Steel Frame Design Manual - Springerextras.springer.com/2001/978-0-7923-7308-7/EtabsStl.pdf · STEEL FRAME DESIGN MANUAL ... ETABS Steel Design Manual. ... CHAPTER IX Check/Design

Steel FrameDesign Manual

ETABS®

IntegratedThree Dimensional

Static and Dynamic Analysis and Designof

Building Systems

STEEL FRAME DESIGN MANUAL

Computers and Structures, Inc.Berkeley, California, USA

Version 7.0October 2000

COPYRIGHT

The computer program ETABS and all associated documentation areproprietary and copyrighted products. Worldwide rights of ownershiprest with Computers and Structures, Inc. Unlicensed use of the programor reproduction of the documentation in any form, without prior writtenauthorization from Computers and Structures, Inc., is explicitly prohib-ited.

Further information and copies of this documentation may be obtainedfrom:

Computers and Structures, Inc.1995 University Avenue

Berkeley, California 94704 USA

Tel: (510) 845-2177Fax: (510) 845-4096

E-mail: [email protected]: www.csiberkeley.com

© Copyright Computers and Structures, Inc., 1978–2000.The CSI Logo is a registered trademark of Computers and Structures, Inc.ETABS is a registered trademark of Computers and Structures, Inc.

DISCLAIMER

CONSIDERABLE TIME, EFFORT AND EXPENSE HAVE GONEINTO THE DEVELOPMENT AND DOCUMENTATION OF ETABS.THE PROGRAM HAS BEEN THOROUGHLY TESTED AND USED.IN USING THE PROGRAM, HOWEVER, THE USER ACCEPTSAND UNDERSTANDS THAT NO WARRANTY IS EXPRESSED ORIMPLIED BY THE DEVELOPERS OR THE DISTRIBUTORS ONTHE ACCURACY OR THE RELIABILITY OF THE PROGRAM.

THIS PROGRAM IS A VERY PRACTICAL TOOL FOR THE DE-SIGN/ CHECK OF STEEL STRUCTURES. HOWEVER, THE USERMUST THOROUGHLY READ THE MANUAL AND CLEARLYRECOGNIZE THE ASPECTS OF STEEL DESIGN THAT THE PRO-GRAM ALGORITHMS DO NOT ADDRESS.

THE USER MUST EXPLICITLY UNDERSTAND THE ASSUMP-TIONS OF THE PROGRAM AND MUST INDEPENDENTLY VER-IFY THE RESULTS.

Table of Contents

CHAPTER I Introduction 1Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Recommended Reading . . . . . . . . . . . . . . . . . . . . . . . . . . 4

CHAPTER II Design Algorithms 5Design Load Combinations . . . . . . . . . . . . . . . . . . . . . . . . 6

Design and Check Stations . . . . . . . . . . . . . . . . . . . . . . . . 8

P- Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Element Unsupported Lengths . . . . . . . . . . . . . . . . . . . . . . 9

Effective Length Factor (K) . . . . . . . . . . . . . . . . . . . . . . . 11

Design of Continuity Plates . . . . . . . . . . . . . . . . . . . . . . . 13

Design of Doubler Plates . . . . . . . . . . . . . . . . . . . . . . . . 15

Choice of Input Units . . . . . . . . . . . . . . . . . . . . . . . . . . 17

CHAPTER III Check/Design for AISC-ASD89 19Design Loading Combinations . . . . . . . . . . . . . . . . . . . . . 22

Classification of Sections . . . . . . . . . . . . . . . . . . . . . . . . 22

Calculation of Stresses . . . . . . . . . . . . . . . . . . . . . . . . . 26

Calculation of Allowable Stresses . . . . . . . . . . . . . . . . . . . 27

Allowable Stress in Tension . . . . . . . . . . . . . . . . . . . . 27Allowable Stress in Compression. . . . . . . . . . . . . . . . . . 27

Flexural Buckling . . . . . . . . . . . . . . . . . . . . . . . 27Flexural-Torsional Buckling . . . . . . . . . . . . . . . . . . 29

Allowable Stress in Bending . . . . . . . . . . . . . . . . . . . . 34I-sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Channel sections . . . . . . . . . . . . . . . . . . . . . . . . 37T-sections and Double angles . . . . . . . . . . . . . . . . . 38

i

Box Sections and Rectangular Tubes . . . . . . . . . . . . . 39Pipe Sections . . . . . . . . . . . . . . . . . . . . . . . . . . 40Round Bars . . . . . . . . . . . . . . . . . . . . . . . . . . 40Rectangular and Square Bars . . . . . . . . . . . . . . . . . 40Single-Angle Sections . . . . . . . . . . . . . . . . . . . . . 41General Sections . . . . . . . . . . . . . . . . . . . . . . . . 43

Allowable Stress in Shear . . . . . . . . . . . . . . . . . . . . . 43

Calculation of Stress Ratios . . . . . . . . . . . . . . . . . . . . . . . 44

Axial and Bending Stresses . . . . . . . . . . . . . . . . . . . . . 45Shear Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

CHAPTER IV Check/Design for AISC-LRFD93 49Design Loading Combinations . . . . . . . . . . . . . . . . . . . . . 52

Classification of Sections . . . . . . . . . . . . . . . . . . . . . . . . 52

Calculation of Factored Forces . . . . . . . . . . . . . . . . . . . . . 56

Calculation of Nominal Strengths . . . . . . . . . . . . . . . . . . . . 58

Compression Capacity . . . . . . . . . . . . . . . . . . . . . . . 58Flexural Buckling . . . . . . . . . . . . . . . . . . . . . . . 58Flexural-Torsional Buckling . . . . . . . . . . . . . . . . . . 62Torsional and Flexural-Torsional Buckling . . . . . . . . . . 62

Tension Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . 64Nominal Strength in Bending. . . . . . . . . . . . . . . . . . . . 65

Yielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65Lateral-Torsional Buckling . . . . . . . . . . . . . . . . . . 65Flange Local Buckling . . . . . . . . . . . . . . . . . . . . . 69Web Local Buckling . . . . . . . . . . . . . . . . . . . . . . 73

Shear Capacities . . . . . . . . . . . . . . . . . . . . . . . . . . 76

Calculation of Capacity Ratios . . . . . . . . . . . . . . . . . . . . . 77

Axial and Bending Stresses . . . . . . . . . . . . . . . . . . . . . 77Shear Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

CHAPTER V Check/Design for UBC-ASD97 79Design Loading Combinations . . . . . . . . . . . . . . . . . . . . . 81

Member Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

Classification of Sections . . . . . . . . . . . . . . . . . . . . . . 82Calculation of Stresses . . . . . . . . . . . . . . . . . . . . . . . 84Calculation of Allowable Stresses . . . . . . . . . . . . . . . . . 84Calculation of Stress Ratios. . . . . . . . . . . . . . . . . . . . . 85

Axial and Bending Stresses . . . . . . . . . . . . . . . . . . 85Shear Stresses . . . . . . . . . . . . . . . . . . . . . . . . . 87

Seismic Requirements . . . . . . . . . . . . . . . . . . . . . . . 88Ordinary Moment Frames . . . . . . . . . . . . . . . . . . . 88Special Moment-Resisting Frames. . . . . . . . . . . . . . . 88Braced Frames . . . . . . . . . . . . . . . . . . . . . . . . . 89Eccentrically Braced Frames. . . . . . . . . . . . . . . . . . 90Special Concentrically Braced Frames . . . . . . . . . . . . 93

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ETABS Steel Design Manual

Joint Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

Design of Continuity Plates. . . . . . . . . . . . . . . . . . . . . 95Design of Doubler Plates . . . . . . . . . . . . . . . . . . . . . . 98Beam/Column Plastic Moment Capacity Ratio . . . . . . . . . . 100Evaluation of Beam Connection Shears . . . . . . . . . . . . . . 102Evaluation of Brace Connection Forces . . . . . . . . . . . . . . 103

CHAPTER VI Check/Design for UBC-LRFD97 105Design Loading Combinations . . . . . . . . . . . . . . . . . . . . . 107

Member Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

Classification of Sections . . . . . . . . . . . . . . . . . . . . . 108Calculation of Factored Forces . . . . . . . . . . . . . . . . . . 110Calculation of Nominal Strengths . . . . . . . . . . . . . . . . . 111Calculation of Capacity Ratios . . . . . . . . . . . . . . . . . . 112

Axial and Bending Stresses. . . . . . . . . . . . . . . . . . 112Shear Stresses . . . . . . . . . . . . . . . . . . . . . . . . . 113

Seismic Requirements . . . . . . . . . . . . . . . . . . . . . . . 114Ordinary Moment Frames . . . . . . . . . . . . . . . . . . 114Special Moment-Resisting Frames . . . . . . . . . . . . . . 114Braced Frames . . . . . . . . . . . . . . . . . . . . . . . . 115Eccentrically Braced Frames . . . . . . . . . . . . . . . . . 116Special Concentrically Braced Frames . . . . . . . . . . . . 119

Joint Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Design of Continuity Plates . . . . . . . . . . . . . . . . . . . . 121Design of Doubler Plates . . . . . . . . . . . . . . . . . . . . . 125Weak Beam Strong Column Measure . . . . . . . . . . . . . . . 128Evaluation of Beam Connection Shears . . . . . . . . . . . . . . 129Evaluation of Brace Connection Forces . . . . . . . . . . . . . . 130

CHAPTER VII Check/Design for CISC94 133Design Loading Combinations . . . . . . . . . . . . . . . . . . . . . 136

Classification of Sections . . . . . . . . . . . . . . . . . . . . . . . 137

Calculation of Factored Forces . . . . . . . . . . . . . . . . . . . . 137

Calculation of Factored Strengths . . . . . . . . . . . . . . . . . . . 140

Compression Strength . . . . . . . . . . . . . . . . . . . . . . . 140Tension Strength. . . . . . . . . . . . . . . . . . . . . . . . . . 141Bending Strengths . . . . . . . . . . . . . . . . . . . . . . . . . 141

I-shapes and Boxes . . . . . . . . . . . . . . . . . . . . . . 142Rectangular Bar. . . . . . . . . . . . . . . . . . . . . . . . 143Pipes and Circular Rods . . . . . . . . . . . . . . . . . . . 143Channel Sections . . . . . . . . . . . . . . . . . . . . . . . 144T-shapes and double angles. . . . . . . . . . . . . . . . . . 144Single Angle and General Sections . . . . . . . . . . . . . . 145

Shear Strengths . . . . . . . . . . . . . . . . . . . . . . . . . . 145


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Table of Contents

Axial and Bending Stresses . . . . . . . . . . . . . . . . . . . . 147Shear Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

CHAPTER VIII Check/Design for BS 5950 151Design Loading Combinations . . . . . . . . . . . . . . . . . . . . . 154


Calculation of Factored Forces. . . . . . . . . . . . . . . . . . . . . 157

Calculation of Section Capacities . . . . . . . . . . . . . . . . . . . 159

Compression Resistance. . . . . . . . . . . . . . . . . . . . . . 159Tension Capacity . . . . . . . . . . . . . . . . . . . . . . . . . 161Moment Capacity . . . . . . . . . . . . . . . . . . . . . . . . . 161

Plastic and Compact Sections . . . . . . . . . . . . . . . . 161Semi-compact Sections . . . . . . . . . . . . . . . . . . . . 162

Lateral-Torsional Buckling Moment Capacity . . . . . . . . . . 162Shear Capacities . . . . . . . . . . . . . . . . . . . . . . . . . . 165


Local Capacity Check . . . . . . . . . . . . . . . . . . . . . . . 167Under Axial Tension . . . . . . . . . . . . . . . . . . . . . 167Under Axial Compression . . . . . . . . . . . . . . . . . . 167

Overall Buckling Check . . . . . . . . . . . . . . . . . . . . . . 167Shear Capacity Check . . . . . . . . . . . . . . . . . . . . . . . 168

CHAPTER IX Check/Design for EUROCODE 3 169Design Loading Combinations . . . . . . . . . . . . . . . . . . . . . 172


Calculation of Factored Forces. . . . . . . . . . . . . . . . . . . . . 177

Calculation of Section Resistances. . . . . . . . . . . . . . . . . . . 178

Tension Capacity . . . . . . . . . . . . . . . . . . . . . . . . . 179Compression Resistance. . . . . . . . . . . . . . . . . . . . . . 179Shear Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . 181Moment Resistance . . . . . . . . . . . . . . . . . . . . . . . . 182Lateral-torsional Buckling. . . . . . . . . . . . . . . . . . . . . 183


Bending, Axial Compression, and Low Shear . . . . . . . . . . 185Bending, Axial Compression, and High Shear . . . . . . . . . . 186Bending, Compression, and Flexural Buckling . . . . . . . . . . 186Bending, Compression, and Lateral-Torsional Buckling . . . . . 187Bending, Axial Tension, and Low Shear . . . . . . . . . . . . . 188Bending, Axial Tension, and High Shear . . . . . . . . . . . . . 188Bending, Axial Tension, and Lateral-Torsional Buckling . . . . 189Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

CHAPTER X Design Output 191Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

iv


Graphical Display of Design Input and Output . . . . . . . . . . . . 192

Tabular Display of Design Input and Output . . . . . . . . . . . . . 193

Member Specific Information . . . . . . . . . . . . . . . . . . . . . 195

References 197Index 199

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Table of Contents

C h a p t e r I

Introduction

OverviewETABS features powerful and completely integrated modules for design of bothsteel and reinforced concrete structures. The program provides the user with op-tions to create, modify, analyze and design structural models, all from within thesame user interface. The program is capable of performing initial member sizingand optimization from within the same interface.

The program provides an interactive environment in which the user can study thestress conditions, make appropriate changes, such as revising member properties,and re-examine the results without the need to re-run the analysis. A single mouseclick on an element brings up detailed design information. Members can begrouped together for design purposes. The output in both graphical and tabulatedformats can be readily printed.

The program is structured to support a wide variety of the latest national and inter-national building design codes for the automated design and check of concrete andsteel frame members. The program currently supports the following steel designcodes:

• U.S. AISC/ASD (1989),

• U.S. AISC/LRFD (1993),

Overview 1

• U.S. UBC/ASD (1997),

• U.S. UBC/LRFD (1997),

• Canadian CAN/CSA-S16.1-94 (1994),

• British BS 5950 (1990), and

• Eurocode 3 (ENV 1993-1-1).

The design is based upon a set of user-specified loading combinations. However,the program provides a set of default load combinations for each design code sup-ported in ETABS. If the default load combinations are acceptable, no definition ofadditional load combination is required.

In the design optimization process the program picks the least weight section re-quired for strength for each element to be designed, from a set of user specified sec-tions. Different sets of available sections can be specified for different groups ofelements. Also several elements can be grouped to be designed to have the samesection.

In the check process the program produces demand/capacity ratios for axial loadand biaxial moment interactions and shear. The demand/capacity ratios are basedon element stress and allowable stress for allowable stress design, and on factoredloads (actions) and factored capacities (resistances) for limit state design.

The checks are made for each user specified (or program defaulted) load combina-tion and at several user controlled stations along the length of the element. Maxi-mum demand/capacity ratios are then reported and/or used for design optimization.

All allowable stress values or design capacity values for axial, bending and shearactions are calculated by the program. Tedious calculations associated with evalu-ating effective length factors for columns in moment frame type structures are auto-mated in the algorithms.

When using 1997 UBC-ASD or UBC-LRFD design codes, requirements for conti-nuity plates at the beam to column connections are evaluated. The program per-forms a joint shear analysis to determine if doubler plates are required in any of thejoint panel zones. Maximum beam shears required for the beam shear connectiondesign are reported. Also maximum axial tension or compression values that aregenerated in the member are reported.

