent point ofzero moment or physical end of the beam top flange, orphysical end of the concrete slab, measured toward the leftend (I-end) of the beam, in.

L1right Distance from an output station to an adjacent point ofzero moment or physical end of the beam top flange, orphysical end of the concrete slab, measured toward theright end (J-end) of the beam, in.

LL Acronym for live load.

M Moment, kip-in.

MAll Other Moment due to all loads except dead load, kip-in.

MDL Moment due to dead load, kip-in.

Mmax station Maximum moment at any output station for a given designload combination, kip-in.

Mstation Moment at the output station considered for the designload combination, kip-in.

M1 Smaller bending moment at the end of the unbraced beamspan, kip-in. This is used when the program calculates theCb factor.

M2 Larger bending moment at the end of an unbraced beamspan, kip-in. This is used when the program calculates theCb factor.

MaxLS Maximum longitudinal spacing of shear studs along thelength of the beam, in. This item is specified on the ShearStuds tab in the composite beam overwrites.

MLS Minimum longitudinal spacing of shear studs along thelength of the beam, in. This item is specified on the ShearStuds tab in the composite beam overwrites.



MSCBS Minimum required number of shear studs in a compositebeam segment, unitless.

MSPR Maximum shear studs per row across the beam top flangeas specified on the Shear Studs tab in the composite beamoverwrites, unitless.

MTS Minimum transverse spacing of shear studs across thebeam top flange as specified on the Shear Studs tab in thecomposite beam overwrites, in.

N The number of shear studs required between an outputstation and adjacent points of zero moment or physical endof the beam top flange, or physical end of the concreteslab, unitless. This number is based on Equation 6, Equa-tion 7, or Equation 9 of Composite Beam Design AISC-ASD89 Technical Note 25 Shear Studs.

NCBS The number of uniformly distributed shear studs that theprogram requires for a composite beam segment, unitless.

Neff The effective number of beams resisting a heel drop im-pact, unitless. This item is used in the vibration calcula-tions.

Nr Number of shear stud connectors in one metal deck rib,but not more than 3 in the calculations even if more than 3studs exist in the rib, unitless. The program uses whatevervalue is specified for the Max Studs per Row item on theShear Studs tab in the composite beam overwrites for Nr,unless that value exceeds 3, in which case the programuses 3.

N1 Number of shear connectors required between the point ofmaximum positive moment and adjacent points of zeromoment for the design load combination, unitless.

N2 Number of shear connectors required between a point loadand the nearest point of zero moment for the design loadcombination, unitless.



NR Number of metal deck ribs within a composite beam seg-ment that are available to receive shear studs when themetal deck span is oriented perpendicular to the beamspan, unitless.

NSmax Maximum number of shear studs that fit in a compositebeam segment, unitless.

PO Heel drop force, kips. This force is taken as 600 poundsconverted to the appropriate units.

PCC Percent composite connection, unitless.

RF Reduction factor for the allowable horizontal load for ashear stud based on the metal deck and shear stud ge-ometry, unitless.

RLL Acronym for reduced live load.

RLLF The reduced live load factor for an element, unitless. TheRLLF is multiplied times the unreduced live load to get thereduced live load.

RSmax Maximum number of rows of shear studs that can fit in acomposite beam segment when there is a solid slab orwhen the metal deck span is oriented parallel to the beamspan, unitless.

S Support distance. This is the assumed distance from thecenter of the support to the face of the support used tocalculate the available length of the beam top flange.

Sbare Section modulus of the steel beam alone (plus cover plate,if it exists) referred to the extreme tension fiber, in3.

Seff Effective section modulus of a partially composite beamreferred to the extreme tension fiber of the steel beamsection (including cover plate, if it exists), in3.



Sr Center-to-center spacing of metal deck ribs, in. This itemmay be different on the left and the right sides of thebeam.

Ss Section modulus of the steel beam alone (not includingcover plate even if it exists), in3.

St-eff The section modulus for the partial composite section re-ferred to the top of the effective transformed section, in3.This item may be different on the left and the right sides ofthe beam.

Str Section modulus for the fully (100%) composite trans-formed section referred to the extreme tension fiber of thesteel section (including cover plate, if it exists), in3. Refer-ring to Figure 1 of Composite Beam Design AISC-ASD89Technical Note 21 Elastic Stresses with Partial CompositeConnection, Str is calculated using Equation 3 of CompositeBeam Design AISC-ASD89 Technical Note 21 ElasticStresses with Partial Composite Connection.

SDL Acronym for superimposed dead load.

SPRmax Maximum number of shear studs that can fit in one rowacross the top flange of a composite beam, unitless.

V Shear force, kips.

Vall Allowable beam shear (end reaction), kips.

Vh Total horizontal shear to be resisted by shear studs be-tween the point of maximum moment and points of zeromoment for full (100%) composite connection, kips.

V'h Total horizontal shear to be resisted by shear studs be-tween the point of maximum moment and points of zeromoment for partial composite connection, kips.



W Total load supported by the beam that is considered whencalculating the first natural frequency of the beam, kips.This is calculated by the program as the sum of all of thedead load and superimposed dead load supported by thebeam plus a percentage of all of the live load and reduciblelive load supported by the beam. The percentage of liveload is specified in the composite beam preferences. Thepercentage is intended to estimate the sustained portion ofthe live load (about 10% to 25% of the total design liveload).

a3 Whichever is smaller of the distance from the top of theconcrete slab to the ENA or the thickness of the concreteabove the metal deck (or the thickness of a solid slab), tc,in. This item may be different on the left and right sides ofthe beam.

a4 Whichever is smaller of the distance from the top of themetal deck to the ENA or the height of the metal deck, hr,in. This item applies when there is metal deck (not a solidslab) and the ENA falls below the top of the metal deck.This item may be different on the left and right sides of thebeam.

b Width, in.

bcp Width of cover plate, in.

beff Effective width of concrete flange of composite beam, in.This item may be different on the left and the right sides ofthe beam.

beff par Effective width of concrete flange of composite beam,when there is partial composite connection, transformed toan equivalent width of steel (that is, multiplied by Ec / Es),in. This item may be different on the left and the rightsides of the beam.

bf Width of flange of a rolled steel beam, in.



bf-bot Width of steel beam bottom flange, in.

bf-top Width of steel beam top flange, in.

b1 Smaller of the width of the beam bottom flange and thewidth of the cover plate, in.

b2 Projection of the cover plate beyond the edge of the beambottom flange, in. See Figure 1 of Composite Beam DesignAISC-ASD89 Technical Note 19 Width to Thickness Checks.

d Depth of steel beam from the top of the beam top flange tothe bottom of the beam bottom flange, in.

davg Average depth of concrete slab, including the concrete inthe metal deck ribs, in.

delement Distance from the ENA of the element considered to theENA of the steel beam alone (including cover plate if it ex-ists), in. Signs are considered for this distance. Elementslocated below the ENA of the steel beam alone (includingcover plate if it exists) have a negative distance and thoseabove have a positive distance.

ds Diameter of a shear stud, in.

f First natural frequency of the beam in cycles per second.

fb Bending stress, ksi.

fbot-bm The maximum tensile stress at the bottom of the bottomflange of the steel beam, ksi.

fbot-st The maximum tensile stress at the bottom of the steelsection (including cover plate, if it exists), ksi.

fc The maximum concrete compressive stress, ksi.

ftop-st The maximum stress at the top of the steel beam (may betension or compression depending on the location of theENA), ksi.



fv Shear stress, ksi.

f'c Specified compressive strength of concrete, ksi.

g Acceleration of gravity, in/seconds2.

h Clear distance between flanges less the fillet of corner ra-dius for rolled shapes and clear distance between flangesfor other shapes, in.

hr Height of metal deck rib, in.

*rh Height of the metal deck ribs above the elastic neutral axis

(i.e., that is in compression) used for calculating thetransformed section properties, in. Note that this could bedifferent on the left and right sides of the beam.

If the deck ribs are oriented perpendicular to the beamspan, *

rh = 0.

If the deck ribs are oriented parallel to the beam span, oneof the following three items applies:

1. If the ENA is below the metal deck, *rh = hr.

2. If the ENA is within the metal deck, *rh equals the

height of the metal deck above the ENA.

3. If the ENA is above the metal deck, *rh = 0.

kc Unitless factor used in AISC-ASD89 specification EquationF1-4.

l Laterally unbraced length of the compression flange, in.

lh The distance from the center of a bolt hole to the end ofthe beam web, in. The program assumes this distance tobe 1.5 inches as shown in Figure 2 of Composite Beam De-sign AISC-ASD89 Technical Note 24 Beam Shear Checks.



lv The distance from the center of the top bolt hole to the topedge of the beam web (at the cope), in. The program as-sumes this distance to be 1.5 inches as shown in Figure 2of Composite Beam Design AISC-ASD89 Technical Note 24Beam Shear Checks.

n The number of bolts as determined from Table 1 of Com-posite Beam Design AISC-ASD89 Technical Note 24 BeamShear Checks, unitless.

q Allowable shear load for one shear stud, kips.

r T Radius of gyration of a section comprising the compressionflange plus one-third of the compression web area takenabout an axis in the plane of the web, in. The cover plate,if it exists, is ignored by the program when calculating r T.

sb Beam spacing, in.

t Thickness, in.

tc Thickness of concrete slab, in. If there is metal deck, thisis the thickness of the concrete slab above the metal deck.If there is a solid slab, this is the thickness of that slab.This item may be different on the left and right sides of thebeam.

*ct Height of the concrete slab above the metal deck (or solid

slab) that lies above the elastic neutral axis (i.e., is incompression) that is used for calculating the transformedsection properties, in. Note that this could be different onthe left and right sides of the beam.

One of the following three items applies:

1. If the ENA is below the top of the metal deck(bottom of the concrete slab), *

ct = tc.

2. If the ENA is within the concrete slab, *ct equals

the height of the concrete slab above the ENA.



3. If the ENA is above the concrete slab, *ct = 0

tcp Thickness of cover plate, in.

tf Thickness of steel beam flange, in.

tf-bot Thickness of steel beam bottom flange, in.

tf-top Thickness of steel beam top flange, in.

tO Time to the maximum initial displacement of a singlebeam due to a heel drop impact, seconds.

tw Thickness of steel beam web, in.

wc Weight per unit volume of concrete, kips/in3. This itemmay be different on the left and right sides of the beam.

wd Weight per unit area of metal deck, ksi. This item maybe different on the left and right sides of the beam.

wr Average width of the metal deck ribs, in. This item maybe different on the left and right sides of the beam.

ws Weight per unit volume of steel, kips/in3.

y Distance from the bottom of the bottom flange of thesteel beam section to the ENA of the fully compositebeam, in.

ybare Distance from the bottom of the bottom flange of thesteel section to the ENA elastic neutral axis of the steelbeam (plus cover plate, if it exists), in.

ye The distance from the ENA of the steel beam (plus coverplate, if it exists) alone to the ENA of the fully compositebeam, in.

yeff The distance from the bottom of the beam bottom flangeto the ENA of a partially composite beam, in.



y1 Distance from the bottom of the bottom flange of thesteel beam section to the centroid of an element of thebeam section, in.

z Distance from the ENA of the steel beam (plus coverplate, if it exists) alone to the top of the concrete slab,in. Note that this distance may be different on the leftand right sides of the beam.

ΣA Sum of the areas of all of the elements of the steel beamsection (including the cover plate, if it exists), in2.

ΣAtr Sum of the areas of all of the elements of the compositesteel beam section, in2.

Σ(Ay1) Sum of the product A times y1 for all of the elements ofthe steel beam section (including the cover plate, if itexists), in3.

Σ(Atry1) Sum of the product Atr times y1 for all of the elements ofthe composite steel beam section, in3.

Σ(Ay12) Sum of the product A times y1

2 for all of the elements ofthe steel beam section (including the cover plate, if itexists), in4.

Σ(Atry12) Sum of the product Atr times y1

2 for all of the elements ofthe composite steel beam section, in4.

ΣIO Sum of the moments of inertia of each element of thebeam section taken about the center of gravity of theelement, in4.

β Unitless factor used in calculating the number of shearstuds between a point load and a point of zero momentequal to Str/Sbare for full composite connection andSeff/Sbare for partial composite connection.




Technical Note 17Preferences

GeneralThe composite beam design preferences are basic assignments that apply toall composite beams. Use the Options menu > Preferences > CompositeBeam Design command to access the Preferences form where you can viewand revise the composite beam design preferences. The Composite Beam De-sign Preferences form has five separate tabs: Factors, Beam, Deflection, Vi-bration, and Price.

Default values are provided for all composite beam design preference items.Thus, it is not required that you specify or change any of the preferences. Youshould, however, at least review the default values for the preference itemsto make sure they are acceptable to you.

Note:

Default values are provided for all preference items. Thus, if you are happy with the de-faults, you do not need to specify any of the composite beam preferences.

Using the Preferences FormTo view preferences, select the Options menu > Preferences > CompositeBeam Design. The Preferences form will display. The first time you enter thePreferences form, review and, if necessary, change the specified design codein the drop-down box near the bottom of the form.

Click on the desired tab: Factors, Beam, Deflection, Vibration or Price. Thepreference options included under each of the tabs are displayed in a two-column spreadsheet. The left column of the spreadsheet displays the prefer-ence item name. The right column of the spreadsheet displays the preferenceitem value.

To change a preference item, left click the desired preference item in eitherthe left or right column of the spreadsheet. This activates a drop-down box or

Preferences Composite Beam Design AISC-ASD89

Technical Note 17 - 2 Preferences

highlights the current preference value. If the drop-down box appears, selecta new value. If the cell is highlighted, type in the desired value. The prefer-ence value will update accordingly. You cannot overwrite values in the drop-down boxes.

When the preference item is clicked in either column, a short description ofthat item displays in the large text box just below the list of items. This de-scription helps you remember the purpose of each preference item withoutreferring to the documentation.

To set all of the composite beam preference items on a particular tab to theirdefault values, click on that tab to view it and then click the Reset Tab but-ton. This button resets the preference values on the currently selected tab.

To set all of the composite beam preference items on all tabs to their defaultvalues, click the Reset All button. This button immediately resets all of thecomposite beam preference items.

Important note about resetting preferences: The defaults for the prefer-ence items are built into the program. The composite beam preference valuesthat were in a .edb file that you used to initialize your model may be differentfrom the built-in default values. Clicking a reset button resets the preferencevalues to built-in values, not to the values that were in the .edb file used toinitialize the model.

When you have finished making changes to the composite beam preferences,click the OK button to close the form. You must click the OK button for thechanges to be accepted by the program. If you click the Cancel button to exitthe form, any changes made to the preferences are ignored and the form isclosed.

PreferencesFor purposes of explanation in this Technical Note, the preference items arepresented in tables. The column headings in these tables are described asfollows:

Item: The name of the preference item as it appears in the cells at theleft side of the Preferences form.

Composite Beam Design AISC-ASD89 Preferences

Factors Tab Technical Note 17 - 3

Possible Values: The possible values that the associated preference itemcan have.

Default Value: The built-in default value that the program assumes forthe associated preference item.

Description: A description of the associated preference item.

Factors TabFor AISC-ASD89 design there are no items on the Factors tab. Thus, if youclick this tab, it will appear blank.

Beam TabTable 1 lists the composite beam preference items available on the Beam tabin the Preferences form.

Table 1: Composite Beam Preferences on the Beam Tab

ItemPossibleValues

DefaultValue Description

Shored? Yes/No No Toggle for shored or unshored con-struction.

Middle Range(%) ≥ 0% 70%

Length in the middle of the beam overwhich the program checks the effectivewidth on each side of the beam, ex-pressed as a percentage of the totalbeam length.

Pattern LiveLoad Factor ≥ 0 0.75

Factor applied to live load for specialpattern live load check for cantileverback spans and continuous spans.

Stress RatioLimit

>0 0.95The acceptable stress ratio limit. Thisitem only applies to design optimiza-tion.

The Shored item affects both the deflection calculations and the flexural cal-culations for the beam. See Composite Beam Design Technical Note 11 BeamDeflection and Camber for a description of beam deflection. Flexural calcula-tions are described in Composite Beam Design AISC-ASD89 Technical Note 20Transformed Section Moment of Inertia, Technical Note 21 Elastic Stresses


Technical Note 17 - 4 Deflection Tab

with Partial Composite Connection, Technical Note 22 Allowable BendingStresses, and Technical Note 23 Bending Stress Checks. If the beam isshored, checks are performed for the construction loading design load combi-nation (see Composite Beam Design Technical Note 10 Design Load Combina-tions ).

The Middle Range item is described in "Location Where Effective Slab Width isChecked" in Composite Beam Design Technical Note 8 Effective Width of theConcrete Slab.

The Pattern Live Load Factor item is described in "Special Live Load Patterningfor Cantilever Back Spans" and "Special Live Load Patterning for ContinuousSpans" in Composite Beam Design Technical Note 10 Design Load Combina-tion.

Deflection TabTable 2 lists the composite beam preference items available on the Deflectiontab in the Preferences form.

Table 2: Composite Beam Preferences on the Deflection Tab

ItemPossibleValues


Live LoadLimit, L/

> 0 360Live load deflection limitation denomi-nator (inputting 360 means that the de-flection limit is L/360).

Total LoadLimit, L/

> 0 240Total load deflection limitation denomi-nator (inputting 240 means that the de-flection limit is L/240).

Camber DL(%)

> 0 100%Percentage of dead load (not includingsuperimposed dead load) on whichcamber calculations are based.

See Composite Beam Design Technical Note 11 Beam Deflection and Camberfor a description of beam deflection and camber.

Composite Beam Design AISC-ASD89 Preferences

Vibration Tab Technical Note 17 - 5

Vibration TabTable 3 lists the composite beam preference items available on the Vibrationtab in the Preferences form.

Table 3: Composite Beam Preferences on the Vibration Tab

ItemPossibleValues


Percent LiveLoad (%) ≥ 0 25%

Percentage of live load plus reducedlive load considered (in addition to fulldead load) when computing weightsupported by the beam for use incalculating the first natural frequency ofthe beam.

ConsiderFrequency? Yes/No No

Toggle to consider the frequency asone of the criteria to be used for deter-mining if a beam section is acceptable.

MinimumFrequency

> 0 Hz 8 Hz

Minimum acceptable first naturalfrequency for a floor beam. This item isused when the Consider Frequencyitem is set to Yes.

ConsiderMurray Damp-

ing?Yes/No No

Toggle to consider Murray's minimumdamping requirement as one of thecriteria to be used for determining if abeam section is acceptable.

InherentDamping (%)

> 0% 4%

Percentage of critical damping that isinherent in the floor system. This item isused when the Consider MurrayDamping item is set to Yes.

See Composite Beam Design Technical Note 12 Beam Vibration for a descrip-tion of beam vibration.


Technical Note 17 - 6 Price Tab

Price TabTable 4 lists the composite beam preference items available on the Price tabin the Preferences form.

Table 4: Composite Beam Preferences on the Price Tab

ItemPossibleValues


Optimize forPrice?

Yes/No No

Toggle to consider price rather thansteel weight when selecting the opti-mum beam section from an auto selectsection list.

Stud Price ($) ≥ 0 $0Installed price for a single shear studconnector.

Camber Price($) ≥ 0 $0

Camber price per unit weight of steelbeam (including cover plate, if itexists).

See "Using Price to Select Optimum Beam Sections" in Composite Beam De-sign Technical Note 1 General Design Information for additional informationon the "Optimize for Price?" item.

Note that the price per unit weight for the steel beam (plus cover plate, if ap-plicable) is input as part of the material property specification for the beam.The material properties can be reviewed or defined using the Define menu >Material Properties command. Be sure that you use the same currencyunits (for example, U.S. dollars) for the steel price in the material properties,the stud price in the preferences, and the camber price in the preferences.




Technical Note 18Overwrites

This Technical Note provides instructions on how to use the Composite BeamOverwrites form and describes the items available on each of the tabs in theform. One section is devoted to each of the tabs.

GeneralThe composite beam design overwrites are basic assignments that apply onlyto those composite beams to which they are assigned. After selecting one ormore composite beams, use the Design menu > Composite Beam Design> View\Revise Overwrites command to access the Composite Beam Over-writes form where you can view and revise the composite beam design over-writes.

Note:

There are default values provided for all overwrite items. Thus, if you are happy with thedefaults, you do not need to specify any of the composite beam overwrites.

The Composite Beam Overwrites form has eight separate tabs. They areBeam, Bracing (C), Bracing, Deck, Shear Studs, Deflection, Vibration and Mis-cellaneous. Descriptions of the various overwrite options available on each tabare provided later in this Technical Note.

Default values are provided for all composite beam overwrite items. Thus, it isnot required that you specify or change any of the overwrites. However, atleast review the default values for the overwrite items to make sure they areacceptable. When changes are made to overwrite items, the program appliesthe changes only to the elements to which they are specifically assigned; thatis, to the elements that are selected when the overwrites are changed.

Overwrites Composite Beam Design AISC-ASD89

Technical Note 18 - 2 Using the Composite Beam Overwrites Form

Using the Composite Beam Overwrites FormAfter selecting one or more composite beams, use the Design menu >Composite Beam Design > View\Revise Overwrites command to accessthe Composite Beam Overwrites form. Click on the desired tab.

The Composite Beam Overwrites are displayed on each tab with a column ofcheck boxes and a two-column spreadsheet. The left column in the spread-sheet contains the name of the overwrite item. The right column in thespreadsheet contains the overwrite value.

Initially, the check boxes are all unchecked and all of the cells in the spread-sheet have a gray background to indicate they are inactive and that the itemsin the cells currently cannot be changed. The names of the overwrite items inthe first column of the spreadsheet are visible. The values of the overwriteitems in the second column of the spreadsheet are visible if only one beamwas selected before the Composite Beam Overwrites form was accessed. Ifmultiple beams were selected, no values show for the overwrite items in thesecond column of the spreadsheet.

After selecting one or multiple beams, check the box to the left of an over-write item to change it. Then left click in either column of the spread sheet toactivate a drop-down box or to highlight the contents of the cell in the rightcolumn of the spreadsheet. If the drop-down box appears, select a value fromthe box. If the cell contents becomes highlighted, type in the desired value.The overwrite will reflect the change. You cannot change the values in thedrop-down boxes.

When you check a check box or left click in one of the columns in the spread-sheet, a short description of the item in that row displays in the large text boxjust below the list of items. This description helps you recall the purpose ofthe overwrite item without referring to the manual.

When changes to the composite beam overwrites have been made, click theOK button to close the form. The program then changes all of the overwriteitems whose associated check boxes are checked for the selected beam(s).You must click the OK button for the changes to be accepted by the program.If you click the Cancel button to exit the form, any changes made to theoverwrites will be ignored and the form will be closed.

Composite Beam Design AISC-ASD89 Overwrites

Overwrites Technical Note 18 - 3

Resetting Composite Beam Overwrites to Default ValuesTo set all of the composite beam overwrite items on a particular tab to theirdefault values, click on the tab and then click the Reset Tab button. Thisbutton resets the overwrite values on the tab currently selected.

To set all of the composite beam overwrite items on all tabs to their defaultvalues, click the Reset All button. This button immediately resets all of thecomposite beam overwrite items. Alternatively, you can click the Designmenu > Composite Beam Design > Reset All Composite Beam Over-writes command to accomplish the same thing.

Important note about resetting overwrites: The defaults for the over-write items are built into the program. The composite beam overwrite valuesthat were in a .edb file that you used to initialize your model may be differentfrom the built-in program default values. When you reset overwrites, the pro-gram resets the overwrite values to its built-in values, not to the values thatwere in the .edb file used to initialize the model.

OverwritesFor purposes of explanation in this Technical Note, the overwrite items arepresented in tables. The column headings in these tables are described asfollows.

Item: The name of the overwrite item as it appears in the cells at the leftside of the Composite Beam Overwrites form.

Possible Values: The possible values for the associated overwrite item.

Default Value: The built-in default value that the program assumes forthe associated overwrite item.

Description: A description of the associated overwrite item.


Technical Note 18 - 4 Beam Tab

Beam TabTable 1 lists the composite beam overwrite items available on the Beam tab inthe Composite Beam Overwrites form.

Table 1: Composite Beam Overwrites on the Beam Tab

ItemPossibleValues


Shored? Yes/No No(unshored)

Toggle for shored or unshored con-struction.

Beam type Composite,NC w studs, orNC w/o studs

Composite Type of beam design. NC w studs isshort for Noncomposite with minimumshear studs. NC w/o studs is short forNoncomposite without shear studs.

b-eff leftCondition

Programcalculated oruser-defined

Programcalculated

Toggle specifying how the effectivewidth of the concrete slab on the leftside of the beam is determined

b-eff left ≥ 0 Programcalculated

value

User-defined effective width of concreteslab on left side of beam, beff left.

b-eff rightCondition


Programcalculated

Toggle specifying how the effectivewidth of the concrete slab on the rightside of the beam is determined

b-eff right ≥ 0 Programcalculated

value

User-defined effective width of concreteslab on right side of beam, beff right

Beam Fy ≥ 0 Specified inMaterial

Properties

Yield stress of the beam, Fy. Specifying0 in the overwrites means that Fy is asspecified in the material properties

Beam Fu ≥ 0 Specified inMaterial

Properties

Minimum tensile strength of the beam,Fu. Specifying 0 means that Fu is asspecified in the material properties


Beam Tab Technical Note 18 - 5


ItemPossibleValues


Cover PlatePresent?

Yes/No No Toggle switch indicating if a full lengthcover plate exists on the bottom of thebeam bottom flange.

Plate width ≥ 0 0 Width of cover plate, bcp.

Plate thickness ≥ 0 0 Thickness of cover plate, tcp.

Plate Fy > 0 0 Cover plate yield stress, Fycp. Specify-ing 0 means that Fycp is set to thatspecified in the beam material proper-ties

The Shored item affects both the deflection calculations and the flexuralstress calculations for the beam. See Composite Beam Design Technical Note11 Beam Deflection and Camber for a description of beam deflection. If thebeam is shored, no checks are performed for the construction loading designload combination.

Note:

The Middle Range item is specified on the Beam tab in the composite beam preferencesand is described in "Location Where Effective Slab Width is Checked" in CompositeBeam Design Technical Note 8 Effective Width of the Concrete Slab.

Typically, when a beam is designed using the Composite Beam Design post-processor that beam is designed as a composite beam if it has a deck section(not slab section) assigned along the full length of the specified Middle Rangeon at least one side of the beam. The Beam Type overwrite allows you tospecify that a beam that would ordinarily be designed as a composite beambe designed as a noncomposite beam. The overwrite does not and cannotforce a beam that has been designed as a noncomposite beam because thereis no deck section along at least one side to be designed as a compositebeam. When using the Composite Beam Design postprocessor, a beam thatdoes not have a deck section along at least one side is always designed as a


Technical Note 18 - 6 Bracing (C) Tab and Bracing Tab

noncomposite beam, regardless of what is specified in the Beam Type over-write.

When a beam is designed as noncomposite with minimum shear studs, thebeam is designed as a noncomposite beam. Then shear studs are specified forthe beam with as large a spacing as possible, without exceeding the specifiedmaximum longitudinal spacing. The maximum longitudinal spacing can beoverwritten on the Shear Studs tab.

See Composite Beam Design Technical Note 8 Effective Width of the ConcreteSlab for a description of the beam effective width.

The beam yield stress and the cover plate yield stress both default to theyield stress specified for the material property associated with the beam sec-tion. When the Define menu > Frame Sections command is used to definea beam section, the material property associated with the beam sectionshould also be defined. The material property is defined using the Definemenu > Material Properties command.

In this program, the cover plate can have a yield stress that is different fromthat of the beam, if desired. The cover plate width, thickness and Fy items arenot active unless the "Cover Plate Present" item is set to Yes. See "CoverPlates" in Composite Beam Design Technical Note 7 Composite Beam Proper-ties for a description of cover plates.

Bracing (C) Tab and Bracing TabThe unbraced length overwrite items included on the Bracing (C) tab and theBracing tab are exactly the same. The items on the Bracing (C) tab apply toconstruction loading design load combinations. The items on the Bracing tabapply to final condition design load combinations.

The first two items that appear in the Bracing (C) tab and the Bracing tab areshown in Table 2a. Additional items may also appear in the tabs, dependingon your choice for the Bracing Condition item. These additional items areshown in Tables 2b and 2c.


Bracing (C) Tab and Bracing Tab Technical Note 18 - 7

Table 2a: First Two Composite Beam Overwrite Items on theBracing (C) Tab and the Bracing Tab

ItemPossibleValues


Cb factor ≥ 0 Programcalculated

Unitless factor used in determining al-lowable bending stress, Cb. Specifying0 in the overwrites means that thisvalue is program calculated

BracingCondition

Programcalculated,

bracingspecified or

lengthspecified

Programcalculated

This item defines how the unbracedlengths are determined for bucklingabout the beam local 2-axis. They areprogram calculated, based on user-specified uniform and point bracing, orbased on a user-specified maximumunbraced length.

When the Cb factor is program calculated, the program uses Equation 1 tocalculate it unless you have specified the Bracing Condition as Length Speci-fied.

2.3M

M0.3

M

M1.051.75C

2

2

1

2

1b ≤

+

+= Eqn. 1

where,

M1 and M2 are the end moments of any unbraced span of the beam. M1 isnumerically less than M2.

The ratio M1/M2 is positive for double curvature bending and negative forsingle curvature bending within the unbraced beam span.

If any moment within the unbraced beam span is greater than M2, thenumeric value of Cb is 1.0.

The numeric value of Cb is 1.0 for cantilever overhangs.

When the Cb factor is program calculated and the Bracing Condition is set inthe overwrites to Length Specified, the programs uses 1.0 for Cb.


Technical Note 18 - 8 Bracing (C) Tab and Bracing Tab

When the Bracing Condition is specified as Program Calculated, the programassumes the beam is braced as described in "Determination of the BracedPoints of a Beam" in Composite Beam Design Technical Note 9 Beam Un-braced Length. Note that the program automatically considers the bracing forconstruction loading and for the final condition separately. For the construc-tion loading condition, the program assumes that the concrete fill does notassist in bracing the beam.

When the Bracing Condition is specified as Bracing Specified, two items ap-pear in the tab in addition to those shown in Table 2a. The two additionalitems are shown in Table 2b.

Table 2b: Additional Composite Beam Overwrite Items On theBracing (C) Tab and the Bracing Tab When the BracingCondition Is Specified As Bracing Specified

ItemPossibleValues


No. PointBraces

≥ 0 0 The number of user-specified pointbrace locations. Clicking in this boxopens the Point Braces form where youspecify the point braces.

No. UniformBraces

≥ 0 0 The number of user-specified uniformbraces. Clicking in this box opens theUniform Braces form where you specifythe uniform braces.

The No. Point Braces and No. Uniform Braces items allow you to specify actualbracing for the beam. These items are described in "User-Specified Uniformand Point Bracing" in Composite Beam Design Technical Note 9 Beam Un-braced Length.

When the Bracing Condition is specified as Length Specified, two items appearin the tab in addition to those shown in Table 2a. The two additional items areshown in Table 2c.


Deck Tab Technical Note 18 - 9

Table 2c: Additional Composite Beam Overwrite Items On the Brac-ing (C) Tab and the Bracing Tab When the Bracing Condi-tion Is Specified As Length Specified

ItemPossibleValues


AbsoluteLength?

Yes/No No Toggle switch for whether the maxi-mum unbraced length is given as anabsolute length or a relative length.

Unbraced L22 ≥ 0 and ≤beam length

Length ofbeam

Maximum unbraced length for bucklingabout the beam local 2 axis.

When the maximum unbraced length is specified as an absolute length, theactual maximum unbraced length is specified. When the maximum unbracedlength is specified as a relative length, the value specified is equal to themaximum unbraced length divided by the length of the beam. The relativelength specified is always between 0 and 1, inclusive.

See Composite Beam Design Technical Note 9 Beam Unbraced Length for ad-ditional information about the unbraced length of the beam.

Deck TabTable 3 lists the composite beam overwrite items available on the Deck tab inthe Composite Beam Overwrites form.

Table 3: Composite Beam Overwrites On the Deck Tab

ItemPossibleValues


Deck ID Left Programcalculated, anydefined deckproperty, or

None

Programcalculated

Deck ID assigned to left side of beam.


Technical Note 18 - 10 Shear Studs Tab

Table 3: Composite Beam Overwrites On the Deck Tab

ItemPossibleValues


Deck directionLeft

Programcalculated,parallel, or

perpendicular

Programcalculated

Span direction of the metal deck ribs onleft side of beam relative to the spandirection of the beam.

Deck ID Right Programcalculated, anydefined deckproperty, or

None

Programcalculated

Deck ID assigned to right side of beam.

Deck directionRight


perpendicular

Programcalculated

Span direction of the metal deck ribs onthe right side of beam relative to thespan direction of beam.

When the Deck ID is program calculated, you must refer to the output data tosee what the program assumed for this item. It is not shown in the over-writes.

If the deck direction is program calculated, do not overlook the importantnote about deck orientation in "Multiple Deck Types or Directions Along theBeam Length" in Composite Beam Design Technical Note 8 Effective Width ofthe Concrete Slab.

Shear Studs TabTable 4 lists the composite beam overwrite items available on the ShearStuds tab in the Composite Beam Overwrites form.

Table 4: Composite Beam Overwrites On the Shear Studs Tab

ItemPossibleValues


User Pattern? Yes/No No Toggle to indicate if a user-definedshear connector pattern is defined.


Shear Studs Tab Technical Note 18 - 11

Table 4: Composite Beam Overwrites On the Shear Studs Tab

ItemPossibleValues


UniformSpacing

≥ 0 0, indicatingthere are no

uniformlyspaced

connectors

Uniform spacing of shear studs alongthe beam. There is one shear stud perrow along the beam.

No. AdditionalSections


additionalconnectorsspecified

Number of sections in which additionaluniformly spaced shear studs arespecified. Clicking in this box opens theAdditional Sections form where youspecify the section length and the num-ber of uniformly spaced connectors inthe section.

Min LongSpacing

> 0 6ds

(i.e., six studdiameters)

Minimum longitudinal spacing of shearstuds along the length of the beam.

Max LongSpacing

> 0 36 inches Maximum longitudinal spacing of shearstuds along the length of the beam.

Min TranSpacing

> 0 4ds

(i.e., four studdiameters)

Minimum transverse spacing of shearstuds across the beam flange.

Max Studsper Row

> 0 3 Maximum number of shear studs in asingle row across the beam flange.

q Programcalculated or

> 0

Programcalculated

Allowable shear load for a single shearstud. Specifying 0 in the overwritesmeans that this value is program cal-culated.

The Uniform Spacing and No. Additional Sections items are only available ifthe User Pattern item is set to Yes. See Composite Beam Design AISC-ASD89Technical Note 24 Beam Shear Checks for discussion of user-defined shearstud patterns.

The program default value for the minimum longitudinal spacing of shearstuds along the length of the beam is six shear stud diameters. Note that thisitem is input as an absolute length, not as a multiplier on the stud diameter.

The program default value for the maximum longitudinal spacing of shearstuds along the length of the beam is 36 inches. The design code used mayspecify the maximum longitudinal spacing is eight times the total slab thick-


Technical Note 18 - 12 Shear Studs Tab

ness (rib height, hr, plus concrete slab above metal deck, tc). AISC-ASD89Specification Section I5.2.2 specifies that the maximum longitudinal spacingof shear studs along the length of a beam shall not exceed 36 inches forbeams when the span of the metal deck is perpendicular to the span of thebeam. If your total slab thickness is less than 36"/8 = 4.5", the program de-fault value may be unconservative and should be revised.

The program default value for the minimum transverse spacing of shear studsacross the beam flange is four shear stud diameters. This is consistent withthe last paragraph of AISC-ASD89 Specification Section I4. Note that thisitem is input as an absolute length, not as a multiplier on the stud diameter.See Composite Beam Design Technical Note 13 Distribution of Shear Studs ona Composite Beam for additional discussion of how shear studs are distributedon composite beams.

The "Max Studs per Row" item indicates the maximum number of shear studsthat is allowed in a row across the beam flange. For wider beams, the MinTran Spacing item might indicate that more studs could be accommodatedacross the beam flange but the Max Studs per Row item will limit the numberof studs in any row. See Composite Beam Design Technical Note 13 Distribu-tion of Shear Studs on a Composite Beam for additional discussion of howshear studs are distributed on beams.

See "Shear Stud Connector" in Composite Beam Design AISC-ASD89 Techni-cal Note 25 Shear Studs for discussion of how the program calculates the al-lowable shear load for a single shear stud. Note that when a q value is speci-fied in the overwrites, the program assumes that the specified value of q hasalready been modified by any applicable reduction factors for the metal deck.Finally, note that specifying 0 (zero) in the overwrites for this item meansthat the allowable shear stud load is calculated by the program, not that it iszero.

Shear studs are discussed in detail in Composite Beam Design Technical Note13 Distribution of Shear Studs on a Composite Beam, Technical Note 14 TheNumber of Shear Studs that Fit in a Composite Beam Segment, and TechnicalNote 15 User-Defined Shear Stud Patterns.


Deflection Tab Technical Note 18 - 13

Deflection TabTable 5 lists the composite beam overwrite items available on the Deflectiontab in the Composite Beam Overwrites form.

Table 5: Composite Beam Overwrites On the Deflection Tab

ItemPossibleValues


DeflectionAbsolute?

Yes/No No Toggle to consider live load and totalload deflection limitations as absoluteor as divisor of beam length (relative).

Live Load Limit > 0 Specified inPreferences

Deflection limitation for live load. Forrelative deflection, inputting 360 meansthat the limit is L/360.

Total LoadLimit

> 0 Specified inPreferences

Deflection limitation for total load. Forrelative deflection, inputting 240 meansthat the limit is L/240.

CalculateCamber?

Yes/No Yes Toggle for the program to calculatebeam camber.

Fixed Camber ≥ 0 0 User-specified camber when the pro-gram does not calculate beam camber

See Composite Beam Design Technical Note 11 Beam Deflection and Camberfor discussion of beam deflection and camber.


Technical Note 18 - 14 Vibration Tab

Vibration TabTable 6 lists the composite beam overwrite items available on the Vibrationtab in the Composite Beam Overwrites form.

Table 6: Composite Beam Overwrites on the Vibration Tab

ItemPossibleValues


Neff Condition User Definedor ProgramCalculated

User Defined Toggle to select user defined or pro-gram calculated based on beam spac-ing, N effective.

No. EffectiveBeams

≥1 1.0 Effective number of beams resisting aheel drop impact.


Miscellaneous TabTable 7 lists the composite beam overwrite items available on the Miscellane-ous tab in the Composite Beam Overwrites form.

Table 7: Composite Beam Overwrites on the Miscellaneous Tab

ItemPossibleValues


ConsiderBeam Depth?

Yes/No No Toggle to select if beam depth is to beconsidered in an auto select sectionlist. If yes, maximum and minimumdepths must be input.

MaximumDepth

>0 44 inches Maximum actual (not nominal) beamdepth to be considered in auto selectsection list.

MinimumDepth

≥0 0 Minimum actual (not nominal) beamdepth to be considered in auto selectsection list.

MaximumPCC(%)

>0 100% Maximum percent composite connec-tion considered for the beam.


EQ Factor Technical Note 18 - 15


ItemPossibleValues


Minimum PCC(%)

>0 25% Minimum percent composite connectionconsidered for the beam.

LL ReductionFactor

0<, >1.0 1.0 Reducible live load is multiplied by thisfactor to obtain the reduced live load. Ifzero is selected, the program calcu-lated valued is used.

Horizontal EQFactor

0<, >1.0 1.0 Multiplier applied to the earthquakeportion of the load in a design loadcombination.

EQ FactorThe EQ (earthquake) factor is a multiplier that is typically applied to theearthquake load in a design load combination. Following are the five types ofloads that can be included in a design load combination, along with an expla-nation of how the EQ factor is applied to each of the load types.

Static Load: The EQ factor is applied to any static loads designated as aQuake-type load. The EQ factor is not applied to any other type of staticload.

Response Spectrum Case: The EQ factor is applied to all responsespectrum cases.

Time History Case: The EQ factor is applied to all time history cases.

Static Nonlinear Case: The EQ factor is not applied to any static nonlin-ear cases.

Load Combination: The EQ factor is not applied to any load combinationthat is included in a design load combination. For example, assume youhave two static load cases labeled DL and EQ. DL is a dead load and EQ isa quake load.


Technical Note 18 - 16 EQ Factor

Now assume that you create a design load combination named DESCOMB1that includes DL and EQ. For design load combination DESCOMB1, the EQload is multiplied by the EQ factor.