Special 1997 UBC-ASD and UBC-LRFD seismic design provisions are imple-mented in the current version of the program. The ratio of the beam flexural capaci-ties with respect to the column reduced flexural capacities (reduced for axial forceeffect) associated with the weak beam-strong column aspect of any beam/column

2 Overview


intersection, are reported for special moment resisting frames. Capacity require-ments associated with seismic framing systems that require ductility are checked.

The presentation of the output is clear and concise. The information is in a form thatallows the designer to take appropriate remedial measures if there is member over-stress. Backup design information produced by the program is also provided forconvenient verification of the results.

English as well as SI and MKS metric units can be used to define the model geome-try and to specify design parameters.

OrganizationThis manual is organized in the following way:

Chapter II outlines various aspects of the steel design procedures of the ETABSprogram. This chapter describes the common terminology of steel design as imple-mented in ETABS.

Each of seven subsequent chapters gives a detailed description of a specific code ofpractice as interpreted by and implemented in ETABS. Each chapter describes thedesign loading combinations to be considered; allowable stress or capacity calcula-tions for tension, compression, bending, and shear; calculations of demand/capac-ity ratios; and other special considerations required by the code. In addition, Chap-ter V and VI describe the determination of continuity plate area, doubler platethickness, beam connection shear, and brace connection force according to theUBC ASD and LRFD codes, respectively.

• Chapter III gives a detailed description of the AISC-ASD code (AISC 1989) asimplemented in ETABS.

• Chapter IV gives a detailed description of the AISC-LRFD code (AISC 1993)as implemented in ETABS.

• Chapter V gives a detailed description of the UBC-ASD steel building code(UBC 1997) as implemented in ETABS.

• Chapter VI gives a detailed description of the UBC-LRFD steel building code(UBC 1997) as implemented in ETABS.

• Chapter VII gives a detailed description of the Canadian code (CISC 1994) asimplemented in ETABS.

• Chapter VIII gives a detailed description of the British code BS 5950 (BSI1990) as implemented in ETABS.

Organization 3

Chapter I Introduction

• Chapter IX gives a detailed description of the Eurocode 3 (CEN 1992) as im-plemented in ETABS.

Chapter X outlines various aspects of the tabular and graphical output from ETABSrelated to steel design.

Recommended ReadingIt is recommended that the user read Chapter II “Design Algorithms” and one ofseven subsequent chapters corresponding to the code of interest to the user. Finallythe user should read “Design Output” in Chapter X for understanding and interpret-ing ETABS output related to steel design. If the user’s interest is in the UBC-ASDsteel design code, it is recommended that the user should also read the chapter re-lated to AISC-ASD. Similarly, if the user’s interest is in the UBC-LRFD steel de-sign code, it is recommended that the user should also read the chapter related toAISC-LRFD.

A steel design tutorial is presented in the ETABS Quick Tutorial manual. It is rec-ommended that first time users follow through the steps of this tutorial before read-ing this manual.

4 Recommended Reading


C h a p t e r II

Design Algorithms

This chapter outlines various aspects of the steel check and design procedures thatare used by the ETABS program. The steel design and check may be performed ac-cording to one of the following codes of practice.

• American Institute of Steel Construction’s “Allowable Stress Design and Plas-tic Design Specification for Structural Steel Buildings”, AISC-ASD (AISC1989).

• American Institute of Steel Construction’s “Load and Resistance Factor De-sign Specification for Structural Steel Buildings”, AISC-LRFD (AISC 1993).

• International Conference of Building Officials’ “1997 Uniform Building Code:Volume 2: Structural Engineering Design Provisions” Chapter 22 Division III“Design Standard for Specification for Structural Steel Buildings AllowableStress Design and Plastic Design”, UBC-ASD (ICBO 1997).

• International Conference of Building Officials’ “1997 Uniform Building Code:Volume 2: Structural Engineering Design Provisions” Chapter 22 Division II“Design Standard for Load and Resistance factor Design Specification forStructural Steel Buildings”, UBC-LRFD (ICBO 1997).

• Canadian Institute of Steel Construction’s “Limit States Design of Steel Struc-tures”, CAN/CSA-S16.1-94 (CISC 1995).

5

• British Standards Institution’s “Structural Use of Steelwork in Building”, BS5950 (BSI 1990).

• European Committee for Standardization’s “Eurocode 3: Design of SteelStructures C Part 1.1: General Rules and Rules for Buildings”, ENV 1993-1-1(CEN 1992).

Details of the algorithms associated with each of these codes as implemented andinterpreted in ETABS are described in subsequent chapters. However, this chapterprovides a background which is common to all the design codes. For referring topertinent sections of the corresponding code, a unique prefix is assigned for eachcode.

– References to the AISC-ASD89 code carry the prefix of “ASD”

– References to the AISC-LRFD93 code carry the prefix of “LRFD”

– References to the UBC-ASD97 code carry the prefix of “UBC”

– References to the UBC-LRFD97 code carry the prefix of “UBC”

– References to the Canadian code carry the prefix of “CISC”

– References to the British code carry the prefix of “BS”

– References to the Eurocode carry the prefix of “EC3”

It is assumed that the user has an engineering background in the general area ofstructural steel design and familiarity with at least one of the above mentioned de-sign codes.

Design Load CombinationsThe design load combinations are used for determining the various combinations ofthe load cases for which the structure needs to be designed/checked. The load com-bination factors to be used vary with the selected design code. The load combina-tion factors are applied to the forces and moments obtained from the associated loadcases and the results are then summed to obtain the factored design forces and mo-ments for the load combination.

For multi-valued load combinations involving response spectrum, time history,moving loads and multi-valued combinations (of type enveloping, square-root ofthe sum of the squares or absolute) where any correspondence between interactingquantities is lost, the program automatically produces multiple sub combinationsusing maxima/minima permutations of interacting quantities. Separate combina-tions with negative factors for response spectrum cases are not required because the

6 Design Load Combinations


program automatically takes the minima to be the negative of the maxima for re-sponse spectrum cases and the above described permutations generate the requiredsub combinations.

When a design combination involves only a single multi-valued case of time his-tory or moving load, further options are available. The program has an option to re-quest that time history combinations produce sub combinations for each time stepof the time history. Also an option is available to request that moving load combina-tions produce sub combinations using maxima and minima of each design quantitybut with corresponding values of interacting quantities.

For normal loading conditions involving static dead load, live load, wind load, andearthquake load, and/or dynamic response spectrum earthquake load, the programhas built-in default loading combinations for each design code. These are based onthe code recommendations and are documented for each code in the correspondingchapters.

For other loading conditions involving moving load, time history, pattern liveloads, separate consideration of roof live load, snow load, etc., the user must definedesign loading combinations either in lieu of or in addition to the default designloading combinations.

The default load combinations assume all static load cases declared as dead load tobe additive. Similarly, all cases declared as live load are assumed additive. How-ever, each static load case declared as wind or earthquake, or response spectrumcases, is assumed to be non additive with each other and produces multiple lateralload combinations. Also wind and static earthquake cases produce separate loadingcombinations with the sense (positive or negative) reversed. If these conditions arenot correct, the user must provide the appropriate design combinations.

The default load combinations are included in design if the user requests them to beincluded or if no other user defined combination is available for concrete design. Ifany default combination is included in design, then all default combinations willautomatically be updated by the program any time the user changes to a differentdesign code or if static or response spectrum load cases are modified.

Live load reduction factors can be applied to the member forces of the live load caseon an element-by-element basis to reduce the contribution of the live load to thefactored loading.

The user is cautioned that if moving load or time history results are not requested tobe recovered in the analysis for some or all the frame members, then the effects ofthese loads will be assumed to be zero in any combination that includes them.

Design Load Combinations 7

Chapter II Design Algorithms

Design and Check StationsFor each load combination, each beam, column, or brace element is designed orchecked at a number of locations along the length of the element. The locations arebased on equally spaced segments along the clear length of the element. By defaultthere will be at least 3 stations in a column or brace element and the stations in abeam will be at most 2 feet (0.5m if model is created in SI unit) apart. The numberof segments in an element can be overwritten by the user before the analysis ismade. The user can refine the design along the length of an element by requestingmore segments. See the section “Frame Output Stations Assigned to Line Objects”in the ETABS User’s Manual Volume 1 (CSI 1999) for details.

The axial-flexure interaction ratios as well as shear stress ratios are calculated foreach station along the length of the member for each load combination. The actualmember stress components and corresponding allowable stresses are calculated.Then, the stress ratios are evaluated according to the code. The controlling com-pression and/or tension stress ratio is then obtained, along with the correspondingidentification of the station, load combination, and code-equation. A stress ratiogreater than 1.0 indicates an overstress or exceeding a limit state.

When using 1997 UBC ASD or LRFD design codes, requirements for continuityplates at the beam to column connections are evaluated at the topmost station ofeach column. The program also performs a joint shear analysis at the same stationto determine if doubler plates are required in any of the joint panel zones. Maxi-mum beam shears required for the beam shear connection design at the two ends arereported. Also maximum axial tension or compression values that are generated atthe two ends in the braces are reported. The ratio of the beam flexural capacitieswith respect to the column reduced flexural capacities (reduced for axial force ef-fect) associated with the weak beam-strong column aspect of any beam/column in-tersection, are reported for special moment resisting frames.

P- EffectsExcept for AISC-ASD and UBC-ASD design codes, the ETABS design algorithmsrequire that the analysis results include the P- effects. The P- effects are consid-ered differently for “braced” or “nonsway” and “unbraced” or “sway” componentsof moments in frames. For the braced moments in frames, the effect of P- is lim-ited to “individual member stability”. For unbraced components, “lateral drift ef-fects” should be considered in addition to “individual member stability” effect. InETABS, it is assumed that “braced” or “nonsway” moments are contributed from

8 Design and Check Stations


the “dead” or “live” loads. Whereas, “unbraced” or “sway” moments are contrib-uted from all other types of loads.

For the individual member stability effects, the moments are magnified with mo-ment magnification factors as in the AISC-LRFD and UBC-LRFD codes or areconsidered directly in the design equations as in the Canadian, British, and Euro-pean codes. No moment magnification is applied to the AISC-ASD and UBC-ASDcodes.

For lateral drift effects of unbraced or sway frames, ETABS assumes that the am-plification is already included in the results because P- effects are considered forall but AISC-ASD and UBC-ASD codes.

The users of ETABS should be aware that the default analysis option in ETABS forP- effect is turned OFF. The default number of iterations for P- analysis is 1.The user should turn the P- analysis ON and set the maximum number of it-erations for the analysis. No P- analysis is required for the AISC-ASD andUBC-ASD codes. For further reference, the user is referred to ETABS User’s Man-ual Volume 2 (CSI 1999). The user is also cautioned that ETABS currently consid-ers P- effects due to axial loads in frame members only. Forces in other types of el-ements do not contribute to this effect. If significant forces are present in othertypes of elements, for example, large axial loads in shear walls modeled as shell ele-ments, then the additional forces computed for P- will be inaccurate.

Element Unsupported LengthsTo account for column slenderness effects, the column unsupported lengths are re-quired. The two unsupported lengths are l33 and l22 . See Figure II-1. These are thelengths between support points of the element in the corresponding directions. Thelength l33 corresponds to instability about the 3-3 axis (major axis), and l22 corre-sponds to instability about the 2-2 axis (minor axis). The length l22 is also used forlateral-torsional buckling caused by major direction bending (i.e., about the 3-3axis). See Figure II-2 for correspondence between the ETABS axes and the axes inthe design codes.

Normally, the unsupported element length is equal to the length of the element, i.e.,the distance between END-I and END-J of the element. See Figure II-1. The pro-gram, however, allows users to assign several elements to be treated as a singlemember for design. This can be done differently for major and minor bending.Therefore, extraneous joints, as shown in Figure II-3, that affect the unsupportedlength of an element are automatically taken into consideration.

Element Unsupported Lengths 9


10 Element Unsupported Lengths


Figure II-1Major and Minor Axes of Bending

Figure II-2Correspondence between ETABS Axes and Code Axes

In determining the values for l22 and l33 of the elements, the program recognizesvarious aspects of the structure that have an effect on these lengths, such as memberconnectivity, diaphragm constraints and support points. The program automati-cally locates the element support points and evaluates the corresponding unsup-ported element length.

Therefore, the unsupported length of a column may actually be evaluated as beinggreater than the corresponding element length. If the beam frames into only one di-rection of the column, the beam is assumed to give lateral support only in that direc-tion. The user has options to specify the unsupported lengths of the elements on anelement-by-element basis.

Effective Length Factor (K)The column K-factor algorithm has been developed for building-type structures,where the columns are vertical and the beams are horizontal, and the behavior is ba-sically that of a moment-resisting nature for which the K-factor calculation is rela-tively complex. For the purpose of calculating K-factors, the elements are identi-fied as columns, beams and braces. All elements parallel to the Z-axis are classified

Effective Length Factor (K) 11


Figure II-3Unsupported Lengths are Affected by Intermediate Nodal Points

as columns. All elements parallel to the X-Y plane are classified as beams. The restare braces.

The beams and braces are assigned K-factors of unity. In the calculation of theK-factors for a column element, the program first makes the following four stiff-ness summations for each joint in the structural model:

S =E I

Lcx

c c

c x

S =E I

Lbxb b

b x

S =E I

Lcy

c c

c y

S =E I

Lbyb b

b y

where the x and y subscripts correspond to the global X and Y directions and the cand b subscripts refer to column and beam. The local 2-2 and 3-3 terms EI l22 22 andEI l33 33 are rotated to give components along the global X and Y directions to formthe ( / )EI l x and ( / )EI l y values. Then for each column, the joint summations atEND-I and the END-J of the member are transformed back to the column local1-2-3 coordinate system and the G-values for END-I and the END-J of the memberare calculated about the 2-2 and 3-3 directions as follows:

G =S

SI

Ic

Ib

2222

22

G =S

SJ

Jc

Jb

2222

22

G =S

SI

Ic

Ib

3333

33

G =S

SJ

Jc

Jb

3333

33

If a rotational release exists at a particular end (and direction) of an element, thecorresponding value is set to 10.0. If all degrees of freedom for a particular joint aredeleted, the G-values for all members connecting to that joint will be set to 1.0 forthe end of the member connecting to that joint. Finally, if G I and G J are known fora particular direction, the column K-factor for the corresponding direction is calcu-lated by solving the following relationship for α:

2 I J

I J

G G

G G

from which K . This relationship is the mathematical formulation for theevaluation of K factors for moment-resisting frames assuming sidesway to be unin-hibited. For other structures, such as braced frame structures, the K-factors for allmembers are usually unity and should be set so by the user. The following are someimportant aspects associated with the column K-factor algorithm:

12 Effective Length Factor (K)


• An element that has a pin at the joint under consideration will not enter the stiff-ness summations calculated above. An element that has a pin at the far end fromthe joint under consideration will contribute only 50% of the calculated EIvalue. Also, beam elements that have no column member at the far end from thejoint under consideration, such as cantilevers, will not enter the stiffness sum-mation.

• If there are no beams framing into a particular direction of a column element,the associated G-value will be infinity. If the G-value at any one end of a col-umn for a particular direction is infinity, the K-factor corresponding to that di-rection is set equal to unity.

• If rotational releases exist at both ends of an element for a particular direction,the corresponding K-factor is set to unity.

• The automated K-factor calculation procedure can occasionally generate artifi-cially high K-factors, specifically under circumstances involving skewedbeams, fixed support conditions, and under other conditions where the programmay have difficulty recognizing that the members are laterally supported andK-factors of unity are to be used.

• All K-factors produced by the program can be overwritten by the user. Thesevalues should be reviewed and any unacceptable values should be replaced.

• The beams and braces are assigned K-factors of unity.

Design of Continuity PlatesIn a plan view of a beam/column connection, a steel beam can frame into a columnin the following ways:

• The steel beam frames in a direction parallel to the column major direction, i.e.the beam frames into the column flange.

• The steel beam frames in a direction parallel to the column minor direction, i.e.the beam frames into the column web.

• The steel beam frames in a direction that is at an angle to both of the principalaxes of the column, i.e. the beam frames partially into the column web and par-tially into the column flange.

To achieve a beam/column moment connection, continuity plates such as shown inFigure II-4 are usually placed on the column, in line with the top and bottom flangesof the beam, to transfer the compression and tension flange forces of the beam intothe column.

Design of Continuity Plates 13


14 Design of Continuity Plates


Figure II-4Plan Showing Continuity Plates for a Column of I-Section

For connection conditions described in the last two items above, the thickness ofsuch plates is usually set equal to the flange thickness of the corresponding beam.

However, for the connection condition described by the first item above, where thebeam frames into the flange of the column, such continuity plates are not alwaysneeded. The requirement depends upon the magnitude of the beam-flange force andthe properties of the column.

When using 1997 UBC ASD or LRFD design codes, the program investigateswhether the continuity plates are required. Columns of I-sections only are investi-gated. The program evaluates the continuity plate requirements for each of thebeams that frame into the column flange (i.e. parallel to the column major direction)and reports the maximum continuity plate area that is needed for each beam flange.The continuity plate requirements are evaluated for moment frames only. No checkis made for braced frames.

Design of Doubler PlatesOne aspect of the design of a steel framing system is an evaluation of the shearforces that exist in the region of the beam column intersection known as the panelzone.

Shear stresses seldom control the design of a beam or column member. However,in a moment resisting frame, the shear stress in the beam-column joint can be criti-cal, especially in framing systems when the column is subjected to major directionbending and the joint shear forces are resisted by the web of the column. In minordirection bending, the joint shear is carried by the column flanges, in which case theshear stresses are seldom critical, and this condition is therefore not investigated bythe program.

Shear stresses in the panel zone, due to major direction bending in the column, mayrequire additional plates to be welded onto the column web, depending upon theloading and the geometry of the steel beams that frame into the column, either alongthe column major direction, or at an angle so that the beams have components alongthe column major direction. See Figure II-5. The program investigates such situa-tions and reports the thickness of any required doubler plates. Only columns withI-shapes are investigated for doubler plate requirements. Also doubler plate re-quirements are evaluated for moment frames only. No check is made for bracedframes. Doubler plate requirements are evaluated when using UBC ASD andLRFD codes.

Design of Doubler Plates 15


16 Design of Doubler Plates


Figure II-5Elevation and Plan of Doubler Plates for a Column of I-Section

Choice of Input UnitsEnglish as well as SI and MKS metric units can be used for input. But the codes arebased on a specific system of units. All equations and descriptions presented in thesubsequent chapters correspond to that specific system of units unless otherwisenoted. For example, AISC-ASD code is published in kip-inch-second units. By de-fault, all equations and descriptions presented in the chapter “Check/Design forAISC-ASD89” correspond to kip-inch-second units. However, any system of unitscan be used to define and design the structure in ETABS.

Choice of Input Units 17


C h a p t e r III

Check/Design for AISC-ASD89

This chapter describes the details of the structural steel design and stress check al-gorithms that are used by ETABS when the user selects the AISC-ASD89 designcode (AISC 1989a). Various notations used in this chapter are described in TableIII-1.

For referring to pertinent sections and equations of the original ASD code, a uniqueprefix “ASD” is assigned. However, all references to the “Specifications for Allow-able Stress Design of Single-Angle Members” (AISC 1989b) carry the prefix of“ASD SAM”.

The design is based on user-specified loading combinations. But the program pro-vides a set of default load combinations that should satisfy requirements for the de-sign of most building type structures.

In the evaluation of the axial force/biaxial moment capacity ratios at a station alongthe length of the member, first the actual member force/moment components andthe corresponding capacities are calculated for each load combination. Then the ca-pacity ratios are evaluated at each station under the influence of all load combina-tions using the corresponding equations that are defined in this chapter. The con-trolling capacity ratio is then obtained. A capacity ratio greater than 1.0 indicatesoverstress. Similarly, a shear capacity ratio is also calculated separately.

19

20


A = Cross-sectional area, in2

Ae = Effective cross-sectional area for slender sections, in2

A f = Area of flange , in2

Ag = Gross cross-sectional area, in2

A Av v2 3, = Major and minor shear areas, in2

Aw = Web shear area, dt w , in2

Cb = Bending Coefficient

Cm = Moment Coefficient

Cw = Warping constant, in6

D = Outside diameter of pipes, in

E = Modulus of elasticity, ksi

Fa = Allowable axial stress, ksi

Fb = Allowable bending stress, ksi

F Fb b33 22, = Allowable major and minor bending stresses, ksi

Fcr = Critical compressive stress, ksi

Fe33¢ =

12

23

2

33 33 33

2

E

K l r

Fe22¢ =

12

23

2

22 22 22

2

E

K l r

Fv = Allowable shear stress, ksi

Fy = Yield stress of material, ksi

K = Effective length factor

K K33 22, = Effective length K-factors in the major and minor directions

M M33 22, = Major and minor bending moments in member, kip-in

M ob = Lateral-torsional moment for angle sections, kip-in

P = Axial force in member, kips

Pe = Euler buckling load, kips

Q = Reduction factor for slender section, = Q Qa s

Qa = Reduction factor for stiffened slender elements

Qs = Reduction factor for unstiffened slender elements

S = Section modulus, in3

S S33 22, = Major and minor section moduli, in3

Table III-1AISC-ASD Notations

21

Chapter III Check/Design for AISC-ASD89

S Seff eff, ,,33 22 = Effective major and minor section moduli for slender sections, in3

S c = Section modulus for compression in an angle section, in3

V V2 3, = Shear forces in major and minor directions, kips

b = Nominal dimension of plate in a section, inlonger leg of angle sections,b tf w2 for welded and b tf w3 for rolled box sections, etc.

be = Effective width of flange, in

b f = Flange width, in

d = Overall depth of member, in

fa = Axial stress either in compression or in tension, ksi

fb = Normal stress in bending, ksi

f fb b33 22, = Normal stress in major and minor direction bending, ksi

fv = Shear stress, ksi

f fv v2 3, = Shear stress in major and minor direction bending, ksi

h = Clear distance between flanges for I shaped sections ( )d t f2 , in

he = Effective distance between flanges less fillets, in

k = Distance from outer face of flange to web toe of fillet , in

kc = Parameter used for classification of sections,

0.46

h t w

if h t w 70 ,

1 if h t w 70 .

l l33 22, = Major and minor direction unbraced member lengths, in

lc = Critical length, in

r = Radius of gyration, in

r r33 22, = Radii of gyration in the major and minor directions, in

rz = Minimum Radius of gyration for angles, in

t = Thickness of a plate in I, box, channel, angle, and T sections, in

t f = Flange thickness, in

t w = Web thickness, in

w = Special section property for angles, in

Table III-1AISC-ASD Notations (cont.)

English as well as SI and MKS metric units can be used for input. But the code isbased on Kip-Inch-Second units. For simplicity, all equations and descriptions pre-sented in this chapter correspond to Kip-Inch-Second units unless otherwisenoted.

Design Loading CombinationsThe design load combinations are the various combinations of the load cases forwhich the structure needs to be checked. For the AISC-ASD89 code, if a structure issubjected to dead load (DL), live load (LL), wind load (WL), and earthquake in-duced load (EL), and considering that wind and earthquake forces are reversible,then the following load combinations may have to be defined (ASD A4):

DL (ASD A4.1)DL + LL (ASD A4.1)

DL WL (ASD A4.1)DL + LL WL (ASD A4.1)

DL EL (ASD A4.1)DL + LL EL (ASD A4.1)

These are also the default design load combinations in ETABS whenever theAISC-ASD89 code is used. The user should use other appropriate loading combi-nations if roof live load is separately treated, if other types of loads are present, or ifpattern live loads are to be considered.

When designing for combinations involving earthquake and wind loads, allowablestresses are increased by a factor of 4/3 of the regular allowable value (ASD A5.2).


Classification of SectionsThe allowable stresses for axial compression and flexure are dependent upon theclassification of sections as either Compact, Noncompact, Slender, or Too Slender.ETABS classifies the individual members according to the limiting width/thick-ness ratios given in Table III-2 (ASD B5.1, F3.1, F5, G1, A-B5-2). The definition

22 Design Loading Combinations


Classification of Sections 23


Figure III-1AISC-ASD Definition of Geometric Properties

24 Classification of Sections


SectionDescription

RatioChecked

CompactSection

NoncompactSection

SlenderSection

I-SHAPE

b tf f2( rolled)

Fy65 Fy95 No limit

b tf f2(welded)

Fy65 F ky c/ No limit

d tw

For f Fa y640

1F

f

Fy

a

y

( ) ,

For f Fa y/257/ Fy .

No limit No limit

h tw No limit

If compression only,Fy253

otherwiseFb760

F Fy y

BOX

b tf Fy190 Fy238 No limit

d tw As for I-shapes No limit No limit

h tw No limit As for I-shapes As for I-shapes

Other t tw f 2 , d bw f None None

CHANNEL

b tf As for I-shapes As for I-shapes No limit

d tw As for I-shapes No limit No limit

h tw No limit As for I-shapes As for I-shapes

Other No limit No limit

If weldedb df w ,t tf w

If rolledb df w ,t tf w

Table III-2Limiting Width-Thickness Ratios for

Classification of Sections Based on AISC-ASD

of the section properties required in this table is given in Figure III-1 and TableIII-1.

If the section dimensions satisfy the limits shown in the table, the section is classi-fied as either Compact, Noncompact, or Slender. If the section satisfies the criteriafor Compact sections, then the section is classified as Compact section. If the sec-tion does not satisfy the criteria for Compact sections but satisfies the criteria for



SectionDescription

RatioChecked

CompactSection

NoncompactSection

SlenderSection

T-SHAPE

b tf f2 Fy65 Fy95 No limit

d tw Not applicable Fy127 No limit

Other No limit No limit

If weldedb df w ,t tf w

If rolledb df w ,t tf w

DOUBLEANGLES

b t Not applicable Fy76 No limit

ANGLE b t Not applicable Fy76 No limit

PIPE D t Fy3 300, Fy3 300,Fy

(Compression only)No limit for flexure

ROUND BAR Assumed Compact

RECTANGLE Assumed Noncompact

GENERAL Assumed Noncompact

Table III-2Limiting Width-Thickness Ratios for

Classification of Sections Based on AISC-ASD (Cont.)

Noncompact sections, the section is classified as Noncompact section. If the sec-tion does not satisfy the criteria for Compact and Noncompact sections but satisfiesthe criteria for Slender sections, the section is classified as Slender section. If thelimits for Slender sections are not met, the section is classified as Too Slender.Stress check of Too Slender sections is beyond the scope of ETABS.

In classifying web slenderness of I-shapes, Box, and Channel sections, it is as-sumed that there are no intermediate stiffeners (ASD F5, G1). Double angles areconservatively assumed to be separated.

Calculation of StressesThe stresses are calculated at each of the previously defined stations. The memberstresses for non-slender sections that are calculated for each load combination are,in general, based on the gross cross-sectional properties.:

f = P/Aa

f = M /Sb33 33 33

f = M /Sb22 22 22

f = V /Av v2 2 2

f = V /Av v3 3 3

If the section is slender with slender stiffened elements, like slender web in I, Chan-nel, and Box sections or slender flanges in Box, effective section moduli based onreduced web and reduced flange dimensions are used in calculating stresses.

f = P/Aa (ASD A-B5.2d)f = M /Sb eff33 33 33, (ASD A-B5.2d)f = M /Sb eff22 22 22, (ASD A-B5.2d)f = V /Av v2 2 2 (ASD A-B5.2d)f = V /Av v3 3 3 (ASD A-B5.2d)

The flexural stresses are calculated based on the properties about the principal axes.For I, Box, Channel, T, Double-angle, Pipe, Circular and Rectangular sections, theprincipal axes coincide with the geometric axes. For Single-angle sections, the de-sign considers the principal properties. For general sections it is assumed that allsection properties are given in terms of the principal directions.

For Single-angle sections, the shear stresses are calculated for directions along thegeometric axes. For all other sections the shear stresses are calculated along thegeometric and principle axes.

26 Calculation of Stresses


Calculation of Allowable StressesThe allowable stresses in compression, tension, bending, and shear are computedfor Compact, Noncompact, and Slender sections according to the following subsec-tions. The allowable flexural stresses for all shapes of sections are calculated basedon their principal axes of bending. For the I, Box, Channel, Circular, Pipe, T, Dou-ble-angle and Rectangular sections, the principal axes coincide with their geomet-ric axes. For the Angle sections, the principal axes are determined and all computa-tions related to flexural stresses are based on that.

If the user specifies nonzero allowable stresses for one or more elements in theETABS “Allowable Stress Overwrites” form, these values will override the abovementioned calculated values for those elements . The specified allowable stressesshould be based on the principal axes of bending.

Allowable Stress in Tension

The allowable axial tensile stress value Fa is assumed to be Fy .

F = Fa y (ASD D1, ASD SAM 2)

It should be noted that net section checks are not made. For members in tension,if l r is greater than 300, a message to that effect is printed (ASD B7, ASD SAM 2).For single angles, the minimum radius of gyration, rz , is used instead of r22 and r33

in computing l r .

Allowable Stress in Compression

The allowable axial compressive stress is the minimum value obtained from flex-ural buckling and flexural-torsional buckling. The allowable compressive stressesare determined according to the following subsections.

For members in compression, if Kl r is greater than 200, a warning message isprinted (ASD B7, ASD SAM 4). For single angles, the minimum radius of gyration,rz , is used instead of r22 and r33 in computing Kl r .

Flexural Buckling

The allowable axial compressive stress value, Fa , depends on the slenderness ratioKl r based on gross section properties and a corresponding critical value, C c ,where

Calculation of Allowable Stresses 27


Kl

r

K l

r

K l

rmax ,33 33

33

22 22

22

, and

c

2 2 E

Fy

. (ASD E2, ASD SAM 4)

For single angles, the minimum radius of gyration, rz , is used instead of r22 and r33

in computing Kl r .

For Compact or Noncompact sections Fa is evaluated as follows:

F =

Kl/r

CF

+Kl/r

C

Ka

c

y

c

( )2

22

5

3

3

8

l/r

C c

3

38

, ifKl

rC c , (ASD E2-1, SAM 4-1)

F =E

Kl ra

12

23

2

2( ), if

Kl

rC c . (ASD E2-2, SAM 4-2)

If Kl r is greater than 200, then the calculated value of Fa is taken not to exceed thevalue of Fa calculated by using the equation ASD E2-2 for Compact and Noncom-pact sections (ASD E1, B7).