Next assume that you create a load combination called COMB2 that in-cludes EQ. Now assume that you create a design load combination calledDESCOMB3 that included DL and COMB2. For design load combinationDESCOMB3, the EQ load that is part of COMB2 is not multiplied by the EQfactor.

The EQ factor allows you to design different members for different levels ofearthquake loads in the same run. It also allows you to specify member-specific reliability/redundancy factors that are required by some codes. The ρfactor specified in Section 1630.1.1 of the 1997 UBC is an example of this.




Technical Note 19Width-to-Thickness Checks

This Technical Note describes how the program checks the AISC-ASD89specification width-to-thickness requirements for compact and noncompactsections. The width-to-thickness requirements for compact and noncompactsections are spelled out in AISC-ASD89 Specification Chapter B, Table B5.1.This program checks the width-to-thickness ratios of the beam flanges andweb, and, if it exists, the cover plate.

OverviewThe program classifies beam sections as either compact, noncompact or slen-der on the basis of their width-to-thickness ratios. The program checks thecompact and noncompact section requirements for each design load combi-nation separately. A beam section may be classified differently for differentdesign load combinations. For example, it may be classified as compact fordesign load combination A and as noncompact for design load combination B.One reason that a beam may be classified differently for different design loadcases is that the compression flange may be different for different design loadcombinations. If the sizes of the top and bottom flanges are not the same,classification of the section as compact or noncompact may depend on whichflange is determined to be the compression flange.

For each design load combination, the program first checks a beam sectionfor the compact section requirements for the compression flange, web andcover plate (if applicable). If the beam section meets all of those require-ments, it is classified as compact for that design load combination. If thebeam section does not meet all of the compact section requirements, it isthen checked for the noncompact requirements for the flanges, web andcover plate (if applicable). If the beam section meets all of those require-ments, it is classified as noncompact for that design load combination. If thebeam section does not meet all of the noncompact section requirements, it isclassified as slender for that design load combination, and the program doesnot consider it for composite beam design.

Width-to-Thickness Checks Composite Beam Design AISC-ASD89

Technical Note 19 - 2 Limiting Width-to-Thickness Ratios for Flanges

Limiting Width-to-Thickness Ratios for FlangesThis section describes the limiting width-to-thickness ratios considered by theprogram for beam compression flanges. The width-to-thickness ratio forflanges is denoted b/t, and is equal to bf/2tf for I-shaped sections and bf/tf forchannel sections.

The program does not check the flange width-to-thickness ratios for compos-ite beams with positive bending. This is consistent with the last sentence ofthe first paragraph in AISC-ASD89 Specification Section I2.2.

Compact Section Limits for FlangesFor compact sections, the width-to-thickness ratio for the compression flangeis limited to that indicated by Equation 1.

yF

65tb ≤ , for compact sections Eqn. 1

where Fy is the specified yield stress of the beam. Equation 1 applies to bothrolled sections selected from the program's database and to user-defined(welded) sections.

Noncompact Section Limits for FlangesFor noncompact sections, the width-to-thickness ratio for the compressionflange is limited to that indicated by Equation 2.

cy kF

95tb ≤ , for noncompact sections Eqn. 2

where Fy is the specified yield stress of the beam and kc is as follows:

kc is equal to one (1.0) for rolled sections selected from the program da-tabase.

kc is equal to one (1.0) for user-defined (welded) sections with h/tw lessthan or equal to 70.

kc is given by Equation 3 for user-defined (welded) sections with h/tw

greater than 70. For h/tw less than or equal to 70 kc = 1.

Composite Beam Design AISC-ASD89 Width-to-Thickness Checks

Limiting Width-to-Thickness Ratios for Webs Technical Note 19 - 3

( )0.46w

cth

4.05k = , for h/tw > 70, Eqn. 3

Limiting Width-to-Thickness Ratios for WebsThis section describes the limiting width-to-thickness ratios considered by theprogram for beam webs.

Compact Section Limits for WebsWhen checking a beam web for compact section requirements, the width-to-thickness ratio used is d/tw as shown in Equation 4.

yw F

640td ≤ Eqn. 4

Noncompact Section Limits for WebsWhen checking a beam web for noncompact section requirements, the width-to-thickness ratio used is h/tw. Note that this is different from the width-to-thickness ratio used for the compact section requirement check. The equationused for checking the noncompact section limits in the web depends on theallowable bending stress, Fb, for the noncomposite steel beam plus coverplate, if it exists. Refer to the Composite Beam Design AISC-ASD89 TechnicalNote 22 Allowable Bending Stresses for a description of how the program cal-culates the allowable bending stress.

Equation 5 defines the noncompact section limit for webs.

bw F

760th ≤ Eqn. 5

The program makes a slight simplifying assumption when using Equation 5 byassuming that Fb = 0.66Fy. In most cases in the Composite Beam Designpostprocessor, this assumption is exactly correct. When the assumption is notexactly correct, it errs on the conservative side.


Technical No

Limiting Width-to-Thickness Ratios for Cover PlatesWidth-to-thickness checks are only performed for the cover plate when thereis negative moment in the beam. In this case, the cover plate is in compres-sion.

The width-to-thickness checks made for the cover plate depend on the widthof the cover plate compared to the width of the beam bottom flange. Figure 1illustrates the conditions considered.

In Case A of the figure, the width of the cover plate is less than or equal tothe width of the beam bottom flange. In this case, the width-to-thickness ra-tio is taken as b1/tcp, and it is checked as a flange cover plate.

In Case B of Figure 1, the width of the cover plate is greater than the width ofthe beam bottom flange. Two conditions are checked in this case. The firstcondition is the same as that shown in Case A, where the width-to-thicknessratio is taken as b1/tcp and is checked as a flange cover plate. The secondcondition checked in Case B takes b2/tcp as the width-to-thickness ratio andchecks it as a plate projecting from a beam. This second condition is onlychecked for the noncompact requirements; it is not checked for compact re-quirements.

Figure 1

te 19 - 4 Limiting Width-to-Thickness Ratios for Cover Plates

Conditions Considered When Checking Width-To-ThicknessRatios of Cover Plates

b1

t cp b1

t cpb2b2

Case A Case B

Beam

Cover plate

Beam

Cover plate

Composite Beam Design AISC-ASD89 Width-to-Thickness Checks

Limiting Width-to-Thickness Ratios for Cover Plates Technical Note 19 - 5

Compact Section Limits for Cover PlatesThe checks made for compact section requirements depend on whether thewidth of the cover plate is less than or equal to that of the bottom flange ofthe beam (Case A in Figure 1), or greater than that of the bottom flange ofthe beam (Case B in Figure 1).

Cover Plate Width Less Than or Equal to Beam Bottom Flange WidthWhen the cover plate width is less than or equal to the width of the beambottom flange, Equation 6 applies for the compact check for the cover plate.

ycpcp

1

F

190tb

≤ Eqn. 6

The term b1 in Equation 6 is defined in Figure 1.

Cover Plate Width Greater than Beam Bottom Flange WidthWhen the cover plate width exceeds the width of the beam bottom flange, theprogram checks both Equations 6 and 7 for the compact check for the coverplate.

ycpcp

2

F

95tb

≤ Eqn. 7


Noncompact Section Limits for Cover PlatesThe checks made for noncompact section requirements depend on whetherthe width of the cover plate is less than or equal to that of the bottom flangeof the beam (Case A in Figure 1), or greater than that of the bottom flange ofthe beam (Case B in Figure 1).

Cover Plate Width Less Than or Equal to Beam Bottom Flange WidthWhen the cover plate width is less than or equal to the width of the beambottom flange, Equation 8 applies for the noncompact check for the coverplate.

ycpcp

1

F

238tb

≤ Eqn. 8


Technical Note 19 - 6 Limiting Width-to-Thickness Ratios for Cover Plates


Cover Plate Width Greater than Beam Bottom Flange WidthWhen the cover plate width exceeds the width of the beam bottom flange,both Equations 8 and 9 apply for the noncompact check for the cover plate.

ycpcp

2

F

95tb

≤ Eqn. 9


Background Technical Note 20 - 1



Technical Note 20Transformed Section Moment of Inertia

This Technical Note describes in general terms how the program calculatesthe transformed moment of inertia for a composite section, Itr. The calculatedtransformed moment of inertia applies for full (100%) composite connection.See Composite Beam AISC-ASD89 Technical Note 21 Elastic Stresses withPartial Composite Connection for a description of partial composite connec-tion.

The Technical Note also describes in detail a method that can be used to cal-culate the transformed section moment of inertia by hand that will yield thesame result as the program. The exact methodology used by the program isoptimized for computer-based calculations and is unsuitable for hand calcula-tions and for presentation in this Technical Note.

Note that for the AISC-ASD89 specification, the transformed section proper-ties used for stress calculations for a beam may be different from those usedfor deflection calculations for the same beam. For AISC-ASD89 compositebeam design stress calculations, the value of Ec is always calculated fromEquation 1, assuming that the unit weight of concrete, wc, is 150 pounds percubic foot, regardless of its actual specified weight.

( ) 'c

1.5cc f33wE = Eqn. 1

In Equation 1, Ec is in pounds per square inch (psi), wc is in pounds per cubic

foot (pcf) and 'cf is in pounds per square inch (psi).

For AISC-ASD89 composite beam design deflection calculations, the value ofEc is taken from the material property specified for the concrete slab.

Transformed Section Moment of Inertia Composite Beam Design AISC-ASD89

Technical Note 20 - 2 Background

BackgroundFigure 1 shows a typical rolled steel composite floor beam with the metal deckribs running parallel to the beam. Figure 2 shows a typical composite user-defined steel beam with the metal deck ribs running parallel to the beam.Note that the user-defined beam may have a different top and bottom flangesize, and that no fillets are assumed in this beam.

For each of these configurations the following items may or may not beincluded when calculating the transformed section moment of inertia:

Concrete in the metal deck ribs: The concrete in the metal deck ribs isincluded in the calculation when the deck ribs are oriented parallel to thebeam (typically the case for girders). It is not included when the deck ribs areoriented perpendicular to the beam (typically the case for infill beams).

• Cover plate: The cover plate is only included if one is specified by you inthe composite beam overwrites.

Note that the deck type and deck orientation may be different on the twosides of the beam as described in "Multiple Deck Types or Directions Alongthe Beam Length" of Composite Beam Design Technical Note 8 EffectiveWidth of the Concrete Slab.

Because composite behavior is only considered for positive bending, thetransformed section moment of inertia is only calculated for positive bending(top of composite section in compression). Calculation of the transformedsection moment of inertia is greatly complicated by the requirement that theconcrete resist no tension.

The first task in calculating the transformed section moment of inertia of thecomposite section is to compute properties for the steel beam alone (plus thecover plate, if it exists). The properties required are the total area, Abare; thelocation of the ENA, ybare; and the moment of inertia, Is.

Composite Beam Design AISC-ASD89 Transformed Section Moment of Inertia

Backgroun

Figure

Figure

��Concrete slab

d

1: Composite Rolled Steel Beam Shown With Metal Deck RibsRunning Parallel To Beam

2:

��

bcp

h rt c

dt cp

Metal deck

Rolled steel beam

Bottom cover plate

�� t c


Composite User-Defined Steel Beam Shown With Metal DeckRibs Running Parallel To Beam

��

bcp

bf-bot

tw

bf-top

h rt f-top

d

h =

d - t

f-top

- t f-b

ott cp

t f-bot

Metal deck

Beam top flange

Beam web

Beam bottom flange

Bottom cover plate

Concrete slab


Technical Note 20 - 4 Properties of Steel Beam (Plus Cover Plate) Alone

Properties of Steel Beam (Plus Cover Plate) AloneThe location of the ENA for the steel beam alone (plus cover plate if applica-ble) is defined by the distance ybare, where ybare is the distance from the bot-tom of the bottom flange of the beam to the ENA, as shown in Figure 3. Ifthere is a cover plate, ybare is still measured from the bottom of the bottomflange of the beam, not the bottom of the cover plate.

Figure 3 also illustrates an example of the dimension y1 that is used in Tables1 and 2. For a given element of a steel section, the dimension y1 is equal tothe distance from the bottom of the beam bottom flange to the centroid ofthe element. Figure 3 illustrates the distance y1 for the beam top flange.

If the beam section is a rolled steel beam or channel chosen from the pro-gram section database, Abare, ybare and Ibare are calculated as shown in Table 1and Equations 1 and 2. If the beam section is a user-defined (welded) beam,they are calculated using Table 2 and Equations 1 and 2.

Elastic neutral axis of steel beamplus cover plate if applicable.Ibare is taken about this axis.

y bar

e y 1 fo

r top

flan

ge

Bottom of bottom flange of steelbeam. Ybare and y1 aremeasured from here

Figure 3: Illustration of ybare and y1


Properties of Steel Beam (Plus Cover Plate) Alone Technical Note 20 - 5

Table 1: Section Properties for Rolled Steel Beam Plus Cover Plate

Item Area, A y1 Ay1 Ay12 IO

Steel beam As 2

dAy1 Ay1

2 Is

Cover plate bcptcp2

t cp− Ay1 Ay12

12

tb 3cpcp

Sums ΣΣΣΣA ΣΣΣΣ(Ay1) ΣΣΣΣ(Ay12) ΣΣΣΣIO

Table 2: Section Properties for User-Defined (Welded) Steel Beam PlusCover Plate

Item Area, A y1 Ay1 Ay12 IO

Top flange bf-toptf-top2

td topf −− Ay1 Ay1

2

12

tb 3topftopf −−

Web htw 2

dAy1 Ay1

2

12

ht 3w

Bottom flange bf-bottf-bot 2

t botf −Ay1 Ay1

2

12

tb 3botfbotf −−

Cover plate bcptcp2

t cp− Ay1 Ay12

12

tb 3cpcp

Sums ΣΣΣΣA ΣΣΣΣ(Ay1) ΣΣΣΣ(Ay12) ΣΣΣΣIO

The area of the steel section (including the cover plate if it exists), Abare, isgiven by Equation 1.

Abare = ΣA Eqn. 1

The ENA of the steel section is located a distance ybare from the bottom of thebottom flange of the steel beam section (not bottom of cover plate) whereybare is determined from Equation 2.


Technical Note 20 - 6 Properties of Steel Beam (Plus Cover Plate) Alone

∑∑=

A

)(Ayy

1bare Eqn. 2

The moment of inertia of the steel section (plus cover plate, if one exists)about its ENA, Ibare, is given by Equation 3.

( ) ( ) 2bareO

21bare yAIAyI ∑∑∑ −+= Eqn. 3

Following is the notation used in Tables 1 and 2 and Equations 1 through 3:

Abare = Area of the steel beam (plus cover plate, if one exists),in2.

As = Area of rolled steel section alone (without the cover plateeven if one exists), in2.

Ibare = Moment of inertia of the steel beam (plus cover plate ifone exists), in4.

IO = The moment of inertia of an element of the beam sectiontaken about the ENA of the element, in4.

Is = Moment of inertia of the steel beam alone (without thecover plate even if one exists), in4.

bcp = Width of steel cover plate, in.

bf-bot = Width of bottom flange of a user-defined steel beam, in.

bf-top = Width of top flange of a user-defined steel beam, in.

d = Depth of steel beam from outside face of top flange tooutside face of bottom flange, in.

h = Clear distance between flanges for user-defined (welded)sections, in.

tcp = Thickness of cover plate, in.

tf-bot = Thickness of bottom flange of a user-defined (welded)section, in.


Properties of the Composite Section General Calculation Method Technical Note 20 - 7

tf-top = Thickness of top flange of a user-defined (welded) section,in.

tw = Thickness of web of user-defined (welded) section, in.

ybare = Distance from the bottom of the bottom flange of the steelsection to the ENA of the steel beam (plus cover plate if itexists), in.

y1 = Distance from the bottom of the bottom flange of the steelbeam section to the centroid of an element of the beamsection, in.

ΣA = Sum of the areas of all of the elements of the steel beamsection, in2.

Σ(Ay1) = Sum of the product A times y1 for all of the elements ofthe steel beam section, in3.

Σ(A 21y ) = Sum of the product A times 2

1y for all of the elements of

the steel beam section, in4.

ΣIO = Sum of the moments of inertia of each element of thebeam section taken about the ENA of the element, in4.

Properties of the Composite Section GeneralCalculation MethodThe first step, and potentially most calculation-intensive step in the process ofdetermining the composite properties is to calculate the distance from theENA of the steel beam (plus cover plate if it exists) to the ENA of the fullcomposite section. This distance is designated ye in Figure 4.

Recall that concrete in tension is ignored when calculating the compositeproperties. Because of the possibility that some of the concrete may be intension, and because the amount of concrete that is in tension is initially un-known (if any), the process for calculating the distance ye is iterative. Afterthe distance ye has been determined, the other calculations to determine thecomposite properties are relatively straight-forward.


Technical Note 20 - 8 Properties of the Composite Section General Calculation Method

The program uses the following method to calculate the properties of thecomposite section.

1. The location of the ENA of the composite section, defined by ye (see Fig-ure 4), is calculated using the following iterative process:

a. The program assumes (guesses) that the ENA of the composite sectionis within the height of the steel beam and uses Equation 4 to calculatethe distance ye that defines the location of the ENA for the compositesection. Note that with this assumption, all of the concrete is abovethe ENA of the composite section and thus it is all in compression andcan be considered.

( )element

elementelemente A

dAy

ΣΣ

= Eqn. 4

where,

Figure 4: Illustration of ye and z

��

Elastic neutral axis of compositebeam

y e

Elastic neutral axis of steel beamalone, including cover plate if itexists

z


Properties of the Composite Section General Calculation Method Technical Note 20 - 9

Aelement = Area of an element in the composite section, ignoring anyarea of concrete that is in tension and ignoring any con-crete in the metal deck ribs when the metal deck span isperpendicular to the beam span, in2.

delement = Distance from the ENA of the element considered to theENA of the steel beam alone (including cover plate, if itexists), in. Signs are considered for this distance. Ele-ments located below the ENA of the steel beam alone (in-cluding cover plate, if it exists) have a negative distanceand those above have a positive distance.

If the ENA as calculated is within the height of the steel beam, as as-sumed, the assumed location of the ENA is correct and the calculationfor ye is complete.

b. If the calculated ENA is not within the height of the steel beam, as as-sumed in Step a, the assumed location of the ENA is incorrect and cal-culation for ye continues.

i Using the incorrect location of the ENA calculated in Step a, theprogram calculates the location of ye again using Equation 4, ig-noring any concrete that is in tension.

ii If the newly calculated location of the ENA is the same as the pre-viously calculated location (Step i), the assumed location of theENA has been identified and the calculation for ye is complete.

c. If the newly calculated location of the ENA is not the same as the pre-viously calculated location (Step i), the most recent assumed locationof the ENA is incorrect and another iteration is made.

The program repeats the iterations until the location of the ENA hasbeen determined. After the location of the ENA is known, the rest ofthe process for calculating the composite properties is non-iterative.

2. Given that the ENA has been located, the program determines if any con-crete is below the ENA. If so, the program ignores it in the remaining cal-culations.


Technical Note 20 - 10 Equivalent Hand Calculation Method to Calculate the Distance ye

3. The program sums the product of the area of each element of the com-posite section (except concrete in tension) times its distance to a conven-ient axis (such as the bottom of the beam bottom flange).

4. The program divides the sum calculated in step 3 by the sum of the areasof each element of the composite section (except concrete in tension).This calculation yields the distance from the convenient axis to the ENA ofthe composite section.

5. After the ENA of the composite section has been determined, the sectionproperties of the composite section are quickly calculated using standardmethods.

A hand calculation method for determining the distance ye described in steps1a through 1c above is presented in the next section entitled "EquivalentHand Calculation Method to Calculate the Distance ye." A hand calculationmethod for the calculation of the composite properties described in steps 2through 5 above is presented in the section entitled "Equivalent Hand Calcu-lation Method to Calculate the Composite Properties" later in this TechnicalNote.

Equivalent Hand Calculation Method to Calculate theDistance ye

The following hand calculation method for determining the distance ye issimilar to and provides the same result as the calculations performed by theprogram.

After ybare has been calculated, ye is calculated by equating the forces aboveand below the ENA using either Equation 5a or Equation 5b. Recall that ye isthe distance from the ENA of the steel beam alone, plus cover plate if it exits,to the ENA of the fully composite section, as illustrated in Figure 4.

8765bare

4321e XXXXA

XXXXy

+++++++

= Eqn. 5a

( )9

4321921010

e 2X

XXXX4XXX-y

+++−±= Eqn. 5b


Equivalent Hand Calculation Method to Calculate the Distance ye Technical Note 20 - 11

Equations for use in calculating values for the variables X1 through X10 inEquations 5a and 5b are presented in the following subsection entitled "Back-ground Equations." The actual process to calculate ye is described in the sub-section of this Technical Note entitled "Hand Calculation Process for ye."

Background EquationsThis subsection presents the equations for the variables X1 through X10 inEquations 5a and 5b. The exact equation to use for the variables X1 throughX10 depends on the assumed location of the ENA.

For the purposes of determining the ye distance, there are nine possible loca-tions for the ENA. Those locations are as follows:

1. The ENA is located within the height of the steel section (includingcover plate, if it exists).

2. The ENA is located within the height of the metal deck on both the leftand the right sides of the beam.

3. The ENA is located within the height of the metal deck on the left sideof the beam and within the height of the concrete above the metaldeck (or within a solid slab) on the right side of the beam.

Note: Recall that you can have different deck properties on the twosides of the beam.

4. The ENA is located within the height of the metal deck on the left sideof the beam and above the concrete on the right side of the beam.

5. The ENA is located within the height of the concrete above the metaldeck (or within a solid slab) on the left side of the beam and within theheight of the metal deck on the right side of the beam.

6. The ENA is located within the height of the concrete above the metaldeck (or within a solid slab) on both sides of the beam.

7. The ENA is located within the height of the concrete above the metaldeck (or within a solid slab) on the left side of the beam and above theconcrete on the right side of the beam.



8. The ENA is located above the concrete on the left side of the beam andwithin the height of the metal deck on the right side of the beam.

9. The ENA is located above the concrete on the left side of the beam andwithin the height of the concrete above the metal deck (or within asolid slab) on the right side of the beam.

The first two columns in Table 3 list the nine possible locations of the ENA ofthe composite section. The columns labeled Left Side and Right Side indicatethe location of the ENA relative to the left and right sides of the beam, re-spectively. The third column of Table 3, labeled "ye Eqn" specifies whetherEquation 5a or 5b should be used to calculate ye. Columns 4 through 13 ofTable 3 list the equation numbers to be used to determine the value of thevariables X1 through X10 for the location of the ENA specified in the first twocolumns of the table.

When using Table 3, the location of the ENA of the composite section and thelocation of the ENA of the composite section relative to the elements thatmake up the composite section are initially unknown. Thus, begin by assum-ing a location of the ENA. It works best if you assume that the ENA of thecomposite section is within the steel section. Then, calculate the actual loca-tion of the ENA and check the validity of the assumption. This process is de-scribed in the subsection entitled "Hand Calculation Process for ye."

Equations 7 through 16 define the terms X1 through X10 in Table 3 and Equa-tions 5a and 5b. A term that is repeatedly used in Equations 7 through 16 isz. As previously illustrated in Figure 4, z is the distance from the ENA of thesteel beam alone (plus cover plate, if it exists) to the top of the concrete slab.The distance z, which can be different on the left and right sides of the beam,is defined by Equations 6a and 6b.

zleft = d + hr left + tc left - ybare Eqn. 6a

zright = d + hr right + tc right - ybare Eqn. 6b

The equations for the variables X1 through X10 in Equations 5a and 5b and Ta-ble 3 follow. In most cases, there are multiple equations for each variable.See Table 3 for specification of which equation to use for any assumed loca-tion of the ENA.



Table 3: Table Identifying Circumstances for Using Equations 5a and 5b andIdentifying Appropriate Equations to Use to Calculate the Values ofVariables X1 through X10 that Appear in Equations 5a and 5b

LeftSide

RightSide

ye

EqnX1

EqnX2

EqnX3

EqnX4

EqnX5

EqnX6

EqnX7

EqnX8

EqnX9

EqnX10

Eqn

Steel section 5a 7a 8a 9a 10a 11a 12a 13a 14a N.A. N.A.

hr hr 5b 7a 8b 9a 10b 11a 12b 13a 14b 15a 16ahr tc 5b 7a 8b 9b 0 11a 12b 13b 14c 15a 16chr >tc 5b 7a 8b 0 0 11a 12b 0 0 15a 16atc hr 5b 7b 0 9a 10b 11b 12c 13a 14b 15a 16dtc tc 5b 7b 0 9b 0 11b 12c 13b 14c 15a 16btc >tc 5b 7b 0 0 0 11b 12c 0 0 15a 16b

>tc hr 5b 0 0 9a 10b 0 0 13a 14b 15a 16a>tc tc 5b 0 0 9b 0 0 0 13b 14c 15a 16b

Table Descriptive Notes:

1. The columns labeled Left Side and Right Side indicate the assumed location of theENA of the composite section relative to the left and right sides of the beam. Steelsection means that the ENA falls within the height of the steel section (including thecover plate, if it exists). The designation hr means that the ENA is within the height ofthe metal deck. The designation tc means that the ENA is within the height of theconcrete slab above metal deck or within the height of a solid slab. The designation>tc means that the ENA is above the concrete slab.

2. The column labeled "ye Eqn" tells you whether to use Equation 5a or Equation 5b tocalculate ye for the assumed location of the ENA listed in the first two columns of thetable.

3. The columns labeled "X1 Eqn" through "X10 Eqn" indicate the equation numbers thatshould be used to calculate the value of the variables X1 through X10 for use in Equa-tions 5a and 5b. If one of the cells for X1 through X8 contains a "0," the value of Xn iszero for that location of the ENA.

4. The variables X9 and X10 are not used if the ENA falls within the height of the steelbeam.

5. The variables X2, X4, X6 and X8 are always taken as zero if the deck span is orientedperpendicular to the beam span.

6. Using this table requires a trial and error process. You must assume a location for theENA and then check if the assumption is correct. See the subsection entitled "HandCalculation Process for ye" later in this chapter for more information.



Important note: The terms X2, X4, X6 and X8 are always taken as zero if thedeck span is oriented perpendicular to the beam span; otherwise they aretaken as given in the equations below.

−=

2

tzXX leftc

left51 Eqn. 7a

=2

zXX left

51 Eqn. 7b

X2 is taken as zero if the deck span is oriented perpendicular to the beamspan; if the deck span is oriented parallel to the beam span, X2 is as specifiedin the equations below.

−−=

2

htzXX leftr

leftcleft62 Eqn. 8a

( )2leftcleft62 tzXX −= Eqn. 8b

−=

2

tzXX rightc

right73 Eqn. 9a

=

2

zXX right

73 Eqn. 9b


−−=

2

htzXX rightr

rightcright84 Eqn. 10a

( )2rightcright84 tzXX −= Eqn. 10b

s

leftcleftclefteff5 E

tEbX = Eqn. 11a



s

leftleftclefteff5 E

zEbX = Eqn. 11b


leftrs

leftrleftrleftclefteff6 SE

hwEbX = Eqn. 12a

leftrs

leftrleftclefteff6 S2E

wEbX = Eqn. 12b

s

leftclefteff6 2E

EbX = Eqn. 12c

s

rightcrightcrighteff7 E

tEbX = Eqn. 13a

s

rightrightcrighteff7 E

zEbX = Eqn. 13b


rightrs

rightrrightrrightcrighteff8 SE

hwEbX = Eqn. 14a

rightrs

rightrrightcrighteff8 S2E

wEbX = Eqn. 14b

s

rightcrighteff8 2E

EbX = Eqn. 14c

869 XXX += Eqn. 15a

89 XX = Eqn. 15b



69 XX = Eqn. 15c

( )( )rightcright87

leftcleft65bare10

tz2XX

tz2XXAX

−−

−−−−−=Eqn. 16a

75bare10 XXAX −−−= Eqn. 16b

( ) 7leftcleft65bare10 XtzXXAX −−−−−= Eqn. 16c

( )rightcright875bare10 tzXXXAX −−−−−= Eqn. 16d

The notation used in equations 5a through 16d are as follows:

Abare = Area of the steel beam (plus cover plate), in2. This areadoes not include the concrete area.

Ec = Modulus of elasticity of concrete slab, ksi. Note that thiscould be different on the left and right sides of the beam.Also note that this it may be different for stress calcula-tions and deflection calculations.

Es = Modulus of elasticity of steel, ksi.

Sr = Center-to-center spacing of metal deck ribs, in. Note thatthis may be different on the left and right sides of thebeam.

beff = Effective width of the concrete flange of the compositebeam, in. This width is code dependent. Note that thiswidth may be different on the left and right sides of thebeam. See Composite Beam Design Technical Note 8 Ef-fective Width of the Concrete Slab for additional informa-tion.


hr = Height of metal deck rib, in. Note that this may be differ-ent on the left and right sides of the beam.


Hand Calculation Process for ye Technical Note 20 - 17

tc = Thickness of concrete slab, in. If there is metal deck, thisis the thickness of the concrete slab above the metaldeck. Note that this may be different on the left and rightsides of the beam.

wr = Average width of a metal deck rib, in. Note that this maybe different on the left and right sides of the beam.

ybare = Distance from the bottom of the bottom flange of thesteel beam to the ENA of the steel beam (plus coverplate, if it exists) alone, in.

ye = The distance from the ENA of the steel beam (plus coverplate, if it exists) alone to the ENA of the fully compositebeam, in.

z = Distance from the ENA of the steel beam (plus coverplate, if it exists) alone to the top of the concrete slab, in.Note that this distance may be different on the left andright sides of the beam.

Hand Calculation Process for ye

The location of the ENA of the composite section, defined by ye, is calculatedusing the following process:

1. Assume the ENA is within the height of the steel beam. Use Equation 5a tocalculate the location of the ENA. Table 3 identifies the equations to use todetermine values for the variables X1 through X8 in Equation 5a.

2. If the location of the ENA calculated in step 1 is within the height of thesteel beam, as initially assumed, the location of the ENA is correct and thecalculation for ye is complete.

3. If the calculated ENA is not within the height of the steel beam, as initiallyassumed, the location is incorrect and a new assumption for the locationof the neutral axis is made. The new assumption for the location of theENA is wherever it was calculated to be in step 1 and is one of the choicesdefined in the first two columns of Table 3.


Technical Note 20 - 18 Equivalent Hand Calculation Method to Calculate the Composite Properties

4. Use Equation 5b to calculate the location of the ENA. Note that Table 3identifies the equations to use to determine values for the variables X1

through X10 for use in solving Equation 5b.

5. If the calculated location of the ENA is the same as the new location as-sumed in step 3, then the assumption is correct and the calculation for ye

is complete.

6. If the calculated location of the ENA is not the same as the location as-sumed in step 3, the location is incorrect and another iteration is made.The new assumption for the location of the ENA is wherever it was calcu-lated to be in step 4 and is one of the choices defined in the first two col-umns of Table 3.

7. Repeat steps 4 through 7 as many times as required until the assumedlocation of the ENA (based on the choices in the first two columns of Table3) and the calculated location of the ENA match.

Equivalent Hand Calculation Method to Calculate theComposite PropertiesAfter the location of the ENA has been calculated, the other calculations todetermine the composite section moment of inertia are non-iterative andrelatively straightforward. The other calculation steps are as follow.

8. Calculate the transformed section properties for full composite connectionas illustrated in Table 4. When reviewing Table 4 note:

a. If the deck spans perpendicular to the beam span, the concrete in themetal deck ribs is ignored. If the deck spans parallel to the beam span,the concrete in the metal deck ribs is considered.

b. The cover plate may or may not be present.

c. The concrete slab and metal deck may not exist on one side of thebeam or the other.


Equivalent Hand Calculation Method to Calculate the Composite Properties Technical Note 20 - 19

Table 4: Transformed Section Properties for a Fully Composite Beam

ItemTransformed

Area, Atr y1 Atry1 Atry12 IO

Concreteslab, left side s

c*ceff

E

Etb

2

tthd

*c

cr −++ Atry1 Atry12

s

3*cceff

12E

tEb

Concreteslab, rightside

s

c*ceff

E

Etb

2

tthd

*c

cr −++ Atry1 Atry12

s

3*cceff

12E

tEb

Concrete inmetal deckribs, left side sr

cr*reff

ES

Ewhb

2

hhd

*r

r −+ Atry1 Atry12

sr

3*rcreff

E12S

hEwb

Concrete inmetal deckribs, right side sr

cr*reff

ES

Ewhb

2

hhd

*r

r −+ Atry1 Atry12

sr

3*rcreff

E12S

hEwb

Steel beamplus coverplate

Abare ybare Atry1 Atry12 Ibare

Sums ΣΣΣΣAtr ΣΣΣΣ(Atry1) ΣΣΣΣ(Atry12) ΣΣΣΣIO

d. The top of the concrete slab may be at a different elevation on the twosides of the beam.

e. Any concrete that is below the ENA of the composite section is not in-cluded in the calculation.

Following is a list of the variables introduced in Table 4 that have not beenmentioned previously in this Technical Note.

Atr = Area of an element of the composite steel beam section, in2.

*rh = Height of the metal deck ribs above the ENA (i.e., that is in

compression) used for calculating the transformed sectionproperties, in. Note that this could be different on the left andright sides of the beam.


Technical Note 20 - 20 Equivalent Hand Calculation Method to Calculate the Composite Properties

If the deck ribs are oriented perpendicular to the beam span,*rh = 0.

If the deck ribs are oriented parallel to the beam span, one ofthe following three items applies:

1. If the ENA is below the metal deck, *rh = hr.

2. If the ENA is within the metal deck, *rh equals the height of

the metal deck above the ENA.

3. If the ENA is above the metal deck, *rh = 0.

*ct = Height of the concrete slab above the metal deck (or solid

slab) that lies above the ENA (i.e., is in compression) that isused for calculating the transformed section properties, in. Notethat this could be different on the left and right sides of thebeam.

One of the following three items applies:

1. If the ENA is below the top of the metal deck (bottom of the

concrete slab), *ct = tc.

2. If the ENA is within the concrete slab, *ct equals the height

of the concrete slab above the ENA.

3. If the ENA is above the concrete slab, *ct = 0

ΣAtr = Sum of the areas of all of the elements of the composite steelbeam section, in2.

Σ(Atry1) =Sum of the product Atr times y1 for all of the elements of thecomposite steel beam section, in3.

Σ(Atry12) =Sum of the product Atr times y1

2 for all of the elements of thecomposite steel beam section, in4.


Equivalent Hand Calculation Method to Calculate the Composite Properties Technical Note 20 - 21

The neutral axis of the transformed composite section is locateda distance y from the bottom of the bottom flange of the steel

beam section (not bottom of cover plate). The distance y can

be determined from either Equation 17a or from Equation 17b.They both give the same result.

∑∑=

tr

1tr

A

)y(Ay Eqn. 17a

y = ybare + ye Eqn. 17b

The distance y is illustrated in Figure 5.

The transformed section moment of inertia about the ENA ofthe composite beam, Itr, is calculated using Equation 18.

( ) 2trO

21trtr yAIyAI ∑∑∑ −+= Eqn. 18

Figure 5 illustrates the axis about which Itr is taken.

��

Elastic neutral axis (ENA) ofcomposite beam. Itr is takenabout this axis.

y y 1 fo

r top

flan

ge

Bottom of bottom flange of steelbeam. The dimensions y, ybare

and y1 are measured from here.

y ey b

are

z

Elastic neutral axis (ENA) of steelbeam alone, including cover plateif it exists

Figure 5: Illustration of y

Effective Moment of Inertia for Partial Composite Connection Technical Note 21 - 1



Technical Note 21Elastic Stresses with Partial Composite Connection

This Technical Note describes how the program calculates elastic stresses inthe steel section and the concrete slab when there is partial composite con-nection. Note that because composite action is only considered by the pro-gram for positive bending, the description in this Technical Note only appliesto positive bending.

When there is partial composite connection, the number of shear connectorsprovided controls the amount of horizontal shear that can be transferred be-tween the steel beam and the concrete slab. For beams with partial compositeconnection, the program checks for deflections and stress assuming an elasticdistribution of stress, where the strain in both the concrete and the steel isproportional to the distance from the elastic neutral axis (ENA) of the trans-formed section.

Effective Moment of Inertia for Partial CompositeConnectionThe effective moment of inertia of the composite section for positive bendingin a partially composite beam is calculated using Equation 1:

( )baretrbareeff IIPCCII −+= Eqn. 1

Note:

Equation 1 is the same as AISC-ASD89 Specification Equation I4-4.

where,

PCC = Percent composite connection, unitless. The percentagevaries between 25% and 100% inclusive.

Ibare = Moment of inertia of the steel beam alone plus coverplate, if it exists, in4.

Elastic Stresses with Partial Composite Connection Composite Beam Design AISC-ASD89

Technical Note 21 - 2 Effective Section Modulus Referred to the Extreme Tension Fiber

Ieff = Effective moment of inertia of a partially compositebeam, in4.

Itr = Transformed section moment of inertia about ENA of thecomposite beam calculated as described in CompositeBeam Design AISC-ASD89 Technical Note 20 Trans-formed Section Moment of Inertia, in4.

Effective Section Modulus Referred to the ExtremeTension FiberThe effective section modulus, Seff, referred to the extreme tension fiber in apartially composite beam is calculated using Equation 2:

( )baretrbareeff SSPCCSS −+= Eqn. 2

Note:

Equation 2 is the same as AISC-ASD89 Specification Equation I2-1.

where,

PCC = Percent composite connection, unitless. The percentagevaries between 25% and 100% inclusive.

Sbare = Section modulus of the steel beam alone (plus coverplate, if it exists) referred to the extreme tension fiber,in3.

Seff = Effective section modulus of a partially composite beamreferred to the extreme tension fiber of the steel beamsection (including cover plate, if it exists), in3.

Str = Section modulus for the fully (100%) composite trans-formed section referred to the extreme tension fiber ofthe steel section (including cover plate, if it exists), in3.Referring to Figure 1, Str is calculated using Equation 3.

Note:

The section moduli Str and Seff are referenced to the bottom of the cover plate, if it exists.Otherwise they are referenced to the bottom of the beam bottom flange.

Composite Beam Design AISC-ASD89 Elastic Stresses with Partial Composite Connection

Location o

w

I

LocatThis secsection

��

Figure

f the ENA for Partial Composite Connection Technical Note 21 - 3

( )cp

trtr

ty

IS

+= Eqn. 3

here,

tr = Transformed section moment of inertia about the ENA ofthe composite beam, calculated as described in Techni-cal Note Composite Beam Design AISC-ASD89 TechnicalNote 20 Transformed Section Moment of Inertia, in4.

y = Distance from the bottom of the beam bottom flange to

the ENA of the composite beam calculated as describedin Technical Note Composite Beam Design AISC-ASD89Technical Note 20 Transformed Section Moment of Iner-tia, in.

ion of the ENA for Partial Composite Connectiontion describes how the location of the ENA of the partially compositeis calculated.

��

Elastic neutral axis (ENA) ofcomposite beam for full (100%)composite connection. Itr is takenabout this axis.

y

d

t cp

1: Figure Demonstrating Variables for Calculating Str in Equation 3


Techn

Refer to Figure 2. In the figure, the distance from the bottom of the beambottom flange to the ENA of the partially composite beam, yeff, is given byEquation 4:

cpeff

effeff t

S

Iy −= Eqn. 4

Note:

The distance yeff is measured from the bottom of the beam bottom flange even whenthere is a cover plate.

CL

Figu

ical Note 21 - 4 Location of the ENA for Partial Composite Connection

��

ENA of fullycomposite beam. Itris taken about thisaxis.

y eff

d

t cp

y

ENA of partiallycomposite beam.

beff left

beff-par left

beff leftEc left

Es

��

��

t ch r

beff-par right

beff rightEc right

Es

beff righty ba

re

ENA of steel beamalone plus coverplate if it exists.

re 2: Composite Beam Section


Steel Section Stresses for Partial Composite Connection Technical Note 21 - 5

where,

yeff = The distance from the bottom of the beam bottom flangeto the ENA of the partially composite beam, in.

Ieff = Effective moment of inertia of a partially compositebeam calculated using Equation 1, in4.

Seff = Effective section modulus of a partially composite beamreferred to the extreme tension fiber of the steel beamsection (including cover plate, if it exists) calculated us-ing Equation 2, in3.

tcp = Thickness of the cover plate if it exists, in.

Steel Section Stresses for Partial CompositeConnectionThe steel section stresses (including those in the cover plate, if it exists) arecalculated as described below.

The steel stresses are checked at the top and bottom of the steel beam and atthe bottom of the cover plate, if it exists. Note that in this program, it is pos-sible for the steel beam section and the cover plate to have a different yieldstress. If there is a cover plate, and if the yield stress of the cover plate islarger than that of the beam, the allowable stress at the bottom of the coverplate is larger than that at the bottom of the beam bottom flange. Thus, thestress at the bottom of the beam bottom flange may control the design.

Equations 5 through 7 show the equations used to determine the stresses forpositive bending.

If a cover plate exists, Equation 5 gives the stress at the bottom of the coverplate. Otherwise, it gives the stress at the bottom of the beam bottom flange.

effst-bot S

Mf = Eqn. 5

If a cover plate exists, Equation 6 gives the stress at the bottom of the beambottom flange. If there is no cover plate, Equations 5 and 6 are the same.


Technical Note 21 - 6 Concrete Slab Stresses for Partial Composite Connection

eff

effbm-bot I

Myf = Eqn. 6

Equation 7 gives the stress at the top of the steel beam section.

( )[ ]eff

effst-top I

y-dAbsMf = Eqn. 7

The term "Abs" in Equation 7 means to take the absolute value of the(d - yeff) term. The following notation that has not been previously introducedin this Technical Note is used in Equations 5 through 7.

M = The design moment, kip-in.


fbot-bm = The maximum tensile stress at the bottom of the bottomflange of the steel beam, ksi.

fbot-st = The maximum tensile stress at the bottom of the steelsection (including cover plate, if it exists), ksi.

ftop-st = The maximum stress at the top of the steel beam (maybe tension or compression, depending on the location ofthe ENA), ksi.

For full (100%) composite connection Ieff and yeff in Equations 6 and 7 aremodified as shown in Composite Beam Design AISC-ASD89 Technical Note 23Bending Stress Checks Equations 1e and 1f.

Concrete Slab Stresses for Partial CompositeConnectionThe calculation of concrete slab stresses for partial composite connection inthe program is based on a published paper covering the topic. See Lorenz andStockwell (1984). The exact methodology used by this program to calculatethe concrete slab stresses for partial composite connection is optimized forcomputer-based calculations and is unsuitable for hand calculations and forpresentation in this Technical Note.


Concrete Slab Stresses for Partial Composite Connection Technical Note 21 - 7

This section describes in detail a method that can be used to calculate theconcrete slab stresses for partial composite connection by hand that will yieldthe same result as the program. The method presented here parallels muchof what is done internally in the program.

Note:

Although the equation for the effective slab width of a partially composite beam is derivedby considering bounding conditions of 0% and 100% composite connection, the programactually limits the minimum percent composite connection to 25%.

Refer to Figure 2. On each side of the beam the effective width of the slab forthe partially composite beam, beff-par left and beff-par right, varies from the valuefor full composite action, beff left(Ec left /Es) and beff right(Ec right /Es), to zero as thepercent composite connection varies from 100% to 0%. Formulas for beff-par left

and beff-par right are derived from the definition of the elastic neutral axis (ENA)together with the assumption that the ratio of the effective widths of the con-crete slab on the left and right sides of the beam remains constant for anypercentage of composite connection. Equation 8 is a formula representing thisassumption.

rightpareff

leftpareff

righteff

lefteff

b

b

b

b

−

−= Eqn. 8

From the definition of the ENA, if you multiply the area of individual elementsof a composite section times their distance to the ENA (considering the sign ofthe distance term), and then sum up these products for all elements of thecomposite section, the result is zero. This statement is shown as a formula inEquation 9.

X1 - beff-par left ( X2 + X4) - beff-par right ( X3 + X5) = 0 Eqn. 9

Note:

See Figures 3, 4 and 5 for illustrations of the physical distances represented by the vari-ables a3 and a4 in Equations 9a through 9e.

where:

X1 = Abare (yeff - ybare) Eqn. 9a

X2 = a3 left (d + hr left + tc left - 2

a left3 - yeff) Eqn. 9b



X3 = a3 right (d + hr right + tc right - 2

a right3 - yeff) Eqn. 9c

−−+= eff

left4leftr

leftr

leftrleft44 y

2

ahd

S

waX Eqn. 9d

−−+= eff

right4rightr

rightr

rightrright45 y

2

ahd

S

waX Eqn. 9e

Table 1 lists the values that should be used for the variables a3 and a4 inEquations 9a through 9e for all possible conditions. The possible conditionsare different combinations of the location of the ENA for the partially compos-ite beam and the deck direction. Note that a3 and a4 are evaluated separatelyfor each side of the beam and can be different for the left and right sides ofthe beam.

Table 1: Values that Should Be Used for the Variables A3 and A4 in Equa-tions 9a through 9e. Physical Representations of A3 and A4 areShown in Figures 3, 4 and 5

ENA LocationDeck

Direction a31, 2 a41, 3

Above the concrete slab over metal deck (orthe solid slab)

Parallel orPerpendicular

N.A.4 N.A.4

In the concrete slab over metal deck (or thesolid slab)

Parallel orPerpendicular

d + hr + tc - yeff N.A.4

Within the height of the metal deck Parallel tc d + hr - yeff

Within the height of the metal deck Perpendicular tc N.A.5

Within the height of the steel beam Parallel tc hr

Within the height of the steel beam Perpendicular tc N.A.5


1. When the cell for an an value indicates "N.A." a value of 0 should be used in Equations 9a through 9efor that item. The notes below explain why the various "N.A." items are indicated.

2. The a3 dimension represents a distance within the height of the concrete slab.

3. The a4 dimension represents a distance within the height of the metal deck ribs.


Concrete

4. The an dimension is not applicable because it would represent concrete below the ENA, which is in ten-sion and thus ignored in the calculations.

5. The a4 dimension is not applicable because it represents concrete in the metal deck ribs. This concreteis ignored in the calculations when the deck span is perpendicular to the beam span.

Figures 3, 4 an 5 illustrate the physical distances represented by the variablesa3, a4 and a5 for various locations of the ENA of the partially composite beam.

��

a 3Figur

Slab Stresses for Partial Composite Connection Technical Note 21 - 9

��

y eff

d

t cp

ENA of partiallycomposite beamlocated withinconcrete slab abovethe metal deck (or ina solid slab)

t ch r

e 3: Illustration of Variable a3 in Equations 9a through 9e When theENA is in the Concrete Slab Above the Metal Deck or in a SolidSlab


Te

Fi

ch

yeff

d

tcp

ENA of partiallycomposite beamlocated within metaldeck

t c

hra 4

a 3

gure 4: Illustration of Variables a3 and a4 in Equations 9a through 9eWhen the ENA is Within the Height of the Metal Deck

��

3

F

nical Note 21 - 10 Concrete Slab Stresses for Partial Composite Connection

��

y eff

d

t cp

ENA of partiallycomposite beamlocated within theheight of the steelsection

t ch ra 4

a

igure 5: Illustration of Variables a3 and a4 in Equations 9a through 9eWhen the ENA is Located Within the Height of the Steel Section



Next we can substitute Equation 8 into Equation 9 and solve for beff-par left andbeff-par right. The resulting equations are shown here as Equations 10a and 10b.

( ) ( )

++

+

=−

53righteff

lefteff42

1rightpareff

XXb

bXX

Xb Eqn. 10a

( ) ( )

++

+

=−

53righteff

lefteff42

righteff

lefteff1

leftpareff

XXb

bXX

b

bX

b Eqn. 10b

Note:

The width beff-par is the effective width of the concrete slab for partial composite connec-tion. It is transformed to an equivalent width of steel.

The following notation is used in Equations 8 through 10b:

Abare = Area of the steel beam (plus cover plate, if one exists),in2.

Sr = Center-to-center spacing of metal deck ribs, in. Notethat this could be different on the left and right sides ofthe beam.

a3 = Whichever is smaller of the distance from the top of theconcrete slab to the ENA or the thickness of the concreteabove the metal deck (or the thickness of a solid slab),tc, in. This item may be different on the left and rightsides of the beam.

a4 = Whichever is smaller of the distance from the top of themetal deck to the ENA or the height of the metal deck,hr, in. This item applies when there is metal deck (not asolid slab) and the ENA is below the top of the metaldeck. This item may be different on the left and rightsides of the beam.



beff = The effective width of the concrete slab for full (100%)composite action, in. Note that this may be different onthe left and right sides of the beam.

beff-par = The effective width of the concrete slab for partial com-posite action transformed to have the same E as thesteel section, in. Note that this item may be different onthe left and right sides of the beam.


hr = Height of the metal deck ribs, in. Note that this itemmay be different on the left and right sides of the beam.

tc = Thickness of concrete slab, in. If there is metal deck,this is the thickness of the concrete slab above themetal deck. Note that this item may be different on theleft and right sides of the beam.

wr = Average width of metal deck rib, in. Note that this itemmay be different on the left and right sides of the beam.

ybare = The distance from the bottom of the beam bottom flangeto the ENA of the steel beam plus cover plate, if it ex-ists, in. See Composite Beam Design AISC-ASD89 Tech-nical Note 20 Transformed Section Moment of Inertia.No composite connection (concrete slab) is consideredwhen calculating this item.

yeff = The distance from the bottom of the beam bottom flangeto the ENA of the partially composite beam, in.



The section moduli on each side of the beam referred to the top of the par-tially composite section, St-eff left and St-eff right, are given by Equations 11a and11b:

( )effleftcleftr

effleftefft ythd

IS

−++=− Eqn. 11a

( )effrightcrightr

effrightefft ythd

IS

−++=− Eqn. 11b

where,

Ieff = Effective moment of inertia of the partially compositebeam calculated using Equation 1, in4.

Finally, the concrete compressive stress, fc, for a partially composite beam iscalculated as the larger of Equations 12a and 12b:

= −

− left eff

leftpar eff

left efftleftc b

b

SM

f Eqn. 12a

= −

− right eff

rightpar eff

right efftrightc b

b

SM

f Eqn. 12b

where,

M = The design moment, kip-in. For unshored beams M =MSDL + MLL + MOther. For shored beams M = MDL + MSDL +MLL + MOther.

St-eff = The section modulus for the partial composite sectionreferred to the top of the equivalent transformed sectioncalculated using Equation 11a or 11b, as appropriate,in3. Note that this item may be different on the left andright sides of the beam. (For full [100%] composite con-nection see Composite Beam Design AISC-ASD89 Tech-nical Note 23 Bending Stress Checks, Equations 1a and1c instead of Equations 11a and 11b.)



beff = The effective width of the concrete slab, in. Note thatthis could be different on the left and right sides of thebeam.

beff-par = The effective width of the concrete slab for partial com-posite action transformed to have the same E as thesteel section, in. This item is calculated using Equation10a for the slab on the right side of the beam and 10bfor the slab on the left side of the beam. (For full[100%] composite connection see Composite Beam De-sign AISC-ASD89 Technical Note 23 Bending StressChecks, Equations 1b and 1d instead of Equations 10aand 10b.)

fc = The maximum concrete compressive stress, ksi.




Technical Note 22Allowable Bending Stresses

GeneralThis Technical Note describes how the program determines the allowablebending stresses using the AISC-ASD89 specification for composite beams.The methodologies for determining the allowable bending stress for both thesteel beam alone and the composite beam are described.

Important note concerning cover plates: This section describes how theallowable bending stresses are determined for steel beams. When a coverplate is present, the program determines the allowable stresses for the beamas if the cover plate were not present, except as noted in Note 3 for Table 1.Based on the allowable bending stress at the bottom of the beam bottomflange, Fb-bbf, which the program determines as described in this TechnicalNote, the allowable bending stress at the bottom of the cover plate, Fb-bcp istaken as shown in Equation 1.

= −

y

cpybbfbbcp-b F

FFF Eqn. 1

where,

Fb-bbf = Allowable bending stress at the bottom of the beambottom flange, ksi.

Fb-bcp = Allowable bending stress at the bottom of the coverplate, ksi.

Fy = Yield stress of beam, ksi.

Fycp = Yield stress of cover plate, ksi.

Allowable Bending Stresses Composite Beam Design AISC-ASD89

Technical Note 22 - 2 Allowable Bending Stress for Steel Beam Alone

Allowable Bending Stress for Steel Beam AloneThis section documents the allowable bending stresses that the program useswhen the steel beam alone (noncomposite) resists the bending. Allowablebending stresses are provided for both compression and tension.

Note:

Allowable stresses for composite beams are described in the section entitled “AllowableBending Stresses for Positive Bending in the Composite Beam” later in this TechnicalNote.

The allowable bending stress for the steel beam alone depends on the type ofbeam section, whether the compression flange and the web are compact ornoncompact, the yield stress of the beam and the unsupported length of thecompression flange, Lb. Table 1 identifies the equations that are used to cal-culate the allowable bending stress of the steel beam alone for various condi-tions.

Table 1 is based on the requirements of Chapter F, Section F1 in the AISC-ASD89 specification. The compact and noncompact requirements that theprograme uses for the flanges, web and the cover plate (if it exists and is incompression) are presented in Composite Beam Design AISC-ASD89 Techni-cal Note 19 Width-to-Thickness Checks.

In the Flange and Cover Plate column of Table 1, if the flange or the coverplate is noncompact, the column entry is noncompact. Both the flange andthe cover plate must be compact for the entry to be compact.

Composite Beam Design AISC-ASD89 Allowable Bending Stresses

Allowable Bending Stress for Steel Beam Alone Technical Note 22 - 3

Table 1 Equations Used by the Program for Allowable BendingStress for Steel Beam Alone

Type ofBeam Section

Flangeand

CoverPlate Web

BeamFy

UnsupportedLength of

CompressionFlange1

Equation(s) for Fb,the Allowable Bending

Stress

compact compact ≤ 65 ksi ≤ Lc3

in tension or compression

compact compact > 65 ksi ≤ Lc6


compact noncompact No limit ≤ Lc6


noncompact compact ≤ 65 ksi ≤ Lc4


noncompact compact > 65 ksi ≤ Lc6


noncompact noncompact No limit ≤ Lc6


Rolled I-shaped orchannel section

from the programdatabase

compact ornoncompact


No limit > Lc

6 for tension; larger of 7 or8, as applicable and 9 for

compression2

compact compact ≤ 65 ksi ≤ Lc3


compact compact > 65 ksi ≤ Lc6


compact noncompact No limit ≤ Lc6


noncompact compact ornoncompact ≤ 65 ksi ≤ Lc

5in tension or compression

noncompact compact ornoncompact

> 65 ksi ≤ Lc6


User defined(welded) section

that isI-shaped or a

channel



No limit > Lc

6 for tension; larger of 7 or8, as applicable and 9 for

compression2, 3


1. See Equation 2 for Lc.2. Equations 7 and 8 do not apply to channels.3. For I-shaped beams, Equation 9 does not apply if the area of the compression flange is less

than the area of the tension flange. For this check the area of the cover plate is included aspart of the flange area.


Technical Note 22 - 4 Allowable Bending Stress for Steel Beam Alone

In the fifth column of Table 1, the unsupported length of the compressionflange is compared to Lc. The length Lc is defined in Equation 2.

( ) yfy

fc FAd

20000and

F

76bofsmallerL = Eqn. 2

The Af and bf terms in Equation 2 are the area and width of the beam com-pression flange (not including cover plate even if it exists), respectively.These terms are never based on the cover plate dimensions. The Fy term isthe yield stress of the beam (not cover plate)

The equations referred to in the last column of Table 1 are listed below.

yb F0.66F = Eqn. 3

−= y

f

fyb F

2tb

0.0020.79FF Eqn. 4

−=

c

y

f

fyb k

F

2tb

0.0020.79FF Eqn. 5

where

( )0.46w

cth

4.05k = , for h/tw > 70, otherwise kc = 1 Eqn. 5a

yb F0.60F = Eqn. 6

In Equation 6, the program takes Fy as the yield stress of the compressionflange for hybrid beams.

( )yy

b3

2Ty

b

y

b3

Ty

b3

0.60FFC10*1,530

rlF

32

F

FC10*510

rl

FC10*102

When

≤

−=

≤≤

Eqn. 7


Allowable Bending Stress for Steel Beam Alone Technical Note 22 - 5

( ) y2T

b3

b

y

b3

T

0.60Frl

C10*170F

FC10*510

rl

When

≤=

>Eqn. 8

( ) yf

b3

b 0.60FAld

C10*12F ≤= Eqn. 9

In Equations 7 and 8, the l term in l/rT is the unbraced length of the compres-sion flange. The rT term is based on the compression flange of the beam. Thisis significant when the dimensions of the top and bottom flanges are different.For rolled sections, the rT term is taken from the program database. For user-defined (welded) sections, the rT term is calculated using Equation 10a or10b. Equation 10a applies for positive bending and Equation 10b applies fornegative bending. If it exists, the cover plate is ignored when calculating rT.

For positive bending:

( )

( )3

ttydtb

36

ttyd

12

tb

rwtopfbare

topftopf

3wtopfbaretopf

3topf

T−

−−

−−−

−−+

−−+

= Eqn. 10a

For negative bending:

( )

( )3

ttytb

36tty

12tb

rwbotfbare

botfbotf

3wbotfbarebotf

3botf

T−

−−

−−−

−+

−+

= Eqn. 10b

The Cb term in Equations 7, 8 and 9 is defined in "Bracing (C) Tab and Brac-ing Tab" in Composite Beam Design AISC-ASC89 Technical Note 18 Over-writes.

In Equation 9 Af is the area of the compression flange (not including the coverplate even if it exists).


Technical Note 22 - 6 Allowable Bending Stresses for Positive Bending in the Composite Beam

The derivation of ybare is provided in "Properties of Steel Beam (Plus CoverPlate) Alone" in Composite Beam Design AISC-ASD89 Technical Note 20Transformed Section Moment of Inertia.

Allowable Bending Stresses for Positive Bending in theComposite BeamNote:

Allowable stresses when composite connection is not considered is described earlier inthis Technical Note in the section entitled “Allowable Bending Stress for Steel BeamAlone.”

Figure 1 shows a typical composite beam. When there is positive bending inthe beam there is compression at the top of the concrete and tension at thebottom of the beam. For positive bending in a composite beam, the programchecks the stresses at the following locations:

Compression stress at the top of the concrete. This stress is limited to

0.45 'cf .

Tension or compression at the top of the top flange of the beam. See Table2 for the allowable stress.

Tension or compression at the bottom of the bottom flange of the beam. Inpractice, it is unlikely that the bottom flange of the beam will ever be incompression for positive bending. It would require an extremely large coverplate, beyond the bounds of practicality. See Table 2 for the allowablestress.

Tension at the bottom of the cover plate. See Table 2 and the section enti-tled “General” at the beginning of this Technical Note for the allowablestress.

Table 2 defines the equations that are used to calculate the allowable bendingstress for the steel beam portion of a composite beam section for variousconditions. The equation used depends on whether the beam web is compactand whether the yield stress is less than or equal to 65 ksi.


Allowable B

Table 2

Type of Secti

Anycomposite

F

F

Concrete slab

Figure

ending Stresses for Positive Bending in the Composite Beam Technical Note 22 - 7

: Equations the Program Uses to Calculate the Allowable Bend-ing Stress in the Steel Beam Portion of a Composite Beam

Equations Used for Allowable StressesBeamon Web Beam Fy Compression Tension

compact ≤ 65 ksi 11 11non-

compact ≤ 65 ksi 12 12 beam


> 65 ksi 12 12

yb F0.66= Eqn.11

yb F0.60= Eqn. 12

��

bcp

h rt c

dt cp

Metal deck

Steel beam

Cover plate

1: Composite Beam

Bending Stress Checks Without Composite Action Technical Note 23 - 1



Technical Note 23Bending Stress Checks

This Technical Note describes how the program checks the bending stress forAISC-ASD89 design. The bending stress checks are described for the caseswith and without composite action.

Bending Stress Checks Without Composite ActionAt each output station where there is negative moment in a composite sectionor there is positive or negative moment in a noncomposite section, the asso-ciated bending stress is checked at the following positions in the beam, asapplicable.

The top of the top flange of the steel beam.

The bottom of the bottom flange of the steel beam.

The bottom of the cover plate if it exists.

Table 1 lists the equations that ETABS uses to calculate both the actualbending stress and the allowable bending stress at each of these positions.

Table 1: Equations for Actual and Allowable Stresses forNoncomposite Bending

Location

Equation forCalculating Actual Bending

Stress

Equation forCalculating Allowable Bending

Stress

Top of beamtop flange ( )

bare

bare

I

ydM −See Table 1 in Composite BeamDesign AISC-ASD89 Technical

Note 22 Allowable BendingStresses.

Bottom ofbeambottomflange

bare

bare

I

yMSee Table 1 in Composite BeamDesign AISC-ASD89 Technical


Bending Stress Checks Composite Beam Design AISC-ASD89

Technical Note 23 - 2 Positive Moment in a Composite Beam

Table 1: Equations for Actual and Allowable Stresses forNoncomposite Bending

Location

Equation forCalculating Actual Bending

Stress

Equation forCalculating Allowable Bending

Stress

Bottom ofcover plate ( )

bare

cpbare

I

tyM +See Table 1 in Composite BeamDesign AISC-ASD89 Technical


The following notation is used in the equations in the second column ofTable 1:

Ibare = Moment of inertia of the steel beam (plus cover plate, ifone exists), in4. See Equation 3 in Composite Beam De-sign AISC-ASD89 Technical Note 20 Transformed SectionMoment of Inertia.

M = The design moment, kip-in.



ybare = Distance from the bottom of the bottom flange of thesteel section to the elastic neutral axis (ENA) of the steelbeam (plus cover plate, if it exists), in. See Equation 2 inComposite Beam Design AISC-ASD89 Technical Note 20Transformed Section Moment of Inertia.

Positive Moment in a Composite BeamAt each output station where there is positive moment in the composite sec-tion, the associated bending stress is checked at the following positions in thecomposite beam, as applicable.

The top of the concrete slab. This check is performed separately on eachside of the beam.

The top of the top flange of the steel beam.

Composite Beam Design AISC-ASD89 Bending Stress Checks

Positive Moment in a Composite Beam Technical Note 23 - 3

The bottom of the bottom flange of the steel beam.

The bottom of the cover plate, if it exists.

Table 2 lists the equations that the program uses to calculate both the actualbending stress and the allowable bending stress at each of these positions. Inaddition to the checks listed in Table 2, if the beam is unshored, the programperforms additional checks. These checks are described in the section entitled"Important Notes Regarding Unshored Composite Beams" later in this Techni-cal Note.

Table 2: Equations for Actual and Allowable Stresses for PositiveBending in a Composite Beam

LocationEquation for CalculatingActual Bending Stress

Equation for CalculatingAllowable Bending Stress

Top of concrete 12a, 12bin Composite Beam Design AISC-ASD89 Technical Note 21 ElasticStresses with Partial Composite

Connection.

0.45f'c

Top of beam topflange

7in Composite Beam Design AISC-ASD89 Technical Note 21 ElasticStresses with Partial Composite

Connection.

11 or 12 in Composite BeamDesign AISC-ASD89 TechnicalNote 22 Allowable Bending

Stresses.See Table 2 in the same Note.

Bottom of beambottom flange

6in Composite Beam Design AISC-ASD89 Technical Note 21 ElasticStresses with Partial Composite

Connection.

11 or 12 in Composite BeamDesign AISC-ASD89 TechnicalNote 22 Allowable Bending


Bottom of coverplate

5 in Composite Beam Design AISC-ASD89 Technical Note 21 ElasticStresses with Partial Composite

Connection.

1 together with 11 or 12 inComposite Beam Design

AISC-ASD89 Technical Note22 Allowable Bending



Technical Note 23 - 4 Positive Moment in a Composite Beam

The equations referred to in the second column of Table 2 for calculating ac-tual bending stress are derived for partial composite connection. When thereis full (100%) composite connection, make the substitutions shown in Equa-tions 1a through 1g into those equations:

Note:

The formulas shown in Equations 1a through 1g are not in general true. They only applyas substitutions into the equations listed in Table 2 when you are considering full (100%)composite connection rather than partial composite connection.

Equations 1a and 1b show the substitutions to make into Equation 12a ofComposite Beam Design AISC-ASD89 Technical Note 21 Elastic Stresses withPartial Composite Connection if you are considering full (100%) compositeconnection.

( )ythdI

Sleftcleftr

trleftefft −++

=− Eqn. 1a

beff par left = beff left (Ec left / Es) Eqn. 1b

Equations 1c and 1d show the substitutions to make into Equations 12b ofComposite Beam Design AISC-ASD89 Technical Note 21 Elastic Stresses withPartial Composite Connection if you are considering full (100%) compositeconnection.

( )ythdI

Srightcrightr

trrightefft −++

=− Eqn. 1c

beff par right = beff right (Ec right / Es) Eqn. 1d

Equations 1e and 1f show the substitutions to make into Equations 6 and 7 ofComposite Beam Design AISC-ASD89 Technical Note 21 Elastic Stresses withPartial Composite Connection if you are considering full (100%) compositeconnection.

yeff = y Eqn. 1e

Ieff = Itr Eqn. 1f

The y term in Equations 1a, 1c and 1e is the distance from the bottom of thebeam bottom flange to the elastic neutral axis (ENA) of the composite beam.

Composite Beam Design AISC-ASD89 Bending Stress Checks

Important Notes Regarding Unshored Composite Beams Technical Note 23 - 5

The distance y can be calculated using Equation 17a or 17b of CompositeBeam Design AISC-ASD89 Technical Note 20 Transformed Section Moment ofInertia.

The Itr term in Equation 1f is the transformed section moment of inertia aboutthe ENA of the composite beam assuming full (100%) composite connection.This moment of inertia can be calculated using Equation 18 of CompositeBeam Design AISC-ASD89 Technical Note 20 Transformed Section Moment ofInertia.

Equation 1g shows the substitution to make into Equation 5 of CompositeBeam Design AISC-ASD89 Technical Note 21 Elastic Stresses with PartialComposite Connection if you are considering full (100%) composite connec-tion.

Seff = Str Eqn. 1g

The Str term in Equation 1g is the section modulus for the fully (100%) com-posite transformed section referred to the extreme tension fiber of the steelsection (including cover plate, if it exists). This section modulus can be calcu-lated using Equation 3 of Composite Beam Design AISC-ASD89 TechnicalNote 21 Elastic Stresses with Partial Composite Connection.

Important Notes Regarding Unshored CompositeBeamsSteel Stress ChecksFor unshored composite beams, the stresses are checked as described above.In addition, for unshored composite beams only (not shored beams and notnoncomposite beams), the program also checks that the bending stresses inthe steel beam do not exceed 0.9 Fy when stresses are computed assumingthe steel section alone resists the DL moment and the composite section re-sists the SDL + LL + Other moment.

Equations 2a through 2c illustrate how these stress checks are performed bythe program.

At the top of the beam top flange:


Technical Note 23 - 6 Important Notes Regarding Unshored Composite Beams

( ) ( )y

eff

effOtherAll

bare

bareDL F0.9I

y-dM

IydM ≤+−

Eqn. 2a

At the bottom of the beam bottom flange:

yeff

effOtherAll

bare

bareDL F0.9I

yM

IyM ≤+ Eqn. 2b

At the bottom of the cover plate, if it exists:

( )y

eff

OtherAll

bare

cpbareDL F0.9S

M

I

tyM≤+

+Eqn. 2c

In Equations 2a through 2c, MDL is the moment due to dead load and MAll Other

is the moment due to all other loads (except dead load).

Concrete Stress ChecksFor unshored composite beams, the bending stress check for the concreteslab is determined based on the SDL + LL + All Other Loads, not the TL mo-ment. In other words, for unshored beams, the steel beam alone is assumedto carry all of the DL moment alone. The composite section carries the rest ofthe moment.

In the above paragraph,

DL = dead load

SDL = superimposed dead load

LL = live load

TL = total load

Shear Stress Check Technical Note 24 - 1



Technical Note 24Beam Shear Checks

This Technical Note describes how the program checks the beam end reactionfor shear for AISC-ASD89 composite beam design.

The program performs two checks for beam end shear. The first is based onthe allowable shear stress specified in AISC-ASD89 Specification Section F4.If the beam does not pass this shear stress check, the program indicates thatthe beam is inadequate. This shear check is described in the section entitled"Shear Stress Check."

The second check the program performs is based on the allowable shearrupture (block shear) specified in AISC-ASD89 Specification Section J4. Thischeck is completed based on several built-in assumptions about bolt size, boltspacing, cope depth, etc. If the beam does not pass this shear rupture check,the program does not indicate that the beam is inadequate. Instead, it issuesa design warning message in the output that the block shear may be high forthe beam. This shear check is described in the section entitled "Shear RuptureCheck" in this Technical Note

Shear Stress CheckTypical CaseFor h/tw ≤ yF380 the allowable shear stress is shown in Equation 1, which is

the same as AISC-ASD89 Specification Equation F4-1.

Fv = 0.40 Fy Eqn. 1

where,

Fv = Allowable shear stress, ksi.

Fy = Beam yield stress, ksi.

The shear stress to which Equation 1 applies is calculated using Equation 2.

Beam Shear Checks Composite Beam Design AISC-ASD89

Technical Note 24 - 2 Shear Stress Check

fv = ( ) wtopbot tCCd

V−−

Eqn. 2

where,

Cbot = Cope depth at bottom of beam, in.

Ctop = Cope depth at top of beam, in.

V = Beam end shear at the inside end of the rigid end offsetalong the length of the beam (if the offset exists), kips.

d = Beam depth, in.

fv = Shear stress, ksi.

tw = Beam web thickness, in.

Note:

The top and bottom copes are internally calculated by the program and reported in thelong- and short-form printed output. See the section entitled "Copes" later in this Techni-cal Note for more information on beam copes.

Note that Equation 2 is based on the full depth of the beam minus the top andbottom copes. The copes are internally calculated by the program and are re-ported in the printed output. See the following section titled "Copes" for in-formation on how the program determines the assumed copes.

Slender WebFor h/tw > yF380 the allowable shear stress is that shown in Equation 3.

Equation 3 is based on AISC-ASD89 Specification Equation F4-2 with kv setequal to 5.34.

Fv = Cv2.89

Fy ≤ 0.40Fy Eqn. 3

where

Cv = ( )2wy thF

5.34*45,000when Cv ≤ 0.8 Eqn. 3a

Composite Beam Design AISC-ASD89 Beam Shear Checks

Copes Technical Note 24 - 3

Cv = yw F

5.34th

190when Cv > 0.8 Eqn. 3b

The shear stress to which Equation 3 applies is calculated using Equation 4.

fv = ( ) w*top

*bot tCCd

V

−−Eqn. 4

where

C*bot = maximum of Cbot or tf bot Eqn. 4a

C*top = maximum of Ctop or tf top Eqn. 4b

Note that Equation 4 is based on the clear distance between the flanges of thebeam minus any portion of the top and bottom copes that extends into thisclear distance. This is different from the typical, non-slender web case.

Finally, note that the value of h/tw is limited by the requirements for a non-compact web. See "Noncompact Section Limits for Webs" in Composite BeamDesign AISC-ASD89 Technical Note 19 Width-to-Thickness Checks for moreinformation.

CopesThe program calculates the default beam copes as follows:

If the beam frames into a column or a brace, by default, no cope is as-sumed at either the top or the bottom of the beam.

If a beam, call it Beam A, frames into another beam, call it Beam B, thefollowing copes are assumed in Beam A, as shown in Figure 1:

The depth of the cope at the top of Beam A is equal to the thickness ofthe Beam B top flange plus 1/4".

If the depth of Beam A is greater than the depth of Beam B minus thebottom flange thickness of Beam B minus 1/4", the depth of the copeat the bottom of Beam A is equal to the depth of Beam A minus thedepth of Beam B plus the bottom flange thickness of Beam B plus1/4".


Technical Note 24 - 4 Shear Rupture Check

Important note: In some cases when you use auto select section lists andyou compare the cope dimensions reported in the output with the cope di-mensions calculated using the above-described method considering the cur-rent design sections for the beam and the girder, you may see different re-sults. The reason for this is that the beam may have been designed beforethe girder, and thus the cope dimensions for the beam were calculated basedon an older design section for the girder. This illustrates that the design is aniterative process. You must cycle through your design and analysis severaltimes before you get final results. Also you should always run one final designcheck with all auto select section lists removed; that is, with actual beamsections assigned to all elements.

Shear Rupture CheckThe program checks for shear rupture based on AISC-ASD89 SpecificationSection J4. The shear rupture check is only performed at the end of a beam ifthe top flange of the beam is coped at that end. Several assumptions are re-quired for the program to perform this check. They include:

1. A single row of 7/8" diameter bolts is assumed.

2. The bolt spacing is assumed to be 3 inches.

Beam ABeam Bt f-top

t f-bot

d B d A

t f-top

+ 1/

4"t f-b

ot+

1/4"

d A -

dB +

t

f-bot

+ 1/

4"Figure 1: Default Beam Copes


Shear Rupture Check Technical Note 24 - 5

3. Standard bolt holes are assumed. The diameter of the bolt hole is as-sumed to be 15/16".

4. The number of bolts assumed is based on the T dimension of the beam asshown in Table 1. For rolled sections, the T dimension, which is tabulatedin the AISC manual, is equal to d -2k. For welded sections, the programassumes that the T dimension equals d - tf-top - tf-bot - 1 inch.

where,

d = Beam depth, in.

k = Distance from outside face of rolled beam flange to toeof web fillet, in.

tf-bot = Thickness of beam bottom flange, in.

tf-top = Thickness of beam top flange, in.

Table 1: Assumed Number of Bolts Based on Beam T Dimension

T Dimension Range Assumed Number of Bolts

T < 6.5" Shear rupture not checked

6.5" ≤ T < 9.5" 2

9.5" ≤ T < 12.5" 3

12.5" ≤ T < 16.5" 4

16.5" ≤ T < 19.5" 5

19.5" ≤ T < 22.5" 6

22.5" ≤ T < 25.5" 7

25.5" ≤ T < 28.5" 8

28.5" ≤ T < 31.5" 9

T ≥ 31.5 10

5. The distance from the center of the top bolt hole to the top edge of thebeam web (at the cope), lv, is 1.5 inches.

6. The distance from the center of any bolt hole to the end of the beam web,lh, is 1.5 inches.


Technical Note 24 - 6 Shear Rupture Check

7. The allowable shear rupture stress is calculated based on shear fracturealong the shear plane and tension yield along the tension plane.

See Figure 2 for an illustration of the assumptions in items 1, 2, 5, 6 and 7.

The allowable beam shear (end reaction) based on shear rupture is calculatedusing Equation 5.

Vall = 0.30 Fu Ans + 0.60 Fy Agt Eqn. 5

where,

Agt = Gross area along the tension plane, in2. See Equation6.

Ans = Net area along the shear plane, in2. See Equation7.

Fu = Minimum specified tensile strength of structural steel,ksi.

Vall = Allowable shear at end of beam, kips.

The gross area along the tension plane, Agt, is given by Equation 6.

Agt = lh tw Eqn. 6

Figure 2: Illustration of Shear Rupture Assumptions and Terms

lh = 1.5"l v =

1.5

"3”

typ.

Tension plane

Shear plane


Limitations of Shear Check Technical Note 24 - 7

where,

lh = The distance from the center of a bolt hole to the end ofthe beam web, in. The program assumes this distance tobe 1.5 inches, as shown in Figure 2.


The net area along the shear plane, Ans, is given by Equation 7.

Ans = [lv + 3(n - 1) - (15/16)(n - 0.5)] tw Eqn. 7

where,

lv = The distance from the center of the top bolt hole to thetop edge of the beam web (at the cope), in. The pro-gram assumes this distance to be 1.5 inches, as shownin Figure 2.

n = The number of bolts as determined from Table 1,unitless.


If the allowable shear at the end of the beam, Vall, is less than the beam endreaction, the program prints a design warning message in the output.

Limitations of Shear CheckFollowing are some limitations of the program check for beam end shear inthe Composite Beam Design postprocessor.

1. You cannot specify transverse web stiffeners.

2. No check is made for shear on the net section considering the bolt holes,except as noted in the following item 3.

3. The shear rupture (block shear) check specified in AISC-ASD89 Specifica-tion Section J4 is performed as described in the section above entitled"Shear Rupture Check." If the beam does not satisfy the shear rupturecheck, only a warning suggesting you should check shear rupture (block


Technical Note 24 - 8 Limitations of Shear Check

shear) is issued in the output. The program does not fail the beam be-cause it does not pass the shear rupture check.

4. Tension field action, as described in AISC-ASD89 specification Chapter Gis not considered.




Technical Note 25Shear Studs

OverviewThis Technical Note begins by defining the program default allowable shearstud horizontal loads for AISC-ASD89 composite beam design. Next some ofthe basic equations used for determining the number of shear studs on thebeam are provided.

Composite Beam Design AISC-ASD89 Technical Note 26 Calculations forNumber of Shear Studs describes how the program determines the distribu-tion of shear studs on a composite beam. It also introduces the concept ofcomposite beam segments. It is very important that you understand the defi-nition of a composite beam segment so that you can properly interpret thereported number of shear studs in the composite beam output.

Composite Beam Design Technical Note 14 The Number of Shear Studs thatFit in a Composite Beam Segment describes how the program determines themaximum number of shear studs that fit in a composite beam segment. Theprogram also checks that the shear studs it specifies can fit on the beam. Seealso Composite Beam Design Technical Note 15 User-Defined Shear StudPatterns for more information.

Shear Stud ConnectorsThe unmodified allowable horizontal load for shear studs is calculated usingEquation 1. As described later, this allowable load may be modified if there isformed metal deck.

q = 0.25Asc c'cEf ≤ 0.5AscFu Eqn. 1

where,

Asc = Cross-sectional area of shear stud, in2.

Shear Studs Composite Beam Design AISC-ASD89

Technical Note 25 - 2 Shear Stud Connectors

f'c = Compressive strength of concrete slab, ksi.

Ec = Young’s modulus for the concrete slab as specified in thematerial property definition associated with the slab, ksi.

Fu = Minimum specified tensile strength of shear stud, ksi.

Equation 1 is based on AISC-LRFD93 Specifications Equation I5-1 with asafety factor of 2 applied to it. Note that this equation is also discussed in theAISC-ASD89 specifications commentary for Chapter I. Equation 1 gives allow-able shear stud loads similar, but not exactly the same, to those obtainedusing Tables I4.1 and I4.2 in the AISC-ASD89 specification. If you want touse values that are exactly the same as those obtained from AISC-ASD89 Ta-bles I4.1 and I4.2, you should assign a value of q in the overwrites.

If there is formed metal deck, the value of q obtained from Equation 1 is re-duced by a reduction factor, RF, whose value depends on the direction of thedeck span relative to the beam span. The reduction factor is different de-pending on whether the span of the metal deck ribs is oriented parallel orperpendicular to the span of the beam. The subsections below entitled “Re-duction Factor when Metal Deck is Perpendicular to Beam” and “ReductionFactor when Metal Deck is Parallel to Beam” describe the reduction factors forthe two deck directions.

Important note #1: The metal deck reduction factor, RF, only applies to the

0.25Asc c'cEf term in Equation 1. It does not apply to the 0.5AscFu term.

Important note #2: When there is slab on both sides of the beam, the pro-gram calculates q for each side of the beam separately using Equation 1 andthe appropriate metal deck reduction factor if applicable. The program thenuses the smaller of the two q values in the calculations.

Important note #3: When you specify a q value in the composite beamoverwrites, the program assumes that the specified value of q already in-cludes a metal deck reduction factor, if applicable. Thus the program does notmodify the specified q value based on the metal deck configuration.

Reduction Factor when Metal Deck is Perpendicular to BeamWhen the span of the metal deck is perpendicular to the beam span, the al-lowable horizontal load per shear stud specified in Equation 1 is multiplied by

Composite Beam Design AISC-ASD89 Shear Studs

Shear Stud Connectors Technical Note 25 - 3

the reduction factor specified in Equation 2 to yield the final allowable hori-zontal load for a single shear stud.

1.01.0hH

hw

N

0.85RF

r

s

r

r

r

≤

−

= Eqn. 2

where,

RF = Reduction factor for the allowable horizontal load for ashear stud, unitless.

hr = Height of metal deck rib, in.

Hs = Length of shear stud after welding, in.

Nr = Number of shear studs in one metal deck rib, but notmore than 3 in the calculations even if more than 3 studsexist in the rib, unitless. The program uses whatevervalue is specified for the Max Studs per Row item on theShear Studs tab in the composite beam overwrites for Nr,unless that value exceeds 3, in which case the programuses 3. Note that the default value for the Max Studs perRow item in the overwrites is 3.