For Slender sections, except slender Pipe sections, Fa is evaluated as follows:

F = Q

Kl/r

CF

+Kl/r

C

ac

y¢

( )2

22

5

3

3

8 c c

Kl/r

C¢

¢

3

38

, ifKl

rC c

¢ , (ASD A-B5-11, SAM 4-1)

F =E

Kl ra

12

23

2

2( ), if

Kl

rC c

¢ . (ASD A-B5-12, SAM 4-2)

where,

CE

Q Fc

y

¢ 2 2

. (ASD A-B5.2c, ASD SAM 4)

28 Calculation of Allowable Stresses


For slender sections, if Kl r is greater than 200, then the calculated value of Fa istaken not to exceed its value calculated by using the equation ASD A-B5-12 (ASDB7, E1).

For slender Pipe sections Fa is evaluated as follows:

F =D t

Fa y (ASD A-B5-9)

The reduction factor, Q, for all compact and noncompact sections is taken as 1. Forslender sections, Q is computed as follows:

Q Q Qs a , where (ASD A-B5.2.c, SAM 4)

Qs = reduction factor for unstiffened slender elements, and (ASD A-B5.2.a)

Qa = reduction factor for stiffened slender elements. (ASD A-B5.2.c)

The Qs factors for slender sections are calculated as described in Table III-3 (ASDA-B5.2a, ASD SAM 4). The Qa factors for slender sections are calculated as theratio of effective cross-sectional area and the gross cross-sectional area.

QA

Aa

e

g

(ASD A-B5-10)

The effective cross-sectional area is computed based on effective width as follows:

A A b b te g e

be for unstiffened elements is taken equal to b, and be for stiffened elements istaken equal to or less than b as given in Table III-4 (ASD A-B5.2b). For webs in I,box, and Channel sections, he is used as be and h is used as b in the above equation.

Flexural-Torsional Buckling

The allowable axial compressive stress value, Fa , determined by the limit states oftorsional and flexural-torsional buckling is determined as follows (ASD E3, C-E3):

F = Q

Kl/r

CF

+Kl/r

C

a

e

c

y

e

¢

2

22

5

3

3

8 c

e

c

Kl/r

C¢

¢

3

38

, if Kl/r Ce c

¢ , (E2-1, A-B5-11)





SectionType

Reduction Factor for Unstiffened Slender Elements(Qs )

EquationReference

I-SHAPEQ

if b t F k

b t F k if Fs

f f y c

f f y c y

2

2

,

k b t F k

k b t F if b t F k

c f f y c

c f f y f f y c

2

2 22

,

.

ASD A-B5-3,ASD A-B5-4

BOX Qs 1 ASD A-B5.2c

CHANNEL As for I-shapes with b tf f2 replaced by b tf f . ASD A-B5-3,ASD A-B5-4

T-SHAPE

For flanges, as for flanges in I-shapes. For web see below.

Q

if d t F

d t F if F d ts

w y

w y y w

,

, F

d t F if d t F

y

w y w y

,

, .2

ASD A-B5-3,ASD A-B5-4,ASD A-B5-5,ASD A-B5-6

DOUBLE-ANGLE

Q

if b t F

b t F if F b ts

y

y y

,

, F

b t F if b t F

y

y y

,

, .2

ASD A-B5-1,ASD A-B5-2,

SAM 4-3

ANGLE Q

if b t F

b t F if F b ts

y

y y

,

, F

b t F if b t F

y

y y

,

, .2

ASD A-B5-1,ASD A-B5-2,

SAM 4-3

PIPE Qs 1 ASD A-B5.2c

ROUNDBAR

Qs 1 ASD A-B5.2c

RECTAN-GULAR

Qs 1 ASD A-B5.2c

GENERAL Qs 1 ASD A-B5.2c

Table III-3Reduction Factor for Unstiffened Slender Elements, Qs



SectionType

Effective Width for Stiffened Sections EquationReference

I-SHAPE h

h ifh

t f

t

f h t fif

h

t

e

w

w

w w

, ,

( ),1

f.

(compression only, fP

Ag

) ASD A-B5-8

BOX

h

h ifh

t f

t

f h t fif

h

t

e

w

w

w w

, ,

( ),1

f.


Ag

)

b

b ifb

t f

t

f h t fif

b

t

e

f

f

f

, ,

( ),1

f.

(compr., flexure, f Fy )

ASD A-B5-8

ASD A-B5-7

CHANNEL h

h ifh

t f

t

f h t fif

h

t

e

w

w

w w

, ,

( ),1

f.


Ag

) ASD A-B5-8

T-SHAPE b beASD A-B5.2c

DOUBLE-ANGLE

b be ASD A-B5.2c

ANGLE b be ASD A-B5.2c

PIPE Qa 1, (However, special expression for allowable axial stress is given.) ASD A-B5-9

ROUNDBAR

Not applicable

RECTAN-GULAR

b be ASD A-B5.2c

GENERAL Not applicable

Note: A reduction factor of 3/4 is applied on f for axial-compression-only cases and if the load combination

includes any wind load or seismic load (ASD A-B5.2b).

Table III-4Effective Width for Stiffened Sections

F =E

Kl/ra

e

12

23

2

2, if Kl/r C

e c¢ . (E2-2, A-B5-12)

where,

CE

Q Fc

y

¢ 2 2

, and (ASD E2, A-B5.2c, SAM 4)

Kl/rE

Fee

2

. (ASD C-E2-2, SAM 4-4)

ASD Commentary (ASD C-E3) refers to the 1986 version of the AISC-LRFD codefor the calculation of Fe . The 1993 version of the AISC-LRFD code is the same asthe 1986 version in this respect. Fe is calculated in ETABS as follows:

• For Rectangular, I, Box, and Pipe sections:

FEC

K lGJ

I Ie

w

z z

2

222 33

1(LRFD A-E3-5)

• For T-sections and Double-angles:

F =F F

H

F F H

F Fe

e ez e ez

e ez

22 22

2222

1 14

(LRFD A-E3-6)

• For Channels:

F =F F

H

F F H

F Fe

e ez e ez

e ez

33 33

3322

1 14

(LRFD A-E3-6)

• For Single-angle sections with equal legs:

F =F F

H

F F H

F Fe

e ez e ez

e ez

33 33

3322

1 14

(ASD SAM C-C4-1)

• For Single-angle sections with unequal legs, Fe is calculated as the minimumreal root of the following cubic equation (ASD SAM C-C4-2, LRFD A-E3-7):



( )( )( ) ( ) (F F F F F F F F Fx

rFe e e e e ez e e e e33 22

222

02

02

2 F Fy

re e 33

02

02

0) ,

where,

x y0 0, are the coordinates of the shear center with respect to the centroid,x 0 0 for double-angle and T-shaped members (y-axis of symmetry),

r x yI I

Ag0 0

202 22 33 = polar radius of gyration about the shear center,

Hx y

r1 0

202

02

, (LRFD A-E3-9)

FE

K l re 33

2

33 33 33

2, (LRFD A-E3-10)

FE

K l re 22

2

22 22 22

2, (LRFD A-E3-11)

FEC

K lGJ

Arez

w

z z

2

202

1, (LRFD A-E3-12)

K K22 33, are effective length factors in minor and major directions,

K z is the effective length factor for torsional buckling, and it is taken equalto K 22 in ETABS,

l l22 33, are effective lengths in the minor and major directions,

l z is the effective length for torsional buckling, and it is taken equal to l22 .

For angle sections, the principal moment of inertia and radii of gyration are used forcomputing Fe (ASD SAM 4). Also, the maximum value of Kl, i .e,max( , )K l K l22 22 33 33 , is used in place of K l22 22 or K l33 33 in calculating Fe 22 and Fe 33

in this case.



Allowable Stress in Bending

The allowable bending stress depends on the following criteria: the geometricshape of the cross-section, the axis of bending, the compactness of the section, anda length parameter.

I-sections

For I-sections the length parameter is taken as the laterally unbraced length, l22 ,which is compared to a critical length, lc . The critical length is defined as

lb

F

A

d Fc

f

y

f

y

min ,,76 20 000

, where (ASD F1-2)

A f is the area of compression flange,

Major Axis of Bending

If l22 is less than lc , the major allowable bending stress for Compact andNoncompact sections is taken depending on whether the section is welded orrolled and whether f y is greater than 65 ksi or not.

For Compact sections:

F = Fb y33 if f y , (ASD F1-1)


For Noncompact sections:

F =b

tF Fb

f

f

y y33 2, if rolled and f y , (ASD F1-3)

F =b

t

F

kFb

f

f

y

c

y33 2, if welded and f y , (ASDF1-4)

F = Fb y33 if f y .. (ASD F1-5)

If the unbraced length l22 is greater than lc , then for both Compact and Non-compact I-sections the allowable bending stress depends on the l rT22 ratio.



Forl

r

C

FT

b

y

22 102 000,,

F Fb y33 , (ASD F1-6)

for102 000 510 00022, ,C

F

l

r

C

Fb

y T

b

y

,

FF l r

CF Fb

y T

b

y y3322

22

3 1530 000

( / )

,, and (ASD F1-6)

forl

r

C

FT

b

y

22 510 000,,

FC

l rFb

b

T

y33

222

170 0000

,

( / ), (ASD F1-7)

and Fb33 is taken not to be less than that given by the following formula:

FC

l d AFb

b

f

y33

22

12 000,

/(ASD F1-8)

where,

rT is the radius of gyration of a section comprising the compression flangeand 1 3 the compression web taken about an axis in the plane of the web,

C = +M

M+

M

Mba

b

a

b

2

, where (ASD F1.3)

M Ma band are the end moments of any unbraced segment of the member andM a is numerically less than M b ; M Ma b being positive for double curvaturebending and negative for single curvature bending. Also, if any moment withinthe segment is greater than M b , C b is taken as 1.0. Also, C b is taken as 1.0 forcantilevers and frames braced against joint translation (ASD F1.3). ETABS de-faults C b to 1.0 if the unbraced length, l22 , of the member is redefined by the



user (i.e. it is not equal to the length of the member). The user can overwrite thevalue of C b for any member by specifying it.

The allowable bending stress for Slender sections bent about their major axis isdetermined in the same way as for a Noncompact section. Then the followingadditional considerations are taken into account.

If the web is slender, then the previously computed allowable bending stress isreduced as follows:

F R R Fb PG e b33 33¢ , where (ASD G2-1)

RA

A

h

t FPG

w

f b

760

33

, (ASD G2)

R

A

A

A

A

e

w

f

w

f

3 3

, (hybrid girders) (ASD G2)

Re , (non-hybrid girders) (ASD G2)

Aw = Area of web, in 2 ,

A f = Area of compression flange, in 2 ,

F

Fy

b33

(ASD G2)

Fb33 = Allowable bending stress assuming the section is non-compact, and

Fb33¢ = Allowable bending stress after considering web slenderness.

In the above expressions, Re is taken as 1, because currently ETABS deals withonly non-hybrid girders.

If the flange is slender, then the previously computed allowable bending stressis taken to be limited as follows.

F Q Fb s y33¢ , where (ASD A-B5.2a, A-B5.2d)

Qs is defined earlier.



Minor Axis of Bending

The minor direction allowable bending stress Fb22 is taken as follows:




For Noncompact and Slender sections:

F =b

tF Fb

f

f

y y22 2, if f y , (ASD F2-3)

F = Fb y22 if f y .. (ASD F2-2)

Channel sections

For Channel sections the length parameter is taken as the laterally unbracedlength, l22 , which is compared to a critical length, lc . The critical length is de-fined as

lb

F

A

d Fc

f

y

f

y

min ,,76 20 000

, where (ASD F1-2)

A f is the area of compression flange,


If l22 is less than lc , the major allowable bending stress for Compact andNoncompact sections is taken depending on whether the section is welded orrolled and whether f y is greater than 65 ksi or not.




For Noncompact sections:

F =b

tF Fb

f

f

y y33 , if rolled and f y , (ASD F1-3)



F =b

t

F

kFb

f

f

y

c

y33 , if welded and f y ,(ASD F1-4)

F = Fb y33 if f y .. (ASD F1-5)

If the unbraced length l22 is greater than lc , then for both Compact andNoncompact Channel sections the allowable bending stress is taken as follows:

FC

l d AFb

b

f

y33

22

12 000,

/(ASD F1-8)

The allowable bending stress for Slender sections bent about their major axis isdetermined in the same way as for a Noncompact section. Then the followingadditional considerations are taken into account.

If the web is slender, then the previously computed allowable bending stress isreduced as follows:

F R R Fb e PG b33 33¢ (ASD G2-1)

If the flange is slender, the previously computed allowable bending stress istaken to be limited as follows:

F Q Fb s y33¢ (ASD A-B5.2a, A-B5.2d)

The definition for rT ,C b , A f , Aw , Re , RPG ,Qs , Fb33 , and Fb33¢ are given earlier.


The minor direction allowable bending stress Fb22 is taken as follows:

F = Fb y22 (ASD F2-2)

T-sections and Double angles

For T sections and Double angles, the allowable bending stress for both majorand minor axes bending is taken as,

F = Fb y .



Box Sections and Rectangular Tubes

For all Box sections and Rectangular tubes, the length parameter is taken as thelaterally unbraced length, l22 , measured compared to a critical length, lc . Thecritical length is defined as

l M /Mb

F,

b

Fc a b

y y

max ( )1950 12001200

(ASD F3-2)

where M a and M b have the same definition as noted earlier in the formula for

C b . If l22 is specified by the user, lc is taken as1200 b

Fy

in ETABS.


If l22 is less than lc , the allowable bending stress in the major direction ofbending is taken as:

F = Fb y33 (for Compact sections) (ASD F3-1)

F = Fb y33 (for Noncompact sections) (ASD F3-3)

If l22 exceeds lc , the allowable bending stress in the major direction of bend-ing for both Compact and Noncompact sections is taken as:

F = Fb y33 (ASD F3-3)

The major direction allowable bending stress for Slender sections is deter-mined in the same way as for a Noncompact section. Then the following addi-tional consideration is taken into account. If the web is slender, then the previ-ously computed allowable bending stress is reduced as follows:

F R R Fb e PG b33 33¢ (ASD G2-1)

The definition for Re , RPG , Fb33 , and Fb33¢ are given earlier.

If the flange is slender, no additional consideration is needed in computing al-lowable bending stress. However, effective section dimensions are calculatedand the section modulus is modified according to its slenderness.


If l22 is less than lc , the allowable bending stress in the minor direction of bend-ing is taken as:



F = Fb y22 (for Compact sections) (ASD F3-1)

F = Fb y22 (for Noncompact and Slender sections) (ASD F3-3)

If l22 exceeds lc , the allowable bending stress in the minor direction of bend-ing is taken, irrespective of compactness, as:

F = Fb y22 (ASD F3-3)

Pipe Sections

For Pipe sections, the allowable bending stress for both major and minor axesof bending is taken as

F = Fb y (for Compact sections), and (ASD F3-1)

F = Fb y (for Noncompact and Slender sections). (ASD F3-3)

Round Bars

The allowable stress for both the major and minor axis of bending of round barsis taken as,

F = Fb y . (ASD F2-1)

Rectangular and Square Bars

The allowable stress for both the major and minor axis of bending of solidsquare bars is taken as,

F = Fb y . (ASD F2-1)

For solid rectangular bars bent about their major axes, the allowable stress isgiven by

F = Fb y , And

the allowable stress for minor axis bending of rectangular bars is taken as,

F = Fb y . (ASD F2-1)



Single-Angle Sections

The allowable flexural stresses for Single-angles are calculated based on their prin-cipal axes of bending (ASD SAM 5.3).