Reduction Factor when Metal Deck is Parallel to BeamWhen the ratio wr/hr is less than 1.5, the allowable horizontal load per shearstud specified in Equation 1 is multiplied by the reduction factor specified inEquation 3.

1.01.0hH

hw

0.6RFr

s

r

r ≤

−

= Eqn. 3

where,

RF = Reduction factor for the allowable horizontal load for ashear stud, unitless.

hr = Height of metal deck rib, in.


Technical Note 25 - 4 Horizontal Shear for Full Composite Connection

Hs = Length of shear stud after welding, in.


Horizontal Shear for Full Composite ConnectionThe total horizontal shear to be resisted between the point of maximum posi-tive moment (where the concrete is in compression) and the points of zeromoment for full composite connection, Vh, is given by the smaller of Equations4, 5a or 5b as applicable. Note that Equation 4 applies to both rolled beamsand user-defined (welded) beams. Equation 5a only applies to rolled beamsand Equation 5b only applies user-defined (welded) beams.

2

A0.85fA0.85fV rightc

'rightcleftc

'leftc

h+

= Eqn. 4

where,

f’c = Compressive strength of the concrete slab, ksi. This itemmay be different on the left and right sides of the beam.

Ac = Area of the concrete slab, in2. When the deck span is per-pendicular to the beam span, this is the area of concrete inthe slab above the metal deck that is above the elasticneutral axis (ENA) of the fully composite beam. When thedeck span is parallel to the beam span, this is the area ofconcrete in the slab, including the concrete in the metaldeck ribs, that is above the ENA of the fully compositebeam. This item may be different on the left and rightsides of the beam.

For rolled beams only:

2

FtbFAV ycpcpcpys

h+

= Eqn. 5a

For user-defined (welded) beams only:


Number of Shear Studs Technical Note 25 - 5

2

Ftb

2

Ftb2

Fht

2

FtbV

ycpcpcpybot-fbot-f

ywytop-ftop-fh

+

++=Eqn. 5b

The following notation is used in Equations 5a and 5b:

As = Area of a rolled steel section (not including the coverplate, if it exists), in2.

Fy = Minimum specified yield stress of steel beam, ksi.

Fycp = Minimum specified yield stress of cover plate, ksi.


bf-bot = Width of bottom flange of a user-defined (welded) steelbeam, in.

bf-top = Width of top flange of a user-defined (welded) steelbeam, in.

h = Clear distance between flanges for a user-defined(welded) steel beam, in.


tf-bot = Thickness of bottom flange of a user-defined (welded)steel beam, in.

tf-top = Thickness of top flange of a user-defined (welded) steelbeam, in.

Number of Shear StudsThe program determines the required number of shear studs on the compos-ite beam based on the moment at each output station. The calculation iscompleted separately at each output station. The program uses (reports) themaximum number of shear studs required on the beam based on the calcula-tion at any output station. See Composite Beam Design Technical Note 13Distribution of Shear Studs on a Composite Beam for more details.


Technical Note 25 - 6 Number of Shear Studs

Between the Output Station with Maximum Moment and the Point of Zero MomentFor full (100%) composite action, the number of shear studs required be-tween the output station with the maximum positive moment and adjacentpoints of zero moment, N1, for a given design load combination is given byEquation 6.

qV

N h1 = Eqn. 6

In Equation 6, Vh is determined as described in the previous section entitled"Horizontal Shear for Full Composite Connection" and q is determined as de-scribed in the previous section entitled "Shear Stud Connectors."

For partial composite connection, the number of shear studs required be-tween the output station with the maximum positive moment and adjacentpoints of zero moment, N1, is given by Equation 7.

qV

N'h

1 = Eqn. 7

In Equation 7, V'h is equal to the percent composite connection times Vh. Forexample, if there is 70% composite connection, V'h = 0.7 Vh. Thus, the per-cent composite connection, PCC, for AISC-ASD89 design is given by Equation8.

h

'h

VV

PCC = Eqn. 8

Between Other Output Stations and Points of Zero MomentThe program uses Equation 9 to determine the number of shear studs, N2,required in a positive bending region between other output stations and adja-cent points of zero moment for a given design load combination using AISC-ASD89 design. Note that the program checks Equation 9 at each output sta-tion.

01β

1M

βMN

N max station

station1

2 ≥−

−

= Eqn. 9

where,


Number of Shear Studs Technical Note 25 - 7

Mstationmax = Maximum moment at any output station for a givendesign load combination, k-in.

Mstation = Moment at the output station considered for the de-sign load combination, k-in.

N1 = Number of shear studs required between the outputstation with the maximum positive moment and ad-jacent points of zero moment for the design loadcombination, unitless.

N2 = Number of shear studs required between the outputstation considered and adjacent points of zero mo-ment for the design load combination, unitless.

β = A term equal to Str/Sbare for full (100%) compositeconnection and Seff/Sbare for partial composite con-nection, unitless.

The Str term is the section modulus for the fully (100%) composite trans-formed section referred to the extreme tension fiber of the steel section(including cover plate, if it exists), in3. This section modulus can be calcu-lated using Equation 3 of Composite Bean Design AISC-ASD89 TechnicalNote 21 Elastic Stresses with Partial Composite Connection.

The Sbare term is the section modulus for the steel section alone (pluscover plate, if it exists) referred to the extreme tension fiber of the steelsection, in3. This section modulus can be calculated as Ibare/ybare where Ibare

is calculated using Equation 3 of Composite Beam Design AISC-ASD89Technical Note 20 Transformed Section Moment of Inertia and ybare is cal-culated using Equation 2 of Composite Beam Design AISC-ASD89 Techni-cal Note 20 Transformed Section Moment of Inertia.

The Seff term is the effective section modulus of the partially compositebeam referred to the extreme tension fiber of the steel beam section (in-cluding cover plate, if it exists), in3. This section modulus can be calcu-lated using Equation 2 of Composite Bean Design AISC-ASD89 TechnicalNote 21 Elastic Stresses with Partial Composite Connection.

Basic Equations Technical Note 26 - 1



Technical Note 26Calculation of the Number of Shear Studs

This Technical Note describes algorithms for determining the placement ofshear studs on a composite beam, including providing three example prob-lems. Also see Composite Beam Design Technical Note 13 Distribution ofShear Studs on a Composite Beam, Technical Note 14 The Number of ShearStuds that Fit in a Composite Beam Segment, and Technical Note 15 User-Defined Shear Stud Patterns for more information.

Basic EquationsEquation 1 applies at the output station with the maximum positive momentwhen there is full (100%) composite connection.

qV

N h1 = Eqn. 1

where,

Vh is the total horizontal shear to be resisted between the point of maximumpositive moment (where the concrete is in compression) and the points ofzero moment for full composite connection. Vh is derived by the smaller ofEquations 1a, 1b or 1c as applicable. Note that Equation 1a applies to bothrolled beams and user-defined (welded) beams. Equation 1b only applies torolled beams and Equation 1c only applies to user-defined (welded) beams.

2

A0.85fA0.85fV rightc

'rightcleftc

'leftc

h

+= Eqn. 1a

where,

f’c = Compressive strength of the concrete slab, ksi. This item maybe different on the left and right sides of the beam.

Ac = Area of the concrete slab, in2.

Calculation of the Number of Shear Studs Composite Beam Design AISC-ASD89

Technical Note 26 - 2 Basic Equations

When the deck span is perpendicular to the beam span, Ac is the area of con-crete in the slab above the metal deck that is above the elastic neutral axis(ENA) of the fully composite beam. When the deck span is parallel to thebeam span, Ac is the area of concrete in the slab, including the concrete in themetal deck ribs, that is above the ENA of the fully composite beam. This itemmay be different on the left and right sides of the beam.

For rolled beams only:

2

FtbFAV

ycpcpcpysh

+= Eqn. 1b

For user-defined (welded) beams only:

2

Ftb

2

Ftb2

Fht

2

FtbV

ycpcpcpybot-fbot-f

ywytop-ftop-fh

+

++=Eqn. 1c

The following notation is used in Equations 1b and 1c:

As = Area of a rolled steel section (not including the cover plate, ifit exists), in2.

Fy = Minimum specified yield stress of steel beam, ksi.


bf-bot = Width of bottom flange of a user-defined (welded) steelbeam, in.

bf-top = Width of top flange of a user-defined (welded) steel beam, in.

h = Clear distance between flanges for a user-defined (welded)steel beam, in.


Fycp = Minimum specified yield stress of cover plate, ksi.

tf-bot = Thickness of bottom flange of a user-defined (welded) steelbeam, in.

Composite Beam Design AISC-ASD89 Calculation of the Number of Shear Studs

Basic Equations Technical Note 26 - 3

tf-top = Thickness of top flange of a user-defined (welded) steelbeam, in.

Equation 2 applies at the output station with the maximum positive momentwhen there is partial composite connection.

qV

N'h

1 = Eqn. 2

In Equation 2, V'h is equal to the percent composite connection times Vh. Forexample, if there is 70% composite connection, V'h = 0.7 Vh.

Equation 3 applies at any other output station regardless of the percent com-posite connection.

01β

1M

βMN

N max station

station1

2 ≥−

−

= Eqn. 3

where,

N2 = Number of shear studs required between the output sta-tion considered and adjacent points of zero moment forthe design load combination, unitless.

N1 = Number of shear studs required between the output sta-tion with the maximum positive moment and adjacentpoints of zero moment for the design load combination,unitless.

Mstation = Moment at the output station considered for the designload combination, k-in.

β = A term equal to Str/Sbare for full (100%) composite con-nection and Seff/Sbare for partial composite connection,unitless. Str is the section modulus for fully (100%) com-posite transformed section referred to the extreme tensionfiber of the steel section (including cover plate, if it ex-ists), in3. Sbare is the section modulus of the steel beamalone (plus cover plate, if it exists) referred to the ex-


Technical Note 26 - 4 Shear Stud Distribution Example 1

treme tension fiber, in3. Seff is the effective sectionmodulus of a partially composite beam referred to the ex-treme tension fiber of the steel beam section (includingcover plate, it if exists), in3.

Mstationmax = Maximum moment at any output station for a given de-sign load combination, k-in.

Shear Stud Distribution Example 1Shear stud distribution example 1 is shown in Figure 1. It is a 30-foot-longsimply supported beam. It has 1 klf uniform loading and a 50 k-ft moment atthe right end. For this example, assume the following:

Output stations occur at every 2 feet along the beam.

The allowable horizontal load for a single shear stud, q, is 12.4 kips.

The horizontal shear to be resisted between the point of maximum mo-ment and adjacent points of zero moment, Vh', is 245 kips.

The support distance, S, plus the gap distance, G, is equal to 0.50 foot (6inches) at each end of the beam.

The maximum longitudinal spacing of shear studs along the length of thebeam is 36 inches.

As shown in Figure 1, this beam has one composite beam segment that has alength, LCBS, of 29 feet.

Note:

Use the Assign menu > Frame/ Line >Frame Output Stations command to modify thenumber of output stations for a beam.


Shear Stu

Figure

1 klf

d Distribution Example 1 Technical Note 26 - 5

1 Example 1, Distribution of Shear Studs on a Composite Beam

30'16.67 k13.33 k

50 k-ft

Shear

16.67 k

13.33 k

13.33'

L1 and LCBS

88.89 k-ft (actual Mmax)

50 k-ft

3.33'

LCBS = 29'

0.5'0.5' L1 left = 13.50' L1 right = 12.63'

Out

put s

tatio

n 14

ftfro

m le

ft en

d of

bea

m

ETAB

S ca

lcul

ated

poin

t of z

ero

mom

ent

End

of b

eam

flan

ge

Cen

ter o

f sup

port

End

of b

eam

flan

ge

Cen

ter o

f sup

port

Moment

L = 30'

2.87'

Actual point ofzero moment



Table 1 illustrates how the bending moment is calculated by the program forthis beam at each output station. Note the following about Figure 1 and Table1:

The actual maximum moment for this beam of 88.89 k-ft occurs at a dis-tance of 13.33 feet from the left end of the beam, as shown in the mo-ment diagram in Figure 1. As shown in Table 1, since the program onlycalculates moment at the designated output stations, it picks up themaximum moment as 88.67 k-ft at the station located 14 feet from the(center of the support at the) left end of the beam. Increasing the numberof output stations will decrease the difference between the program-calculated maximum moment and the actual maximum moment.

The actual point of zero moment near the right end of the beam occurs26.67 feet from the left end of the beam (3.33 feet from the right end ofthe beam), as shown in the moment diagram in Figure 1. Referring to Ta-ble 1, the program calculates the point of zero moment by assuming a lin-ear variation of moment between output stations located 26 and 28 feetfrom the left end of the beam. This assumption yields a point of zero mo-ment that is 26.63 feet from the left end of the beam (3.37 feet from theright end of the beam). The dimensions shown in the bottom sketch ofFigure 1 reflect this program-calculated point of zero moment.

Table1 Example 1, Distribution of Shear Studs on aComposite Beam

Station(ft)

Moment(k-ft)

0 0.00

2 24.67

4 45.33

6 62.00

8 74.67

10 83.33

12 88.00

14 88.67

16 85.33

18 78.00

20 66.67


Shear Stud Distribution Example 1 Technical Note 26 - 7

Table1 Example 1, Distribution of Shear Studs on aComposite Beam

Station(ft)

Moment(k-ft)

22 51.33

24 32.00

26 8.67

28 -18.67

30 -50.00

The program calculates the maximum moment as 88.67 k-ft at the outputstation located 14 feet from the left end of the beam. Multiplying Mmax by0.999 yields 0.999 *88.67 = 88.58 k-ft. Because no other output station hasa moment that exceeds 0.999Mmax (88.58 k-ft) and no point loads are on thisbeam (for any load case), the only output station that is considered whendetermining the shear stud distribution is the station 14 feet from the left endof the beam (the maximum moment location).

The required number of shear studs between the maximum moment and ad-jacent points of zero moment, N1, is calculated using Equation 2 as:

studs19.76studperkips12.4

kips245qV

N'h

1 ===

The distances L1 left and L1 right for the output station located 14 feet from theleft end of the beam are shown in Figure 1.

= CBS1

right1left1CBS1 L*

LN

,L

NMaxRoundupN

= ft29*

ft12.63studs19.76

,ft13.50

studs19.76MaxRoundupNCBS1

= ft29*

ft12.63studs19.76

RoundupNCBS1

NCBS1 = Roundup (45.37 studs)



NCBS1 = 46 studs

The minimum number of studs required in the composite beam segment forthis beam is calculated using Equation 5 of Composite Beam Design TechnicalNote 13 Distribution of Shear Studs on a Composite Beam as:

=

MaxLSL

RoundupMS CBSCBS

studs10ft1in12

in36ft29

RoundupMSCBS =

=

Thus, the number of shear studs does not need to be increased to meet theminimum requirements. Assuming that the shear studs are found to fit on thebeam, the final number of uniformly spaced shear studs specified for thebeam is 46.

Shear Stud Distribution Example 2Shear stud distribution example 2 is shown in Figure 2. It is a 30-foot-longsimply supported beam. It has point loads at the beam one-third points. Forthis example, assume the following:

The point loads do not come from other beams in the program model.Thus, this beam has one composite beam segment instead of three com-posite beam segments.




The ratio β = Seff/Sbare is equal to 1.40.


Shear Stud Dis

Figure 2:

5 k 20 k

tribution Example 2 Technical Note 26 - 9

Example 2, Distribution of Shear Studs on a Composite Beam

LCBS = 29'

30'15 k10 k

Shear

15 k

10 k

Moment

100 k-ft

150 k-ft (Mmax)

0.5'0.5' L1 left = 9.5'

Out

put s

tatio

n 10

ftfro

m le

ft en

d of

bea

m

End

of b

eam

flan

ge

Cen

ter o

f sup

port

End

of b

eam

flan

ge

Cen

ter o

f sup

port

10' 10'10'

5 k

L1 right = 19.5'

Out

put s

tatio

n 20

ftfro

m le

ft en

d of

bea

m

L = 30'

L1 left = 19.5' L1 right = 9.5'





As shown in Figure 2, this beam has one composite beam segment that has alength, LCBS, of 29 feet.

Table 2 shows the bending moment calculated by the program for this beamat each output station.

Table 2: Example 2, Distribution of Shear Studs on aComposite Beam

Station(ft)

Moment(k-ft)

L1 left

(ft)L1 right

(ft)

0 0.00 N.A. N.A.

2 20.00 N.A. N.A.

4 40.00 N.A. N.A.

6 60.00 N.A. N.A.

8 80.00 N.A. N.A.

10 100.00 9.5 19.5

12 110.00 N.A. N.A.

14 120.00 N.A. N.A.

16 130.00 N.A. N.A.

18 140.00 N.A. N.A.

20 150.00 19.5 9.5

22 120.00 N.A. N.A.

24 90.00 N.A. N.A.

26 60.00 N.A. N.A.

28 30.00 N.A. N.A.

30 0.00 N.A. N.A.



The required number of shear studs between the maximum moment (locatedat the output station 20 feet from the left end of the beam) and adjacentpoints of zero moment, N1, is calculated using Equation 2 as:

studs00.01studperkips12.4

kips241qV

N'h

1 ===

The required number of shear studs between the point load located at theoutput station 10 feet from the left end of the beam and adjacent points ofzero moment, N2, is calculated using Equation 3 as:

01

1M

βMN

N max station

station1

2 ≥=−β

−

=

Negative11.40

1ft-k1501.40*ft-k100

studs10.00

N2 =−

−

=

N2 = 0 studs

The distances L1 left and L1 right for the output stations located 10 feet and 20feet from the left end of the beam are shown in Figure 2.

For the output station located 10 feet from the left end of the beam:

= CBS1

right1left1CBS1 L*

LN

,L

NMaxRoundupN

= ft29*

ft19.50studs0

,ft9.50

studs0MaxRoundupNCBS1

NCBS1 = 0 studs

For the output station located 20 feet from the left end of the beam:

= CBS1

right1left1CBS1 L*

LN

,L

NMaxRoundupN



= ft29*

ft9.50studs10.00

,ft19.50

studs10.00MaxRoundupNCBS1

= ft29*

ft9.50studs00.01

RoundupNCBS1

NCBS1 = Roundup (30.53 studs)

NCBS1 = 31 studs

The minimum number of studs required in the composite beam segment forthis beam is calculated using Equation 5 of Composite Beam Design TechnicalNote 13 Distribution of Shear Studs on a Composite Beam as:

=

MaxLSL

RoundupMS CBSCBS

studs10ft1in12

in36ft29

RoundupMSCBS =

=

Thus, the number of shear studs does not need to be increased to meet theminimum requirements. Assuming that the shear studs are found to fit on thebeam, the final number of uniformly spaced shear studs specified for thebeam is 31.



Shear Stud Distribution Example 3Shear stud distribution example 3 is shown in Figure 3. It is identical to Ex-ample 2, except that the point loads are assumed to come from end reactionsof other beams that are included in the program model. Thus, three compos-ite beam segments are in this example instead of the one composite beamsegment that was in Example 2. For this example, assume the following:




The ratio β = Seff/Sbare is equal to 1.40.



As shown in Figure 3, this beam has three composite beam segments labeled1, 2 and 3 from the left end of the beam to the right end of the beam. Thelengths of these composite beam segments are LCBS1 = 9.5 feet, LCBS2 = 10feet and LCBS3 = 9.5 feet.

Table 2 shows the bending moment calculated by the program for this beamat each output station. Table 3 summarizes how the shear stud distribution isdetermined for this beam.



Figure 3 Exa

5 k 20 k

4 Shear Stud Distribution Example 3

mple 3, Distribution of Shear Studs on a Composite Beam

LCBS1 = 9.5'

30'15 k10 k

Shear

15 k

10 k

Moment

100 k-ft

150 k-ft (Mmax)

0.5'0.5' L1 left = 9.5'

Out

put s

tatio

n 10

ftfro

m le

ft en

d of

bea

m

End

of b

eam

flan

ge

Cen

ter o

f sup

port

End

of b

eam

flan

ge

Cen

ter o

f sup

port

10' 10'10'

5 k

L1 right = 19.5'

Out

put s

tatio

n 20

ftfro

m le

ft en

d of

bea

m

L = 30'

L1 left = 19.5' L1 right = 9.5'

LCBS3 = 9.5'LCBS2 = 10'



Table 3: Example 3, Distribution of Shear Studs on a Composite BeamLeft to Right Along the Beam

Station Moment L1 left L1 right Studs NCBS1 NCBS2 NCBS3

10 ft 100 k-ft 9.5 ft 19.5 ft 0.00 0 (1) N.A. N.A.

20 ft 150 k-ft 19.5 ft 9.5 ft 10.00 5 (2a) 5 (2b) N.A.

Right to Left Along the BeamStation Moment L1 left L1 right Studs NCBS1 NCBS2 NCBS3

20 ft 150 k-ft 19.5 ft 9.5 ft 10.00 5 (3b) 5 (3b) 10 (3a)

10 ft 100 k-ft 9.5 ft 19.5 ft 0.00 5 (4d) 5 (4b) 10 (4a)

The numbers in parenthesis identify equations from Composite Beam Design TechnicalNote 13 Distribution of Shear Studs on a Composite Beam.

The number of shear studs listed in the Studs column of Table 3 is calculatedexactly as described for Example 2. Equation 3 is used at the station 10 feetfrom the left end of the beam, and Equation 2 is used at the station 20 feetfrom the left end of the beam.

The columns labeled NCBS1, NCBS2 and NCBS3 show the number of studs requiredin composite beam segments 1, 2 and 3, respectively, along with the equationused to calculate that number of studs. The equation number is shown in pa-renthesis.

The calculation proceeds from left to right along the beam and then backalong the beam from right to left. The detailed calculations associated withTable 3 are shown in the next subsection entitled "Detailed Calculations."

The final required number of shear studs for each of the composite beamsegments is shown in the last row of Table 3. Composite beam segments 1, 2and 3 require 5, 5 and 10 shear studs, respectively. This is a total of 20 shearstuds. This compares with 31 studs required in Example 2, where a uniformintensity of shear studs is assumed over the entire beam rather than overeach of the three composite beam segments.

Detailed CalculationsThis subsection shows the calculations required to obtain the values in thecolumns labeled NCBS1, NCBS2 and NCBS3 in Table 3.



Left to Right at 10 Feet from Left EndWe begin by working from left to right along the beam. The first output sta-tion considered is 10 feet from the left end of the beam. This output station isconsidered to be in composite beam segment 1. Equation 1 of CompositeBeam Design Technical Note 13 Distribution of Shear Studs on a CompositeBeam is used to calculate the studs required in composite beam segment 1.

= CBS1

right1left1CBS1 L*

LN

,L

NMaxRoundupN

= ft9.5*

ft19.5studs0

,ft9.5

studs0MaxRoundupNCBS1

NCBS1 = 0 studs

Thus, NCBS1 is calculated as zero studs. Because the output station consideredis in composite beam segment 1 and we are working from left to right alongthe beam, NCBS2 and NCBS3 are not yet applicable.

Left to Right at 20 Feet from Left EndThe next output station considered is 20 feet from the left end of the beam.This output station is considered to be in composite beam segment 2. Equa-tion 2a of Composite Beam Design Technical Note 13 Distribution of ShearStuds on a Composite Beam is used to calculate the studs required in com-posite beam segment 1.

PrevCBS1CBS1left1

CBS1 NL*L

NRoundupN ≥

=

studs0ft9.5*ft19.5

studs10.00RoundupNCBS1 ≥

=

NCBS1 = 5 studs

Next, we need to determine whether to use Equation 2b or Equation 2c ofComposite Beam Design Technical Note 13 Distribution of Shear Studs on aComposite Beam for composite beam segment 2.



∑∑−

=

−

=

<1n

1iCBSi

?1n

1iCBSi

left1NL*

LN

∑∑==

<1

1iCBSi

?1

1iCBSi NL*

ft19.5studs10.00

CBS1

?

CBS1 NL*ft19.5

studs10.00 <

studs5ft9.5*ft19.5

studs10.00 ?<

4.87 studs < 5 studs → Use Equation 2b of Composite Beam De-sign Technical Note 13 Distribution of Shear Studs on a CompositeBeam.

Thus, Equation 2b of Composite Beam Design Technical Note 13 Distributionof Shear Studs on a Composite Beam is used to calculate the studs requiredin composite beam segment 2.

PrevCBS2CBS21

1iCBSileft1

1

1iCBSi

CBS2 NL*

LL

N-N

RoundupN ≥

−

=

∑

∑

=

=

studs0ft10*ft9.5ft19.5studs5-studs10.00

RoundupNCBS2 ≥

−

=

NCBS2 = 5 studs

Because the output station considered is in composite beam segment 2 andwe are working from left to right along the beam, NCBS3 is not yet applicable.

Right to Left at 20 Feet from Left EndNow we work back along the beam from right to left. Thus, the next outputstation considered is the one 20 feet from the left end of the beam. This out-put station is now considered to be in composite beam segment 3.



Equation 3a of Composite Beam Design Technical Note 13 Distribution ofShear Studs on a Composite Beam is used to calculate the shear studs re-quired in composite beam segment 3.

PrevCBS3CBS3right1left1

CBS3 NL*L

N,

L

NMaxRoundupN ≥

=

studs0ft9.5*ft9.5

studs10,

ft19.5

studs10MaxRoundupN 3CBS ≥

=

studs0ft9.5*ft9.5

studs10RoundupN 3CBS ≥

=

NCBS3 = 10 studs

Equation 3b of Composite Beam Design Technical Note 13 Distribution ofShear Studs on a Composite Beam is used to calculate the shear studs re-quired in composite beam segments 1 and 2.

NCBS1 = NCBS1 Prev = 5 studs


Right to Left at 10 Feet from Left EndThe final output station considered is 10 feet from the left end of the beam.This output station is now considered to be in composite beam segment 2.

Equation 4a of Composite Beam Design Technical Note 13 Distribution ofShear Studs on a Composite Beam is used to calculate the shear studs re-quired in composite beam segment 3.

PrevCBS3CBS3right1

CBS3 NL*L

NRoundupN ≥

=

studs10ft9.5*ft19.5

studs0RoundupNCBS3 ≥

=

NCBS3 = 0 studs but must be at least 10 studs.



Therefore, use 10 studs.

Next we determine whether to use Equation 4b or Equation 4c of CompositeBeam Design Technical Note 13 Distribution of Shear Studs on a CompositeBeam for composite beam segment 2.

∑∑+=+=

<rightmost

1niCBSi

?rightmost

1niCBSi

right1NL*

LN

CBS3

?

CBS3 NL*ft19.5

studs0 <

studs10ft9.5*ft19.5

studs0 ?<

0 studs < 10 studs → Use Equation 7b.

Thus, Equation 4b of Composite Beam Design Technical Note 13 Distributionof Shear Studs on a Composite Beam is used to calculate the studs requiredin composite beam segment 2.

PrevCBS2CBS2rightmost

3iCBSiright1

rightmost

3iCBSi

CBS2 NL*

LL

N-N

RoundupN ≥

−

=

∑

∑

=

=

PrevCBS2CBS2CBS3right1

CBS3CBS2 NL*

LLN-N

RoundupN ≥

−=

studs5ft10*ft9.5ft19.5

10-0RoundupNCBS2 ≥

−

=

NCBS2 = Negative ≥ 5 studs, use 5 studs

Equation 4d of Composite Beam Design Technical Note 13 Distribution ofShear Studs on a Composite Beam is used to calculate the shear studs re-quired in composite beam segment 1.




Minimum Studs RequiredThe minimum number of studs required in the three composite beam seg-ments for this beam is calculated using Equation 5 of Composite Beam DesignTechnical Note 13 Distribution of Shear Studs on a Composite Beam.

studs4ft1in12

in36ft5.9

MaxLSL

RoundupMS CBS1CBS1 =

=

=

studs4ft1in12

in36ft10

MaxLSL


=

=

studs4ft1in12

in36ft5.9

MaxLSL


=

=

Thus, the number of shear studs does not need to be increased to meet theminimum requirements. Assuming that the shear studs are found to fit on thebeam, the final number of uniformly spaced shear studs specified for thebeam is 5 in composite beam segment 1, 5 in composite beam segment 2 and10 in composite beam segment 3, for a total of 20 shear studs.

Beam Overwrites Input Data Technical Note 27 - 1




This Technical Note describes the composite beam design input data for AISC-ASD89. The input can be printed to a printer or to a text file when you clickthe File menu > Print Tables > Composite Beam Design command. Aprintout of the input data provides the user with the opportunity to carefullyreview the parameters that have been input into the program and upon whichprogram design is based. See Composite Beam Design Technical Note 5 InputData for further information about using the print Composite Beam DesignTables Form, as well as other non-code-specific input data for compositebeam design.

Beam Overwrites Input DataThe program provides the printout of the input data in a series of tables. Thetables typically correspond to the tabs used in the Composite Beam Over-writes form. The column headings for input data and a description of what isincluded in the columns of the tables are provided in Table 1 of this TechnicalNote.

Recall that the composite beam overwrites apply to all beams to which theyhave been specifically assigned. To access the composite beam overwrites,select one or more beams and then click the Design menu > CompositeBeam Design > View/Revise Overwrites command. Information aboutcomposite beam overwrites is available in Composite Beam Design AISC-ASD89 Technical Note 18 Overwrites.

Input Data Composite Beam Design AISC-ASD89

Technical Note 27 - 2 Table 1 Beam Overwrites Input Data

Table 1 Beam Overwrites Input DataCOLUMN HEADING DESCRIPTIONBeam Location InformationThis information does not correspond to one of the tabs in the composite beam over-writes. This data is provided to help identify the beam to which printed overwrites apply.

XGlobal X coordinate of the center of the beam to which theoverwrites apply.

YGlobal Y coordinate of the center of the beam to which theoverwrites apply.

Length Length of the beam to which the overwrites apply.

Beam PropertiesComposite Type Type of beam design. The choices are Composite, NC w/ studs

and NC w/o studs. NC w/ studs is short for noncomposite withminimum shear studs. NC w/o studs is short for noncompositewithout shear studs. Note that this option allows you to design anoncomposite floor beam in the Composite Beam Design post-processor.

Shoring Provided This item is Yes if the composite beam is shored. Otherwise, itis No. Note that this item supersedes the Shored Floor item inthe composite beam preferences.

b-eff Left If the beff left width is program calculated, this item reads "ProgCalc." Otherwise, this item is the user-defined width for beff left.See Composite Beam Design Technical Note 8 Effective Widthof the Concrete Slab for description of the effective width of theslab.

b-eff Right If the beff right width is program calculated, this item reads "ProgCalc." Otherwise, this item is the user-defined width for beff right.See Composite Beam Design Technical Note 8 Effective Widthof the Concrete Slab for description of the effective width of theslab.

Beam Fy If the beam yield stress is based on the material property speci-fied for the beam, this item reads "Prog Calc." Otherwise, thisitem is the user-defined yield stress of the beam.

Beam Fu If the beam minimum tensile strength is based on the materialproperty specified for the beam, this item reads "Prog Calc."Otherwise, this item is the user-defined minimum tensilestrength of the beam.

Composite Beam Design AISC-ASD89 Input Data

Table 1 Beam Overwrites Input Data Technical Note 27 - 3

Table 1 Beam Overwrites Input DataCOLUMN HEADING DESCRIPTIONCover PlateThis information is included on the Beam tab of the overwrites.

Plate Width Width of the cover plate.

Plate Thick Thickness of the cover plate.

Plate Fy Yield stress of the cover plate.

Consider Cover Plate If this item is "Yes," the specified cover plate is considered inthe design of the beam. Otherwise, the cover plate is not con-sidered in the beam design.

Beam Unbraced LengthBeam unbraced length data is provided for both the construction condition and the finalcondition. The headings for these two types of beam unbraced lengths are “Beam Un-braced Length (Construction Loading)” and “Beam Unbraced Length (Final Loading).”The types of data provided in each of these tables is identical and is documented oncehere.

Bracing State This item can be "Prog Calc," "User Bracing," or "LengthGiven." Prog Calc means that the program determines thebraced points of the beam. User Bracing means that you havespecified the actual bracing for the beam. The user-definedbracing may be point or uniform bracing along the top and bot-tom flange of the beam. Length Given means that you havespecified a single maximum unbraced length for the beam.

Unbraced L22 If the Bracing State item is "Length Given," this item is the user-specified maximum unbraced length of the beam. Otherwise,this item is specified as N/A.

L22 Absolute If the Bracing State item is "Length Given," this item indicateswhether the user-specified maximum unbraced length of thebeam (the Unbraced L22 item) is an absolute (actual) length ora relative length. A relative length is the maximum unbracedlength divided by the length of the beam. If the Bracing Stateitem is not Length Given, this item is specified as N/A.

Cb Factor If the Cb factor is calculated by the program, this item reads"Prog Calc." Otherwise, the user-defined Cb factor that is usedin determining the allowable bending stress is displayed. (Notethat when the Cb factor is program calculated, it may be differ-ent for each design load combination, and, for a given designload combination, it may be different for each station consid-ered along the length of the beam.)



Table 1 Beam Overwrites Input DataCOLUMN HEADING DESCRIPTIONPoint BracesThe heading of the point braces data table specifies whether the point braces are pro-gram calculated or user-defined, and whether the distances used to locate the pointbraces (Location item) are absolute (actual) distances or relative distances. A relativedistance is the distance divided by the length of the beam.

Location This is the distance from the I-end of the beam to the pointbrace. As described in the preceding paragraph, it may be anabsolute or a relative distance.

Type The choices for this item are TopFlange, BotFlange orBothFlngs. TopFlange means only the top flange is braced atthis point. BotFlange means only the bottom flange is braced atthis point. BothFlngs means both the top and bottom flangesare braced at this point.

Uniform BracesThe heading of the uniform braces data table specifies whether the point braces are pro-gram calculated or user-defined, and whether the distances used to define the extent ofthe uniform braces (Start and End items) are absolute (actual) distances or relative dis-tances. A relative distance is the distance divided by the length of the beam.

Note:Details about the location and type of program calculated point and uniformbraces is only reported after you have run the design. Before you run the de-sign, this information is not available.

Start This is the distance from the I-end of the beam to the startingpoint of the uniform brace. As described in the preceding para-graph, it may be an absolute or a relative distance.

End This is the distance from the I-end of the beam to the endingpoint of the uniform brace. This distance is always larger thanthe Start item. As described previously, it may be an absoluteor a relative distance.

Type The choices for this item are TopFlange, BotFlange orBothFlngs. TopFlange means only the top flange is uniformlybraced along the specified length. BotFlange means only thebottom flange is uniformly braced along the specified length.BothFlngs means both the top and bottom flanges are uniformlybraced along the specified length.



Table 1 Beam Overwrites Input DataCOLUMN HEADING DESCRIPTIONDeck PropertiesBeam Side This item is either Left or Right. It indicates to which side of the

beam the deck label and deck direction specified in the samerow apply.

Deck Label This item is either “Prog Calc,” if the deck label is determinedby the program, or it is the label (name) of a defined deck sec-tion, if this is a user-specified overwrite, or it is "None" if nocomposite deck has been specified on the side of the beam.

Deck Direction This item is “Prog Calc,” “Parallel,” or “Perpendclr.” Prog Calcmeans that the direction of the deck span (parallel or perpen-dicular to the beam span) is program determined. Parallelmeans that the span of the metal deck is parallel to the beamspan. Perpendclr means that the span of the metal deck is per-pendicular to the beam span.

Shear Stud PropertiesMin Long Spacing Minimum longitudinal spacing of shear studs along the beam.

Max Long Spacing Maximum longitudinal spacing of shear studs along the beam.

Min Tran Spacing Minimum transverse spacing of shear studs across the beamflange.

Max Conn in a Row Maximum number of shear studs in a single row across thebeam flange.

Stud q This item is “Prog Calc” if the allowable horizontal load for asingle shear stud is determined by the program, or it is a user-defined allowable horizontal load for a single shear stud.

User-Defined Shear Stud PatternUniform Spacing The uniform spacing of single shear studs along the length of

the beam.User-Defined Uniform Stud SectionsThe heading of the uniform stud sections data table specifies whether the distances usedto define the extent of the stud sections (Start, End and Length items) are absolute (ac-tual) distances or relative distances. A relative distance is the distance divided by thelength of the beam.

Note:User-defined shear stud patterns are described in Composite Beam DesignTechnical Note 15 User-Defined Shear Stud Patterns.



Table 1 Beam Overwrites Input DataCOLUMN HEADING DESCRIPTION

Start This is the distance from the I-end of the beam to the startingpoint of the uniform stud section. As described previously, itmay be an absolute or a relative distance.

End This is the distance from the I-end of the beam to the endingpoint of the uniform stud section. As described previously, itmay be an absolute or a relative distance.

Length This is the length of the uniform stud section. As described pre-viously, it may be an absolute or a relative distance.

Number The number of uniformly spaced shear studs in the uniformstud section.

Deflection, Camber and VibrationDeflection Absolute If the live load and total load deflection limits are specified as

absolute (actual) distances, this item is Yes. If they are speci-fied as a divisor of beam length (relative), this item is No.

Live Load Limit The live load deflection limit for the beam.

Total Load Limit The total load deflection limit for the beam.

Calculate Camber If this item is Yes, the program calculates the camber for thebeam. If it is No, the program does not calculate a camber, butif desired, the user can specify the camber.

Specified Camber User-specified camber when the program does not calculatethe beam camber.

Neff Beams This item is “Prog Calc” if the number of effective beams forvibration calculations is determined by the program, or it is auser-defined number of effective beams.

Other RestrictionsLimit Beam Depth This item is Yes if the beam depth limitations (Minimum Depth

and Maximum Depth items) are considered by the program forbeams with auto select section lists. This item is No if the beamdepth limitations are not considered.

Minimum Depth Minimum actual (not nominal) beam depth considered in theauto select section list if the Limit Beam Depth item is Yes.

Maximum Depth Maximum actual (not nominal) beam depth considered in theauto select section list if the Limit Beam Depth item is Yes.




Minimum PCC Minimum percent composite connection considered by the pro-gram for the beam.

Maximum PCC Maximum percent composite connection considered by theprogram for the beam.

RLLF This represents the reducible live load factor. A reducible liveload is multiplied by this factor to obtain the reduced live load.This item is “Prog Calc” if the reducible live load factor is de-termined by the program, or it is a user-defined reducible liveload factor.

EQF The EQ Factor is a multiplier applied to earthquake loads. Thisitem corresponds to the EQ Factor item in the composite beamdesign overwrites. More information about the EQ Factor isavailable from Composite Beam Design AISC-ASD89 TechnicalNote 18 Overwrites.

1/3 Increase This item is “Active” if the one-third increase in allowablestresses for design load combinations, including wind or seis-mic loads, is considered for the beam. The item is “Inactive” ifthe one-third increase is not considered.

Short Form Output Details Technical Note 28 - 1




This Technical Note describes the composite beam output for AISC-ASD89that can be printed to a printer or to a text file in either short form or longform. See Composite Beam Design Technical Note 6 Output Data for informa-tion about using the Print Composite Beam Design Tables Form, as well as theSummary of Composite Beam Output.

The program provides the output data in a series of tables. The columnheadings for output data and a description of what is included in the columnsof the tables are provided in Table 1 of this Technical Note.

Short Form Output DetailsThis output is printed when you click the File menu > Print Tables > Com-posite Beam Design command and select Short Form in the Output Detailsarea of the resulting form. Similar output also appears on screen if you clickthe Details button in the Show Details area of the Interactive CompositeBeam Design and Review form. See Composite Beam Design Technical Note 3Interactive Composite Beam Design for more details on the interactive design.

Table 1 Output DetailsCOLUMN HEADING DESCRIPTIONBasic Beam Information

Beam Label Label associated with the line object that represents the beam.A typical label beam would appear as "B23." Do not confusethis with the Section Label, which would be identified as"W18X35."

Group Name of the design group (if any) to which the beam has beenassigned.

Beam Beam section label (name).

Output Details Composite Beam Design AISC-ASD89

Technical Note 28 - 2 Table 1 Output Details

Table 1 Output DetailsCOLUMN HEADING DESCRIPTION

Fy Beam yield stress, Fy.

Fu Beam minimum tensile strength, Fu.


Seg. Length Length of each composite beam segment separated by com-mas. The lengths are listed starting with the composite beamsegment at the I-end of the beam and working toward the J-endof the beam.

Stud Ratio This item has a slightly different meaning, depending onwhether the shear studs are user-defined or calculated by theprogram.

When the number of shear studs is calculated by the program,a stud ratio is reported for each composite beam segment. It isequal to the number of shear studs required in the segmentdivided by the maximum number of studs that fit in the seg-ment.