The allowable stress for major axis bending is the minimum considering the limitstate of lateral-torsional buckling and local buckling (ASD SAM 5.1).

The allowable major bending stress for Single-angles for the limit state of lateral-torsional buckling is given as follows (ASD SAM 5.1.3):

F =F

FFb major

ob

yob, , if F Fob y (ASD SAM 5-3a)

F =F

FF Fb major

y

ob

y y, , if F Fob y (ASD SAM 5-3b)

where, Fob is the elastic lateral-torsional buckling stress as calculated below.

The elastic lateral-torsional buckling stress, Fob , for equal-leg angles is taken as

F Cl tob b , (ASD SAM 5-5)

and for unequal-leg angles Fob is calculated as

F CI

S llt rob b

major

w wmin

min2

2 2( ) , (ASD SAM 5-6)

where,

t t tw fmin , ,

l l lmax ,22 33 ,

Imin

= minor principal moment of inertia,

Imax

= major principal moment of inertia,

S major = major section modulus for compression at the tip of one leg,

rmin

= radius of gyration for minor principal axis,



w AIz w z dA z

122 2

0max

( ) , (ASD SAM 5.3.2)

z = coordinate along the major principal axis,

w = coordinate along the minor principal axis, and

z 0 = coordinate of the shear center along the major principal axis with respectto the centroid.

w is a special section property for angles. It is positive for short leg in compression,negative for long leg in compression, and zero for equal-leg angles (ASD SAM5.3.2). However, for conservative design in ETABS, it is always taken as negativefor unequal-leg angles.

In the above expressions C b is calculated in the same way as is done for I sectionswith the exception that the upper limit of C b is taken here as 1.5 instead of 2.3.

C = +M

M+

M

Mba

b

a

b

2

(ASD F1.3, SAM 5.2.2)

The allowable major bending stress for Single-angles for the limit state of localbuckling is given as follows (ASD SAM 5.1.1):

F = Fb major y, , ifb

t Fy

, (ASD SAM 5-1a)

F = Fb major y, , ifF

b

t Fy y

, (ASD SAM 5-1b)

F = Q Fb major y, , ifb

t Fy

, (ASD SAM 5-1c)

where,

t = thickness of the leg under consideration,

b = length of the leg under consideration, and

Q = slenderness reduction factor for local buckling. (ASD A-B5-2, SAM 4)

In calculating the allowable bending stress for Single-angles for the limit state of lo-cal buckling, the allowable stresses are calculated considering the fact that either of



the two tips can be under compression. The minimum allowable stress is consid-ered.


The allowable minor bending stress for Single-angles is given as follows (ASDSAM 5.1.1, 5.3.1b, 5.3.2b):

F = Fyb,minor, if

b

t Fy

, (ASD SAM 5-1a)

F = Fyb,minor, if

F

b

t Fy y

, (ASD SAM 5-1b)

F = Q Fyb,minor, if

b

t Fy

, (ASD SAM 5-1c)

In calculating the allowable bending stress for Single-angles it is assumed that thesign of the moment is such that both the tips are under compression. The minimumallowable stress is considered.

General Sections

For General sections the allowable bending stress for both major and minoraxes bending is taken as,

F = Fb y .

Allowable Stress in Shear

The allowable shear stress is calculated along the geometric axes for all sections.For I, Box, Channel, T, Double angle, Pipe, Circular and Rectangular sections, theprincipal axes coincide with their geometric axes. For Single-angle sections, princi-pal axes do not coincide with the geometric axes.


The allowable shear stress for all sections except I, Box and Channel sections istaken in ETABS as:

F Fv y (ASD F4-1, SAM 3-1)



The allowable shear stress for major direction shears in I-shapes, boxes and chan-nels is evaluated as follows:

F Fv y , ifh

t Fw y

380, and (ASD F4-1)

FC

F Fvv

y y , ifF

h

ty w

. (ASD F4-2)

where,

C

k

F h tif

h

t

k

F

h t

k

Fif

h

t

v

v

y w w

v

y

w

v

y

45 0002

,, ,

,w

v

y

k

F,

(ASD F4)

ka h

ifa

h

a hif

a

h

v

2

2

1

1

, ,

, ,(ASD F4)

tw = Thickness of the web,

a = Clear distance between transverse stiffeners, in. Currently it is takenconservatively as the length, l22 , of the member in ETABS,

h = Clear distance between flanges at the section, in.


The allowable shear stress for minor direction shears is taken as:

F Fv y (ASD F4-1, SAM 3-1)

Calculation of Stress RatiosIn the calculation of the axial and bending stress ratios, first, for each station alongthe length of the member, the actual stresses are calculated for each load combina-tion. Then the corresponding allowable stresses are calculated. Then, the stress ra-tios are calculated at each station for each member under the influence of each of

44 Calculation of Stress Ratios


the design load combinations. The controlling stress ratio is then obtained, alongwith the associated station and load combination. A stress ratio greater than 1.0 in-dicates an overstress.

During the design, the effect of the presence of bolts or welds is not considered.Also, the joints are not designed.

Axial and Bending Stresses

With the computed allowable axial and bending stress values and the factored axialand bending member stresses at each station, an interaction stress ratio is producedfor each of the load combinations as follows (ASD H1, H2, SAM 6):

• If f a is compressive and f Fa a , the combined stress ratio is given bythe larger of

f

F+

C f

f

F'F

+C fa

a

m b

a

e

b

m b33 33

33

33

22 22

1 1f

F'Fa

e

b

22

22

, and (ASD H1-1, SAM 6.1)

f

F

f

F

f

Fa

y

b

b

b

b

33

33

22

22

, where (ASD H1-2, SAM 6.1)

f a , f b33 , f b22 , Fa , Fb33 , and Fb22 are defined earlier in this chapter,

C m33 and C m22 are coefficients representing distribution of moment along themember length.

C mM

aM

b

,(ASD H1)

For sway frame C m , for nonsway frame without transverse loadC M Mm a b , for nonsway frame with transverse load and end re-strained compression member C m , and for nonsway frame with trans-verse load and end unrestrained compression member C m (ASD H1),where M Ma b is the ratio of the smaller to the larger moment at the ends of the

Calculation of Stress Ratios 45


member, M Ma b being positive for double curvature bending and negativefor single curvature bending. When M b is zero, C m is taken as 1.0. The pro-gram defaults C m to 1.0 if the unbraced length factor, l, of the member is rede-fined by either the user or the program, i.e., if the unbraced length is not equal tothe length of the member. The user can overwrite the value ofC m for any mem-ber. C m assumes two values, C m22 and C m33 , associated with the major and mi-nor directions.

Fe¢ is given by

FE

Kl re¢

12

23

2

2( / ). (ASD H1)

A factor of 4/3 is applied on Fe¢ and Fy if the load combination includes any

wind load or seismic load (ASD H1, ASD A5.2).

• If f a is compressive and f Fa a , a relatively simplified formula isused for the combined stress ratio.

f

F+

f

F+

f

Fa

a

b

b

b

b

33

33

22

22

(ASD H1-3, SAM 6.1)

• If f a is tensile or zero, the combined stress ratio is given by the larger of

f

F

f

F

f

Fa

a

b

b

b

b

33

33

22

22


f

F

f

Fb

b

b

b

33

33

22

22

, where

f a , f b33 , f b22 , Fa , Fb33 , and Fb22 are defined earlier in this chapter. However,either Fb33 or Fb22 need not be less than Fy in the first equation (ASD H2-1).The second equation considers flexural buckling without any beneficial effectfrom axial compression.

For circular and pipe sections, an SRSS combination is first made of the two bend-ing components before adding the axial load component, instead of the simple addi-tion implied by the above formulae.

For Single-angle sections, the combined stress ratio is calculated based on the prop-erties about the principal axis (ASD SAM 5.3, 6.1.5). For I, Box, Channel, T, Dou-ble-angle, Pipe, Circular and Rectangular sections, the principal axes coincide withtheir geometric axes. For Single-angle sections, principal axes are determined in

46 Calculation of Stress Ratios


ETABS. For general sections no effort is made to determine the principal direc-tions.

When designing for combinations involving earthquake and wind loads, allowablestresses are increased by a factor of 4/3 of the regular allowable value (ASD A5.2).

Shear Stresses

From the allowable shear stress values and the factored shear stress values at eachstation, shear stress ratios for major and minor directions are computed for each ofthe load combinations as follows:

f

Fv

v

2 , and

f

Fv

v

3 .

For Single-angle sections, the shear stress ratio is calculated for directions along thegeometric axis. For all other sections the shear stress is calculated along the princi-ple axes which coincide with the geometric axes.

When designing for combinations involving earthquake and wind loads, allowableshear stresses are increased by a factor of 4/3 of the regular allowable value (ASDA5.2).

Calculation of Stress Ratios 47


C h a p t e r IV

Check/Design for AISC-LRFD93

This chapter describes the details of the structural steel design and stress check al-gorithms that are used by ETABS when the user selects the AISC-LRFD93 designcode (AISC 1993). Various notations used in this chapter are described in TableIV-1.

For referring to pertinent sections and equations of the original LRFD code, aunique prefix “LRFD” is assigned. However, all references to the “Specificationsfor Load and Resistance Factored Design of Single-Angle Members” (AISC 1994)carry the prefix of “LRFD SAM”.


In the evaluation of the axial force/biaxial moment capacity ratios at a station alongthe length of the member, first the actual member force/moment components andthe corresponding capacities are calculated for each load combination. Then the ca-pacity ratios are evaluated at each station under the influence of all load combina-tions using the corresponding equations that are defined in this chapter. The con-trolling capacity ratio is then obtained. A capacity ratio greater than 1.0 indicatesexceeding a limit state. Similarly, a shear capacity ratio is also calculated sepa-rately.

49

50


A = Cross-sectional area, in2

Ae = Effective cross-sectional area for slender sections, in2

Ag = Gross cross-sectional area, in2

A Av v2 3, = Major and minor shear areas, in2

Aw = Shear area, equal dt w per web, in2

B1 = Moment magnification factor for moments not causing sidesway

B2 = Moment magnification factor for moments causing sidesway

Cb = Bending coefficient

Cm = Moment coefficient

Cw = Warping constant, in6

D = Outside diameter of pipes, in

E = Modulus of elasticity, ksi

Fcr = Critical compressive stress, ksi

Fr = Compressive residual stress in flange assumed 10.0 for rolledsections and 16.5 for welded sections, ksi

Fy = Yield stress of material, ksi

G = Shear modulus, ksi

I 22 = Minor moment of inertia, in4

I 33 = Major moment of inertia, in4

J = Torsional constant for the section, in4


K K33 22, = Effective length K-factors in the major and minor directions

Lb = Laterally unbraced length of member, in

Lp = Limiting laterally unbraced length for full plastic capacity, in

Lr = Limiting laterally unbraced length for inelastic lateral-torsionalbuckling, in

M cr = Elastic buckling moment, kip-in

M lt = Factored moments causing sidesway, kip-in

M nt = Factored moments not causing sidesway, kip-in

M Mn n33 22, = Nominal bending strength in major and minor directions, kip-in

M ob = Elastic lateral-torsional buckling moment for angle sections, kip-in

M Mr r33 22, = Major and minor limiting buckling moments, kip-in

M u = Factored moment in member, kip-in

M Mu u33 22, = Factored major and minor moments in member, kip-in

Pe = Euler buckling load, kips

Pn = Nominal axial load strength, kip

Pu = Factored axial force in member, kips

Py = A Fg y , kips

Q = Reduction factor for slender section, = Q Qa s

Table IV-1AISC-LRFD Notations

51

Chapter IV Check/Design for AISC-LRFD93

Qa = Reduction factor for stiffened slender elements

Qs = Reduction factor for unstiffened slender elements

S = Section modulus, in3

S S33 22, = Major and minor section moduli, in3

S Seff eff, ,,33 22 = Effective major and minor section moduli for slender sections, in3

S c = Section modulus for compression in an angle section, in3

V Vn n2 3, = Nominal major and minor shear strengths, kips

V Vu u2 3, = Factored major and minor shear loads, kips

Z = Plastic modulus, in3

Z Z33 22, = Major and minor plastic moduli, in3

b = Nominal dimension of plate in a section, inlonger leg of angle sections,b tf w2 for welded and b tf w3 for rolled box sections, etc.

be = Effective width of flange, in

b f = Flange width, in

d = Overall depth of member, in

d e = Effective depth of web, in

hc = Clear distance between flanges less fillets, inassumed d k2 for rolled sections, and d t f2 for welded sections

k = Distance from outer face of flange to web toe of fillet, in

kc = Parameter used for section classification,4 h t w , kc

l l33 22, = Major and minor direction unbraced member lengths, in

r = Radius of gyration, in

r r33 22, = Radii of gyration in the major and minor directions, in

t = Thickness, in

t f = Flange thickness, in

t w = Thickness of web, in

w = Special section property for angles, in

= Slenderness parameter

c e, = Column slenderness parameters

p = Limiting slenderness parameter for compact element

r = Limiting slenderness parameter for non-compact element

s = Limiting slenderness parameter for seismic element

slender = Limiting slenderness parameter for slender element

b = Resistance factor for bending, 0.9

c = Resistance factor for compression, 0.85

t = Resistance factor for tension, 0.9

v = Resistance factor for shear, 0.9

Table IV-1AISC-LRFD Notations (cont.)


Design Loading CombinationsThe design load combinations are the various combinations of the load cases forwhich the structure needs to be checked. For the AISC-LRFD93 code, if a structureis subjected to dead load (DL), live load (LL), wind load (WL), and earthquake in-duced load (EL), and considering that wind and earthquake forces are reversible,then the following load combinations may have to be defined (LRFD A4.1):

1.4 DL (LRFD A4-1)1.2 DL + 1.6 LL (LRFD A4-2)

0.9 DL 1.3 WL (LRFD A4-6)1.2 DL 1.3 WL (LRFD A4-4)1.2 DL + 0.5 LL 1.3 WL (LRFD A4-4)

0.9 DL 1.0 EL (LRFD A4-6)1.2 DL 1.0 EL (LRFD A4-4)1.2 DL + 0.5 LL 1.0 EL (LRFD A4-4)

These are also the default design load combinations in ETABS whenever theAISC-LRFD93 code is used. The user should use other appropriate loading combi-nations if roof live load is separately treated, if other types of loads are present, or ifpattern live loads are to be considered.


When using the AISC-LRFD93 code, ETABS design assumes that a P- analysishas been performed so that moment magnification factors for moments causingsidesway can be taken as unity. It is recommended that the P- analysis be done atthe factored load level of 1.2 DL plus 0.5 LL (White and Hajjar 1991).

Classification of SectionsThe nominal strengths for axial compression and flexure are dependent on the clas-sification of the section as Compact, Noncompact, Slender or Too Slender. ETABS





Figure IV-1AISC-LRFD Definition of Geometric Properties



Descriptionof Section

Check COMPACT( p )

NONCOMPACT

r

SLENDER( slender )

I-SHAPE

b tf f2(rolled)

Fy65 F - .y141 10 0 No limit

b tf f2(welded)

Fy65F -

ky

c

162 No limit

h tc w

For P Pu b y ,640

1F

-P

Py

u

b y

For P Pu b y

191

253

F-

P

P

F

y

u

b y

y

F

P

Py

u

b y

970 F Fy y

BOXb tf

h tc w

Fy190

As for I-shapes

Fy238

As for I-shapes

No limit

Fy

CHANNELb tf f

h tc w

As for I-shapesAs for I-shapes


No limitAs for I-shapes

T-SHAPEb tf f2d tw

As for I-ShapesNot applicable

As for I-ShapesFy127

No limitNo limit

ANGLE b t Not applicable Fy76 No limit

DOUBLE-ANGLE

(Separated)b t Not applicable Fy76 No limit

PIPE D t Fy Fy

Fy

(Compression only)No limit for flexure


RECTAN-GULAR Assumed Noncompact


Table IV-2Limiting Width-Thickness Ratios for

Classification of Sections in Flexure based on AISC-LRFD




Width-Thickness

Ratio

NONCOMPACT(Uniform Compression)

(M M22 33 0)( r )

I-SHAPE

b tf f2(rolled)

Fy95

b tf f2(welded)

Fy95

h tc w Fy253

BOXb tf

h tc w

Fy238

Fy253

CHANNELb tf f

h tc w


T-SHAPEb tf f2d tw

As for I-shapesFy127

ANGLE b t Fy76

DOUBLE-ANGLE(Separated)

b t Fy76

PIPE D t Fy3300


RECTANGULAR Assumed Noncompact


Table IV-3Limiting Width-Thickness Ratios for

Classification of Sections (Special Cases) based on AISC-LRFD

classifies individual members according to the limiting width/thickness ratiosgiven in Table IV-2 and Table IV-3 (LRFD B5.1, A-G1, Table A-F1.1). The defini-tion of the section properties required in these tables is given in Figure IV-1 andTable IV-1. Moreover, special considerations are required regarding the limits ofwidth-thickness ratios for Compact sections in Seismic zones and Noncompact sec-tions with compressive force as given in Table IV-3. If the limits for Slender sec-tions are not met, the section is classified as Too Slender. Stress check of TooSlender sections is beyond the scope of ETABS.

In classifying web slenderness of I-shapes, Box, and Channel sections, it is as-sumed that there are no intermediate stiffeners. Double angles are conservativelyassumed to be separated.

Calculation of Factored ForcesThe factored member loads that are calculated for each load combination are Pu ,M u33 , M u22 , Vu2 and Vu3 corresponding to factored values of the axial load, themajor moment, the minor moment, the major direction shear force and the minor di-rection shear force, respectively. These factored loads are calculated at each of thepreviously defined stations.

For loading combinations that cause compression in the member, the factored mo-ment M u (M u33 and M u22 in the corresponding directions) is magnified to considersecond order effects. The magnified moment in a particular direction is given by:

M = B M + B Mu nt lt1 2 , where (LRFD C1-1, SAM 6)

B1 = Moment magnification factor for non-sidesway moments,B2 = Moment magnification factor for sidesway moments,M nt = Factored moments not causing sidesway, andM lt = Factored moments causing sidesway.

The moment magnification factors are associated with corresponding directions.The moment magnification factor B1 for moments not causing sidesway is given by

B =C

P Pm

u e1 1

, where (LRFD C1-2, SAM 6-2)

Pe is the Euler buckling load (PA F Kl

r

F

Ee

g y y

2, ), and

56 Calculation of Factored Forces


C m33 and C m22 are coefficients representing distribution of moment along themember length.

C m M

Ma

b

,(LRFD C1-3)

M Ma b is the ratio of the smaller to the larger moment at the ends of the mem-ber, M Ma b being positive for double curvature bending and negative for sin-gle curvature bending. For tension members C m is assumed as 1.0. For com-pression members with transverse load on the member, C m is assumed as 1.0for members with any unrestrained end and as 0.85 for members with two unre-strained ends. When M b is zero, C m is taken as 1.0. The program defaults C m

to 1.0 if the unbraced length factor, l, of the member is redefined by either theuser or the program, i.e., if the unbraced length is not equal to the length of themember. The user can overwrite the value of C m for any member. C m assumestwo values, C m22 and C m33 , associated with the major and minor directions.

The magnification factor B1 , must be a positive number. Therefore Pu must be lessthan Pe . If Pu is found to be greater than or equal to Pe , a failure condition is de-clared.

ETABS design assumes the analysis includes P- effects, therefore B2 is taken asunity for bending in both directions. It is suggested that the P- analysis be done atthe factored load level of 1.2 DL plus 0.5 LL (LRFD C2.2). See also White andHajjar (1991).

For single angles, where the principal axes of bending are not coincident with thegeometric axes (2-2 and 3-3), the program conservatively uses the maximum ofK l22 22 and K l33 33 for determining the major and minor direction Euler buckling ca-pacity.

If the program assumptions are not satisfactory for a particular structural model ormember, the user has a choice of explicitly specifying the values of B1 and B2 forany member.

Calculation of Factored Forces 57


Calculation of Nominal StrengthsThe nominal strengths in compression, tension, bending, and shear are computedfor Compact, Noncompact, and Slender sections according to the following subsec-tions. The nominal flexural strengths for all shapes of sections are calculated basedon their principal axes of bending. For the Rectangular, I, Box, Channel, Circular,Pipe, T, and Double-angle sections, the principal axes coincide with their geometricaxes. For the Angle sections, the principal axes are determined and all computa-tions except shear are based on that.

For Single-angle sections, the nominal shear strengths are calculated for directionsalong the geometric axes. For all other sections the shear stresses are calculatedalong their geometric and principle axes.

The strength reduction factor, , is taken as follows (LRFD A5.3):

t = Resistance factor for tension, 0.9 (LRFD D1, H1, SAM 2, 6)

c = Resistance factor for compression, 0.85 (LRFD E2, E3, H1)

c = Resistance factor for compression in angles, 0.90 (LRFD SAM 4, 6)

b = Resistance factor for bending, 0.9 (LRFD F1, H1, A-F1, A-G2, SAM 5)

v = Resistance factor for shear, 0.9 (LRFD F2, A-F2, A-G3, SAM 3)

If the user specifies nonzero factored strengths for one or more elements in the“Capacity Overwrites” form, these values will override the above mentioned cal-culated values for those elements. The specified factored strengths should bebased on the principal axes of bending.

Compression Capacity

The nominal compression strength is the minimum value obtained from flexuralbuckling, torsional buckling and flexural-torsional buckling. The strengths are de-termined according to the following subsections.

For members in compression, if Kl r is greater than 200, a message to that effect isprinted (LRFD B7, SAM 4). For single angles, the minimum radius of gyration, rz ,is used instead of r22 and r33 in computing Kl r .

Flexural Buckling

The nominal axial compressive strength, Pn , depends on the slenderness ratio, Kl r,and its critical value, c , where

58 Calculation of Nominal Strengths


Kl

r

K l

r

K l

rmax ,33 33

33

22 22

22

, and

c

Kl

r

F

Ey . (LRFD E2-4, SAM 4)

For single angles, the minimum radius of gyration, rz , is used instead of r22 and r33

in computing Kl r .

Pn for Compact or Noncompact sections is evaluated for flexural buckling as fol-lows:

P = A Fn g cr , where (LRFD E2-1)

F = Fcr ycl2

, for c , and (LRFD E2-2)

F = Fcr y

c

2, for c . (LRFD E2-3)

Pn for Slender sections is evaluated for flexural buckling as follows:

P = A Fn g cr , where (LRFD A-B3d, SAM 4)

F = Q Fcr ycQl2

, for c Q , and (LRFD A-B5-15, SAM 4-1)

F = Fcr y

c

2, for c Q . (LRFD A-B5-16, SAM 4-2)

The reduction factor, Q, for all compact and noncompact sections is taken as 1. Forslender sections, Q is computed as follows:

Q Q Qs a , where (LRFD A-B5-17, SAM 4)

Qs = reduction factor for unstiffened slender elements, and (LRFD A-B5.3a)

Qa = reduction factor for stiffened slender elements. (LRFD A-B5.3c)

TheQs factors for slender sections are calculated as described in Table IV-4 (LRFDA-B5.3a). The Qa factors for slender sections are calculated as the ratio of effectivecross-sectional area and the gross cross-sectional area (LRFD A-B5.3c).

QA

Aa

e

g

(LRFD A-B5-14)

Calculation of Nominal Strengths 59




SectionType

Reduction Factor for Unstiffened Slender Elements(Qs )

EquationReference

I-SHAPE

Q

if b t F

b t F if Fs

f f y

f f y y

2

2

,

, b t F

b t F if b t F

f f y

f f y f f y

2

2 22

,

, .

(rolled)

LRFD A-B5-5,LRFD A-B5-6

Q

if b t F k

b t F k if Fs

f f y c

f f y c

2

2

,

y c f f y c

c f f y f f y c

k b t F k

k b t F if b t F k

2

2 22

,

.

(welded)


BOX Qs 1 LRFD A-B5.3d

CHANNEL As for I-shapes with b tf f2 replaced by b tf f .

LRFD A-B5-5,LRFD A-B5-6,LRFD A-B5-7,LRFD A-B5-8

T-SHAPE

For flanges, as for flanges in I-shapes. For web see below.

Q

if d t F

d t F if F d ts

w y

w y y w

,

, F

d t F if d t F

y

w y w y

,

, .2

LRFD A-B5-5,LRFD A-B5-6,LRFD A-B5-7,LRFD A-B5-8,LRFD A-B5-9,LRFDA-B5-10

DOUBLE-ANGLE

(Separated)

Q

if b t F

b t F if F b ts

y

y y

,

, F

b t F if b t F

y

y y

,

, .2


ANGLE Q

if b t F E

b t F E if F E bs

y

y y

,

, t F E

b t F E if b t F E

y

y y

,

, .2

LRFD SAM4-3

PIPE Qs 1 LRFD A-B5.3d

ROUNDBAR

Qs 1 LRFD A-B5.3d

RECTAN-GULAR

Qs 1 LRFD A-B5.3d

GENERAL Qs 1 LRFD A-B5.3d

Table IV-4Reduction Factor for Unstiffened Slender Elements, Qs



SectionType

Effective Width for Stiffened Sections EquationReference

I-SHAPE h

h ifh

t f

t

f h t fif

h

t

e

w

w

w w

, ,

( ),1

f.


Ag

) LRFD A-B5-12

BOX

h

h ifh

t f

t

f h t fif

h

t

e

w

w

w w

, ,

( ),1

f.


Ag

)

b

b ifb

t f

t

f b t fif

b

t

e

f

f

f f

, ,

( ),1

f.

(compr. or flexure, f Fy )

LRFD A-B5-12

LRFD A-B5-11

CHANNEL h

h ifh

t f

t

f h t fif

h

t

e

w

w

w w

, ,

( ),1

f.


Ag

) LRFD A-B5-12

T-SHAPE b be LRFD A-B5.3b

DOUBLE-ANGLE

(Separated)b be LRFD A-B5.3b

ANGLE b be LRFD A-B5.3b

PIPE Q

ifD

t F

D t Fif

D

t F

ay

y y

1 , ,

, .(compression only) LRFD A-B5-13

ROUNDBAR

Not applicable

RECTAN-GULAR

b be LRFD A-B5.3b

GENERAL Not applicable

Table IV-5Effective Width for Stiffened Sections

The effective cross-sectional area is computed based on effective width as follows:

A A b b te g e

be for unstiffened elements is taken equal to b, and be for stiffened elements istaken equal to or less than b as given in Table IV-5 (LRFD A-B5.3b). For webs in I,box, and Channel sections, he is used as be and h is used as b in the above equation.

Flexural-Torsional Buckling

Pn for flexural-torsional buckling of Double-angle and T-shaped compressionmembers whose elements have width-thickness ratios less than r is given by

P = A Fn g crft , where (LRFD E3-1)

F =F F

H

F F H

F Fcrft

cr crz cr crz

cr cr

2 2

22

1 14

z2

, where (LRFD E3-1)

FGJ

Arcrz

02

,

Hx y

r1 0

202

02

,

r0 = Polar radius of gyration about the shear center,


Fcr 2 is determined according to the equation LRFD E2-1 for flexural

buckling about the minor axis of symmetry for cyKl

r

F

E22

.

Torsional and Flexural-Torsional Buckling

The strength of a compression member, Pn , determined by the limit states of tor-sional and flexural-torsional buckling is determined as follows:

P = A Fn g cr , where (LRFD A-E3-1)



F = Q Fcr yeQl2

, for e Q , and (LRFD A-E3-2)

F = Fcr y

e

2, for e Q . (LRFD A-E3-3)

In the above equations, the slenderness parameter e is calculated as

e

F

Fy

e

, (LRFD A-E3-4)

where Fe is calculated as follows:

• For Rectangular, I, Box, and Pipe sections:

FEC

K lGJ

I Ie

w

z z

2

222 33

1(LRFD A-E3-5)

• For T-sections and Double-angles:

F =F F

H

F F H

F Fe

e ez e ez

e ez

22 22

2222

1 14

(LRFD A-E3-6)

• For Channels:

F =F F

H

F F H

F Fe

e ez e ez

e ez

33 33

3322

1 14

(LRFD A-E3-6)

• For Single-angles sections with equal legs:

F =F F

H

F F H

F Fe

e ez e ez

e ez

33 33

3322

1 14

(LRFD A-E3-6)

• For Single-angle sections with unequal legs, Fe is calculated as the minimumreal root of the following cubic equation (LRFD A-E3-7):

( )( )( ) ( ) (F F F F F F F F Fx

rFe e e e e ez e e e e33 22

222

02

02

2 F Fy

re e 33

02

02

0) ,

where,




r x yI I

Ag0 0

202 22 33 = polar radius of gyration about the shear center,

Hx y

r1 0

202

02

, (LRFD A-E3-9)

FE

K l re 33

2

33 33 33

2, (LRFD A-E3-10)

FE

K l re 22

2

22 22 22

2, (LRFD A-E3-11)

FEC

K lGJ

Arez

w

z z

2

202

1, (LRFD A-E3-12)

K K22 33, are effective length factors in minor and major directions,

K z is the effective length factor for torsional buckling, and it is taken equalto K 22 in ETABS,

l l22 33, are effective lengths in the minor and major directions,

l z is the effective length for torsional buckling, and it is taken equal to l22 .

For angle sections, the principal moment of inertia and radii of gyration are used forcomputing Fe . Also, the maximum value of Kl, i.e, max( , )K l K l22 22 33 33 , is used inplace of K l22 22 or K l33 33 in calculating Fe 22 and Fe 33 in this case.

Tension Capacity

The nominal axial tensile strength value Pn is based on the gross cross-sectionalarea and the yield stress.

P A Fn g y (LRFD D1-1)

It should be noted that no net section checks are made. For members in tension,if l r is greater than 300, a message to that effect is printed (LRFD B7, SAM 2). For



single angles, the minimum radius of gyration, rz , is used instead of r22 and r33 incomputing Kl r .

Nominal Strength in Bending

The nominal bending strength depends on the following criteria: the geometricshape of the cross-section, the axis of bending, the compactness of the section, anda slenderness parameter for lateral-torsional buckling. The nominal strengths for allshapes of sections are calculated based on their principal axes of bending. For theRectangular, I, Box, Channel, Circular, Pipe, T, and Double-angle sections, theprincipal axes coincide with their geometric axes. For the Single Angle sections,the principal axes are determined and all computations related to flexural strengthsare based on that. The nominal bending strength is the minimum value obtained ac-cording to the limit states of yielding, lateral-torsional buckling, flange local buck-ling, and web local buckling, as follows:

Yielding

The flexural design strength of beams, determined by the limit state of yielding is:

M Z F S Fp y y (LRFD F1-1)

Lateral-Torsional Buckling

Doubly Symmetric Shapes and Channels

For I, Channel, Box, and Rectangular shaped members bent about the major axis,the moment capacity is given by the following equation (LRFD F1):

M =

M if L L

C M - M - ML - L

L -n

p b p

b p p rb p

r33

33

33 33 33

, ,

LM if L L L

M M if L

pp p b r

cr p

33

33 33

, ,

, b rL .