When the shear studs are user-defined, the total number ofstuds is reported instead of the stud ratio

Story Story level associated with the beam.

Length Length of the beam.

Loc X Global X coordinate of the center of the beam.

Loc Y Global Y coordinate of the center of the beam.

RLLF A reducible live load is multiplied by this factor to obtain the re-duced live load.

Shored This item is Yes if the beam is shored and No if it is unshored.

Composite Beam Design AISC-ASD89 Output Details

Table 1 Output Details Technical Note 28 - 3


Camber The camber for the beam. This item may be calculated by theprogram or it may be user-specified.

Comparative Price of the beam using the input price parameters for steel,shear studs and camber. This price is intended for comparisonof alternative designs only. It is not intended to be used for costestimating purposes.

Stud Diam Diameter of shear studs.

EQ Factor A multiplier applied to earthquake loads. This item correspondsto the EQ Factor item in the composite beam design overwrites.More information about the EQ Factor is available CompositeBeam Design AISC-ASD89 Technical Note 18 Overwrites.

Overwrites If this item is Yes, one or more items have been overwritten forthis beam. If it is No, nothing has been overwritten. The valuesfor all overwrite items are included in the long form output.Thus, if this item is "Yes," you may want to print the long formoutput.

b-cp Width of the cover plate. If no cover plate is specified by theuser, N/A is reported for this item.

t-cp Thickness of the cover plate. If no cover plate is specified bythe user, N/A is reported for this item.

Fy-cp Yield stress for the cover plate. If no cover plate is specified bythe user, N/A is reported for this item.

Consider-cp This item is Yes if the specified cover plate is considered in thedesign. Otherwise, it is No.

Deck Left and DeckRight

The deck section labels (names) on the left and right sides ofthe beam.

Dir. Left and Dir. Right The deck directions on the left and right sides of the beam.Perpendclr means that the deck span is perpendicular to thebeam span. Parallel means that the deck span is parallel to thebeam span.




beff Left and beff Right The slab effective widths on the left and right sides of the beam.

Ctop Left and CtopRight

The program calculated cope of the beam top flange at the leftand right ends of the beam. Do not confuse the left and rightends of the beam with the left and right sides of the beam. Theleft end of the beam is the I-end and the right end of the beamis the J-end.

Cbot Left and CbotRight

The program calculated cope of the beam bottom flange at theleft and right ends of the beam. Do not confuse the left and rightends of the beam with the left and right sides of the beam. Theleft end of the beam is the I-end and the right end of the beamis the J-end.

Itrans Transformed section moment of inertia for full (100%) compos-ite connection for positive bending, Itr.

Ibare Moment of inertia of the steel beam, including cover plate, if itexists.

Is Moment of inertia of the steel beam alone, not including coverplate, even if it exists.

Ieff Effective moment of inertia for partial composite connection.

PCC Percent composite connection.

ytrans Distance from the bottom of the beam bottom flange (not bot-tom of cover plate, even if it exists) to the elastic neutral axis(ENA) of the beam, with full (100%) composite connection, y .

ybare Distance from the bottom of the beam bottom flange (not bot-tom of cover plate, even if it exists) to the ENA of the beam,plus cover plate alone (if it exists).

yeff Distance from the bottom of the beam bottom flange (not bot-tom of cover plate, even if it exists) to the ENA of the beam,with partial composite connection.

q Allowable horizontal shear load for a single shear stud.



Table 1 Output DetailsCOLUMN HEADING DESCRIPTIONMoment DesignThis table of output data reports the controlling moments for both construction loads andfinal loads.

Pmax The largest axial load in the beam for any design load combi-nation.

Important note: This value is not used in the Composite BeamDesign postprocessor design. It is reported to give you a senseof how much axial load, if any, is in the beam. If there is a sig-nificant amount of axial load in the beam, you may want to de-sign it noncompositely using the Steel Frame Design postpro-cessor. The Steel Frame Design postprocessor does consideraxial load.

Pmax Combo The design load combination associated with Pmax.

Type This item is either Constr Pos, Constr Neg, Final Pos or FinalNeg. Const Pos means it is a positive moment for constructionloading. Const Neg means it is a negative moment for con-struction loading. Final Pos means it is a positive moment forfinal loading. Final Neg means it is a negative moment for finalloading.

Combo Design load combination that causes the controlling moment forthe moment type considered in the table row.

Location The critical location over the height of the beam section forbending stress. Possible values for this are:

ConcLeft: The top of the concrete slab on the left side of thebeam.

ConcRight: The top of the concrete slab on the right side ofthe beam.

TopFlange: The top of the beam top flange.

BotFlange: The bottom of the beam bottom flange.

CoverPlate: The bottom of the cover plate.




M The controlling moment for the moment type considered in thetable row.

fb The bending stress associated with the controlling moment.The location over the height of the beam where this bendingstress occurs is given in the Location column.

Fb The allowable bending stress associated with the controllingbending stress. The location where this allowable bendingstress applies is given in the Location column. This allowablestress reported here never includes the 1/3 increase that mayapply.

1/3 Factor This item is either Yes or No. It indicates whether a 1/3 allow-able stress increase was used for the ratio calculated in thisrow in the table.

Ratio This is the bending stress, fb, divided by the allowable bendingstress, Fb. If the 1/3 allowable stress increase applies to thedesign load combination, the result is further divided by 1.33.

Shear DesignThis table of output data reports the controlling shears for both construction loads andfinal loads.

Type This item is either Constr Left, Constr Right, Constr Worst, FinalLeft or Final Right. Constr Left means it is a construction load-ing shear at the left end of the beam. Constr Right means it is aconstruction loading shear at the right end of the beam. ConstrWorst means it is a construction loading shear somewhere inthe middle of the beam and it is the worst-case shear.

Final Left means it is a final loading shear at the left end of thebeam. Final Rght means it is a final loading shear at the rightend of the beam. Final Worst means it is a construction loadingshear somewhere in the middle of the beam and it is the worst-case shear.




The Constr Worst and Final Worst items only appear when theycontrol the design. The shear checks at the left and right endsof the beam always appear.

Combo Design load combination that causes the controlling shear forthe shear type considered in the table row.

Block This item is either OK or NG. It indicates whether the programcheck for block shear (shear rupture) passed or failed. OKmeans that the beam passes the Check, and NG (no good)means it did not. If the item indicates NG, you should check theblock shear by hand for the beam.

V The controlling shear for the shear type considered in the tablerow.

fv The shear stress associated with the controlling shear.

Fv The allowable shear stress associated with the controllingbending stress. This allowable stress never includes the 1/3increase that may apply.

1/3 Factor This item is either Yes or No. It indicates whether a 1/3 allow-able stress increase was used for the ratio calculated in thisrow in the table.

Ratio This is the bending stress, fv, divided by the allowable bendingstress, Fv. If the 1/3 allowable stress increase applies to thedesign load combination, the result is further divided by 1.33.

Deflection DesignThis table of output data reports the controlling deflections for both live load and totalload.

Type This item is either Live Load or Total Load.

Consider This item is always Yes, indicating that deflection is one of thecriteria checked when determining if a beam section is consid-ered acceptable.




Combo Design load combination that causes the controlling deflectionfor the deflection type considered in the table row.

Deflection The controlling deflection for the deflection type considered inthe table row. The computed camber is subtracted from the to-tal load deflection before the total load deflection is reported.

Note:Deflection is described in Composite Beam Design Technical Note 11 Beam De-flection and Camber.

Limit The deflection limit for the deflection type considered in the ta-ble row.

Ratio This is the controlling deflection divided by the deflection limit.



COMPOSITE BEAM DESIGN AISC-LRFD93

Technical Note 29General and Notation

This Technical Note provides an overview of composite beam design using theAISC-LRFD93 design specification.

AISC-LRFD93 Design MethodologyThe flowchart in Figure 1 shows the general methodology for composite beamdesign of a single beam element using the AISC-LRFD93 specification. Thenumbered boxes in the flowchart correspond to the "Box" identifiers used inthe text of this Technical Note. The flowchart is intended to convey the im-portant features of the AISC-LRFD93 design methodology. It should not beliterally construed as a flowchart for the actual computer code included in theprogram.

Box 1 - Start HereBefore you begin, note that the flowchart is set up for a single beam. Thusyou must apply the flow process shown to each beam designed. Do not con-fuse the beam that is being designed with a trial section for that beam. Thebeam that is being designed is an actual element in the model. A trial sectionis simply a beam section size that is checked for the beam that is being de-signed.

Box 2 - Design Load CombinationsThe program creates default design load combinations for composite beamdesign using the AISC-LRFD93 specification. Also any user-specified designload combinations can be interpreted and implemented. Refer to CompositeBeam Design AISC-LRFD93 Technical Note 32 Design Load Combinations for adescription of the AISC-LRFD93 default design load combinations.

Box 3 - Design Check LocationsThe program determines all of the design check locations for a given beam.Also refer Composite Beam Design Technical Note 9 Beam Unbraced Lengthand Design Check Locations.

General and Notation Composite Beam Design AISC-LRFD93


Figure 1: Flowchart for AISC-LRFD93 Design of a Single Beam

11 12

19

No

Start here to designa beam element.

Determine designload combinations.

Determine designcheck locations.

Determine checkingorder for beams.

Select a trial beamsection.

Is the sectioncompact or

noncompact?

Yes No

The design for thisbeam element is

complete.

Considering fullcomposite

connection, are themaximum moment

and deflectionacceptable?

No

Is the vibrationcriteria satisfied?

No

Yes

Yes

Considering fullcomposite action, is

the interaction for thecombined stresses

acceptable?

Determine price ofsection.

Calculate requiredcamber.

Is beam shearacceptable?

YesNo

Determine if trialsection is the current

optimum section.

YesDo the required

shear connectors fiton the beam?

Determine therequired number ofshear connectors.

Determine theminimum acceptablepercent composite

connectionconsidering

combined stressesand deflection

criteria.

No

No

Yes

123

4

5

6

8

9

10 13

14

15

16

17

18

20

On the basis ofcompact section

requirements,determine whetherto use a plastic oran elastic stress

distribution tocalculate the

moment capacity,Mn.

Yes

7

Determinetransformed section

properties for fullcomposite action.

Is there another trialsection available that

may qualify as theoptimum beam

section?

Composite Beam Design AISC-LRFD93 General and Notation


Box 4 - Checking Order for BeamsYou must determine the checking order for a beam if the beam is assigned anauto selection property. The program considers the beams in the auto selectlist in the order described in the section entitled “How ETABS Optimizes De-sign Groups” in Composite Beam Design Technical Note 1 General Design In-formation.

Box 5 - Trial Beam SectionThe program allows you to select the next trial beam section to be checkedfor conformance with the AISC-LRFD93 specification and any additional user-defined criteria. Refer to the section entitled “How ETABS Optimizes DesignGroups” in Composite Beam Design Technical Note 1 General Design Infor-mation for a description of this selection process.

Box 6 - Compact and Noncompact RequirementsFor AISC-LRFD93 design of composite beams, the program requires that thebeam section be either compact or noncompact. Slender sections are not de-signed. The program checks to make sure the beam is not slender. Refer toComposite Beam Design AISC-LRFD93 Technical Note 33 Compact and Non-compact Requirements for a description of how the program checks compactand noncompact requirements.

Box 7 - Stress Distribution Used to Calculate Moment CapacityThe program determines whether to use a plastic or an elastic stress distribu-tion when calculating the moment capacity for AISC-LRFD93 design. SeeComposite Beam Design AISC-LRFD93 Technical Note 33 Compact and Non-compact Requirements for more information.

Box 8 - Transformed Section PropertiesThe program computes the transformed section properties of the trial beamsection. If there is only positive bending in the beam, only the transformedsection properties for positive bending are calculated. Similarly, if there isonly negative bending in the beam, only the transformed section propertiesfor negative bending are calculated. If there is both positive and negativebending in the beam, transformed section properties for both positive andnegative bending are calculated.

Refer to Composite Beam Design Technical Note 8 Effective Width of the Con-crete Slab for a description of how the program calculates the effective widthof the concrete slab for the composite beam. Refer to Composite Beam De-



sign AISC-ASD89 Technical Note 20 Transformed Section Moment of Inertiafor description of how the program calculates the transformed section proper-ties.

In AISC-LRFD93 design, the transformed section properties are used for cal-culating deflection, and they are used when the moment capacity is deter-mined based on an elastic stress distribution; that is, when the web is non-compact.

Box 9 - Initial Moment Capacity and Deflection CheckThe program checks that the moment capacity of the beam using full com-posite connection is greater than or equal to the applied factored moment. Italso checks if the deflection using full composite connection is acceptable. Themain purpose of this check is to quickly eliminate inadequate beam sections.Refer to Composite Beam Design AISC-LRFD93 Technical Note 38 Bendingand Deflection Checks for more information.

Box 10 - Vibration Criteria CheckThe program calculates the vibration parameters. If vibration is specified tobe used as one of the tools for selecting the optimum beam size, the programchecks if the vibration parameters satisfy the specified limits. If the vibrationcheck is satisfied, the design using the current trial section continues; other-wise, the design for this section is terminated. For more detailed informationon the vibration checks, refer to Composite Beam Design Technical Note 12Beam Vibration.

Box 11 - P-M Interaction CheckIf there is axial load on the beam, the program checks the P-M interactionequations. If the interaction check is satisfied, the design using the currenttrial section continues; otherwise, the design for this section is terminated.Refer to Composite Beam Design AISC-LRFD93 Technical Note 36 MomentCapacity for Steel Section Alone for more information.

Box 12 - Partial Composite ActionA significant amount of design is performed at this point in the process. Theprogram determines the smallest amount of composite connection for whichthe beam is adequate. Both flexural checks and deflection checks are made atthis point. Flexural checks are also made for the construction loads.



For more information refer to Composite Beam Design AISC-LRFD93 TechnicalNote 37 Partial Composite Connection with a Plastic Stress Distribution andComposite Beam Design AISC-LRFD93 Technical Note 38 Bending and Deflec-tion Checks. Also refer to Composite Beam Design AISC-ASD89 TechnicalNote 21 Elastic Stresses with Partial Composite Connection.

Box 13 - Required Number of Shear ConnectorsThe program calculates the required number of shear connectors on the beamand the distribution of those shear connectors. For more information refer toComposite Beam Design AISC-LRFD93 Technical Note 39 Shear Connectors.Also refer to Composite Beam Design Technical Note 13 Distribution of ShearStuds on a Composite Beam and Composite Beam Design Technical Note 14The Number of Shear Studs that Fit in a Composite Beam Segment. Finallyrefer to Composite Beam Design Technical Note 8 Effective Width of the Con-crete Slab for limitations associated with composite beams and formed metaldeck.

Box 14 - Checking if Shear Connectors Fit on the BeamThe program checks if the number of shear connectors calculated (box 14)actually fit on the beam. For more information refer to Composite Beam De-sign Technical Note 14 The Number of Shear Studs that Fit in a CompositeBeam Segment. If the connectors fit on the beam, the design using the cur-rent trial section continues; otherwise, the design for this section is termi-nated.

Box 15 - Beam ShearThe program checks the beam shear for the reactions at each end of thebeam. See Composite Beam Design AISC-LRFD93 Technical Note 40 BeamShear Capacity for more information. If the beam shear check is satisfied, thedesign using the current trial section continues; otherwise, the design for thissection is terminated.

Box 16 - CamberThe program determines the camber for the beam, if it is specified to havecamber. Refer to Composite Beam Design Technical Note 11 Beam Deflectionand Camber for more information.

Box 17 - Section PriceDetermination of price of section applies only when price has been specifiedby the user as the method of selecting the optimum section. In such cases,



the program determines the price of the current beam. Refer to “Using Priceto Select Optimum Beam Sections” in Composite Beam Design Technical Note1 General Design Information for more information.

Box 18 - Check if a Section is the Current Optimum SectionThis check applies only if price has been specified as the method of selectingthe optimum section. The program checks if the price of the current trialbeam is less than that of any other beam that satisfied the design criteria. Ifso, the current beam section becomes the current optimum beam section.Refer to “Using Price to Select Optimum Beam Sections” in Composite BeamDesign Technical Note 1 General Design Information for more information

If the optimum beam size is to be selected by weight, this check becomes ir-relevant because the beams are checked in order from the lightest to theheaviest beams and thus the first beam found to work is the optimum beam.

Box 19 - Checking for Possible Additional Optimum SectionsThis check applies only if the beam has been assigned an auto selection prop-erty. The program checks if another section in the auto selection list mightqualify as the optimum beam section. Refer to the section titled “How ETABSOptimizes Design Groups” in Composite Beam Design Technical Note 1 Gen-eral Design Information for more information.

Box 20 - Design CompleteAt this point, the design for this particular beam element is complete. If thebeam has been assigned an auto selection property, the current optimumsection, assuming one has been found, is the optimum section for the beam.The program will indicate if no beam with an optimum section is included inthe auto selection list.

If the beam is assigned a regular, non-auto selection property, the design forthat beam property will be provided or the beam will be indicated to be in-adequate.

There are some additional aspects included in the composite beam designmodule that are not directly addressed in the flowchart shown in Figure 1.Those include designing beams in groups and designing beams with partiallength cover plates.



For more information on the design by group feature, refer to the section"How the Program Optimizes Design Groups" in Composite Beam DesignTechnical Note 1 General Design Informaiton. The extension of the methodol-ogy described in Part 3 to designing by groups is relatively simple and is as-sumed to be apparent to the reader.

NotationAbare Area of the steel beam (plus coverplate) alone, in2.

Ac Area of concrete within slab effective width that is above theelastic neutral axis (ENA) for full composite action, in2. Forbeams with metal deck ribs running perpendicular to the beamspan, only the concrete above the metal deck and above theENA is included. For beams with metal deck ribs running par-allel to the beam span, the concrete above the metal deck andthe concrete in the deck ribs are included if it is above theENA. This value may be different on the left and right sides ofthe beam.

Af Area of compression flange, in2.

Ag Gross area of steel member, in2.

As Area of rolled steel section, or the total area (excluding coverplate) of a user-defined steel section, in2. Note that the totalarea of a user-defined steel section is found by summing thearea of the top flange, web and bottom flange.

ASb Initial displacement amplitude of a single beam resulting froma heel drop impact, in.

Asc Cross-sectional area of a shear stud connector, in2.

Atr Area of an element of the composite steel beam section, in2.

Aw Area of the web equal to the overall depth d times the webthickness tw, in2.

B1 Moment magnifier, unitless.



Cb Bending coefficient dependent on moment gradient, unitless.

Cbot Cope depth at bottom of beam, in.

CC1 Compressive force in concrete slab above metal deck, kips. Ifno metal deck exists, this is the compressive force in the slab.

CC2 Compressive force in concrete that is in the metal deck ribs,kips. This force only occurs when the metal deck ribs are ori-ented parallel to the steel beam, and the plastic neutral axis isbelow the top of the metal deck.

CFT Compressive force in the top flange of the steel beam, kips.This force only occurs when the plastic neutral axis is belowthe top of the beam.

CKT Compressive force in the top fillets of a rolled steel beam,kips. This force only occurs when the plastic neutral axis isbelow the bottom of the top flange of the beam.

CR Compressive force in the slab rebar, kips. This force only oc-curs when the plastic neutral axis is below the rebar, and youhave specified the rebar to be considered.

Ctop Cope depth at top of beam, in.

Cw Warping constant for a section, in6.

CWeb Compressive force in the steel beam web, kips. This force onlyoccurs when the plastic neutral axis is within the beam web.

D Damping ratio, percent critical damping inherent in the floorsystem, unitless.

Ec Modulus of elasticity of concrete slab, ksi. Note that this couldbe different on the left and right sides of the beam. Also notethat this is different for stress calculations and deflection cal-culations.

Es Modulus of elasticity of steel, ksi.



Fcr Critical stress for columns in compression, ksi.

FL Smaller of (Fyf - Fr) or Fyw, ksi.

Fr Compressive residual stress in flange, ksi. Taken as 10 kipsper square inch for rolled shapes and 16.5 kips per squareinch for welded shapes converted to the appropriate.

Fu Minimum specified tensile strength of structural steel or shearstud, ksi.

Fy Minimum specified yield stress of structural steel, ksi.

Fycp Minimum specified yield stress of cover plate, ksi.

Fyf-bot Minimum specified yield stress of steel in beam bottom flange,ksi.

Fyf-top Minimum specified yield stress of steel in beam top flange, ksi.

Fyw Minimum specified yield stress of steel in beam web, ksi.

G Shear modulus of elasticity of steel, ksi.

Hs Length of shear stud connector after welding, in.

Ieff Effective moment of inertia of a partially composite beam, in4.

IO Moment of inertia of an element of the composite steel beamsection taken about its own center of gravity, in4.

Is Moment of inertia of the steel beam alone plus cover plate ifapplicable, in4.

Itr Transformed section moment of inertia about elastic neutralaxis of the composite beam, in4.

Ix, Iy Moment of inertia about the x and y axes of the beam respec-tively, in4.

Iyc Moment of inertia of compression flange about the y-axis, or ifthere is both positive and negative bending in the beam, the



smaller moment of the two flanges, in4.

J Torsional constant for a section, in4.

K Effective length factor for prismatic member, unitless.

Kf A unitless coefficient typically equal to 1.57 unless the beam isthe overhanging portion of a cantilever with a backspan, inwhich case Kf is as defined in Figure 1 of Composite Beam De-sign Technical Note 12 Beam Vibration, or the beam is a can-tilever that is fully fixed at one end and free at the other end,in which case Kf is 0.56.

L Center-of-support to center-of-support length of the beam, in.

Lb Laterally unbraced length of beam; length between points thatare braced against lateral displacement of the compressionflange or braced against twist of the cross section, in.

Lc Limiting unbraced length for determining allowable bendingstress, in.

LCBS Length of a composite beam segment, in. A composite beamsegment spans between any of the following: (1) physical endof the beam top flange; (2) another beam framing into thebeam being considered; (3) physical end of concrete slab. Fig-ure 1 Composite Beam Design Technical Note Distribution ofShear Studs on a Composite Beam illustrates some typicalcases for LCBS.

Lcsc Length of channel shear connector, in.

Lp Limiting laterally unbraced length of beam for full plasticbending capacity, uniform moment case (Cb = 1.0), in.

Lr Limiting laterally unbraced length of beam for inelastic lateral-torsional buckling, in.

Ls Distance between two points used when the program is calcu-lating the maximum number of shear studs that can fit be-tween those points, in. If the deck span is oriented parallel to



the beam span and at least one of the points is at the end ofthe beam, then Ls is taken as the distance between the twopoints minus 3 inches.

L1 Distance from point of maximum moment to the closest pointof zero moment or physical end of beam top flange, or physi-cal end of concrete slab, in.

L2 Distance from point of maximum moment to the nearest pointof zero moment or physical end of beam top flange, or physi-cal end of concrete slab measured on the other side of thepoint of maximum moment from the distance L1, in.

L3 Distance from point load to the point of zero moment, physicalend of beam top flange, or physical end of concrete slabmeasured on the appropriate side of the point load, in. If thepoint load is located on the left side of the point of maximummoment, the distance is measured from the point load towardthe left end of the beam. If the point load is located on theright side of the point of maximum moment, the distance ismeasured toward the right end of the beam.

M Moment, kip-in.

MA Absolute value of moment at the quarter point of the unbracedbeam segment, kip-in.

MB Absolute value of moment at the centerline of the unbracedbeam segment, kip-in.

MC Absolute value of moment at the three-quarter point of theunbraced beam segment, kip-in.

Mcr Elastic buckling moment, kip-in.

Mmax Maximum positive moment for a beam, kip-in.

Mn Nominal flexural strength, kip-in.

Mp Plastic bending moment, kip-in.



Mpt load Moment at the location of a point load, kip-in.

Mr Limiting buckling moment, Mcr, when λ = λr and Cb = 1.0, kip-in.

Mu Required flexural strength, kip-in.

MPFconc Maximum possible force that can be developed in the concreteslab, and rebar in slab, if applicable, kips.

MPFsteel Maximum possible force that can be developed in the steelsection, and cover plate, if applicable, kips.

NCBS The number of uniformly distributed shear connectors the pro-gram specifies for a composite beam segment, unitless.

Neff The effective number of beams resisting the heel drop impact,unitless.

Nr Number of shear stud connectors in one rib at a beam inter-section; not to exceed three in computations, although morethan three studs may be installed, unitless.

N1 Required number of shear connectors between the point ofmaximum moment and an adjacent point of zero moment (orend of slab), unitless.

N2 Required number of shear connectors between a point loadand a point of zero moment (or end of slab), unitless.

NR Available number of metal deck ribs between two points,unitless.

NSmax Maximum number of shear stud connectors between twopoints a distance of Ls apart, unitless.

P Axial load, kips.

Pe Euler buckling load, kips.

Pn Nominal axial strength (tension or compression), kips.



Pnc Nominal compressive axial strength, kips.

Pnt Nominal tensile axial strength, kips.

PO Heel drop force, kips. This force is taken as 0.6 kips.

Pu Required axial strength (tension or compression), kips.

Py Axial compressive yield strength , kips.

PCC Percent composite connection, unitless. The exact formula forthis term is code dependent.

Qn Nominal strength of one shear connector (shear stud or chan-nel), kips.

R Wiss-Parmelee rating factor, unitless.

RF Reduction factor for horizontal shear capacity of shear con-nectors, unitless.

RSmax Maximum number of rows of shear stud connectors that can fitbetween two points a distance of Ls apart, unitless.

Sed Minimum edge distance from midheight of a metal deck rib tothe center of a shear stud, in. For an example see paragraph1b of the section Solid Slab or Deck Ribs Oriented Parallel toBeam Span in Composite Beam Design Technical Note 14Number of Shear Studs that Fit in a Composite Beam Seg-ment. The default value is 1 inch. You can change this in thepreferences and the overwrites.

Seff Effective section modulus of a partially composite beam re-ferred to the extreme tension fiber of the steel beam section(including cover plate), in3.

Sr Center to center spacing of metal deck ribs, in.

Ss Section modulus of the steel beam alone plus cover plate ifapplicable referred to the tension flange, in3.



St-eff The section modulus for the partial composite section referredto the top of the equivalent transformed section, in3.

Stop Section modulus for the fully composite uncracked trans-formed section referred to the extreme compression fiber, in3.

Str Section modulus for the fully composite uncracked trans-formed section referred to the the extreme tension fiber of thesteel beam section (including cover plate), in3.

Sx, Sy Section modulus about the x and y axes of the beam respec-tively, in3.

Sxc Section modulus about the x axis of the outside fiber of thecompression flange, in3.

Sxt Section modulus about the x axis of the outside fiber of thetension flange, in3.

SRmax Maximum number of shear stud connectors that can fit in onerow across the top flange of a composite beam, unitless.

TB Tensile force in a composite rolled steel beam when the plasticneutral axis is above the top of the beam, kips.

TCP Tensile force in the cover plate, kips.

TFB Tensile force in the bottom flange of a steel beam, kips.

TFT Tensile force in the top flange of a steel beam, kips.

TKB Tensile force in the bottom fillets of a rolled steel beam, kips.

TKT Tensile force in the top fillets of a rolled steel beam, kips.

TWeb Tensile force in the web of a steel beam, kips.

V Shear force, kips.

Vn Nominal shear strength, kips.

Vu Required shear strength, kips.



W Total load supported by the beam, kips. You specify a loadcombination that the program uses to determine this weight.

X1 Beam buckling factor defined by AISC-LRFD93 equation F1-8.

X2 Beam buckling factor defined by AISC-LRFD93 equation F1-9.

Z Plastic section modulus of the steel beam alone plus coverplate if applicable, in3.

Zx, Zy Plastic section modulus about the x and y axes of the beamrespectively, in3.

a clear distance between transverse stiffeners, in.

ar For a user-defined section, ratio of web area to flange area,but not more than 10, unitless.

a1 Distance from top of concrete to bottom of effective concretefor partial composite connection when bottom of effective con-crete is within the slab above the metal deck (or there is asolid slab with no metal deck), in.

a2 Distance from top of metal deck to bottom of effective con-crete for partial composite connection when bottom of effec-tive concrete is within the height of the metal deck, in.

a3 Distance from top of metal deck to elastic neutral axis whenelastic neutral axis is located in slab above metal deck, in.

a4 Distance from top of concrete slab to elastic neutral axis whenelastic neutral axis is located in slab above metal deck, in.

a5 Distance from bottom of metal deck to elastic neutral axiswhen elastic neutral axis is located within height of metaldeck, in.

a6 Distance from top of metal deck to elastic neutral axis whenelastic neutral axis is located within height of metal deck, in.

b Width, in.



bcp Width of steel cover plate, in.

beff Effective width of concrete flange of composite beam, in.

bf Width of flange of a rolled steel beam, in.

bf-bot Width of bottom flange of a user-defined steel beam, in.

bf-top Width of top flange of a user-defined steel beam, in.

d Depth of steel beam from outside face of top flange to outsideface of bottom flange, in.

davg Average depth of concrete slab, including the concrete in themetal deck ribs, in.

dsc Diameter of a shear stud connector, in.

f First natural frequency of the beam in cycles per second.

f'c Specified compressive strength of concrete, ksi.

g Acceleration of gravity, in/seconds2.

h Clear distance between flanges less the fillet or corner radiusat each flange for rolled shapes and clear distance betweenflanges for other shapes, in.

hc For rolled shapes, twice the distance from the beam centroidto the inside face of the compression flange less the fillet orcorner radius. In a user-defined section, twice the distancefrom the centroid of the steel beam alone, not including thecover plate even if it exists, to the inside face of the compres-sion flange, in.

hr Height of metal deck rib, in.

k Distance from outer face of a rolled beam flange to the webtoe of a fillet, in.

kc Unitless factor used in AISC-LRFD93 Table B5.1, 0.35 ≤ kc ≤0.763.



kdepth Distance from inner face of a rolled beam flange to the webtoe of a fillet, in.

kwidth Width of idealized fillet of rolled beam section, in.

l Controlling laterally unbraced length of a member, in.

l22, l33 Laterally unbraced length of a member for buckling about thelocal 2 and 3 axes of the beam respectively, in.

lx, ly Laterally unbraced length of a member for buckling about thex and y axes of the beam respectively, in.

m For a user-defined section, ratio of web yield stress to flangeyield stress, unitless.

r Governing radius of gyration, in.

rd Distance from top of beam flange to bottom of metal deck, in.

r22, r33 Radius of gyration about the local 2 and 3 axes of the beamrespectively, in.

r T Radius of gyration of a section comprising the compressionflange plus one-third of the compression web area taken aboutan axis in the plane of the web, in.

rx, ry Radius of gyration about the x and y axes of the beam respec-tively, in.

ryc Radius of gyration of the compression flange about the y-axis,in.

sb Beam spacing, in.

t Thickness, in.

tc Thickness of concrete slab, in. If there is metal deck this is thethickness of the concrete slab above the metal deck.

tcp Thickness of cover plate, in.



tf Thickness of steel beam flange, in.

tf-bot Thickness of bottom flange of a user-defined steel beam, in.

tf-top Thickness of top flange of a user-defined steel beam, in.

tO Time to the maximum initial displacement of a single beamresulting from a heel drop impact, seconds.

tw Thickness of web of user-defined steel beam, in.

wa Additional metal deck rib width, in. This term is used to specifymetal deck ribs that are split over the beam. The width wa isadded to the width wr when determining the width of deck ribavailable for shear studs.

wc Unit weight per volume of concrete, pounds/feet3.

wd Unit weight per area of metal deck, ksi.

wr Average width of metal deck rib, in.

x1 The assumed gap distance from the supporting beam or col-umn flange to the end of the beam flange, in. The defaultvalue for this length is 0.5 inches.

y Distance from the bottom of the bottom flange of the steelbeam section to the elastic neutral axis of the fully compositebeam, in.

ybare The distance from the bottom of the bottom flange of the steelbeam to the neutral axis of the noncomposite steel beam pluscover plate if applicable, in.

ye The distance from the elastic neutral axis of the bare steelbeam alone (plus cover plate, if applicable) to the elastic neu-tral axis of the fully composite beam, in.

yeff The distance from the bottom of the bottom flange of the steelbeam to the neutral axis of the partially composite beam, in.



y1 Distance from the bottom of the bottom flange of the steelbeam section to the centroid of an element of the compositebeam section, in.

y2 Distance from the top of the top flange of the steel beam sec-tion to the plastic neutral axis when the plastic neutral axis iswithin the beam top flange, in.

y3 Distance from the bottom of the top flange of a rolled steelbeam section to the plastic neutral axis when the plastic neu-tral axis is within the fillets, in.

y4 For a rolled steel beam, the distance from the bottom of thetop fillet to the plastic neutral axis when the plastic neutralaxis is within the beam web, in. For a user-defined steel beam,the distance from the bottom of the top flange to the plasticneutral axis when the plastic neutral axis is within the beamweb, in.

yp Distance from the plastic neutral axis of composite section tothe bottom of the beam bottom flange (not cover plate), in.

z Distance from the elastic neutral axis of the steel beam (pluscover plate, if it exists) alone to the top of the concrete slab,in. Note that this distance may be different on the left andright sides of the beam.

zp Distance from the plastic neutral axis of composite section tothe top of the concrete slab, in. Note that this distance may bedifferent on the left and right sides of the beam.

ΣA Sum of the areas of all of the elements of the steel beam sec-tion, in2.

ΣAtr Sum of the areas of all of the elements of the composite steelbeam section, in2.

Σ(Atry1) Sum of the product Atr times y1 for all of the elements of thecomposite steel beam section, in3.



Σ(Ay1) Sum of the product A times y1 for all of the elements of thesteel beam section, in3.

Σ(Ay12) Sum of the product A times y1

2 for all of the elements of thesteel beam section, in4.

Σ(Atry12)= Sum of the product Atr times y1

2 for all of the elements of thecomposite steel beam section, in4.

ΣIO Sum of the moments of inertia of each element of the com-posite steel beam section taken about the center of gravity ofthe element, in4.

ΣQn Sum of nominal strength of shear connectors (shear stud orchannel) between point considered and point of zero moment,kips.

ΣQn-pcc Required nominal strength of shear connectors (shear stud orchannel) between point considered and point of zero momentfor partial composite connection percentage, PCC, kips.

ΣQn-100 Required nominal strength of shear connectors (shear stud orchannel) between point considered and point of zero momentfor full (100%) composite action, kips.

β Unitless factor used in calculating number of shear studs be-tween a point load and a point of zero moment equal to Str/Ss

for full composite connection and Seff/Ss for partial compositeconnection.

φ Resistance factor, unitless.

φb Resistance factor for bending in a noncomposite beam,unitless. The default value is 0.9.

φbcne Resistance factor for negative bending in a composite beamwhen Mn is determined from an elastic stress distribution,unitless. The default value is 0.9.

φbcnp Resistance factor for negative bending in a composite beamwhen Mn is determined from a plastic stress distribution,



unitless. The default value is 0.85.

φbcpe Resistance factor for positive bending in a composite beamwhen Mn is determined from an elastic stress distribution,unitless. The default value is 0.9.

φbcpp Resistance factor for positive bending in a composite beamwhen Mn is determined from a plastic stress distribution,unitless. The default value is 0.85.

φbs Resistance factor for strength of shear studs, unitless. Notethat this is a resistance factor that is not defined by AISC. It isincluded by CSI to give you more control over the strength ofthe composite section. The default value is 1.0.

φc Resistance factor for axial compression, unitless. The defaultvalue is 0.85.

φt Resistance factor for axial tension, unitless. The default valueis 0.9.

φv Resistance factor for beam shear, unitless. The default value is0.9.

λ Controlling slenderness parameter, unitless. It is the minoraxis slenderness ratio Lb/ry for lateral-torsional buckling. It isthe flange width-thickness ratio b/t as defined in AISC LRFDManual Specification section B5.1 for flange local buckling. It isthe web depth-thickness ratio h/tw as defined in AISC LRFDManual Specification section B5.1 for web local buckling.

λc Column slenderness parameter, unitless.

λp Limiting slenderness parameter for a compact element, largestvalue of λ for which Mn = Mp, unitless.

λr Limiting slenderness parameter for a noncompact element,largest value of λ for which buckling is inelastic, unitless.

Preferences Technical Note 30 - 1



Technical Note 30Preferences

GeneralThe composite beam design preferences are basic assignments that apply toall composite beams. Use the Options menu > Preferences > CompositeBeam Design command to access the Preferences form where you can viewand revise the composite beam design preferences. The Composite Beam De-sign Preferences form has five separate tabs: Factors, Beam, Deflection, Vi-bration, and Price.

Default values are provided for all composite beam design preference items.Thus, it is not required that you specify or change any of the preferences. Youshould, however, at least review the default values for the preference itemsto make sure they are acceptable to you.

Using the Preferences FormTo view preferences, select the Options menu > Preferences > CompositeBeam Design. The Preferences form will display. The first time you enter thePreferences form, review and, if necessary, change the specified design codein the drop-down box near the bottom of the form.

Click on the desired tab: Factors, Beam, Deflection, Vibration or Price. Thepreference options included under each of the tabs are displayed in a two-column spreadsheet. The left column of the spreadsheet displays the prefer-ence item name. The right column of the spreadsheet displays the preferenceitem value.

To change a preference item, left click the desired preference item in eitherthe left or right column of the spreadsheet. This activates a drop-down box orhighlights the current preference value. If the drop-down box appears, selecta new value. If the cell is highlighted, type in the desired value. The prefer-ence value will update accordingly. You cannot overwrite values in the drop-down boxes.

Preferences Composite Beam Design AISC-LRFD93


When the preference item is clicked in either column, a short description ofthat item displays in the large text box just below the list of items. This de-scription helps you remember the purpose of each preference item withoutreferring to the documentation.

To set all of the composite beam preference items on a particular tab to theirdefault values, click on that tab to view it and then click the Reset Tab but-ton. This button resets the preference values on the currently selected tab.

To set all of the composite beam preference items on all tabs to their defaultvalues, click the Reset All button. This button immediately resets all of thecomposite beam preference items.

Important note about resetting preferences: The defaults for the prefer-ence items are built into the program. The composite beam preference valuesthat were in a .edb file that you used to initialize your model may be differentfrom the built-in default values. Clicking a reset button resets the preferencevalues to built-in values, not to the values that were in the .edb file used toinitialize the model.

When you have finished making changes to the composite beam preferences,click the OK button to close the form. You must click the OK button for thechanges to be accepted by the program. If you click the Cancel button to exitthe form, any changes made to the preferences are ignored and the form isclosed.

PreferencesFor purposes of explanation in this Technical Note, the preference items arepresented in tables. The column headings in these tables are described asfollows:

• Item: The name of the preference item as it appears in the cells at theleft side of the Preferences form.

• Possible Values: The possible values that the associated preferenceitem can have.

• Default Value: The built-in default value that the program assumes forthe associated preference item.

Composite Beam Design AISC-LRFD93 Preferences


• Description: A description of the associated preference item.

Factors TabPhi FactorsTable 1 lists the preference items available for phi factors in AISC-LRFD93 de-sign. Some of those phi factors are specified by the AISC specification. Othershave been created by CSI to give you more control over the capacities for thecomposite section.

Table 1 AISC-LRFD93 Phi Factor Preferences

ItemPossibleValues


phi-b >0 0.9 Resistance factor for bending capacityin a steel beam alone, φb. See AISC-

LRFD93 Composite Beam DesignTechnical Note 36 Moment Capacity for

Steel Section Alone.

phi-bcne > 0 0.9 Resistance factor applied to the nega-tive bending capacity in a composite

beam section when the bending capac-ity, Mn, is determined from an elasticstress distribution, φbcne. See AISC-LRFD93 Composite Beam Design

Technical Note 35 Composite SectionElastic Moment Capacity.

phi-bcnp > 0 0.85 Resistance factor applied to the nega-tive bending capacity in a composite

beam section when the bending capac-ity, Mn, is determined from a plastic

stress distribution, φbcnp.

phi-bcpe > 0 0.9 Resistance factor applied to the posi-tive bending capacity in a composite

beam section when the bending capac-ity, Mn, is determined from an elasticstress distribution, φbcne. See AISC-LRFD93 Composite Beam Design

Technical Note 35 Composite SectionElastic Moment Capacity.



Table 1 AISC-LRFD93 Phi Factor Preferences

ItemPossibleValues


phi-bcpp > 0 0.85 Resistance factor applied to the posi-tive bending capacity in a composite

beam section when the bending capac-ity, Mn, is determined from a plasticstress distribution, φbcnp. See AISC-LRFD93 Composite Beam Design

Technical Note 34 Composite PlasticMoment Capacity for Positive Bending.

phi-v > 0 0.9 Resistance factor for shear capacity insteel beam, φv. See AISC-LRFD93Composite Beam Design Technical

Note 40 Beam Shear Capacity.