(LRFD F1-1, F1-2, F1-12)

where,

M n33 = Nominal major bending strength,M p33 = Major plastic moment, Z F S Fy y33 33 , (LRFD F1.1)



M r 33 = Major limiting buckling moment,( )F F Sy r 33 for I-shapes and channels, (LRFD F1-7)and F Sy eff , 33 for rectangular bars and boxes, (LRFD F1-11)

M cr 33 = Critical elastic moment,

C

LEI GJ +

E

LI Cb

b b

w22

2

22

for I-shapes and channels, and (LRFD F1-13)57000

22

C JA

L rb

b

for boxes and rectangular bars, (LRFD F1-14)

Lb = Laterally unbraced length, l22 ,

Lp = Limiting laterally unbraced length for full plastic capacity,300 22r

Fy

for I-shapes and channels, and (LRFD F1-4)

3750 22

33

r

MJA

p


Lr = Limiting laterally unbraced length forinelastic lateral-torsional buckling,

r X

F F+ X F - F

y r

y r22 1

21 212

12

for I-shapes and channels, and (LRFD F1-6)

57000 22

33

r JA

M r


X 1 =S

EGJA

33 2, (LRFD F1-8)

X 2 = 422

33

2C

I

S

GJw , (LRFD F1-9)

C b =M

M + M + M + MA B C

max

max3 4 3

, and (LRFD F1-3)

Mmax

, M M MA B C, ,and are absolute values of maximum moment, 1/4 point, cen-ter of span and 3/4 point major moments respectively, in the member. C b should betaken as 1.0 for cantilevers. However, the program is unable to detect whether themember is a cantilever. The user should overwrite C b for cantilevers. The pro-

gram also defaults C b to 1.0 if the minor unbraced length, l22 , of the member is re-



defined by the user (i.e. it is not equal to the length of the member). The user canoverwrite the value of C b for any member.

For I, Channel, Box, and Rectangular shaped members bent about the minor axis,the moment capacity is given by the following equation:

M = M = Z F S Fn p y y22 22 22 22 (LRFD F1)

For pipes and circular bars bent about any axis,

M = M = Z F S Fn p y y . (LRFD F1)

T-sections and Double Angles

For T-shapes and Double-angles the nominal major bending strength is given as,

M =EI GJ

LB + + Bn

b

3322 21 , where (LRFD F1-15)

M F Sn y33 33 , for positive moment, stem in tension (LRFD F1.2c)

M F Sn y33 33 , for negative moment, stem in compression (LRFD F1.2c)

Bd

L

I

Jb

22 . (LRFD F1-16)

The positive sign for B applies for tension in the stem of T-sections or the out-standing legs of double angles (positive moments) and the negative sign applies forcompression in stem or legs (negative moments).

For T-shapes and double angles the nominal minor bending strength is assumed as,

M = S Fn y22 22 .

Single Angles

The nominal strengths for Single-angles are calculated based on their principal axesof bending. The nominal major bending strength for Single-angles for the limitstate of lateral-torsional buckling is given as follows (LRFD SAM 5.1.3):



M =M

MM Mn major

ob

y major

ob,

,

y major ob y majorif M M, ,, ,

M =M

MMn major

y major

ob

y major,,

, M if M My major ob y major, ,, ,

where,

M y major, = yield moment about the major principal axis of bending,considering the possibility of yielding at the heel and both of theleg tips,

M ob = elastic lateral-torsional buckling moment as calculated below.

The elastic lateral-torsional buckling moment, M ob , for equal-leg angles is taken as

M CE b t

lob b

2 2

, (LRFD SAM 5-5)

and for unequal-leg angles the M ob is calculated as

M ECI

llt rob b w w

min

min2

2 2( ) , (LRFD SAM 5-6)

where,

t t tw fmin , ,

l l lmax ,22 33 ,

Imin

= minor principal axis moment of inertia,

Imax

= major principal axis moment of inertia,

rmin

= radius of gyration for minor principal axis,

w AIz w z dA z

122 2

0max

( ) , (LRFD SAM 5.3.2)

z = coordinate along the major principal axis,

w = coordinate along the minor principal axis, and

z 0 = coordinate of the shear center along the major principal axis with respectto the centroid.



w is a special section property for angles. It is positive for short leg in compression,negative for long leg in compression, and zero for equal-leg angles (LRFD SAM5.3.2). However, for conservative design in ETABS, it is always taken as negativefor unequal-leg angles.

General Sections

For General sections the nominal major and minor direction bending strengths areassumed as,

M = S Fn y .

Flange Local Buckling

The flexural design strength, M n , of Noncompact and Slender beams for the limitstate of Flange Local Buckling is calculated as follows (LRFD A-F1):

For major direction bending,

M =

M if

M M Mn

p p

p p r

p

r p33

33

33 33 33

, ,

, ,

, .

if

M M if

p r

cr p r33 33

(A-F1-3)

and for minor direction bending,

M =

M if

M M Mn

p p

p p r

p

r p22

22

22 22 22

, ,

, ,

, .

if

M M if

p r

cr p r22 22

(A-F1-3)

where,

M n33 = Nominal major bending strength,M n22 = Nominal minor bending strength,M p33 = Major plastic moment, Z F S Fy y33 33 ,M p22 = Minor plastic moment, Z F S Fy y22 22 ,



M r 33 = Major limiting buckling moment,M r 22 = Minor limiting buckling moment,M cr 33 = Major buckling moment,M cr 22 = Minor buckling moment,

= Controlling slenderness parameter,

p = Largest value of for which M Mn p , and

r = Largest value of for which buckling is inelastic.

The parameters , p , r , M r 33 , M r 22 , M cr 33 , and M cr 22 for flange local bucklingfor different types of shapes are given below:

I Shapes, Channels

b

tf

f2, (for I sections) (LRFD B5.1, Table A-F1.1)

b

tf

f

, (for Channel sections) (LRFD B5.1, Table A-F1.1)

p

yF, (LRFD B5.1, Table A-F1.1)

r

y r

y r c

F F

F F k

,

,(LRFD Table A-F1.1)

M F F Sr y r33 33( ) , (LRFD Table A-F1.1)

M F Sr y22 22 , (LRFD Table A-F1.1)

MS

kS

crc

33

2 33

2 33

,


MS

kS

crc

22

2 22

2 22

,




Fr (LRFD A-F1)

Boxes

b t

tb t

t

f w

f

f w

f

3

2

,

,

(LRFD B5.1, Table A-F1.1)

p


r


M F F Sr y r eff33 33( ) , , (LRFD Table A-F1.1)

M F F Sr y r eff22 22( ) , , (LRFD Table A-F1.1)

M F S S Scr y eff eff33 33 33 33, , , (LRFD Table A-F1.1)

M F Scr y eff22 22, , (LRFD Table A-F1.1)

Fr (LRFD A-F1)

S eff , 33 = effective major section modulus considering slenderness, and

S eff , 22 = effective minor section modulus considering slenderness.


No local buckling is considered for T sections and Double angles in ETABS. If spe-cial consideration is required, the user is expected to analyze this separately.

Single Angles

The nominal strengths for Single-angles are calculated based on their principal axesof bending. The nominal major and minor bending strengths for Single-angles forthe limit state of flange local buckling are given as follows (LRFD SAM 5.1.1):



M =

F S ifb

t F

F S

F

n

y c

y

y c

, ,

y

y

ifF

b

t1 ,

F

F S ifb

t F

y

y c

y

,

, ,

where,

S c = section modulus for compression at the tip of one leg,

t = thickness of the leg under consideration,

b = length of the leg under consideration, and

Q = strength reduction factor due to local buckling.

In calculating the bending strengths for Single-angles for the limit state of flange lo-cal buckling, the capacities are calculated for both the principal axes consideringthe fact that either of the two tips can be under compression. The minimum capaci-ties are considered.

Pipe Sections

t, (LRFD Table A-F1.1)

p

yF, (LRFD Table A-F1.1)

r

yF(LRFD Table A-F1.1)

M = M =D t

+ F Sr r y33 22 , (LRFD Table A-F1.1)

M = M =D t

Scr cr33 22 , (LRFD Table A-F1.1)



Circular, Rectangular, and General Sections

No consideration of local buckling is required for solid circular shapes, rectangularplates (LRFD Table A-F1.1). No local buckling is considered in ETABS for circu-lar, rectangular, and general shapes. If special consideration is required, the user isexpected to analyze this separately.

Web Local Buckling

The flexural design strengths are considered in ETABS for only the major axisbending (LRFD Table A-F1.1).

I Shapes, Channels, and Boxes

The flexural design strength for the major axis bending, M n , of Noncompact andSlender beams for the limit state of Web Local Buckling is calculated as follows(LRFD A-F1-1, A-F1-3, A-G2-2):

M =

M if

M M Mn

p p

p p r

p

r p33

33

33 33 33

, ,

, ,

, ,

if

S R R F if

p r

PG e cr r33

(A-F1,A-G1)

where,

M n33 = Nominal major bending strength,M p33 = Major plastic moment, Z F S Fy y33 33 , (LRFD F1.1)M r 33 = Major limiting buckling moment,R S Fe y33 ,(LRFD TableA-F1.1)

= Web slenderness parameter,

p = Largest value of for which M Mn p ,

r = Largest value of for which buckling is inelastic,RPG = Plate girder bending strength reduction factor,Re = Hybrid girder factor, andFcr = Critical compression flange stress, ksi.

The web slenderness parameters are computed as follows, where the value of Pu istaken as positive for compression and zero for tension:

h

tc

w

,



py

u

b y

u

b yF-

P

P

P

P1 ,

F-

P

P F

P

Py

u

b y y

u

b y

253,

r

y

u

b yF-

P

P1 .

The parameters RPG , Re , and Fcr for slender web sections are calculated in ETABSas follows:

Ra

a

h

t FPG

r

r

c

w cr

, (LRFD A-G2-3)

Ra m m

ae

r

r

3

(for hybrid sections), (LRFD A-G2)

Re , (for non-hybrid section), where (LRFD A-G2)

ar , and (LRFD A-G2)

mF

F Fy

cr ymin( , ), taken as 1.0. (LRFD A-G2)

In the above expressions, Re is taken as 1, because currently ETABS deals withonly non-hybrid girders.

The critical compression flange stress, Fcr , for slender web sections is calculatedfor limit states of lateral-torsional buckling and flange local buckling for the corre-sponding slenderness parameter in ETABS as follows:



F =

F if

C F F ifcr

y p

b yp

r p

y p

, ,

,11

2

Cif

r

PGr

,

, ,2

(LRFD A-G2-4, 5, 6)

The parameters , p , r , and C PG for lateral-torsional buckling for slender web I,Channel and Box sections are given below:

L

rb

T

, (LRFD A-G2-7)

p

yF, (LRFD A-G2-8)

r

yF, (LRFD A-G2-9)

C CPG b , and (LRFD A-G2-10)

rT = radius of gyration of the compression flange plus one-third of thecompression portion of the web, and it is taken as b f 12 in ETABS.

C b = a factor which depends on span moment. It is calculated usingthe equation given in page 66.

The parameters , p , r , and C PG for flange local buckling for slender web I,Channel and Box sections are given below:

b

t, (LRFD A-G2-11)

p

yF, (LRFD A-G2-12)

r

y cF k, (LRFD A-G2-13)

C kPG c , and (LRFD A-G2-14)

C b 1. (LRFD A-G2-15)




No local buckling is considered for T-sections and Double-angles in ETABS. Ifspecial consideration is required, the user is expected to analyze this separately.

Single Angles

The nominal major and minor bending strengths for Single-angles for the limit stateof web local buckling are the same as those given for flange local buckling (LRFDSAM 5.1.1). No additional check is considered in ETABS.

Pipe Sections

The nominal major and minor bending strengths for Pipe sections for the limit stateof web local buckling are the same as those given for flange local buckling (LRFDTable A-F1.1). No additional check is considered in ETABS.

Circular, Rectangular, and General Sections

No web local buckling is required for solid circular shapes and rectangular plates(LRFD Table A-F1.1). No web local buckling is considered in ETABS for circular,rectangular, and general shapes. If special consideration is required, the user is ex-pected to analyze them separately.

Shear Capacities

The nominal shear strengths are calculated for shears along the geometric axes forall sections. For I, Box, Channel, T, Double angle, Pipe, Circular and Rectangularsections, the principal axes coincide with their geometric axes. For Single-anglesections, principal axes do not coincide with their geometric axes.


The nominal shear strength,Vn2 , for major direction shears in I-shapes, boxes andchannels is evaluated as follows:

Forh

t Fw y

,

V = F An y w2 , (LRFD F2-1)

forF

<h

t Fy w y

,



V = F AF

h

tn y w

y w2 , and (LRFD F2-2)

forF

<h

ty w

,

V =A

h tn

w

w

2 2. (LRFD F2-3 and A-F2-3)

The nominal shear strength for all other sections is taken as:

V = F An y v2 2 .


The nominal shear strength for minor direction shears is assumed as:

V = F An y v3 3

Calculation of Capacity RatiosIn the calculation of the axial force/biaxial moment capacity ratios, first, for eachstation along the length of the member, the actual member force/moment compo-nents are calculated for each load combination. Then the corresponding capacitiesare calculated. Then, the capacity ratios are calculated at each station for each mem-ber under the influence of each of the design load combinations. The controlling ca-pacity ratio is then obtained, along with the associated station and load combina-tion. A capacity ratio greater than 1.0 indicates exceeding a limit state.



The interaction ratio is determined based on the ratio P Pu n . If Pu is tensile, Pn

is the nominal axial tensile strength and t ; and if Pu is compressive,Pn is the nominal axial compressive strength and c , except for anglesections c (LRFD SAM 6). In addition, the resistance factor forbending, b .

Calculation of Capacity Ratios 77


ForP

Pu

n

, the capacity ratio is given as

P

P+

M

M+

M

Mu

n

u

b n

u

b n

8

933

33

22

22

. (LRFD H1-1a, SAM 6-1a)

ForP

P<u

n


P

P+

M

M+

M

Mu

n

u

b n

u

b n233

33

22

22

. (LRFD H1-1b, SAM 6-1a)

For circular sections an SRSS (Square Root of Sum of Squares) combination is firstmade of the two bending components before adding the axial load component in-stead of the simple algebraic addition implied by the above formulas.

For Single-angle sections, the combined stress ratio is calculated based on the prop-erties about the principal axis (LRFD SAM 5.3, 6). For I, Box, Channel, T, Doubleangle, Pipe, Circular and Rectangular sections, the principal axes coincide withtheir geometric axes. For Single-angle sections, principal axes are determined inETABS. For general sections it is assumed that the section properties are given interms of the principal directions.

Shear Stresses

Similarly to the normal stresses, from the factored shear force values and the nomi-nal shear strength values at each station for each of the load combinations, shear ca-pacity ratios for major and minor directions are calculated as follows:

V

Vu

v n

2

2

, and

V

Vu

v n

3

3

,

where v .


78 Calculation of Capacity Ratios


C h a p t e r V

Check/Design for UBC-ASD97

This chapter describes the details of the structural steel design and stress check al-gorithms that are used by ETABS when the user selects the UBC-ASD97 designcode. The UBC-ASD97 design code in ETABS implements the International Con-ference of Building Officials’ 1997 Uniform Building Code: Volume 2: StructuralEngineering Design Provisions, Chapter 22, Division III, “Design Standard forSpecification for Structural Steel Buildings Allowable Stress Design and PlasticDesign” (ICBO 1997).