Refer to the Technical Notes mentioned in the Description column of the tablefor more information.

Beam TabTable 2 lists the composite beam preference items available on the Beam tabin the Preferences form.

Table 2: Composite Beam Preferences on the Beam Tab

ItemPossibleValues


Shored? Yes/No No Toggle for shored or unshored con-struction.

Middle Range(%) ≥ 0% 70%

Length in the middle of the beam overwhich the program checks the effectivewidth on each side of the beam, ex-pressed as a percentage of the totalbeam length.

Pattern LiveLoad Factor ≥ 0 0.75

Factor applied to live load for specialpattern live load check for cantileverback spans and continuous spans.

Stress RatioLimit >0 0.95

The acceptable stress ratio limit. Thisitem only applies to design optimiza-tion.



Deflection TabTable 3 lists the composite beam preference items available on the Deflectiontab in the Preferences form.

Table 3: Composite Beam Preferences on the Deflection Tab

ItemPossibleValues


Live LoadLimit, L/

> 0 360Live load deflection limitation denomi-nator (inputting 360 means that the de-flection limit is L/360).

Total LoadLimit, L/

> 0 240Total load deflection limitation denomi-nator (inputting 240 means that the de-flection limit is L/240).

Camber DL(%)

> 0 100%Percentage of dead load (not includingsuperimposed dead load) on whichcamber calculations are based.

See Composite Beam Design Technical Note 11 Beam Deflection and Camberfor description of beam deflection and camber.

Vibration TabTable 4 lists the composite beam preference items available on the Vibrationtab in the Preferences form.


ItemPossibleValues


Percent LiveLoad (%) ≥ 0 25%

Percentage of live load plus reducedlive load considered (in addition to fulldead load) when computing weightsupported by the beam for use incalculating the first natural frequency ofthe beam.

ConsiderFrequency?

Yes/No NoToggle to consider the frequency asone of the criteria to be used for deter-mining if a beam section is acceptable.




ItemPossibleValues


MinimumFrequency

> 0 Hz 8 Hz

Minimum acceptable first naturalfrequency for a floor beam. This item isused when the Consider Frequencyitem is set to Yes.

ConsiderMurray Damp-

ing?Yes/No No

Toggle to consider Murray's minimumdamping requirement as one of thecriteria to be used for determining if abeam section is acceptable.

InherentDamping (%) > 0% 4%

Percentage of critical damping that isinherent in the floor system. This item isused when the Consider MurrayDamping item is set to Yes.


Price TabTable 5 lists the composite beam preference items available on the Price tabin the Preferences form.

Table 5: Composite Beam Preferences on the Price Tab

ItemPossibleValues


Optimize forPrice?

Yes/No No

Toggle to consider price rather thansteel weight when selecting the opti-mum beam section from an auto selectsection list.

Stud Price ($) ≥ 0 $0Installed price for a single shear studconnector.

Camber Price($) ≥ 0 $0

Camber price per unit weight of steelbeam (including cover plate, if itexists).

See "Using Price to Select Optimum Beam Sections" in Composite Beam De-sign Technical Note 1 General Design Information for additional informationon the "Optimize for Price?" item.



Note that the price per unit weight for the steel beam (plus cover plate, if ap-plicable) is input as part of the material property specification for the beam.The material properties can be reviewed or defined using the Define menu >Material Properties command. Be sure that you use the same currencyunits (for example, U.S. dollars) for the steel price in the material properties,the stud price in the preferences, and the camber price in the preferences.




Technical Note 31Overwrites

This Technical Note provides instructions on how to use the Composite BeamOverwrites form and describes the items available on each of the tabs in theform. One section is devoted to each of the tabs.

GeneralThe composite beam design overwrites are basic assignments that apply onlyto those composite beams to which they are assigned. After selecting one ormore composite beams, use the Design menu > Composite Beam Design> View\Revise Overwrites command to access the Composite Beam Over-writes form where you can view and revise the composite beam design over-writes.

Note:

There are default values provided for all overwrite items. Thus, if you are happy with thedefaults, you do not need to specify any of the composite beam overwrites.

The Composite Beam Overwrites form has eight tabs. They are Beam, Bracing(C), Bracing, Deck, Shear Studs, Deflection, Vibration and Miscellaneous. De-scriptions of the various overwrite options available on each tab are providedlater in this Technical Note.

Default values are provided for all composite beam overwrite items. Thus, it isnot required that you specify or change any of the overwrites. However, atleast review the default values for the overwrite items to make sure they areacceptable. When changes are made to overwrite items, the program appliesthe changes only to the elements to which they are specifically assigned; thatis, to the elements that are selected when the overwrites are changed.

Overwrites Composite Beam Design AISC-LRFD93

Technical Note 31 - 2 Overwrites

Using the Composite Beam Overwrites FormAfter selecting one or more composite beams, use the Design menu >Composite Beam Design > View\Revise Overwrites command to accessthe Composite Beam Overwrites form. Click on the desired tab.

The Composite Beam Overwrites are displayed on each tab with a column ofcheck boxes and a two-column spreadsheet. The left column in the spread-sheet contains the name of the overwrite item. The right column in thespreadsheet contains the overwrite value.

Initially, the check boxes are all unchecked and all of the cells in the spread-sheet have a gray background to indicate they are inactive and that the itemsin the cells currently cannot be changed. The names of the overwrite items inthe first column of the spreadsheet are visible. The values of the overwriteitems in the second column of the spreadsheet are visible if only one beamwas selected before the Composite Beam Overwrites form was accessed. Ifmultiple beams were selected, no values show for the overwrite items in thesecond column of the spreadsheet.

After selecting one or multiple beams, check the box to the left of an over-write item to change it. Then left click in either column of the spread sheet toactivate a drop-down box or to highlight the contents of the cell in the rightcolumn of the spreadsheet. If the drop-down box appears, select a value fromthe box. If the cell is highlighted, type in the desired value. The overwrite willreflect the change. You cannot change the values in the drop-down boxes.

When you check a check box or left click in one of the columns in the spread-sheet, a short description of the item in that row displays in the large text boxjust below the list of items. This description helps you recall the purpose ofthe overwrite item without referring to the manual.

When changes to the composite beam overwrites have been made, click theOK button to close the form. The program then changes all of the overwriteitems whose associated check boxes are checked for the selected beam(s).You must click the OK button for the changes to be accepted by the program.If you click the Cancel button to exit the form, any changes made to theoverwrites will be ignored and the form will be closed.

Composite Beam Design AISC-LRFD93 Overwrites


Resetting Composite Beam Overwrites to DefaultValuesTo set all of the composite beam overwrite items on a particular tab to theirdefault values, click on the tab and then click the Reset Tab button. Thisbutton resets the overwrite values on the tab currently selected.

To set all of the composite beam overwrite items on all tabs to their defaultvalues, click the Reset All button. This button immediately resets all of thecomposite beam overwrite items. Alternatively, you can click the Designmenu > Composite Beam Design > Reset All Composite Beam Over-writes command to accomplish the same thing.

Important note about resetting overwrites: The defaults for the over-write items are built into the program. The composite beam overwrite valuesthat were in a .edb file that you used to initialize your model may be differentfrom the built-in program default values. When you reset overwrites, the pro-gram resets the overwrite values to its built-in values, not to the values thatwere in the .edb file used to initialize the model.

OverwritesFor purposes of explanation in this Technical Note, the overwrite items arepresented in tables. The column headings in these tables are described asfollows.

Item: The name of the overwrite item as it appears in the cells at the leftside of the Composite Beam Overwrites form.

Possible Values: The possible values for the associated overwrite item.

Default Value: The built-in default value that the program assumes forthe associated overwrite item.

Description: A description of the associated overwrite item.



Beam TabTable 1 lists the composite beam overwrite items available on the Beam tab inthe Composite Beam Overwrites form.


ItemPossibleValues


Shored? Yes/No No(unshored)

Toggle for shored or unshored con-struction.

Beam type Composite,NC w studs, orNC w/o studs

Composite Type of beam design. NC w studs isshort for Noncomposite with minimumshear studs. NC w/o studs is short forNoncomposite without shear studs.

b-eff leftCondition


Programcalculated

Toggle specifying how the effectivewidth of the concrete slab on the leftside of the beam is determined

b-eff left ≥ 0 Programcalculated

value

User-defined effective width of concreteslab on left side of beam, beff left.

b-eff rightCondition


Programcalculated

Toggle specifying how the effectivewidth of the concrete slab on the rightside of the beam is determined

b-eff right ≥ 0 Programcalculated

value

User-defined effective width of concreteslab on right side of beam, beff right

Beam Fy ≥ 0 Specified inMaterial

Properties

Yield stress of the beam, Fy. Specifying0 in the overwrites means that Fy is asspecified in the material properties

Beam Fu ≥ 0 Specified inMaterial

Properties

Minimum tensile strength of the beam,Fu. Specifying 0 means that Fu is asspecified in the material properties




ItemPossibleValues


Cover PlatePresent?

Yes/No No Toggle switch indicating if a full lengthcover plate exists on the bottom of thebeam bottom flange.

Plate width ≥ 0 0 Width of cover plate, bcp.

Plate thickness ≥ 0 0 Thickness of cover plate, tcp.

Plate Fy > 0 0 Cover plate yield stress, Fycp. Specify-ing 0 means that Fycp is set to thatspecified in the beam material proper-ties

The Shored item affects both the deflection calculations and the flexuralstress calculations for the beam. See Composite Beam Design Technical Note11 Beam Deflection and Camber for a description of beam deflection. If thebeam is shored, no checks are performed for the construction loading designload combination.

Note:

The Middle Range item is specified on the Beam tab in the composite beam preferencesand is described in "Location Where Effective Slab Width is Checked" of CompositeBeam Design Technical Note 8 Effective Width of the Concrete Slab.

Typically, when a beam is designed using the Composite Beam Design post-processor that beam is designed as a composite beam if it has a deck section(not slab section) assigned along the full length of the specified Middle Rangeon at least one side of the beam. The Beam Type overwrite allows you tospecify that a beam that would ordinarily be designed as a composite beambe designed as a noncomposite beam. The overwrite does not and cannotforce a beam that has been designed as a noncomposite beam, because thereis no deck section along at least one side, to be designed as a compositebeam. When using the Composite Beam Design postprocessor, a beam thatdoes not have a deck section along at least one side is always designed as a



noncomposite beam, regardless of what is specified in the Beam Type over-write.

When a beam is designed as noncomposite with minimum shear studs, thebeam is designed as a noncomposite beam. Then shear studs are specified forthe beam with as large a spacing as possible, without exceeding the specifiedmaximum longitudinal spacing. The maximum longitudinal spacing can beoverwritten on the Shear Studs tab.

See Composite Beam Design Technical Note 8 Effective Width of the Concrete Slab fora description of the beam effective width.

The beam yield stress and the cover plate yield stress both default to theyield stress specified for the material property associated with the beam sec-tion. When the Define menu > Frame Sections command is used to definea beam section, the material property associated with the beam sectionshould also be defined. The material property is defined using the Definemenu > Material Properties command.

In this program, the cover plate can have a yield stress that is different fromthat of the beam, if desired. The cover plate width, thickness and Fy items arenot active unless the "Cover Plate Present" item is set to Yes. See "CoverPlates" in Composite Beam Design Technical Note 7 Composite Beam Proper-ties for a description of cover plates.

Bracing (C) Tab and Bracing TabThe unbraced length overwrite items included on the Bracing (C) tab and theBracing tab are exactly the same. The items on the Bracing (C) tab apply toconstruction loading design load combinations. The items on the Bracing tabapply to final condition design load combinations.

The first two items that appear in the Bracing (C) tab and the Bracing tab areshown in Table 2a. Additional items may also appear in the tabs, dependingon your choice for the Bracing Condition item. These additional items areshown in Tables 2b and 2c.



Table 2a: First Two Composite Beam Overwrite Items on theBracing (C) Tab and the Bracing Tab

ItemPossibleValues


Cb factor ≥ 0 Programcalculated

Unitless factor used in determining al-lowable bending stress, Cb. Specifying0 in the overwrites means that thisvalue is program calculated

BracingCondition

Programcalculated,

bracingspecified or

lengthspecified

Programcalculated

This item defines how the unbracedlengths are determined for bucklingabout the beam local 2-axis. They areprogram calculated, based on user-specified uniform and point bracing, orbased on a user-specified maximumunbraced length.

When the Cb factor is program calculated, the program uses Equation 1 tocalculate it unless you have specified the Bracing Condition as Length Speci-fied.

C max

maxb

3M 4 3 5.2

5.12C

+++=

BA MMM

MEqn. 1

where,

Mmax is the maximum moment.

MA is the moment at the one-quarter point.

MB is the moment at the center or one-half point.

MC is the moment at the three-quarter point.

When the Bracing Condition is specified as Program Calculated, the programassumes the beam is braced as described in "Determination of the BracedPoints of a Beam" in Composite Beam Design Technical Note 9 Beam Un-braced Length. Note that the program automatically considers the bracing forconstruction loading and for the final condition separately. For the construc-



tion loading condition, the program assumes that the concrete fill does notassist in bracing the beam.

When the Bracing Condition is specified as Bracing Specified, two items ap-pear in the tab in addition to those shown in Table 2a. The two additionalitems are shown in Table 2b.

Table 2b: Additional Composite Beam Overwrite Items on theBracing (C) Tab and the Bracing Tab When the BracingCondition Is Specified as Bracing Specified

ItemPossibleValues


No. PointBraces

≥ 0 0 The number of user-specified pointbrace locations. Clicking in this boxopens the Point Braces form where youspecify the point braces.

No. UniformBraces

≥ 0 0 The number of user-specified uniformbraces. Clicking in this box opens theUniform Braces form where you specifythe uniform braces.

The No. Point Braces and No. Uniform Braces items allow you to specify actualbracing for the beam. These items are described in "User-Specified Uniformand Point Bracing" in Composite Beam Design Technical Note 9 Beam Un-braced Length.

When the Bracing Condition is specified as Length Specified, two items appearin the tab in addition to those shown in Table 2a. The two additional items areshown in Table 2c.



Table 2c: Additional Composite Beam Overwrite Items on the Brac-ing (C) Tab and the Bracing Tab When the Bracing Condi-tion Is Specified as Length Specified

ItemPossibleValues


AbsoluteLength?

Yes/No No Toggle switch for whether the maxi-mum unbraced length is given as anabsolute length or a relative length.

Unbraced L22 ≥ 0 and ≤beam length

Length ofbeam

Maximum unbraced length for bucklingabout the beam local 2 axis.

When the maximum unbraced length is specified as an absolute length, theactual maximum unbraced length is specified. When the maximum unbracedlength is specified as a relative length, the value specified is equal to themaximum unbraced length divided by the length of the beam. The relativelength specified is always between 0 and 1, inclusive.

See Composite Beam Design Technical Note 9 Beam Unbraced Length for ad-ditional information about the unbraced length of the beam.

Deck TabTable 3 lists the composite beam overwrite items available on the Deck tab inthe Composite Beam Overwrites form.

Table 3: Composite Beam Overwrites on the Deck Tab

ItemPossibleValues


Deck ID Left Programcalculated, anydefined deckproperty, or

None

Programcalculated

Deck ID assigned to left side of beam.



Table 3: Composite Beam Overwrites on the Deck Tab

ItemPossibleValues


Deck directionLeft


perpendicular

Programcalculated

Span direction of the metal deck ribs onleft side of beam relative to the spandirection of the beam.

Deck ID Right Programcalculated, anydefined deckproperty, or

None

Programcalculated

Deck ID assigned to right side of beam.

Deck directionRight


perpendicular

Programcalculated

Span direction of the metal deck ribs onthe right side of beam relative to thespan direction of beam

When the Deck ID is program calculated, you must refer to the output data tosee what the program assumed for this item. It is not shown in the over-writes.

If the deck direction is program calculated, do not overlook the importantnote about deck orientation in "Multiple Deck Types or Directions Along theBeam Length" in Composite Beam Design Technical Note 8 Effective Width ofthe Concrete Slab.

Shear Studs TabTable 4 lists the composite beam overwrite items available on the ShearStuds tab in the Composite Beam Overwrites form.

Table 4: Composite Beam Overwrites on the Shear Studs Tab

ItemPossibleValues


User Pattern? Yes/No No Toggle to indicate if a user-definedshear connector pattern is defined.



Table 4: Composite Beam Overwrites on the Shear Studs Tab

ItemPossibleValues


UniformSpacing


uniformlyspaced

connectors

Uniform spacing of shear studs alongthe beam. There is one shear stud perrow along the beam.

No. AdditionalSections


additionalconnectorsspecified

Number of sections in which additionaluniformly spaced shear studs arespecified. Clicking in this box opens theAdditional Sections form where youspecify the section length and the num-ber of uniformly spaced connectors inthe section.

Min LongSpacing

> 0 6ds

(i.e., six studdiameters)

Minimum longitudinal spacing of shearstuds along the length of the beam.

Max LongSpacing

> 0 36 inches Maximum longitudinal spacing of shearstuds along the length of the beam.

Min TranSpacing

> 0 4ds

(i.e., four studdiameters)

Minimum transverse spacing of shearstuds across the beam flange.

Max Studsper Row

> 0 3 Maximum number of shear studs in asingle row across the beam flange.

Qn Programcalculated or

> 0

Programcalculated

Capacity of a single shear stud. Speci-fying 0 in the overwrites means that thisvalue is program calculated.

The Uniform Spacing and No. Additional Sections items are only available ifthe User Pattern item is set to Yes. See Composite Beam Design TechnicalNote 15 User-Defined Shear Stud Patterns for a more information.

The program default value for the minimum longitudinal spacing of shearstuds along the length of the beam is six shear stud diameters. Note that thisitem is input as an absolute length, not as a multiplier on the stud diameter.

The program default value for the maximum longitudinal spacing of shearstuds along the length of the beam is 36 inches. The design code used mayspecify the maximum longitudinal spacing is eight times the total slab thick-ness (rib height, hr, plus concrete slab above metal deck, tc). AISC-LRFD-93Specification Section I5 specifies that the maximum longitudinal spacing of



shear studs along the length of a beam shall not exceed 36 inches for beamswhen the span of the metal deck is perpendicular to the span of the beam. Ifyour total slab thickness is less than 36"/8 = 4.5", the program default valuemay be unconservative and should be revised.

The program default value for the minimum transverse spacing of shear studsacross the beam flange is four shear stud diameters. This is consistent withthe last paragraph of AISC-LRFD-93 Specification Section I5. Note that thisitem is input as an absolute length, not as a multiplier on the stud diameter.See Composite Beam Design Technical Note 13 Distribution of Shear Studs ona Composite Beam for an additional description of how shear studs are dis-tributed on composite beams.

The "Max Studs per Row" item indicates the maximum number of shear studsthat is allowed in a row across the beam flange. For wider beams, the MinTran Spacing item might indicate that more studs could be accommodatedacross the beam flange but the Max Studs per Row item will limit the numberof studs in any row. See Composite Beam Design Technical Note 13 Distribu-tion of Shear Studs on a Composite Beam for an additional description of howshear studs are distributed on beams.

See "Shear Stud Connector" in Composite Beam Design AISC-ASD89 Techni-cal Note 25 Shear Studs for a description of how the program calculates theallowable shear load for a single shear stud. Note that when a q value isspecified in the overwrites, the program assumes that the specified value of qhas already been modified by any applicable reduction factors for the metaldeck. Finally, note that specifying 0 (zero) in the overwrites for this itemmeans that the allowable shear stud load is calculated by the program, notthat it is zero.

Shear studs are described in more detail in Composite Beam Design TechnicalNote 13 Distribution of Shear Studs on a Composite Beam, Technical Note 14The Number of Shear Studs that Fit in a Composite Beam Segment, andTechnical Note 15 User-Defined Shear Stud Patterns.

Deflection TabTable 5 lists the composite beam overwrite items available on the Deflectiontab in the Composite Beam Overwrites form.



Table 5: Composite Beam Overwrites on the Deflection Tab

ItemPossibleValues


DeflectionAbsolute?

Yes/No No Toggle to consider live load and totalload deflection limitations as absoluteor as divisor of beam length (relative).

Live Load Limit > 0 Specified inPreferences

Deflection limitation for live load. Forrelative deflection, inputting 360 meansthat the limit is L/360.

Total LoadLimit

> 0 Specified inPreferences

Deflection limitation for total load. Forrelative deflection, inputting 240 meansthat the limit is L/240.

CalculateCamber?

Yes/No Yes Toggle for the program to calculatebeam camber.

Fixed Camber ≥ 0 0 User-specified camber when the pro-gram does not calculate beam camber

See Composite Beam Design Technical Note 11 Beam Deflection and Camberfor a description of beam deflection and camber.

Vibration TabTable 6 lists the composite beam overwrite items available on the Vibrationtab in the Composite Beam Overwrites form.

Table 6: Composite Beam Overwrites on the Vibration Tab

ItemPossibleValues


Neff Condition User Definedor ProgramCalculated

User Defined Toggle to select user defined or pro-gram calculated based on beam spac-ing, N effective.

No. EffectiveBeams

≥1 1.0 Effective number of beams resisting aheel drop impact.




Miscellaneous TabTable 7 lists the composite beam overwrite items available on the Miscellane-ous tab in the Composite Beam Overwrites form.


ItemPossibleValues


ConsiderBeam Depth?

Yes/No No Toggle to select if beam depth is to beconsidered in an auto select sectionlist. If yes, maximum and minimumdepths must be input.

MaximumDepth

>0 44 inches Maximum actual (not nominal) beamdepth to be considered in auto selectsection list.

MinimumDepth

≥0 0 Minimum actual (not nominal) beamdepth to be considered in auto selectsection list.

MaximumPCC(%)

>0 100% Maximum percent composite connec-tion considered for the beam.

Minimum PCC(%)

>0 25% Minimum percent composite connectionconsidered for the beam.

LL ReductionFactor

0<, >1.0 1.0 Reducible live load is multiplied by thisfactor to obtain the reduced live load. Ifzero is selected, the program calcu-lated valued is used.

Horizontal EQFactor

0<, >1.0 1.0 Multiplier applied to the earthquakeportion of the load in a design loadcombination.

Ignore Similar-ity

Yes/No No Defines if the story level similarity to amaster story level is to be ignored whendesigning the beam.

Design Load Combinations Technical Note 32 - 1



Technical Note 32Design Load Combinations

This Technical Note defines the default AISC-LRFD93 composite beam designload combinations. General information about composite beam design loadcombinations is provided by Composite Beam Design Technical Note 10 De-sign Load Combinations.

You may use the default composite beam design load combinations for yourdesign, or you may define your own design load combinations, or you can useboth default combinations and your own combinations. You can modify thedefault design load combinations and you can delete them if you wish. Usethe Design Menu > Composite Beam Design > Select Design Combocommand to access the design load combinations selection form.

Strength Check for Construction LoadsThe program only performs the check using the construction load design loadcombination if the beam is unshored. If the beam is shored, the check forconstruction loads is not performed and any specified design load combina-tions for construction loads are not relevant.

The automatically created design load combination, using the AISC-LRFD93specification, for checking the strength of an unshored beam subjected toconstruction loads is given by Equation 1.

1.6 (ΣWDL) + 1.6 [0.2 (ΣLL + ΣRLL)] Eqn. 1

where,

ΣWDL = The sum of all wet dead load (WDL) load cases defined forthe model. Note that if a load case is simply defined as deadload, it is assumed to be a WDL load case.

ΣLL = The sum of all live load (LL) load cases defined for themodel.

Design Load Combinations Composite Beam Design AISC-LRFD93

Technical Note 32 - 2 Design Load Combinations

ΣRLL = The sum of all reducible live load (RLL) load cases definedfor the model.

In Equation 1 the term 0.2 (ΣLL + ΣRLL) is an assumed construction live load.Note that the load factor for dead loads is assumed the same as that for liveload when considering construction loads (e.g., placing of concrete, etc.). SeeR. Vogel (1991).

Strength Check for Final LoadsThe automatically created design load combinations for checking the strengthof a composite beam under final loads are given by Equations 2 and 3.

1.4 (ΣWDL + ΣSDL) Eqn. 2

1.2 (ΣWDL + ΣSDL) + 1.6 (ΣLL + ΣRLL) Eqn. 3

where,

ΣSDL = The sum of all superimposed dead load (SDL) load casesdefined for the model.

and the remainder of the terms are as defined for Equation 1.

Deflection Check for Final LoadsThe automatically created design load combination for checking the deflectionof a composite beam under final loads is given by Equation 4.

ΣWDL + ΣSDL + ΣLL + ΣRLL Eqn. 4

where all of the terms are as described for Equations 1 through 3. Note thatall of the load factors for this servicability check are 1.0.

If the beam is unshored, the WDL portion of the deflection is based on themoment of inertia of the steel beam alone and the remainder of the deflectionis based on the effective moment of inertia of the composite section. If thebeam is shored, the entire deflection is based on the effective moment of in-ertia of the composite section.

Composite Beam Design AISC-LRFD93 Design Load Combinations

Design Load Combinations Technical Note 32 - 3

ReferenceVogel, R. 1991. “LRFD-Composite Beam Design with Metal Deck,” Steel Tips,

Technical Information & Product Service, Steel Committee of Califor-nia, March.

Compact and Noncompact Requirements Technical Note 33 - 1



Technical Note 33Compact and Noncompact Requirements

This Technical Note describes how the program checks the AISC-LRFD93specification requirements for compact and noncompact beams. The basiccompact and noncompact requirements checked are in AISC-LRFD93 specifi-cation Chapter B, Table B5.1. The program checks the width-to-thickness ra-tios of the beam compression flange, beam web, and, if it exists and is incompression, the cover plate. When a singly symmetric beam is designed fornoncomposite behavior, it is also checked for lateral torsional buckling re-quirements.

OverviewThe program classifies beam sections as either compact, noncompact or slen-der. It checks the compact and noncompact section requirements at each de-sign location along the beam for each design load combination separately. Abeam section may be classified differently for different design load combina-tions. For example, a beam may be classified as compact for design loadcombination A and as noncompact for design load combination B. Two rea-sons that a beam may be classified differently for different design load casesare:

The compact section requirements for beam webs depend on the axialload in the beam. Different design load combinations may produce differ-ent axial loads in the beam.

The compression flange may be different for different design load combi-nations. If the sizes of the top and bottom flanges are not the same, clas-sification of the section may depend on which flange is determined to bethe compression flange.

At each design location, for each design load combination, the program firstchecks a beam section for the compact section requirements for the compres-sion flange, web, cover plate (if applicable) and lateral torsional buckling (ifapplicable) described herein. If the beam section meets all of those require-

Compact and Noncompact Requirements Composite Beam Design AISC-LRFD93

Technical Note 33 - 2 Compact and Noncompact Requirements

ments, it is classified as compact for that design load combination. If thebeam section does not meet all of the compact section requirements, it ischecked for the noncompact requirements for the flanges, web, cover plate (ifapplicable) and lateral torsional buckling (if applicable) described herein. Ifthe beam section meets all of those requirements, it is classified as noncom-pact for that design load combination. If the beam section does not meet allof the noncompact section requirements, it is classified as slender for that de-sign load combination and the program does not consider it for compositebeam design.

Limiting Width-to-Thickness Ratios for FlangesThis section describes the limiting width-to-thickness ratios considered by theprogram for beam compression flanges. The width-to-thickness ratio forflanges is denoted b/t, and is equal to bf/2tf for I-shaped sections and bf/tf forchannel sections.

Compact Section Limits for FlangesFor compact sections, the width-to-thickness ratio for the compression flangeis limited to that indicated by Equation 1.

yfF

65

t

b ≤ , for compact sections Eqn. 1

where Fyf is the specified yield stress of the flange considered. Equation 1 ap-plies to both rolled sections selected from the program's database and touser-defined sections.

Noncompact Section Limits for FlangesI-Shaped Rolled Beams and ChannelsFor noncompact I-shaped rolled beams and channels, the width-to-thicknessratio for the compression flange is limited to that indicated by Equation 2.

10-F

141

t

b

y

≤ , for noncompact sections Eqn. 2

where Fy is the specified yield stress of the beam or channel.

Composite Beam Design AISC-LRFD93 Compact and Noncompact Requirements


User-Defined and Hybrid BeamsFor noncompact user-defined and hybrid beams, the width-to-thickness ratiofor the compression flange is limited to that indicated by Equation 3.

c

yf

k

16.5-F

162

t

b ≤ , for noncompact sections Eqn. 3

where Fyf is the yield stress of the compression flange and,

0.763k0.35thanlessnotbut

t

h

4k c

w

c ≤≤= Eqn. 4

Limiting Width-to-Thickness Ratios for WebsThis section describes the limiting width-to-thickness ratios considered by theprogram for beam webs.

Compact Section Limits for WebsWhen checking a beam web for compact section requirements, the width-to-thickness ratio used is h/tw. The equation used for checking the compact sec-tion limits in the web depends on the magnitude of the axial compressionstress ratio, (Pu / φbPy) in the beam. When calculating the axial compressionstress ratio, the following two rules are used:

The program takes Py as AsFy for rolled sections and bf-toptf-topFyf-top +htwFyw + bf-bottf-botFyf-bot for user-defined sections.

The program uses φb = 0.85 if a plastic stress distribution is used for mo-ment and φb = 0.9 if an elastic stress distribution is used for moment.

The program computes the axial compression stress ratio (Pu / φbPy) basedon the area of the steel beam alone not including the cover plate, even ifit exists, and not including the concrete slab.

When (Pu / φbPy) ≤ 0.125, Equation 5a defines the compact section limit forwebs. When (Pu / φbPy) > 0.125, Equation 5b defines the compact section limitfor webs.


Technical Note 33 - 4 Compact and Noncompact Requirements

0.125P

Pwhen,

P

P75.21

F

640

t

h

y

u

y

u

yw

≤

−≤

bb φφEqn. 5a

0.125P

Pwhen

,F

253

P

P33.2

F

191

t

h

y

u

yy

u

yw

>

≥

−≤

b

b

φ

φEqn. 5b

In Equations 5a and 5b, the value of Fy used is the largest of the Fy values forthe beam flanges and the web.

If there is no axial force, or if there is axial tension only (i.e., no axial com-pressive force), only Equation 5a applies.

Noncompact Section Limits for WebsWhen checking a beam web of a beam for noncompact section requirements,the width-to-thickness ratio checked is h/tw. The noncompact section limitsdepend on whether the flanges of the beam are of equal or unequal size.

Beams with Equal Sized FlangesEquation 6 defines the noncompact section limit for webs in beams with equalsized flanges.

−≤

y

u

yw P

.74P01

F

970

t

h

bφEqn. 6

In Equation 6, the value of Fy used is the largest of the Fy values for the beamflanges and the web.

Beams with Unequal Sized FlangesEquation 7 defines the noncompact section limit for webs in beams with une-qual sized flanges



2

3

h

h

4

3

where,

,P

.74P01

h

h83.21

F

253

t

h

c

y

u

cyw

≤≤

−

+≤

bφ

Eqn. 7

In Equation 7, the value of Fy used is the largest of the Fy values for the beamflanges and the web. Equation 7 is Equation A-B5-1 in the AISC-LRFD93specification.

Limiting Width-to-Thickness Ratios for Cover PlatesThe width-to-thickness checks made for the cover plate depend on the widthof the cover plate compared to the width of the beam bottom flange. Figure 1illustrates the conditions considered.

In Case A of the figure, the width of the cover plate is less than or equal tothe width of the beam bottom flange. In that case, the width-to-thickness ra-tio is taken as b1/tcp, and it is checked as a flange cover plate.

In Case B of Figure 1, the width of the cover plate is greater than the width ofthe beam bottom flange. Two conditions are checked in that case. The firstcondition is the same as that shown in Case A, where the width-to-thicknessratio is taken as b1/tcp and is checked as a flange cover plate. The secondcondition checked in Case B takes b2/tcp as the width-to-thickness ratio andchecks it as a plate projecting from a beam. This second condition is onlychecked for the noncompact requirements; it is not checked for compact re-quirements.

Compact Section Limits for Cover PlatesFor both cases A and B shown in Figure 1, the cover plate is checked for com-pact section requirements as shown in Equation 8.

ycpcp

1

F

190

t

b ≤ Eqn. 8

where b1 is defined in Figure 1.


Te

Fi

NoThthofth

CoWbopl

Th

chnical Note 33 - 6 Compact and Noncompact Requirements

gure 1: Conditions Considered When Checking Width-to-ThicknessRatios of Cover Plates

ncompact Section Limits for Cover Platese checks made for noncompact section requirements depend on whethere width of the cover plate is less than or equal to that of the bottom flange the beam, Case A in Figure 1, or greater than that of the bottom flange ofe beam, Case B in Figure 1.

ver Plate Width ≤ Beam Bottom Flange Widthhen the cover plate width is less than or equal to the width of the beamttom flange, Equation 9 applies for the noncompact check for the coverate.

ycpcp

1

F

238

t

b ≤ Eqn. 9

e term b1 in Equation 9 is defined in Figure 1.

b1

t cp

b1

t cp

b2b2

Case A Case B

Beam

Cover plate

Beam

Cover plate



Cover Plate Width > Beam Bottom Flange WidthWhen the cover plate width exceeds the width of the beam bottom flange,both Equations 9 and 10 apply for the noncompact check for the cover plate.

ycpcp

2

F

95

t

b ≤ Eqn. 10


Composite Plastic Moment Capacity for Positive Bending Technical Note 34 - 1



Technical Note 34Composite Plastic Moment Capacity for

Positive Bending

This Technical Note describes how the program calculates the positive bend-ing moment capacity for a composite section assuming a plastic stress distri-bution.

OverviewFigure 1 illustrates a generic plastic stress distribution for positive bending.Note that the concrete is stressed to 0.85 f'c and the steel is stressed to Fy.The distance yp is measured from the bottom of the beam bottom flange (notcover plate) to the plastic neutral axis (PNA). The distance zp is measuredfrom the top of the concrete slab to the PNA; it can be different on the twosides of the beam as described later. The illustrated plastic stress distributionis the basic distribution of stress used by the program when considering aplastic stress distribution for positive bending. Note that if the metal deck ribsare parallel to the beam, the concrete in the ribs is also considered.

Figure 1: Generic Plastic Stress Distribution for Positive Bending

��

��

Beam Section Beam Elevation Plastic StressDistribution

CConc

CSteel

TSteel

0.85f’c

Fy

Fy

a

Plastic neutral axis (PNA)

y pz p

Composite Plastic Moment Capacity for Positive Bending Composite Beam Design AISC-LRFD93

Technical Note 34 - 2 Composite Plastic Moment Capacity for Positive Bending

Figure 2 illustrates how the program idealizes a steel beam for calculating theplastic stress distribution. Two different cases are shown, one for a rolledsection and the other for a user-defined section. The idealization for the rolledsection considers the fillets whereas the idealization for the user-defined sec-tion assumes there are no fillets because none are specified in the sectiondefinition. Although not shown in those figures, the deck type and orientationmay be different on the left and right sides of the beam as shown in Figure 2of Composite Beam Design Technical Note 8 Effective Width of the ConcreteSlab.

For a rolled steel section, the fillets are idealized as a rectangular block ofsteel. The depth of this rectangular block, kdepth, is:

kdepth = k - tf Eqn. 1

The width of this rectangular block, kwidth, is:

kwidth = (As - 2bftf - twh) / 2kdepth Eqn. 2

The basic steps in computing the positive plastic moment capacity are:

Determine the location of the PNA using Equations 3a through 10.

Calculate the plastic moment capacity of the composite section using Equa-tion 11 together with the appropriate table chosen from Tables 2 through11 depending on the location of the PNA. Note that for user-defined sec-tions, the terms related to the top and bottom fillets are ignored.

Location of the Plastic Neutral AxisThe program determines the location of the PNA by comparing the maximumpossible compressive force that can be developed in the concrete, MPFconc,with the maximum possible tensile force that can be developed in the steelsection (including the cover plate, if applicable), MPFsteel.

The maximum concrete force, MPFconc, is calculated from Equation 3a if thereis no metal deck, or if the metal deck ribs are oriented perpendicular to thebeam span. Equation 3b is used if the deck ribs are oriented parallel to thebeam span. Note that the maximum concrete force has contributions from theleft and right sides of the beam that are treated separately and may be dif-ferent.

Composite Beam Design AISC-LRFD93 Composite Plastic Moment Capacity for Positive Bending


Figure 2: Idealization of a Rolled Section and a User-Defined Section usedfor Calculating the Plastic Stress Distribution

��

bcp

bf-bot

kwidth

kwidth

tw

bf-top

h rt c

t f-top

kk

dh

k dep

thk d

epth

t cp

t f-bot

Idealization for Rolled Section

��

bcp

bf-bot

tw

bf-top

h rt c

t f-top

dht cp

t f-bot

Idealization for User-Defined Section



MPFconc = [(0.85f'c beff tc)left + (0.85f'c beff tc)right] Eqn. 3a

MPFconc = [(0.85f'c beff

+

r

rrc S

hwt )left +

(0.85f'c beff

+

r

rrc S

hwt )right Eqn. 3b

The maximum steel force, MPFsteel, is calculated from Equation 4a if the beamis a rolled section or Equation 4b if it is a user-defined section.

MPFsteel = (AsFy + bcp tcp Fycp) Eqn. 4a

MPFsteel = (bf-toptf-topFyf-top + twh +

bf-bottf-botFyf-bot + bcp tcp Fycp) Eqn. 4b

When computing the location of the PNA, it important to remember that theconcrete is assumed to take no tension. Also, the concrete in the metal deckribs is only considered effective in compression if the metal deck ribs are ori-ented parallel to the beam span.

The maximum concrete and steel forces are compared to determine whetherthe PNA is within the concrete slab or the steel section. If MPFconc > MPFsteel,the PNA is within the concrete slab. If MPFsteel > MPFconc, the PNA is within thesteel section. If MPFsteel = MPFconc, the PNA is at the top of the steel beam ifthere is full composite connection and within the steel beam if there is partialcomposite connection.

If the PNA is within the slab, the fact that the concrete slab can be differenton each side of the beam complicates locating the PNA. If the PNA is withinthe steel section, there are several general locations for it. After the generallocations have been identified, it is a straightforward process to determine thelocation of the PNA. The general locations are:

Within the beam top flange.

Within the beam top fillet (applies to rolled shapes from the program'ssection database only).



Within the beam web.

Within the beam bottom fillet (applies to rolled shapes from the program'ssection database only).

Within the beam bottom flange.

Within the cover plate (if one is specified).

Note it is very unlikely that the PNA would be below the beam web but thereis nothing in the program to prevent it. This condition would require a verylarge beam bottom flange and/or cover plate. Each of the PNA locations in thesteel section is described following the description of the PNA in the concreteslab.

PNA in the Concrete Slab Above the Steel BeamThe program considers the condition where the slab on the left and right sidesof the beam are different. When the program determines that the PNA isabove the top of the steel section, that is, when MPFconc > MPFsteel, it puts thefollowing four items in order, from highest elevation to lowest:

Top of concrete slab on the left side of the beam.

Top of concrete slab on the right side of the beam.

Top of metal on the left side of the beam.

Top of metal on the right side of the beam.

Next the program sums the compressive forces of those four items, startingwith the item at the highest elevation and proceeding downward. As eachitem is added into the sum, the sum of compressive forces is compared withthe maximum tension value, which is the sum of MPFsteel. As soon as the sumof forces exceeds MPFsteel, the program recognizes that the last location con-sidered is below the PNA, and the second to last location considered is abovethe PNA. Using this information, the program can solve directly for the loca-tion of the PNA.

Figures 3a and 3b show the internal forces for a rolled steel section and auser-defined steel section, respectively, for the condition where the PNA is inthe concrete slab above the metal deck.



Figure 3a: Rolled Steel Section with PNA in Concrete Slab Above MetalDeck, Positive Bending

Figure 3b: User-Defined Steel Section with PNA in Concrete Slab AboveMetal Deck, Positive Bending

��

��

CC 1

Beam Section Beam Elevation Beam Internal Forces

TC P


TF B

TK B

TWeb

TK T

TF T

y pz p

��

��

CC 1


TF T

TF B

TWeb

TC P


y pz p



Figures 4a and 4b show the internal forces for a rolled steel section and auser-defined steel section, respectively, for the condition where the PNA iswithin the height, hr, of the metal deck ribs.

Figure 4a: Rolled Steel Section with PNA within Height, hr, of Metal Deck,Positive Bending

Figure 4b: User-Define Steel Section with PNA within Height, hr, of MetalDeck, Positive Bending

��

��

CC 1


CC 2

TF T

TF B

TWeb

TC P


y pz p

��

��

CC 1


CC 2

TC P


TF B

TK B

TWeb

TK T

TF T

y pz p



Note that in Figures 3a through 4b, the concrete compression forces (CC1 andCC2) may have different magnitudes and locations (elevations) for the left andright sides of the beam.

PNA within the Beam Top FlangeFigures 5a and 5b show the internal forces for a rolled steel section and auser-defined steel section, respectively, for the condition where the PNA iswithin the beam top flange. The term y2, which is the distance from the top ofthe steel beam to the PNA, is shown in these figures and is defined by Equa-tion 5.

topyftopf

concsteel2 F2b

MPFMPFy

−−

−= Eqn. 5

Figure 5a: Rolled Steel Section with PNA within Beam Top Flange,Positive Bending

��

��

CC 1


CC 2

TF TTK T

TF B

TK B

TWeb

TC P


CF T

y 2

y pz p



Figure 5b: User-Defined Steel Section with PNA within Beam Top Flange,Positive Bending

PNA within the Beam Top FilletThe PNA lies within the beam top fillet only if the beam section is a rolled sec-tion. Figure 6 shows the internal forces for this condition.

Figure 6: Rolled Steel Section with PNA within Beam Top Fillet, PositiveBending

��

��

CC 1


CC 2

TF T

TF B

TWeb

TC P


CF T

y 2

y pz p

��

��

CC 1


CC 2

CK TTK T

TF B

TK B

TWeb

TC P


CF Ty 3

y pz p



The term y3, which is the distance from the bottom side of the beam topflange to the PNA, is shown in Figure 6 and is defined by Equation 6.

ywwidth

topyftopftopfconcsteel3 F2k

Ft2bMPFMPFy

−−−−−= Eqn. 6

PNA within the Beam WebFigures 7a and 7b show the internal forces for a rolled steel section and auser-defined steel section, respectively, for the condition where the PNA iswithin the beam web. The term y4, which for a rolled steel beam is the dis-tance from the web toe of the top fillet to the PNA, and for a user-definedbeam is the distance from the bottom side of the beam top flange to the PNA,is shown in Figures 7a and 7b and is defined by Equation 7.

yww

ywdepthwidth

yww

topyftopftopfconcsteel4

F2t

Fk2k

F2t

Ft2bMPFMPFy −

−−= −−−

Eqn. 7

The last term in Equation 7 only applies to rolled steel beams; it reduces tozero for user-defined beams.

Figure 7a: Rolled Steel Section with PNA within Beam Web, PositiveBending

��

��

CC 1


CC 2

CK T

CWeb

TF B

TK B

TWeb

TC P


CF T

y 4

y pz p



Figure 7b: User-Defined Steel Section with PNA within Beam Web,Positive Bending

PNA within the Beam Bottom FilletThe PNA is within the beam bottom fillet only if the beam section is a rolledsection. Figure 8 shows the internal forces for this condition.

Figure 8: Rolled Steel Section with PNA within Beam Bottom Fillet, Posi-tive Bending

��

��

CC 1


CC 2

CWeb

TF B

TWeb

TC P


CF T

y 4

y pz p

��

��

CC 1


CC 2

CK T

CK B

TF B

TK B

CWeb

TC P

CF T

y 5


y pz p



The term y5, which is the distance from the top side of the beam bottom filletto the PNA, is shown in Figure 8 and is defined by Equation 8.

ywwidth

yww

ywwidth

ywdepthwidth

ywwidth


F2k

F2ht

F2k

Fk2k

F2k

Ft2bMPFMPFy

−

−−−

= −−−

Eqn. 8

Note that it is unlikely that the PNA will be this low. It requires a very largebeam bottom flange and/or cover plate.

PNA within the Beam Bottom FlangeFigures 9a and 9b show the internal forces for a rolled steel section and auser-defined steel section, respectively, for the condition where the PNA lieswithin the beam bottom flange.

Figure 9a: Rolled Steel Section with PNA within Beam Bottom Flange,Positive Bending

��

��

CC 1


CC 2

CK T

CK B

TF B

CF B

CWeb

TC P

CF Ty 6


y pz p



Figure 9b: User-Defined Steel Section with PNA within Beam BottomFlange, Positive Bending

The term y6, which is the distance from the top of the beam bottom flange tothe PNA, is shown in Figure 9 and 9b and is defined by Equation 9.

bot-yfbot-f

yww

bot-yfbot-f

ywdepthwidth

bot-yfbot-f


F2b

F2ht

F2b

Fk4k

F2b

Ft2bMPFMPFy

−

−−−

= −−−

Eqn. 9

Note that it is unlikely that the PNA will be this low. It requires a very largebeam bottom flange and/or cover plate.

PNA within the Cover PlateFigures 10a and 10b show the internal forces for a rolled steel section and auser-defined steel section, respectively, for the condition where the PNA lieswithin the cover plate.

��

��


CC 1

CC 2

TF B

CF B

CWeb

TC P

CF T

y 6


y pz p



Figure 10a: Rolled Steel Section with PNA within Cover Plate, PositiveBending

Figure 10b: User-Defined Steel Section with PNA within Cover Plate, Posi-tive Bending

��

��

CC 1


CC 2

CK T

CK B

CCP

CF B

CWeb

TC P

CF T

y 7

Plastic neutral axis (PNA)y pz p

��

��

Beam Section Beam Elevation Beam Internal ForcesPlastic neutral axis (PNA)

CC 1

CC 2

CCP

CF B

CWeb

TC P

CF T

y 7

y pz p



The term y7, which is the distance from the top of the cover plate to the PNA,is shown in Figure 10a and 10b and is defined by Equation 10.

ycpcp

botyfbotfbotf

ycpcp

yww

ycpcp

ywdepthwidth

ycpcp


F2b

Ft2b

F2b

F2ht

F2b

Fk4k

F2b

Ft2bMPFMPFy

−−−

−−−

−−

−−−

=

Eqn. 10

Note that it is unlikely that the PNA will be this low. It requires an extremelylarge cover plate. In the event that the PNA were in the cover plate, the dis-tance yp would become negative.

Calculating the PNA LocationTo calculate the location of the PNA for positive bending, the program startsby comparing the value of MPFconc to that of MPFsteel to determine whether thePNA is in the steel section or in the concrete slab above the steel section. Asdescribed in an earlier section of this Technical Note, if MPFconc > MPFsteel, thePNA is within the concrete slab. If MPFsteel > MPFconc, the PNA is within thesteel section. If MPFsteel = MPFconc, the PNA is at the top of the steel beam.

If the PNA is in the concrete slab above the steel section, the procedure de-scribed in the previous subsection of this Technical Note entitled "PNA in theConcrete Slab Above the Steel Beam" is followed.

If the PNA is within the steel section, the program assumes that the PNA oc-curs in the top flange of the beam. The distance y2 is calculated using Equa-tion 5. The calculated distance y2 is then checked to see if it actually is withinthe beam top flange. If it is, the location of the PNA has been identified.

If the calculated distance y2 is not within the beam top flange, the programcontinues by assuming that the PNA occurs in the beam top fillet. (Note that ifthe beam is a user-defined beam, there is no top fillet and the program skipsdirectly to assuming that the PNA is in the beam web.) The distance y3 is cal-culated using Equation 6. The calculated distance y3 is then checked to see ifit actually is within the beam top fillet. If it does, the location of the PNA hasbeen identified.



If the calculated distance y3 is not within the beam top fillet, the programcontinues by assuming that the PNA occurs in the beam web. The distance y4

is calculated using Equation 7. The calculated distance y4 is then checked tosee if it actually is within the beam web. If it is, the location of the PNA hasbeen identified.

In any practical case, the PNA is not expected to be below the beam web.However, in the event the PNA has not yet been located, the program contin-ues down the beam section through the bottom fillet, the bottom flange andfinally the cover plate until the location of the PNA has been identified.

Plastic Moment Capacity for Positive BendingThe plastic moment capacity for positive bending in a composite section iscalculated from Equation 11:

∑

∑

=−

=− +=

10

1PiecepiecePNApiecebcpp

10

1PiecepiecePNApiecebcppnbcpp

xC

xTM

φ

φφ

Eqn. 11

where:

Cpiece = Compression force in a piece of the composite beam,kips.

Mn = Plastic moment capacity for positive bending, kip-in.

Tpiece = Tension force in a piece of the composite beam, kips.

xPNA-piece = Distance from centroid of tension or compression forcein a piece of a composite beam to the PNA, in.

φbcpp = Resistance factor for positive bending when plasticstress distribution is assumed, unitless.

In Equation 11, the ten pieces are:



Concrete above the metal deck, not including rebar, on the left sideof the beam: The concrete can only carry a compression force; tension isnot allowed in the concrete.

Concrete above the metal deck, not including rebar, on the rightside of the beam: The concrete can only carry a compression force; ten-sion is not allowed in the concrete.

Concrete within height of metal deck on the left side of the beam:The concrete can only carry a compression force; tension is not allowed inthe concrete.

Concrete within height of metal deck on the right side of the beam:The concrete can only carry a compression force; tension is not allowed inthe concrete.

Beam top flange: The force in the beam top flange can be tension, com-pression, or compression in the upper portion of the flange and tension inthe lower portion.

Beam top fillet: The force in the beam top fillet can be tension, compres-sion, or compression in the upper portion of the fillet and tension in thelower portion.

Beam web: The force in the beam web can be tension, compression, orcompression in the upper portion of the web and tension in the lower por-tion.

Beam bottom fillet: The force in the beam bottom fillet can be tension,compression, or compression in the upper portion of the fillet and tension inthe lower portion.

Beam bottom flange: The force in the beam bottom flange can be ten-sion, compression, or compression in the upper portion of the flange andtension in the lower portion.

Cover plate: The force in the cover plate can be tension, or compression inthe upper portion of the cover plate and tension in the lower portion.

In Equation 11 the values used for Tpiece, Cpiece and xPNA-piece depend on the lo-cation of the PNA. The appropriate values for these items are given in Tables



2 through 11. Table 1 serves as a guide to which of those tables to use basedon the location of the PNA.

Note, because the metal deck and concrete slab can be in different locationsrelative to the PNA on the two sides of the beam, you may need to use valuesfrom two different tables listed in Table 1.

Table 1:Table to determine which table to use in conjunction with Equation 11 to determinethe plastic moment capacity of composite section for positive bending.

Location of PNA Table

Above rebar in concrete above metal deck 2

In concrete within metal deck 3

In beam top flange 4

In beam top fillet 5

In beam web 6

In beam bottom fillet 7

In beam bottom flange 8

In cover plate 9

Table 2:When the PNA is above the centroid of the rebar in the concrete above the metal deck,use the equations specified in this table together with Equation 11 to determine theplastic moment capacity of composite section for positive bending.

Piece T xPNA C xPNA

Concrete above metal deck (left) N. A. N. A. 12a 21a

Concrete above metal deck (right) N. A. N. A. 12a 21a

Concrete in metal deck (left) N. A. N. A. 0 N. A.

Concrete in metal deck (right) N. A. N. A. 0 N. A.

Beam top flange 15a 23a 0 N. A.

Beam top fillet 16a 24a 0 N. A.

Beam web 17a 25a 0 N. A.

Beam bottom fillet 18a 26a 0 N. A.

Beam bottom flange 19a 27a 0 N. A.

Cover plate 20a 28a 0 N. A.



Table 3:When the PNA is in the concrete within the metal deck, use the equations specified inthis table together with Equation 11 to determine the plastic moment capacity of com-posite section for positive bending.

Piece T xPNA C xPNA

Concrete above metal deck (left) N. A. N. A. 12b 21b

Concrete above metal deck (right) N. A. N. A. 12b 21b

Concrete in metal deck (left) N. A. N. A. 14a 22a

Concrete in metal deck (right) N. A. N. A. 14a 22a

Beam top flange 15a 23a 0 N. A.






Table 4:When the PNA is in the beam top flange, use the equations specified in this table to-gether with Equation 11 to determine the plastic moment capacity of composite sectionfor positive bending.

Piece T xPNA C xPNA



Concrete in metal deck (left) N. A. N. A. 14b 22b


Beam top flange 15b 23b 15c 23c








Table 5:When the PNA is in the beam top fillet, use the equations specified in this table togetherwith Equation 11 to determine the plastic moment capacity of composite section forpositive bending.

Piece T xPNA C xPNA




Concrete in metal deck (right) N. A. N. A. 14b 22b

Beam top flange 0 N. A. 15d 23d

Beam top fillet 16b 24b 16c 24c





Table 6:When the PNA is in the beam web, use the equations specified in this table togetherwith Equation 11 to determine the plastic moment capacity of composite section forpositive bending.

Piece T xPNA C xPNA






Beam top fillet 0 N. A. 16d 24d

Beam web 17b 25b 17c 25c






Table 7:When the PNA is in the beam bottom fillet, use the equations specified in this table to-gether with Equation 11 to determine the plastic moment capacity of composite sectionfor positive bending.

Piece T xPNA C xPNA







Beam web 0 N. A. 17d 25d

Beam bottom fillet 18b 27b 18c 26c



Table 8:When the PNA is in the beam bottom flange, use the equations specified in this tabletogether with Equation 11 to determine the plastic moment capacity of composite sec-tion for positive bending.

Piece T xPNA C xPNA








Beam bottom fillet 0 N. A. 18d 26d

Beam bottom flange 19b 27b 19c 27c




Table 9:When the PNA is in the cover plate, use the equations specified in this table togetherwith Equation 11 to determine the plastic moment capacity of composite section forpositive bending.

Piece T xPNA C xPNA








Beam bottom fillet 0 N. A. 18d 26d

Beam bottom flange 0 N. A. 19d 27d

Cover plate 20b 28b 20c 28c

Equations 12a and 12b are used for the compression force in the concreteabove the metal deck. Note that these equations are applied to each side ofthe beam separately.

CC1 = 0.85 f'c beff zp Eqn. 12a

CC1 = 0.85 f'c beff tc Eqn. 12b

Note that for partial composite connection Equation 12b is replaced withEquation 3 of Composite Beam Design AISC-LRFD93 Technical Note 37 PartialComposite Connection with a Plastic Stress Distribution.

Equations 13a and 13b are used for the tension and compression forces in therebar in the concrete slab above the metal deck. Note that these equationsare applied to each side of the beam separately.

TR = ArFyr Eqn. 13a

CR = ArFyr Eqn. 13b



Equations 14a and 14b are used for the compression force in the concretewithin the metal deck. Note that these equations are applied to each side ofthe beam separately. Also note that these equations only apply if the span ofthe metal deck ribs is oriented parallel to the beam span. If the metal deckribs are oriented perpendicular to the beam span, there is no compressionforce allowed on the concrete within the metal deck ribs.

( )r

cpreff

'cC2 S

tzwb0.85fC

−= Eqn. 14a

r

rreff

'cC2

S

hwb0.85fC = Eqn. 14b

Note that for partial composite connection Equation 14b is replaced withEquation 4 in Composite Beam Design AISC-LRFD93 Technical Note 37 PartialComposite Connection with a Plastic Stress Distribution.

Equations 15a through 15d are used for the tension and compression forcesin the beam top flange.

TFT = bf-top tf-top Fyf-top Eqn. 15a

TFT = bf-top (tf-top - y2) Fyf-top Eqn. 15b

CFT = bf-top y2 Fyf-top Eqn. 15c

CFT = bf-top tf-top Fyf-top Eqn. 15d

Equations 16a through 16d are used for the tension and compression forcesin the beam top fillet. Note that these equations do not apply to user-definedsections.

TKT = kwidth kdepth Fyw Eqn. 16a

TKT = kwidth (kdepth - y3) Fyw Eqn. 16b

CKT = kwidth y3 Fyw Eqn. 16c

CKT = kwidth kdepth Fyw Eqn. 16d



Equations 17a through 17d are used for the tension and compression forcesin the beam web.

TWeb = tw h Fyw Eqn. 17a

TWeb = tw (h - y4) Fyw Eqn. 17b

CWeb = tw y4 Fyw Eqn. 17c

CWeb = tw h Fyw Eqn. 17d

Equations 18a through 18d are used for the tension and compression forcesin the beam bottom fillet. Note that these equations do not apply to user-defined sections.

TKB = kwidth kdepth Fyw Eqn. 18a

TKB = kwidth (kdepth - y5) Fyw Eqn. 18b

CKB = kwidth y5 Fyw Eqn. 18c

CKB = kwidth kdepth Fyw Eqn. 18d

Equations 19a through 19d are used for the tension and compression forcesin the beam bottom flange.

TFB = bf-bot tf-bot Fyf-bot Eqn. 19a

TFB = bf-bot (tf-bot - y6) Fyf-bot Eqn. 19b

CFB = bf-bot y6 Fyf-bot Eqn. 19c

CFB = bf-bot tf-bot Fyf-bot Eqn. 19d

Equations 20a through 20c are used for the tension and compression forces inthe cover plate.

TCP = bcp tcp Fycp Eqn. 20a

TCP = bcp (tcp - y7) Fycp Eqn. 20b

CCP = bcp y7 Fycp Eqn. 20c



Equations 21a and 21b are used for the distance from the center of the forcein the concrete above the metal deck to the PNA. Note that these equationsare applied to each side of the beam separately.

xPNA = 2

zp Eqn. 21a

xPNA = 2

tz cp − Eqn. 21b

Note that for partial composite connection Equation 21b is replaced withEquation 5 in Composite Beam Design AISC-LRFD93 Technical Note 37 PartialComposite Connection with a Plastic Stress Distribution.

Equations 22a and 22b are used for the distance from the center of the forcein the concrete within the metal deck ribs to the PNA. Note that these equa-tions are applied to each side of the beam separately.

xPNA = 2

tz cp −Eqn. 22a

xPNA = 2

htz rcp −− Eqn. 22b

Note that for partial composite connection, Equation 22b is replaced withEquation 6 in Composite Beam Design AISC-LRFD93 Technical Note 37 PartialComposite Connection with a Plastic Stress Distribution.

Equations 23a through 23d are used for the distance from the center of theforce(s) in the beam top flange to the PNA.

xPNA = 2

tdy

top-fp +− Eqn. 23a

xPNA = 2

y-t 2top-f Eqn. 23b

xPNA = 2

y2 Eqn. 23c



xPNA = 2

trhtz

topfdrcp

−−−−− Eqn. 23d

Note the terms zp, tc, hr and rd in Equation 23d must all be for the left side ofthe beam or all for the right side of the beam. It does not matter which sideof the beam is used, but all of the terms must be consistent.

Equations 24a through 24d are used for the distance from the center of theforce(s) in the beam top fillet to the PNA.

xPNA = 2

ktdy

depthtopfp ++− − Eqn. 24a

xPNA = 2

y-k 3depth Eqn. 24b

xPNA = 2

y3 Eqn. 24c

xPNA = 2

ktrhtz

depthtopfdrcp −−−−− − Eqn. 24d


Equations 25a through 25d are used for the distance from the center of theforce(s) in the beam web to the PNA.

xPNA = 2

hktdy depthtopfp +++− − Eqn. 25a

xPNA = 2

y-h 4 Eqn. 25b

xPNA = 2

y4 Eqn. 25c

xPNA = 2

hktrhtz depthtopfdrcp −−−−−− − Eqn. 25d




Equations 26a through 26d are used for the distance from the center of theforce(s) in the beam bottom fillet to the PNA.

xPNA = h2

3ktdy

depthtopfp +++− − Eqn. 26a

xPNA = 2

y-k 5depth Eqn. 26b

xPNA = 2

y5 Eqn. 26c

xPNA = h2

3ktrhtz

depthtopfdrcp −−−−−− − Eqn. 26d


Equations 27a through 27d are used for the distance from the center of theforce(s) in the beam bottom flange to the PNA.

xPNA = 2

th2ktdy bot-f

depthtopfp ++++− − Eqn. 27a

xPNA = 2

y-t 6bot-f Eqn. 27b

xPNA = 2

y6 Eqn. 27c

2

t-h2k

trhtzx

bot-fdepth

topfdrcpPNA

−

−−−−−= −

Eqn. 27d




Equations 28a through 28c are used for the distance from the center of theforce(s) in the cover plate to the PNA.

2

tth

2ktdyx

cpbot-f

depthtopfpPNA

++

+++−= −

Eqn. 28a

xPNA = 2

y-t 7cp Eqn. 28b

xPNA = 2

y7 Eqn. 28c

Composite Section Elastic Moment Capacity Technical Note 35 - 1



Technical Note 35Composite Section Elastic Moment Capacity

This Technical Note describes how the program calculates the moment capac-ity of a composite section when an elastic stress distribution is assumed.

Positive Moment Capacity with an Elastic StressDistributionTo calculate the positive moment capacity with an elastic stress distribution,the program first calculates the location of the elastic neutral axis (ENA) andthe transformed section moment of inertia. Information on how the programcalculates the location of the ENA and the transformed section moment of in-ertia for full composite connection is provided in Composite Beam DesignAISC-ASD89 Technical Note 20 Transformed Section Moment of Inertia. In-formation on how the program calculates the location of the ENA and thetransformed section moment of inertia for partial composite connection isprovided in Composite Beam Design AISC-ASD89 Technical Note 21 ElasticStresses with Partial Composite Connection.

The positive moment capacity for a composite beam with an elastic stressdistribution is determined by considering five locations in the composite sec-tion. These locations are:

The top of the concrete on the left side of the beam.

The top of the concrete on the right side of the beam.

The top of the top flange of the beam.

The bottom of the bottom flange of the beam.

The bottom of the cover plate.

A moment capacity is calculated based on the allowable stress and the sectionmodulus at each of these five locations that is applicable to the beam consid-ered. The smallest moment capacity calculated is the positive moment capac-

Composite Section Elastic Moment Capacity Composite Beam Design AISC-LRFD93

Technical Note 35 - 2 Composite Section Elastic Moment Capacity

ity for the beam. Figure 1 illustrates the allowable stress assumed for each ofthese locations.

Figure 1: Allowable Stresses for Positive Bending at Various Key Locations ofthe Composite Beam Section

Equations 1a through 1e are used to calculate the positive moment capacityat the seven key locations in the beam section. Table 1 lists the location towhich each equation applies. Note that in these equations, if there is fullcomposite connection, the term y is substituted for the term yeff.

Table 1:Table to determine which of Equations 1a through 1e apply to a particular location ina composite beam

Location in Beam Equation

Top of concrete on left side of beam 1a

Top of concrete on right side of beam 1b

Top of beam top flange 1c

Bottom of beam bottom flange 1e

Bottom of cover plate 1f

�� h r

t cd

t cp

y eff

Elastic neutral axis (ENA)

Fycp

Fyf-bot

Fyf-top

Fyr

0.85f’cEsEc

Composite BeamAllowable Elastic

Stress at Key Points

Compression

Tension

Note: For a fully composite beam yeff = y.

Composite Beam Design AISC-LRFD93 Composite Section Elastic Moment Capacity

Composite Section Elastic Moment Capacity Technical Note 35 - 3

++

=

effleft-cleft-r

eff

left-c

s'left-cbcpenbcpe

y-thd

I

*E

E0.85fM φφ

Eqn. 1a

++

=

effright-cright-r

eff

left-c

s'right-cbcpenbcpe

y-thd

I

*E

E0.85fM φφ

Eqn. 1b

In Equation 1c, the term "ABS" means to take the absolute value of theamount in the associated brackets.

[ ]eff

efftop-yfbcpenbcpe y-dABS

IFM φφ = Eqn. 1c

eff

effbot-yfbcpenbcpe y

IFM φφ = Eqn. 1d

cpeff

effycpbcpenbcpe ty

IFM

+= φφ Eqn. 1e

The positive moment capacity of a composite beam with an elastic stress dis-tribution is the smallest of the moment capacities obtained from the equationsincluded in Equations 1a through 1e that are applicable to the beam consid-ered. If the denominator of Equation 1c is zero, the program does not need toconsider the moment capacity associated with that equation.

Note that the term φbcpe in these equations is the resistance factor for positivebending in a composite beam when Mn is determined from an elastic stressdistribution.

Moment Capacity for Steel Section Alone Technical Note 36 - 1



Technical Note 36Moment Capacity for Steel Section Alone

This Technical Note describes how the program calculates the moment capac-ity of a noncomposite steel beam, including a cover plate, if applicable.

OverviewThe program only calculates the moment capacity, Mn, if the beam is compactor noncompact. It does not calculate Mn if the section is slender.

The plastic moment, Mp, for a noncomposite rolled steel beam section withouta cover plate is calculated as Mp = ZFy.

The exact methodology used to compute the plastic moment capacity in theother cases depends on whether the beam, including the cover plate if it ex-ists, is doubly or singly symmetric, and whether the beam web is classified ascompact or noncompact.

Figure 1 shows a flowchart that directs you to the appropriate section in thischapter for calculating the moment capacity of the steel section alone. Thefigure has boxes labeled a through g; start in the box labeled a. Note that thecriteria used by the program to determine if a section is compact or noncom-pact for the AISC-LRFD93 specification is described in Composite Beam De-sign AISC-LRFD93 Technical Note 33 Compact and Noncompact Require-ments.

Steel Beam PropertiesIf properties for the steel section alone are available directly from the pro-gram's section database, then those properties are used to compute the mo-ment capacity. For other cases such as a user-defined section or a sectionwith a cover plate, the section properties are calculated in a manner similar tothat described in Composite Beam Design AISC-ASD89 Technical Note 20Transformed Section Moment of Inertia, except that there is no concrete orreinforcing steel to consider.

Moment Capacity for Steel Section Alone Composite Beam Design AISC-LRFD93

Techn

Aftediuspeatminesectsectsumplica

MoChFiguto caalon

Infopactcal N

The that

Is section doublysymmetric or a

No Is the beam web No Is the beam web No Beam section is

channel?

Yes

Refer to“Moment

Capacity for aDoubly Symmetric

Beam or aChannel Section”

in thisTechnical Note.

compact?

Yes

noncompact?

Yes

classified asslender and is notdesigned. Go to

next trial section.

Refer to“Moment

Capacity for aSingly Symmetric

Beam with aCompact Web”

in thisTechnical Note.

Refer to“Moment

Capacity for aSingly Symmetric

Beam with aNoncompactWeb” in this

Technical Note.

a b c

d

e f g

Figure 1: Flowchart For Determining Which Section of this Chapter Applies inCalculating Plastic Moment for Steel Section Alone

ical Note 36 - 2 Moment Capacity for Steel Section Alone

r the moment of inertia has been calculated, the section moduli and ra- of gyration are calculated using standard formulas. This process is re-ed to get properties about both axes. The torsional constant is deter-d by summing the torsional constants for the various components of the

ion. For example, it may be determined by summing the J's of a rolledion and the cover plate, if applicable, or in a user-defined section, byming the J's for the top flange, web, bottom flange and cover plate, if ap-ble.

ment Capacity for a Doubly Symmetric Beam or aannel Sectionre 2 shows a flowchart that determines the equations the program useslculate Mn for a doubly symmetric steel section alone or a channel sectione. The figure has boxes labeled a through k; start in the box labeled a.

rmation relating to how the program calculates the compact and noncom- section requirements is in Composite Beam Design AISC-LRFD93 Techni-ote 33 Compact and Noncompact Requirements.

following subsection discusses the unbraced length checks in the program are used to determine how to calculate Mn for a doubly symmetric beam

Composite Beam Design AISC-LRFD93 Moment Capacity for Steel Section Alone

Are the web,compressionflange and

compressioncover platecompact?

Yes

No

Is Lb ≤ Lp?

Yes

Is Lb ≤ Lr?No

Yes

Determine Mnbased on smallestof yielding criteriain AISC-LRFD93Section F1.1 andlateral torsionalbuckling criteriain AISC-LRFD93

Section F1.2a.

No

Determine Mnbased on yieldingcriteria in AISC-LRFD93 Section

F1.1.

Is Lb ≤ Lr?

Yes

Determine Mnbased on smallestof yielding criteriain AISC-LRFD93

Section F1.1,lateral torsionalbuckling criteriain AISC-LRFD93Section F1.2a and

flange and weblocal buckling

criteria in AISC-LRFD93 AppendixF1(b) equation (A-

F1-3).

Are thecompressionflange and


Yes

No

Beam section notdesigned. Go to

next trial section.

No

Is the webnoncompact?

No

Yes

a

b

c

d

e

f

g

h

i

j

k


next trial section.

Figure 2: Flowchart For Calculating Mn for a Doubly Symmetric SteelSection Alone or a Rolled Channel Steel Section Alone

Moment Capa

or a channtions ment

Lateral UnbThe unbrathese item

city for Steel Section Alone Technical Note 36 - 3

el section. Subsequent subsections discuss each of the code sec-ioned in Figure 2 that are used to calculate the moment capacity.

raced Length Checksced lengths listed in Figure 2 are Lb, Lp and Lr. Definitions of each ofs are listed below.


Technical Note 36 - 4 Moment Capacity for Steel Section Alone

Lb = Laterally unbraced length of beam; length between pointswhich are braced against lateral displacement of the com-pression flange, in.

Lp = Limiting laterally unbraced length of beam for full plasticbending capacity, in.

Lr = Limiting laterally unbraced length of beam for inelastic lat-eral-torsional buckling, in.

The unbraced length of a beam, or a beam segment, Lb is determined fromthe input data. The limiting unbraced length for full plastic capacity, Lp, isdetermined from Equation 1 which is also Equation F1-4 in AISC-LRFD93.

yf

yp

F

300rL = Eqn. 1

In Equation 1, ry is taken for the steel beam section including the cover plate,if applicable. The Fyf term in Equation 1 is for the compression flange.

The limiting unbraced length for lateral torsional buckling, Lr, is determinedfrom Equation 2 which is also Equations F1-6 through F1-8 in AISC-LRFD93.

ywryfL

2x

y

w2

x1

2L2

L

1yr

Fand)F(FofsmallerF

GJ

S

I

C4Xand

2

EGJA

S

πX

where,FX11F

XrL

−=

==

++=

Eqn. 2

In Equation 2, Fr, the compressive residual stress in the flange is taken as 10ksi for rolled shapes and 16.5 ksi for user-defined shapes. The warping con-stant, Cw, is based on the steel beam alone ignoring the cover plate if it ex-ists. For rolled sections, including channels, the program takes Cw from itsbuilt-in database. For user-defined sections Cw is calculated using Equation 3.Note that Equation 3 actually applies to symmetrical sections but it is alsoused when the flanges have different dimensions.



4

2

t

2

tdI

C

2

botftopfy

w

−−

=

−−

Eqn. 3

Yielding Criteria in AISC-LRFD93 Section F1.1The yielding criteria is that Mn = Mp. The process for determining Mp has beenpreviously described in the section entitled "Overview" in this technical note.

Lateral Torsional Buckling Criteria in AISC-LRFD93 Section F1.2aThe lateral torsional buckling criteria in AISC LRFD F1.2a is based on AISC-LRFD93 Equation F1-2. In this case Mn is given by Equation 4.

( ) pMLL

LLMMMCM

pr

pbrppbn ≤

−−

−−= Eqn. 4

In Equation 4, Cb is calculated using Equation 5, which is also AISC-LRFD93Equation F1-3.

CBAmax

maxb

3M4M3M2.5M

12.5MC

+++= Eqn. 5

Refer to the notation in Composite Beam Design AISC-LRFD93 Technical Note29 General and Notation for an explanation of the terms in Equation 5.

In Equation 4, Lr is calculated using Equation 2, Lp is calculated from Equation1 and Mr comes from Equation 6.

xLr SFM = Eqn. 6

where FL is as described for Equation 2.

AISC-LRFD Appendix F1(b) Equation A-F1-3The limit state for flange and web local buckling is based on AISC-LRFD93Equation A-F1-3, which is shown herein as Equation 7.

( )

−−

−−=pr

p

λλλλ

rppn MMMM Eqn. 7

Equation 7 applies to both flange local buckling and web local buckling.



Flange Local BucklingFor flange local buckling using Equation 7:

Mr is calculated per Equation 6.

λ is equal to bf /(2tf) for I-sections and bf/tf for channels. The bf and tf

terms are for the compression flange.

λp is given by Equation 8a if the section is a rolled or user-defined I-section, or Equation 8b if the section is a rolled channel. The Fyf in theseequations is for the compression flange.

yff

f

F

65

2t

b ≤ Eqn. 8a

yff

f

F

65

t

b ≤ Eqn. 8b

λr is given by Equation 9a if the section is a rolled beam or channel, orEquation 9b if it is a user-defined section.

LF

141=rλ , for rolled shapes Eqn. 9a

c

Lk

F

162=rλ , for user-defined shapes Eqn. 9b

In Equation 9a and 9b, FL is as defined for Equation 2. In Equation 9b,

wc th4k = but not less than 0.35 ≤ kc ≤ 0.763. Equations 9a and 9b are

taken from AISC-LRFD93 Table A-F1.1.

Web Local BucklingFor web local buckling using Equation 7:

Mr is calculated using Equations 10 and 11 for both the top and bottomflanges separately. The smaller value of Mr is used.

Mr = ReFyfSx Eqn. 10



In Equation 10, Re is equal to 1.0 for rolled shapes and is given by Equation11 for user-defined shapes. Equation 10 is taken from AISC-LRFD93 Table A-F1.1.

( )1.0

2a12

m3ma12R

r

3r

e ≤+

−+= Eqn. 11

Equation 11 comes from the definition of Re given with Equation A-G2-3 inAISC-LRFD93 Appendix G. In Equation 11 the term ar is the ratio of the webarea (htw) to the flange area (bftf), but not more than 10, and m is the ratioof the web yield stress to the flange yield stress.

λ is equal to h/tw.

λp is given by Equation 5a, or 5b in Composite Beam Design AISC-LRFD93Technical Note 33 Compact and Noncompact Requirements depending onthe axial load in the member, if any. See the description accompanyingthese equations for more information.

λr is given by one of Equations 6 and 7 in Composite Beam Design AISC-LRFD93 Technical Note 33 Compact and Noncompact Requirements de-pending on the type of member and the amount of axial compression, ifany. See the description accompanying these equations for more informa-tion.

Moment Capacity for a Singly Symmetric Beam with aCompact WebFigure 3 shows a flowchart that determines the equations the program usesto calculate Mn for a singly symmetric steel section alone with a compact web.The figure has boxes labeled a through n; start in the box labeled a.

Most of the formulas associated with this flowchart are based on AISC-LRFD93 Specification Appendix F section F1and Table A-F1.1.

Information relating to how the program calculates the compact and noncom-pact section requirements is in Composite Beam Design AISC-LRFD93 Techni-cal Note 33 Compact and Noncompact Requirements.


T

Tisot

AF

AF

Yes

Determine Mnbased on smallestof the followingAISC-LRFD93

Appendix Fequations:

A-F1-1 for WLBA-F1-1 for FLBA-F1-1 for LTB.

Is web compact?

Yes

Is beam compactfor LTB?

Yes

No

No Is beamnoncompact for

LTB?

No






Yes

No

Yes





Yes


LTB?

No




No

Note: WLB = Web local bucklingFLB = Flange local bucklingLTB = Lateral torsional buckling

This is the wrongflowchart. See

Figure 1.a

b

c

d

e

g

h

i

j

k

l

m

n


next trial section.


next trial section.Yes f


compressioncover plate

noncompact?

Figure 3: Flowchart For Calculating Mn for a Singly Symmetric Steel SectionAlone with a Compact Web

echnical

he folln the pymmetf the Ahat are

ISC-LRor this

ISC-LRor this

Note 36 - 8 Moment Capacity for Steel Section Alone

owing subsection describes the lateral torsional buckling (LTB) checksrogram that are used to determine how to calculate Mn for a singlyric beam with a compact web. Subsequent subsections describe eachISC-LRFD93 Specification Appendix F equations mentioned in Figure 3 used to calculate the moment capacity.

FD93 Equation A-F1-1 for WLB case Mn is equal to Mp, the plastic moment capacity of the section.

FD93 Equation A-F1-1 for FLB case Mn is equal to Mp, the plastic moment capacity of the section.



AISC-LRFD93 Equation A-F1-3 for FLBAISC-LRFD93 Equation A-F1-3 for flange local buckling is interpreted by theprogram as shown in Equations 12a through 12f.

( ) prppn MMMMM ≤

−−

−−=pr

p

λλλλ

Eqn. 12a

where

xLr SFM = Eqn. 12b

f

f

2t

b=λ Eqn. 12c

yfp F

65=λ Eqn. 12d

L

rF

141=λ , rolled beams and channels Eqn. 12e

c

L

k

F

162=rλ , user-defined beams Eqn. 12f

In Equation 12b, FL and Sx are for the beam compression flange (not coverplate).

In Equations 12c and 12d, bf, tf and Fyf are for the beam compression flange(not cover plate).

In Equation 12e, FL is for the beam compression flange (not cover plate).

In Equation 12f, FL is for the beam compression flange (not cover plate), and

wc th4k = but not less than 0.35 ≤ kc ≤ 0.763.

AISC-LRFD93 Equation A-F1-1 for LTBFor this case Mn is equal to Mp, the plastic moment capacity of the section.



AISC-LRFD93 Equation A-F1-2 for LTBAISC-LRFD93 Equation A-F1-2 for lateral torsional buckling is interpreted bythe program as shown in Equations 13a through 13d and Equations 14athrough 14c.

( ) prppbn MMMMCM ≤

−−

−−=pr

p

λλλλ

Eqn. 13a

where,

xtyfxcLr SFSFM ≤= Eqn. 13b

yc

b

r

L=λ Eqn. 13c

yf

pF

300=λ Eqn. 13d

The term λr in Equation 13a is the value of λ for which Mcr as defined byEquations 14a through 14c is equal to the smaller of FLSxc and FyfSxt where FL

is the smaller of (Fyf - Fr) and Fyw. When calculating FL, the term Fyf is theyield stress of the compression flange and when calculating FyfSxt, the term Fyf

is the yield stress of the tension flange.

( ) ( )

+++= 2

121yb

cr BB1BJIL

157000M Eqn. 14a

where,

J

I

L

h1

I

I22.25B

y

by

yc1

−

= Eqn. 14b

2

b

yc

y

yc2 L

h

J

I

I

I125B

−= Eqn. 14c



To calculate λr for Equation 13a, the program determines the value of Lb forwhich Mcr is equal to the smaller of FLSxc and FyfSxt. Then it divides that valueof Lb by ryc to get λr.

Moment Capacity for a Singly Symmetric Beam with aNoncompact WebFigure 4 shows a flowchart that determines the equations the program usesto calculate Mn for a singly symmetric steel section alone with a noncompactweb. The figure has boxes labeled a through n; start in the box labeled a.

Most of the formulas associated with this flowchart are based on AISC-LRFD93 Specification Appendix F section F1and Table A-F1.1.

Figure 4: Flowchart for Calculating Mn for a Singly Symmetric SteelSection Alone with a Noncompact Web

Yes




Is webnoncompact?

Yes


Yes

No


LTB?

No




Yes



Yes

No

Yes





Yes


LTB?

No




No

Note: WLB = Web local bucklingFLB = Flange local bucklingLTB = Lateral torsional buckling

This is the wrongflowchart. See

Figure 1.a

b

c

d

e

f

g

h

i

j

k

l

m

n


next trial section.


next trial section.


compressioncover plate

noncompact?



Information relating to how the program calculates the compact and noncom-pact section requirements is in Composite Beam Design AISC-LRFD93 Techni-cal Note 33 Compact and Noncompact Requirements.

The lateral torsional buckling checks and all but one of the Appendix F equa-tions mentioned in Figure 4 are described in the previous section entitled,"Moment Capacity for a Singly Symmetric Beam with a Compact Web." Referto that section for more information.

The one equation that has not been described previously is AISC-LRFD93Specification Appendix F Equation A-F1-3. This equation is described in thefollowing subsection.

AISC-LRFD93 Equation A-F1-3 for WLBAISC-LRFD93 Equation A-F1-3 for web local buckling is interpreted by theprogram as shown in Equations 15a through 15g.

( ) prppn MMMMM ≤

−−

−−=pr

p

λλλλ

Eqn. 15a

In Equation 15a:

Mr is calculated using Equations 15b and 15c for both the top and bottomflanges separately. The smaller value of Mr is used.

Mr = ReFyfSx Eqn. 15b

In Equation 15b, Re is given by Equation 15c. Equation 15b is taken fromAISC-LRFD93 Table A-F1.1.

( )1.0

2a12

m3ma12R

r

3r

e ≤+

−+= Eqn. 15c

Equation 15c comes from the definition of Re given with Equation A-G2-3 inAISC-LRFD93 Appendix G. In Equation 15c, the term ar is the ratio of the webarea (htw) to the flange area (bftf), but not more than 10, and m is the ratioof the web yield stress to the flange yield stress.

λ is equal to h/tw.



λp is given by Equation 15d, or 15e depending on the axial load in themember, if any.

0.125P

Pfor,

P

P75.21

F

640

y

u

y

u

y

p ≤

−=

bb φφλ Eqn. 15d

0.125P

Pfor

,F

253

P

P33.2

F

191

y

u

yy

u

y

p

>

≥

−=

b

b

φ

φλ

Eqn. 15e

λr is given by either Equation 15f or Equation 15g.

Equation 15f defines λr for beams with equal sized flanges.

−=

y

u

y

r P

.74P01

F

970

bφλ Eqn. 15f

In Equation 15f, the value of Fy used is the largest of the Fy values for thebeam flanges and the web.

Equation 15g defines the noncompact section limit for webs in beams withunequal size flanges:

2

3

h

h

4

3

where,

,P

.74P01

h

h83.21

F

253

c

y

u

cy

r

≤≤

−

+=

bφλ

Eqn. 15g

In Equation 15g, the value of Fy used is the largest of the Fy values for thebeam flanges and the web. Equation 15g is based on Equation A-B5-1 in theAISC-LRFD93 specification.

Partial Composite Connection with a Plastic Stress Distribution Technical Note 37 - 1



Technical Note 37Partial Composite Connection with a Plastic

Stress Distribution

Partial composite connection for an elastic stress distribution is described inComposite Beam Design AISC-ASD89 Technical Note 21 Elastic Stresses withPartial Composite Connection and Composite Beam Design AISC-LFRD93Technical Note 35 Composite Section Elastic Moment Capacity. This TechnicalNote describes partial composite connection for a plastic stress distribution. Inparticular, it describes how the positive moment capacity of the compositebeam using a plastic stress distribution is calculated for partial compositeconnection.

Estimating the Required Percent Composite ConnectionThe program uses Equation 1 to estimate the required percent compositeconnection (PCC) for a composite beam.

X%*MM

MMPCC

2

beamsteelncomp%Xn

beamsteelnu

−−

=φφ

φEqn. 1

where,

PCC = Required percent composite connection, unitless.

Mu = Required flexural strength, that is, the applied factoredmoment, kip-in.

Mn X% comp = Nominal flexural strength (capacity) of composite sectionwith X% composite connection, kip-in.

Mn steel beam = Nominal flexural strength (capacity) of the steel beamsection alone as determined from Composite Beam DesignAISC-LRFD93 Technical Note 36 Moment Capacity forSteel Section Alone, kip-in.

Partial Composite Connection with a Plastic Stress Distribution Composite Beam Design AISC-LRFD93

Technical Note 37 - 2 Partial Composite Connection with a Plastic Stress Distribution

X% = Percent composite connection that Mn X% comp is basedon, unitless. For 50% composite connection use X% =0.50.

φ = Resistance factor that was used when calculating Mn forfull composite connection, unitless. It is either φbcpe orφbcpp.

Equation 1 is based on Example 3 in Vogel (1991). Equation 1 might be con-sidered the LRFD equivalent to Equation 2 in Composite Beam Design AISC-ASD89 Technical Note 21 Elastic Stresses with Partial Composite Connection,with some rearrangement of terms.

The program initially uses Equation 1 with Mn X% comp equal to the Mn for full(100%) composite connection to estimate the required percent compositeconnection (PCC) for a composite beam. The program checks the moment ca-pacity using this PCC. If the moment capacity is adequate, the iteration iscomplete. If the moment capacity is not adequate, the program calculates anew PCC, using the last considered PCC for X% and Mn X% comp, and deter-mines a new moment capacity. This process continues until a PCC that pro-vides an adequate moment capacity is found.

Calculating MPFconc

The program calculates MPFconc as the smaller of the values obtained from theequations specified in Table 1 for the particular circumstances of the beamconsidered.

Table 1:Table identifying equations to be used to calculate initial value of ΣQn for partial com-posite connection

Deck Orientation

Beam Type Deck Ribs Parallelto Beam Span

Deck Ribs Perpendicularto Beam Span, or

No Metal Deck Exists(Solid Concrete Slab)

Rolled Beam from Database 2b, 2c 2a, 2c

User-Defined Beam 2b, 2d 2a, 2d

Composite Beam Design AISC-LRFD93 Partial Composite Connection with a Plastic Stress Distribution


MPFconc = (PCC) [(0.85f'c beff tc)left + (0.85f'c beff tc)right] Eqn. 2a

MPFconc = (PCC) [(0.85f'c beff

+

r

rrc S

hwt left +

(0.85f'c beff

+

r

rrc S

hwt right ] Eqn. 2b

MPFconc = (PCC) (AsFy + bcp tcp Fycp) Eqn. 2c

MPFconc = (PCC) (bf-toptf-topFyf-top +

twh + bf-bottf-botFyf-bot + bcp tcp Fycp) Eqn. 2d

In Equations 1a through 1d, the term PCC is the percent composite connec-tion. For 50 percent composite connection PCC is 0.5, not 50. The next sub-section describes how the program initially estimates PCC.

Location of the PNAThe location of the PNA for partial composite connection with a plastic stressdistribution is calculated using the method described in Composite Beam De-sign AISC-LFRD93 Technical Note 34 Composite Plastic Moment Capacity forPositive Bending for full composite connection except that the value used forMPFconc is that obtained from one of Equations 2a through 2d, as appropriate,instead of that obtained from Equation 3a or 3b of Composite Beam DesignAISC-LFRD93 Technical Note 34 Composite Plastic Moment Capacity for Posi-tive Bending, as appropriate.



Determining the Effective Portion of the Concrete SlabWhen different composite decks and or spans are specified on each side ofthe beam, the effective portion of the slab is determined as follows: The pro-gram first puts the following six items in order, from highest elevation to low-est, to determine how much of the concrete slab is effective for partial com-posite connection:

Top of concrete slab on the left side of the beam.

Top of concrete slab on the right side of the beam.

Top of metal on the left side of the beam.

Top of metal on the right side of the beam.

Bottom of metal on the left side of the beam.

Bottom of metal on the right side of the beam.

Next the program sums the compressive forces of these six items, startingwith the item at the highest elevation and proceeding downward. As eachitem is added into the sum, the sum of compressive forces is compared withthe MPFconc as determined in one of Equations 2a through 2d.

As soon as the sum of forces exceeds MPFconc, the program recognizes thatthe last location considered is below the bottom of the effective concrete, andthe second to last location considered is above the bottom of the effectiveconcrete. Using this information, the program can solve directly for the loca-tion of the bottom of the effective concrete.

Figure 1a shows the internal concrete forces for a rolled steel section (a user-defined steel section is similar) for the condition where the bottom of the ef-fective concrete is in the concrete slab above the metal deck. In this case, a1

represents the distance from the top of the concrete slab to the bottom of theeffective concrete. Note that the distance a1 can be different on the left andright sides of the beam.



Figure 1a: Rolled Steel Section With Bottom of Effective Concrete in ConcreteSlab Above Metal Deck, Positive Bending With Partial CompositeConnection

Figure 1b shows the internal concrete forces for a rolled steel section (a user-defined steel section is similar) for the condition where the bottom of the ef-fective concrete is within the height, hr, of the metal deck ribs. In this case, a2

represents the distance from the top of the metal deck ribs to the bottom ofthe effective concrete. Note that the distance a2 can be different on the leftand right sides of the beam.

Figure 1b: Rolled Steel Section With Bottom of Effective Concrete Within theHeight, hr, of the Metal Deck Ribs, Positive Bending With PartialComposite Connection

CC 1


Bottom of effective concrete

a 1

CC 1


CC 2

Bottom of effective concrete

a 2



The program obtains the distances a1 and/or a2 using an iterative solutiontechnique.

If the bottom of effective concrete is in the concrete above the metal deck, a2

is set equal to 0. If the bottom of effective concrete is within the height of themetal deck, a1 is set equal to tc.

Moment Capacity of a Partially Composite Beam with aPlastic Stress DistributionThe moment capacity for partial composite connection with a plastic stressdistribution is calculated using the method described for full composite con-nection in the section entitled "Plastic Moment Capacity for Positive Bending"in Composite Beam Design AISC-LFRD93 Technical Note 34 Composite PlasticMoment Capacity for Positive Bending with the following changes:

Equation 12b in Composite Beam Design AISC-LFRD93 Technical Note 34Composite Plastic Moment Capacity for Positive Bending is replaced withEquation 3.

CC1 = 0.85f'c beff a1 Eqn. 3


r

2reff

'cC2

S

awb0.85fC = Eqn. 4


xPNA = 2

az 1p − Eqn. 5




xPNA = 2

aaz 21p −− Eqn. 6

When calculating the moment capacity, concrete or reinforcing steel belowthe bottom of the effective concrete is not considered in the calculation.

Note that the PNA for a partially composite beam always lies within the steelbeam section, not the concrete slab. Thus it is not necessary to check for thePNA location within the concrete slab.

ReferenceVogel, R. 1991. “LRFD-Composite Beam Design with Metal Deck,” Steel Tips,

Technical Information & Product Service, Steel Committee of Califor-nia, March.

Bending and Deflection Checks Technical Note 38 - 1



Technical Note 38Bending and Deflection Checks

This Technical Note describes how the program checks bending and deflectionfor AISC-LRFD93 design.

Bending Check LocationsFor each design load combination the program checks bending at the follow-ing locations:

Point of maximum moment for the design load combination considered.

Point load locations for the design load combination considered.

Bending CheckThe program uses Equation 1 to perform bending checks for both compositeand noncomposite beams.

0.1M

M

n

u ≤φ

Eqn. 1

where,

Mu = The maximum required flexural strength, that is, the maximumapplied factored moment, kip-in.

Mn = Moment capacity for full composite connection or partial com-posite connection, as applicable, kip-in.

φ = Resistance factor for bending, unitless. For positive bending in acomposite beam with an assumed plastic stress distribution,φbcpp is used. For negative bending in a composite beam with anassumed plastic stress distribution, φbcnp is used. For positivebending in a composite beam with an assumed elastic stressdistribution, φbcpe is used. For negative bending in a composite

Bending and Deflection Checks Composite Beam Design AISC-LRFD93

Technical Note 38 - 2 Bending and Deflection Checks

beam with an assumed elastic stress distribution, φbcne is used.If the beam is specified to be noncomposite, φb is used.

Deflection CheckDeflection is calculated as described in Composite Beam Design TechnicalNote 11 Beam Deflection and Camber. For full composite connection Itr isused in the deflection calculations. For partial composite connection Ieff isused in the deflection calculations.

Note that camber is subtracted from the total load deflection for checking.

Shear Connectors Technical Note 39 - 1



Technical Note 39Shear Connectors

This Technical Note begins by defining the program's default allowable shearconnector loads for AISC-LRFD93 composite beam design. Shear connectorcapacities are defined for both shear studs. Next the equations used for de-termining the number of shear connectors on the beam are provided.

Shear Stud ConnectorsThe capacity for a single shear stud is calculated using Equation 1.

Qn = 0.5Asc c'cEf ≤ AscFu Eqn. 1

Equation 1 is based on AISC-LRFD93 specifications Equation I5-1.

If there is formed metal deck, the value of Qn obtained from either Equation 1or from the overwrites, if specified, is reduced by a reduction factor, RF thatis specified in Composite Beam Design AISC-ASD89 Technical Note 25 ShearStuds. Note that the reduction factor is different depending on whether thespan of the metal deck ribs is oriented parallel or perpendicular to the span ofthe beam.

The reduction factor, RF, only applies to the 0.5Asc c'cEf term in Equation 1.

It does not apply to the AscFu term.

The terms f’c and Ec can be different on the two sides of the beam. The pro-gram calculates Qn for each side of the beam separately using Equation 1 anduses the smaller value in the calculations.

Horizontal Shear for Full Composite ConnectionBetween Maximum Moment and Point of Zero MomentPositive BendingThe total horizontal shear to be resisted between the point of maximumpositive moment (where the concrete is in compression) and the points of

Shear Connectors Composite Beam Design AISC-LRFD93

Technical Note 39 - 2 Shear Connectors

zero moment for full composite connection, ΣQn-100, is given by the smaller ofEquations 3, 4a or 4b as applicable. Table 1 defines the conditions where thevarious equations are applicable and it defines what to use for Ac left and Ac right

(both simply called Ac in the table) in Equation 3 for each condition.

Table 1: Table Defining Equations to be used to Calculate Horizontal Shear forFull Composite Connection

Deck RibSpan Relativeto Beam Span Beam Section

Use Smallerof These

EquationsNote About Ac in

Equation 3

Rolled sectionfrom the pro-

gram database

3 as notedand 4a

Perpendicular

User-defined3 as noted

and 4b

Ac in Eqn. 3 is the area of con-crete in the slab above the metaldeck

Rolled sectionfrom the pro-

gram database

3 as notedand 4a

Parallel

User-defined3 as noted

and 4b

Ac in Eqn. 3 is the area of con-crete in the slab, including theconcrete in the metal deck ribs

rightc'rightcleftc

'leftc100n A0.85fA0.85fQ +=Σ − Eqn. 3

ycpcpcpys100n FtbFAQ +=Σ − Eqn. 4a

ycpcpcpbot-yfbot-fbot-fywwtop-yftop-ftop-f100n FtbFtbFhtFtbQ +++=Σ − Eqn. 4b

Number of Shear ConnectorsBetween Maximum Moment and Point of Zero MomentFor full composite action, the number of shear connectors between a point ofmaximum positive or negative moment and adjacent points of zero moment,N1, is given by Equation 5.

n

100n1

Q

QN −Σ

= Eqn. 5

Composite Beam Design AISC-LRFD93 Shear Connectors

Shear Connectors Technical Note 39 - 3

In Equation 5, ΣQn-100 is as determined in the previous section entitled "Hori-zontal Shear for Full Composite Connection" and Qn is determined as de-scribed in the previous section entitled "Shear Stud Connectors."

For partial composite connection, the number of shear connectors between apoint of maximum positive (not negative) moment and adjacent points ofzero moment, N1, is given by Equation 6.

n

PCCn1

Q

QN −Σ

= Eqn. 6

In Equation 6, ΣQn-PCC is equal to the percent composite connection times ΣQn-

100. For example, if there is 70% composite connection, ΣQn-PCC = 0.7 ΣQn-100.Thus, the percent composite connection, PCC, for AISC-LRFD93 design isgiven by Equation 7.

001n

PCCn

Q

QPCC

−

−

ΣΣ

= Eqn. 7

Between Point Load and Point of Zero MomentThe program uses Equation 8 to check that the number of shear connectorsprovided between a point load and a point of zero moment is sufficient. Equa-tion 8 is not specified by AISC but is used by CSI as the LRFD equivalent ofEquation I4-5 in the AISC-ASD89 specification.

−

−=

alonesteelncompn

alonesteelnu12 MM

MMNN

φφφ

Eqn. 8

In Equation 8,

Mn comp = Maximum moment capacity of composite beam, consider-ing partial composite connection if applicable, kip-in.

Mn steel alone = Moment capacity of steel beam alone, kip-in.

Mu = Moment at point load location, kip-in.

N1 = Number of shear connectors required between the point ofmaximum moment and the point of zero moment, or endof the slab, unitless.

Shear Connectors Composite Beam Design AISC-LRFD93

Technical Note 39 - 4 Shear Connectors

N2 = Number of shear connectors required between the pointload considered and the point of zero moment, or end ofthe slab, unitless.

φ = Resistance factor used to determine moment capacity ofcomposite beam, unitless. This is equal to either φbcpe, φbcpp,φbcne, or φbcnp depending on whether there is positive ornegative bending and whether the stress distribution con-sidered is elastic or plastic.

Equation 8 is checked at each point load location.

Beam Shear Capacity Technical Note 40 - 1



Technical Note 40Beam Shear Capacity

This Technical Note describes how the program calculates the allowable shearstress for AISC-LRFD93 composite beam design.

Shear CapacityRefer to Figure 1 for a flowchart showing how the program considers beamvertical shear. AISC-LRFD93 Equations F2-1 through F2-3 are reproducedhere as Equations 1 through 3 respectively.

For yww F

418

t

h ≤ , Vn = 0.6 Fyw Aw Eqn. 1

For ywwyw F

523

t

h

F

418 ≤< ,

w

yw

wyw

n

t

h

F

418A0.6F

V

= Eqn. 2

For 602t

h

F

523

wyw

≤< , 2

w

wn

t

h

132,000AV

= Eqn. 3

Note that in Equations 1 through 3, Aw, the area of the web, is calculated asshown in Equation 4 where Ctop and Cbot are the depths of copes, if any, at thetop and bottom of the beam section. The copes are specified in the over-writes.

Aw = (d - Ctop - Cbot) tw Eqn. 4

Beam Shear Capacity Composite Beam Design AISC-LRFD93

Tec

Fig

ChThe5.

wh

LiFolpos

N

Nd

No No?

418hIs ≤ ?

523h418Is ≤<

No Beam section notdesigned.

?602h523

Is ≤<

hnical Note 40 - 2 Beam Shear Capacity

ure 1: Flow Chart for Calculating Beam Vertical Shear Capacity

ecking the Beam Shear program checks the beam shear at the ends of the beam using Equation

0.1V

V

nv

u ≤φ

Eqn. 5

ere,

Vu = The required shear strength, that is, the applied factoredshear, kips.

Vn = Shear capacity, kips. This term is calculated from Equation 1,2 or 3, as appropriate, and as indicated in Figure 1.

φv = Resistance factor for shear, unitless.

mitations of Beam Shear Checklowing are some limitations of the program's beam shear check for com-ite beams.

o check is made for shear on the net section considering the bolt holes.

o check is made for shear rupture on a beam with the top flange coped asescribed in AISC-LRFD93 specification Chapter J, section J4.

Yes Yes

Determine Vn fromLRFD Section F2.2equation F2-3;, see

Equation 3.

Yes

Determine Vn fromLRFD Section F2.2equation F2-1; see

Equation 1.

Determine Vn fromLRFD Section F2.2equation F2-2; see

Equation 2.

ywFtw ywyw FtF w tF wyw

Input Data Technical Note 41 - 1




This Technical Note describes the composite beam design input data for AISC-LRFD93. The input can be printed to a printer or to a text file when you clickthe File menu > Print Tables > Composite Beam Design command. Aprintout of the input data provides the user with the opportunity to carefullyreview the parameters that have been input into the program and upon whichprogram design is based. See Composite Beam Design Technical Note 5 InputData for further information about using the print Composite Beam DesignTables Form, as well as other non-code-specific input data for compositebeam design.

Beam Overwrites Input DataThe program provides the printout of the input data in a series of tables. Thetables typically correspond to the tabs used in the Composite Beam Over-writes form. The column headings for input data and a description of what isincluded in the columns of the tables are provided in Table 1 of this TechnicalNote.

Recall that the composite beam overwrites apply to all beams to which theyhave been specifically assigned. To access the composite beam overwrites,select one or more beams and then click the Design menu > CompositeBeam Design > View/Revise Overwrites command. Information aboutcomposite beam overwrites is available in Composite Beam Design AISC-LRFD93 Technical Note 31 Overwrites.

Input Data Composite Beam Design AISC-LRFD93

Technical Note 41 - 2 Input Data

Table 1 Beam Overwrites Input DataCOLUMN HEADING DESCRIPTIONBeam Location InformationThis information does not correspond to one of the tabs in the composite beam over-writes. This data is provided to help identify the beam to which printed overwrites apply.

XGlobal X coordinate of the center of the beam to which theoverwrites apply.

YGlobal Y coordinate of the center of the beam to which theoverwrites apply.

Length Length of the beam to which the overwrites apply.

Beam PropertiesComposite Type Type of beam design. The choices are Composite, NC w/ studs

and NC w/o studs. NC w/ studs is short for noncomposite withminimum shear studs. NC w/o studs is short for noncompositewithout shear studs. Note that this option allows you to design anoncomposite floor beam in the Composite Beam Design post-processor.

Shoring Provided This item is Yes if the composite beam is shored. Otherwise, itis No. Note that this item supersedes the Shored Floor item inthe composite beam preferences.

b-eff Left If the beff left width is program calculated, this item reads "ProgCalc." Otherwise, this item is the user-defined width for beff left.See Composite Beam Design Technical Note 8 Effective Widthof the Concrete Slab for description of the effective width of theslab.

b-eff Right If the beff right width is program calculated, this item reads "ProgCalc." Otherwise, this item is the user-defined width for beff right.See Composite Beam Design Technical Note 8 Effective Widthof the Concrete Slab for description of the effective width of theslab.

Beam Fy If the beam yield stress is based on the material property speci-fied for the beam, this item reads "Prog Calc." Otherwise, thisitem is the user-defined yield stress of the beam.

Beam Fu If the beam minimum tensile strength is based on the materialproperty specified for the beam, this item reads "Prog Calc."Otherwise, this item is the user-defined minimum tensilestrength of the beam.

Composite Beam Design AISC-LRFD93 Input Data


Table 1 Beam Overwrites Input DataCOLUMN HEADING DESCRIPTIONCover PlateThis information is included on the Beam tab of the overwrites.

Plate Width Width of the cover plate.

Plate Thick Thickness of the cover plate.

Plate Fy Yield stress of the cover plate.

Consider Cover Plate If this item is "Yes," the specified cover plate is considered inthe design of the beam. Otherwise, the cover plate is not con-sidered in the beam design.

Beam Unbraced LengthBeam unbraced length data is provided for both the construction condition and the finalcondition. The headings for these two types of beam unbraced lengths are “Beam Un-braced Length (Construction Loading)” and “Beam Unbraced Length (Final Loading).”The types of data provided in each of these tables is identical and is documented oncehere.

Bracing State This item can be "Prog Calc," "User Bracing," or "LengthGiven." Prog Calc means that the program determines thebraced points of the beam. User Bracing means that you havespecified the actual bracing for the beam. The user-definedbracing may be point or uniform bracing along the top and bot-tom flange of the beam. Length Given means that you havespecified a single maximum unbraced length for the beam.

Unbraced L22 If the Bracing State item is "Length Given," this item is the user-specified maximum unbraced length of the beam. Otherwise,this item is specified as N/A.

L22 Absolute If the Bracing State item is "Length Given," this item indicateswhether the user-specified maximum unbraced length of thebeam (the Unbraced L22 item) is an absolute (actual) length ora relative length. A relative length is the maximum unbracedlength divided by the length of the beam. If the Bracing Stateitem is not Length Given, this item is specified as N/A.

Cb Factor If the Cb factor is calculated by the program, this item reads"Prog Calc." Otherwise, the user-defined Cb factor that is usedin determining the allowable bending stress is displayed. (Notethat when the Cb factor is program calculated, it may be differ-ent for each design load combination, and for a given designload combination, it may be different for each station consid-ered along the length of the beam.)



Table 1 Beam Overwrites Input DataCOLUMN HEADING DESCRIPTIONPoint BracesThe heading of the point braces data table specifies whether the point braces are pro-gram calculated or user-defined, and whether the distances used to locate the pointbraces (Location item) are absolute (actual) distances or relative distances. A relativedistance is the distance divided by the length of the beam.

Location This is the distance from the I-end of the beam to the pointbrace. As described in the preceding description, it may be anabsolute or a relative distance.


Uniform BracesThe heading of the uniform braces data table specifies whether the point braces are pro-gram calculated or user-defined, and whether the distances used to define the extent ofthe uniform braces (Start and End items) are absolute (actual) distances or relative dis-tances. A relative distance is the distance divided by the length of the beam.

Note:Details about the location and type of program calculated point and uniformbraces is only reported after you have run the design. Before you run the de-sign, this information is not available.

Start This is the distance from the I-end of the beam to the startingpoint of the uniform brace. As described in a previous descrip-tion, it may be an absolute or a relative distance.

End This is the distance from the I-end of the beam to the endingpoint of the uniform brace. This distance is always larger thanthe Start item. As described previously, it may be an absoluteor a relative distance.




Table 1 Beam Overwrites Input DataCOLUMN HEADING DESCRIPTIONDeck PropertiesBeam Side This item is either Left or Right. It indicates to which side of the

beam the deck label and deck direction specified in the samerow apply.

Deck Label This item is either “Prog Calc,” if the deck label is determinedby the program, or it is the label (name) of a defined deck sec-tion, if this is a user-specified overwrite, or it is "None" if nocomposite deck has been specified on the side of the beam.

Deck Direction This item is “Prog Calc,” “Parallel,” or “Perpendclr.” Prog Calcmeans that the direction of the deck span (parallel or perpen-dicular to the beam span) is program determined. Parallelmeans that the span of the metal deck is parallel to the beamspan. Perpendclr means that the span of the metal deck is per-pendicular to the beam span.

Shear Stud PropertiesMin Long Spacing Minimum longitudinal spacing of shear studs along the beam.

Max Long Spacing Maximum longitudinal spacing of shear studs along the beam.

Min Tran Spacing Minimum transverse spacing of shear studs across the beamflange.

Max Conn in a Row Maximum number of shear studs in a single row across thebeam flange.

Stud Qn This item is “Prog Calc” if the allowable horizontal load for asingle shear stud is determined by the program, or it is a user-defined allowable horizontal load for a single shear stud.

User-Defined Shear Stud PatternUniform Spacing The uniform spacing of single shear studs along the length of

the beam.User-Defined Uniform Stud SectionsThe heading of the uniform stud sections data table specifies whether the distances usedto define the extent of the stud sections (Start, End and Length items) are absolute (ac-tual) distances or relative distances. A relative distance is the distance divided by thelength of the beam.

Note:User-defined shear stud patterns are described in Composite Beam DesignTechnical Note 15 User-Defined Shear Stud Patterns.




Start This is the distance from the I-end of the beam to the startingpoint of the uniform stud section. As described previously, itmay be an absolute or a relative distance.

End This is the distance from the I-end of the beam to the endingpoint of the uniform stud section. As described previously, itmay be an absolute or a relative distance.

Length This is the length of the uniform stud section. As described pre-viously, it may be an absolute or a relative distance.

Number The number of uniformly spaced shear studs in the uniformstud section.

Deflection, Camber and VibrationDeflection Absolute If the live load and total load deflection limits are specified as

absolute (actual) distances, this item is Yes. If they are speci-fied as a divisor of beam length (relative), this item is No.

Live Load Limit The live load deflection limit for the beam.

Total Load Limit The total load deflection limit for the beam.

Calculate Camber If this item is Yes, the program calculates the camber for thebeam. If it is No, the program does not calculate a camber, butif desired, the user can specify the camber.

Specified Camber User-specified camber when the program does not calculatethe beam camber.

Neff Beams This item is “Prog Calc” if the number of effective beams forvibration calculations is determined by the program, or it is auser-defined number of effective beams.

Other RestrictionsLimit Beam Depth This item is Yes if the beam depth limitations (Minimum Depth

and Maximum Depth items) are considered by the program forbeams with auto select section lists. This item is No if the beamdepth limitations are not considered.

Minimum Depth Minimum actual (not nominal) beam depth considered in theauto select section list if the Limit Beam Depth item is Yes.

Maximum Depth Maximum actual (not nominal) beam depth considered in theauto select section list if the Limit Beam Depth item is Yes.




Minimum PCC Minimum percent composite connection considered by the pro-gram for the beam.

Maximum PCC Maximum percent composite connection considered by theprogram for the beam.

RLLF This represents the reducible live load factor. A reducible liveload is multiplied by this factor to obtain the reduced live load.This item is “Prog Calc” if the reducible live load factor is de-termined by the program, or it is a user-defined reducible liveload factor.

EQF The EQ Factor is a multiplier applied to earthquake loads. Thisitem corresponds to the EQ Factor item in the composite beamdesign overwrites. More information about the EQ Factor isavailable from Composite Beam Design AISC-LRFD93 Techni-cal Note 42 Overwrites.

Output Details Technical Note 42 - 1




This Technical Note describes the composite beam output for AISC-LRFD93that can be printed to a printer or to a text file in either short form or longform. See Composite Beam Design Technical Note 6 Output Data for informa-tion about using the Print Composite Beam Design Tables Form, as well as theSummary of Composite Beam Output.

The program provides the output data in a series of tables. The columnheadings for output data and a description of what is included in the columnsof the tables are provided in Tables 1 and 2 of this Technical Note.

Short Form Output DetailsThis output is printed when you click the File menu > Print Tables > Com-posite Beam Design command and select Short Form in the Output Detailsarea of the resulting form. Similar output also appears on screen if you clickthe Details button in the Show Details area of the Interactive CompositeBeam Design and Review form. See Composite Beam Design Technical Note 3Interactive Composite Beam Design for more details on the interactive design.

Table 1 Output Details - Short FormCOLUMN HEADING DESCRIPTIONBasic Beam Information

Beam Label Label associated with the line object that represents the beam.A typical label beam would appear as "B23." Do not confusethis with the Section Label, which would be identified as"W18X35."

Group Name of the design group (if any) to which the beam has beenassigned.

Beam Beam section label (name).

Output Details Composite Beam Design AISC-LRFD93

Technical Note 42 - 2 Output Details

Table 1 Output Details - Short FormCOLUMN HEADING DESCRIPTION

Fy Beam yield stress, Fy.

Fu Beam minimum tensile strength, Fu.


Seg. Length Length of each composite beam segment separated by com-mas. The lengths are listed starting with the composite beamsegment at the I-end of the beam and working toward the J-endof the beam.

Stud Ratio This item has a slightly different meaning, depending onwhether the shear studs are user-defined or calculated by theprogram.

When the number of shear studs is calculated by the program,a stud ratio is reported for each composite beam segment. It isequal to the number of shear studs required in the segmentdivided by the maximum number of studs that fit in the seg-ment.

When the shear studs are user-defined, the total number ofstuds is reported instead of the stud ratio.

Story Story level associated with the beam.

Length Length of the beam.

Loc X Global X coordinate of the center of the beam.

Loc Y Global Y coordinate of the center of the beam.


Shored This item is Yes if the beam is shored and No if it is unshored.

Composite Beam Design AISC-LRFD93 Output Details



Camber The camber for the beam. This item may be calculated by theprogram or it may be user-specified.

Comparative Price of the beam using the input price parameters for steel,shear studs and camber. This price is intended for comparisonof alternative designs only. It is not intended to be used for costestimating purposes.

Stud Diam Diameter of shear studs.

EQ Factor A multiplier applied to earthquake loads. This item correspondsto the EQ Factor item in the composite beam design overwrites.

Overwrites If this item is Yes, one or more items have been overwritten forthis beam. If it is No, nothing has been overwritten. The valuesfor all overwrite items are included in the long form output.Thus, if this item is "Yes," you may want to print the long formoutput.

b-cp Width of the cover plate. If no cover plate is specified by theuser, N/A is reported for this item.

t-cp Thickness of the cover plate. If no cover plate is specified bythe user, N/A is reported for this item.

Fy-cp Yield stress for the cover plate. If no cover plate is specified bythe user, N/A is reported for this item.

Consider-cp This item is Yes if the specified cover plate is considered in thedesign. Otherwise, it is No.

Deck Left and DeckRight

The deck section labels (names) on the left and right sides ofthe beam.

Dir. Left and Dir. Right The deck directions on the left and right sides of the beam.Perpendclr means that the deck span is perpendicular to thebeam span. Parallel means that the deck span is parallel to thebeam span.

beff Left and beff Right The slab effective widths on the left and right sides of the beam.




Ctop Left and CtopRight

The program calculated cope of the beam top flange at the leftand right ends of the beam. Do not confuse the left and rightends of the beam with the left and right sides of the beam. Theleft end of the beam is the I-end and the right end of the beamis the J-end.

Cbot Left and CbotRight

The program calculated cope of the beam bottom flange at theleft and right ends of the beam. Do not confuse the left and rightends of the beam with the left and right sides of the beam. Theleft end of the beam is the I-end and the right end of the beamis the J-end.

Itrans Transformed section moment of inertia for full (100%) compos-ite connection for positive bending, Itr.

Ibare Moment of inertia of the steel beam, including cover plate, if itexists.

Is Moment of inertia of the steel beam alone, not including coverplate, even if it exists.

Ieff Effective moment of inertia for partial composite connection.

PCC Percent composite connection.

ytrans Distance from the bottom of the beam bottom flange (not bot-tom of cover plate, even if it exists) to the elastic neutral axis(ENA) of the beam, with full (100%) composite connection, y .

ybare Distance from the bottom of the beam bottom flange (not bot-tom of cover plate, even if it exists) to the ENA of the beam,plus cover plate alone (if it exists).

yeff Distance from the bottom of the beam bottom flange (not bot-tom of cover plate, even if it exists) to the ENA of the beam,with partial composite connection.

q Allowable horizontal shear load for a single shear stud.



Table 1 Output Details - Short FormCOLUMN HEADING DESCRIPTIONMoment DesignThis table of output data reports the controlling moments for both construction loads andfinal loads.

Pmax The largest axial load in the beam for any design load combi-nation.

Important note: This value is not used in the Composite BeamDesign postprocessor design. It is reported to give you a senseof how much axial load, if any, is in the beam. If there is a sig-nificant amount of axial load in the beam, you may want to de-sign it noncompositely using the Steel Frame Design postpro-cessor. The Steel Frame Design postprocessor does consideraxial load.

Pmax Combo The design load combination associated with Pmax.

PCC PNA Location of plastic neutral axis (PNA) for partial composite con-nection (PCC).

PCC phi Mn Factored nominal flexural strength with partial composite con-nection.

Full PNA Location of plastic neutral axis (PNA) for full composite connec-tion.

Full phi Mn Factored nominal flexural strength with full composite connec-tion.

Type This item is either Constr Pos, Constr Neg, Final Pos or FinalNeg. Const Pos means it is a positive moment for constructionloading. Const Neg means it is a negative moment for con-struction loading. Final Pos means it is a positive moment forfinal loading. Final Neg means it is a negative moment for finalloading.

Combo Design load combination that causes the controlling moment forthe moment type considered in the table row.

Mu The controlling factored design moment for the moment typeconsidered in the table row.




phi Mn Maximum factored flexural strength associated with this loadcombination.

Ratio This is Mu divided by φMn.

Shear DesignThis table of output data reports the controlling shears for both construction loads andfinal loads.

Type This item is either Constr Left, Constr Right, Final Left or FinalRight. Constr Left means it is a construction loading shear atthe left end of the beam. Constr Right means it is a constructionloading shear at the right end of the beam.

Final Left means it is a final loading shear at the left end of thebeam. Final Rght means it is a final loading shear at the rightend of the beam.

Combo Design load combination that causes the controlling shear forthe shear type considered in the table row.

Block This item is either OK or NG. It indicates whether the programcheck for block shear (shear rupture) passed or failed. OKmeans that the beam passes the Check, and NG (no good)means it did not. If the item indicates NG, you should check theblock shear by hand for the beam.

Vu The controlling factored shear for the shear type considered inthe table row.

phi VN The maximum factored shear strength associated with the con-trolling moment.

Ratio This is the bending stress, fv, divided by the allowable bendingstress, Fv.



Table 1 Output Details - Short FormCOLUMN HEADING DESCRIPTIONDeflection DesignThis table of output data reports the controlling deflections for both live load and totalload.

Type This item is either Live Load or Total Load.

Consider This item is always Yes, indicating that deflection is one of thecriteria checked when determining if a beam section is consid-ered acceptable.

Combo Design load combination that causes the controlling deflectionfor the deflection type considered in the table row.

Deflection The controlling deflection for the deflection type considered inthe table row. The computed camber is subtracted from the to-tal load deflection before the deflection is reported.

Note:Deflection is described in Composite Beam Design Technical Note 11 BeamDeflection and Camber.

Limit The deflection limit for the deflection type considered in the ta-ble row.

Ratio This is the controlling deflection divided by the deflection limit.

Vibration Design

Neff The effective number of beams used in the vibration evalua-tions.

Type Frequency or Murray Damping.

Consider Indicates whether vibration was considered in the design.

Actual Calculate vibration frequency or percent damping of the beam.

Target Minimum acceptable frequency or damping required.




Ratio Target divided by actual.

Ok Indicates whether the member is acceptable for vibration re-quirements.

Long Form Output DetailsThis output is printed when you click the File menu > Print Tables > Com-posite Beam Design command to open the Print Composite Beam DesignTables form and select Long Form under Output Details. The long form outputdetails report provides all of the data described in Table 1 for the Short FormOutput as well as the data described in Table 2 Output Details - Long Form.

Table 2 Output Details - Long FormCOLUMN HEADING DESCRIPTION

Beam Property Over-writes

Indicates user-specified overwrite values or program calculatedvalues.

Composite Type Either composite or noncomposite (NC) with studs, or noncom-posite without studs.

Shoring Provided Yes or No.

beff Left Program calculated or user-defined effective width of concreteslab on left side of beam.

beff Right Program calculated or user-defined effective width of concreteslab on right side of beam.

Fy Yield stress of beam.

Fu Minimum tensile strength of the beam.




Beam Unbraced Length Overwrites (Construction Loading):

Bracing State User defined or program calculated.

Unbraced L22 Maximum unbraced length for buckling about the 2-2 axis of thebeam. This item is filled with "N/A" unless the unbraced lengthfor buckling about the local 2-2 axis is user defined and is asingle maximum unbraced length for the entire beam.

Absolute L22 A "Yes" for this item indicates that the unbraced lengths arespecified as absolute distances form the left end of the beam. A"No" indicates that they are specified as relative distances fromthe left end of the beam, with 0 indicating the left end of thebeam and 1 indicating the right end of the beam.

Cb Factor Unitless factor used in determining allowable bending stress.Program calculated if zero is specified.

Program Calculated Point Braces for Construction Loading:



Program Calculated Uniform Braces for Construction Loading:

Start Distance from the left end of the beam to the starting point ofthe uniform brace that braces the beam for buckling about the2-2 axis.

End Distance from the left end of the beam to the ending point of theuniform brace that braces the beam for buckling about the 2-2axis.





Beam Unbraced Length Overwrites (Final Loading):

Bracing State User defined or program calculated.

Unbraced L22 Maximum unbraced length for buckling about the 2-2 axis of thebeam. This item is filled with "N/A" unless the unbraced lengthfor buckling about the local 2-2 axis is user-defined and is asingle maximum unbraced length for the entire beam.

Absolute L22 A "Yes" for this item indicates that the unbraced lengths arespecified as absolute distances form the left end of the beam. A"No" indicates that they are specified as relative distances fromthe left end of the beam, with 0 indicating the left end of thebeam and 1 indicating the right end of the beam.

Cb Factor Unitless factor used in determining allowable bending stress.Program calculated if zero is specified.

Program Calculated Point Braces for Final Loading:



Program Calculated Uniform Braces for Final Loading:

Start Distance from the left end of the beam to the starting point ofthe uniform brace that braces the beam for buckling about the2-2 axis.




End Distance from the left end of the beam to the ending point of theuniform brace that braces the beam for buckling about the 2-2axis.


Deck Property Overwrites:

Beam Side Left and right.

Deck Label User defined or program calculated.

Deck Direction User defined or program calculated.

Shear Stud Property Overwrites:

Min. Long Spacing Minimum allowed longitudinal spacing of the shear stud con-nectors.

Max. Long Spacing Maximum allowed longitudinal spacing of the shear stud con-nectors.

Min. Tran Spacing Minimum allowed transverse spacing of shear stud connectors.

Max. Conn. in a Row Maximum allowed number of shear stud connectors in a singlerow across the beam flange.

Qn Horizontal shear capacity of a single stud.

Deflection, Camber and Vibration Overwrites:

Deflection Absolute A "Yes" for this item indicates that the deflection limits arespecified as absolute distances. A "No" indicates that they arespecified as the length of the beam, L, divided by some num-ber, e.g., L/360




Live Load Limit Limiting live load deflection used when deflection limitations areconsidered in selecting the optimum beam.

Total Load Limit Limiting total load deflection used when deflection limitationsare considered in selecting the optimum beam.

Calculated Camber Yes or No.

Specified Camber Specified value or N/A if not specified.

Neff Beam Effective number of beams used in the vibration calculations.

Other Restriction Overwrites:

Limit Beam Depth Yes if user inputs depth limit.

Minimum Depth Minimum shown if specified. Zero is not specified.

Maximum Depth Maximum shown, if specified; 44 inches is not specified.

Maximum PCC Maximum percent composite connection considered by theprogram

Minimum PCC Minimum percent composite connection considered by the pro-gram


EQF A multiplier applied to earthquake loads.

ETABS Composite Floor Frame Design Manual

Documents

composite beam overview

composite beam segments

beam user

design data

beam length

beam span

aspects of composite

composite beam segment