Chapter 22, Division III, of UBC adopted the American Institute of Steel Construc-tion’s Specification for Structural Steel Buildings: Allowable Stress Design andPlastic Design, June 1, 1989 with Commentary (AISC 1989a), which has been im-plemented in the AISC-ASD89 code in ETABS. The ETABS implementation ofAISC-ASD89 is described in Chapter III “Design/Check for AISC-ASD89” of thismanual. The current chapter frequently refers to Chapter III. It is suggested that theuser read Chapter III before continuing to read this chapter.

For referring to pertinent sections and equations of the UBC code, a unique prefix“UBC” is assigned. For referring to pertinent sections and equations of theAISC-ASD code, a unique prefix “ASD” is assigned. However, all references to the“Specifications for Allowable Stress Design of Single-Angle Members” (AISC1989b) carry the prefix of “ASD SAM”.

79

Various notations used in this chapter are described in Table III-1.

When using the UBC-ASD97 option, the following Framing Systems are recog-nized (UBC 1627, 2213):

• Ordinary Moment Frame (OMF)

• Special Moment-Resisting Frame (SMRF)

• Concentrically Braced Frame (CBF)

• Eccentrically Braced Frame (EBF)

• Special Concentrically Braced Frame (SCBF)

By default the frame type is taken as Special Moment-Resisting Frame (SMRF) inthe program. However, the frame type can be overwritten in the Preference form tochange the default and in the Overwrites form on a member by member basis. If anymember is assigned with a frame type, the change of the frame type in the Prefer-ence will not modify the frame type of the individual member for which it is as-signed.

When using the UBC-ASD97 option, a frame is assigned to one of the followingfive Seismic Zones (UBC 2213, 2214):

• Zone 0

• Zone 1

• Zone 2

• Zone 3

• Zone 4

By default the Seismic Zone is taken as Zone 4 in the program. However, the frametype can be overwritten in the Preference form to change the default.



80


Design Loading CombinationsThe design load combinations are the various combinations of the load cases forwhich the structural members and joints needs to be designed or checked. For theUBC-ASD97 code, if a structure is subjected to dead load (DL), live load (LL),wind load (WL), and earthquake induced load (EL), and considering that wind andearthquake forces are reversible, then the following load combinations may have tobe defined (UBC 1612.3):

DL (UBC 1612.3.1 12-7)DL + LL (UBC 1612.3.1 12-8)

DL WL (UBC 1612.3.1 12-9)DL + 0.75 LL 0.75 WL (UBC 1612.3.1 12-11)

DL EL/1.4 (UBC 1612.3.1 12-9)0.9 DL EL/1.4 (UBC 1612.3.1 12-10)DL + 0.75 LL 0.75 EL/1.4 (UBC 1612.3.1 12-11)

These are also the default design load combinations in ETABS whenever theUBC-ASD89 code is used. The user should use other appropriate loading combina-tions if roof live load is separately treated, if other types of loads are present, or ifpattern live loads are to be considered.

When designing for combinations involving earthquake and wind loads, allowablestresses are NOT increased by a factor of 4/3 of the regular allowable value (UBC1612.3.1, 2209.3).


It is noted here that whenever special seismic loading combinations are requiredby the code for special circumstances, the program automatically generates thoseload combinations internally. The following additional seismic load combinationsare frequently checked for specific types of members and special circumstances.

1.0 DL + 0.7 LL 0 EL (UBC 2213.5.1.1)0.85 DL 0 EL (UBC 2213.5.1.2)

where, 0 is the seismic force amplification factor which is required to account forstructural overstrength. The default value of 0 is taken as 2.8 in the program.However, 0 can be overwritten in the Preference form to change the default andin the Overwrites form on a member by member basis. If any member is assigned a

Design Loading Combinations 81

Chapter V Check/Design for UBC-ASD97

value for 0 , the change of 0 in the Preference form will not modify the 0 ofthe individual member for which 0 is assigned. The guideline for selecting a rea-sonable value can be found in UBC 1630.3.1 and UBC Table 16-N. There are othersimilar special loading combinations which are described latter in this chapter.

These above special seismic loading combinations are internal to the program. Theuser does NOT need to create additional load combinations for these load combina-tions. The special circumstances for which these load combinations are additionallychecked are described later in this chapter as appropriate. The special loading com-bination factors are applied directly to the ETABS load cases. It is assumed that anyrequired scaling (such as may be required to scale response spectra results) has al-ready been applied to the ETABS load cases.

Member DesignA member is recognized in the program as either a beam, column, or brace. In thecalculation of the axial and bending stress ratios, first, for each station along thelength of the member, the actual stresses are calculated for each load combination.Then the corresponding allowable stresses are calculated. Then, the stress ratios arecalculated at each station for each member under the influence of each of the designload combinations. The controlling stress ratio is then obtained, along with the as-sociated station and load combination. A stress ratio greater than 1.0 indicates anoverstress. Similarly, a shear capacity ratio is also calculated separately. IN addi-tion, if required for seismic design, members are checked for special loading com-binations, l r ratio, section slenderness ratio, etc.

Classification of Sections

The allowable stresses for axial compression and flexure depend upon the classifi-cation of sections. The sections are classified in UBC-ASD97 as either Compact,Noncompact, Slender or Too Slender in the same way as described in section“Classification of Sections” of Chapter III with some exceptions as described in thenext paragraph. ETABS classifies the individual sections according to the limitingwidth/thickness ratios given in Table III-2 (UBC 2208, 2212, 2213, ASD B5.1,F3.1, F5, G1, A-B5-2). The definition of the section properties required in this ta-ble is given in Figure III-1 and Table III-1 of Chapter III.

In general the design sections need not necessarily be Compact to satisfyUBC-ASD97 codes (UBC 2213.4.2). However, for certain special seismic casesthey have to be Compact and have to satisfy special slenderness requirements. Seesubsection “Seismic Requirements” later in this chapter. The sections which do sat-

82 Member Design


Member Design 83



Width-Thickness

Ratio

SEISMIC(Special requirements in

seismic design )( p )

Section References

I-SHAPE

b tf f2(beam)

Fy52 UBC 2213.7.3 (SMRF)UBC 2213.10.2 (EBF)

b tf f2(column)

8.5 for Fy 368.0 for 36 42Fy

7.4 for 42 45Fy

7.0 for 45 50Fy

6.6 for 50 55Fy

6.3 for 55 60Fy

6.0 for Fy 60

UBC 2213.7.3 (SMRF)UBC 2213.9.5 (SCBF)

ASD N7

BOX

b tf

andh tc w

(column)

Fy110 UBC 2213.7.3 (SMRF),UBC 2213.9.5 (SCBF)

b tf

andh tc w

(brace)

Fy110 UBC 2213.8.2.5 (BF),UBC 2213.9.2.4 (SCBF)

ANGLEb t

(brace)Fy52 UBC 2213.8.2.5 (BF)

UBC 2213.9.2.4 (SCBF)

DOUBLE-ANGLEb t

(brace)Fy52 UBC 2213.8.2.5 (BF)

UBC 2213.9.2.4 (SCBF)

PIPED t

(brace)Fy

UBC 2213.8.2.5 (BF)UBC 2213.9.2.4 (SCBF)

CHANNELb tf f

h tc w

No special requirementNo special requirement

T-SHAPEb tf f2d tw


ROUND BAR No special requirement

RECTANGULAR No special requirement

GENERAL No special requirement

Table V-1Limiting Width-Thickness Ratios for Classification of Sections when Special Seismic

Conditions Apply as per UBC-ASD

isfy these additional requirements are classified and reported as “SEISMIC” inETABS. These special requirements for classifying the sections as “SEISMIC” inETABS ( “Compact” in UBC) are given in Table V-1 (UBC 2213.7.3, 2213.8.2.5,2213.9.2.4, 2213.9.5, 2213.10.2). If these criteria are not satisfied, when the coderequires them to be satisfied, the user must modify the section property. In this caseETABS gives a warning message in the output file.

Calculation of Stresses

The axial, flexural, and shear stresses at each of the previously defined stations foreach load combination in UBC-ASD97 are calculated in the same way as describedin section “Calculation of Stresses” of Chapter III without any exception (UBC2208, ASD A-B5.2d). For nonslender sections, the stresses are based on the grosscross-sectional areas (ASD A-B5.2c), for slender sections the stresses are based oneffective section properties (ASD A-B5.2c), and for Single-angle sections thestresses are based on the principal properties of the sections (ASD SAM 6.1.5).

The flexural stresses are calculated based on the properties about the principal axes.For I, Box, Channel, T, Double-angle, Pipe, Circular and Rectangular sections, theprincipal axes coincide with the geometric axes. For Single-angle sections, the de-sign considers the principal properties. For general sections it is assumed that allsection properties are given in terms of the principal directions.

The shear stresses for Single-angle sections are calculated for directions along thegeometric axes. For all other sections the shear stresses are calculated along thegeometric/principle axes.

Calculation of Allowable Stresses

The allowable stresses in compression, tension, bending, and shear for Compact,Noncompact, and Slender sections according to the UBC-ASD97 are calculated inthe same way as described in section “Calculation of Allowable Stresses” of Chap-ter III without any exception (UBC 2208, ASD A-B5.2d). The allowable stressesfor Seismic sections are calculated in the same way as for Compact sections.

The allowable flexural stresses for all shapes of sections are calculated based ontheir principal axes of bending. For the I, Box, Channel, Circular, Pipe, T, Dou-ble-angle and Rectangular sections, the principal axes coincide with their geomet-ric axes. For the Angle sections, the principal axes are determined and all computa-tions related to flexural stresses are based on that.

84 Member Design


The allowable shear stress is calculated along the geometric axes for all sections.For I, Box, Channel, T, Double angle, Pipe, Circular and Rectangular sections, theprincipal axes coincide with their geometric axes. For Single-angle sections, princi-pal axes do not coincide with the geometric axes.

All limitations and warnings related to allowable stress calculation inAISC-ASD89 also apply in this code.

If the user specifies nonzero allowable stresses for one or more elements in theETABS “Allowable Stress Overwrites” form, these values will override the abovementioned calculated values for those elements . The specified allowable stressesshould be based on the principal axes of bending.

Calculation of Stress Ratios

The stress ratios in UBC-ASD97 are calculated in the same way as described insection “Calculation of Stress Ratios” of Chapter III with some modifications asdescribed below.

In the calculation of the axial and bending stress ratios, first, for each station alongthe length of the member, the actual stresses are calculated for each load combina-tion. Then the corresponding allowable stresses are calculated. Then, the stress ra-tios are calculated at each station for each member under the influence of each ofthe design load combinations. The controlling stress ratio is then obtained, alongwith the associated station and load combination. A stress ratio greater than 1.0 in-dicates an overstress. Similarly, a shear capacity ratio is also calculated separately.

During the design, the effect of the presence of bolts or welds is not considered.


With the computed allowable axial and bending stress values and the factored axialand bending member stresses at each station, an interaction stress ratio is producedfor each of the load combinations as follows (ASD H1, H2, SAM 6):

• If f a is compressive and f Fa a , the combined stress ratio is given bythe larger of

f

F+

C f

f

F'F

+C fa

a

m b

a

e

b

m b33 33

33

33

22 22

1 1f

F'Fa

e

b

22

22


Member Design 85


f

F

f

F

f

Fa

y

b

b

b

b

33

33

22

22

, where (ASD H1-2, SAM 6.1)

f a , f b33 , f b22 , Fa , Fb33 , Fb22 , and Fe¢ are defined earlier in Chapter III. A factor

of 4/3 is NOT applied on Fe¢ and Fy if the load combination includes any

wind load or seismic load (UBC 1612.3.1).

C m33 and C m22 are coefficients representing distribution of moment along themember length. They are calculated in the same way as in Chapter III.

When the stress ratio is calculated for Special Seismic Load Combinations, thecolumn axial allowable stress in compression is taken to be1.7 Fa instead of Fa

(UBC 2213.4.2).

• If f a is compressive and f Fa a , a relatively simplified formula isused for the combined stress ratio.

f

F+

f

F+

f

Fa

a

b

b

b

b

33

33

22

22

(ASD H1-3, SAM 6.1)

• If f a is tensile or zero, the combined stress ratio is given by the larger of

f

F

f

F

f

Fa

a

b

b

b

b

33

33

22

22


f

F

f

Fb

b

b

b

33

33

22

22

, where

f a , f b33 , f b22 , Fa , Fb33 , and Fb22 are defined earlier in Chapter III. However, ei-ther Fb33 or Fb22 need not be less than Fy in the first equation (ASD H2-1).The second equation considers flexural buckling without any beneficial effectfrom axial compression.

When the stress ratio is calculated for Special Seismic Load Combinations, thecolumn axial allowable stress in tension is taken to be Fy instead of Fa (UBC2213.4.2)

For circular and pipe sections, an SRSS combination is first made of the two bend-ing components before adding the axial load component, instead of the simple addi-tion implied by the above formulae.

For Single-angle sections, the combined stress ratio is calculated based on the prop-erties about the principal axes (ASD SAM 5.3, 6.1.5). For I, Box, Channel, T, Dou-ble-angle, Pipe, Circular and Rectangular sections, the principal axes coincide with

86 Member Design


their geometric axes. For Single-angle sections, principal axes are determined inETABS. For general sections it is assumed that all section properties are given interms of the principal directions and consequently no effort is made to determinethe principal directions.

In contrast to the AISC-ASD code, when designing for combinations involvingearthquake and wind loads, allowable stresses are NOT increased by a factor of 4/3of the regular allowable value (UBC 1612.3.1, 2209.3).

Shear Stresses

From the allowable shear stress values and the factored shear stress values at eachstation, shear stress ratios for major and minor directions are computed for each ofthe load combinations as follows:

f

Fv

v

2 , and

f

Fv

v

3 .


In contrast to AISC-ASD code, when designing for combinations involving earth-quake and wind loads, allowable shear stresses are NOT increased by a factor of 4/3of the regular allowable value (UBC 1612.3.1, 2209.3).

Member Design 87


Seismic Requirements

The special seismic requirements checked by the program for member design aredependent on the type of framing used and are described below for each type offraming. The requirements checked are based on UBC Section 2213 for frames inSeismic Zones 3 and 4 and on UBC Section 2214 for frames in Seismic Zones 1 and2 (UBC 2204.2, 2205.2, 2205.3, 2208, 2212, 2213, 2214). No special requirementis checked for frames in Seismic Zone 0.

Ordinary Moment Frames

For this framing system, the following additional requirements are checked and re-ported:

• In Seismic Zones 3 and 4, whenever the axial stress, f a , in columns due to theprescribed loading combinations exceeds Fy , the Special Seismic LoadCombinations as described below are checked with respect to the column axialload capacity only (UBC 2213.5.1).


In this case column forces are replaced by the column forces for the SpecialSeismic Load Combinations, whereas the other forces are taken as zeros. Forthis case the column axial allowable stress in compression is taken to be1.7 Fa

instead of Fa and the column axial allowable stress in tension is taken to be Fy

instead of Fa (UBC 2213.5.1, 2213.4.2).

Special Moment-Resisting Frames

For this framing system, the following additional requirements are checked or re-ported:



In this case column forces are replaced by the column forces for the SpecialSeismic Load Combinations, whereas the other forces are taken as zeros. For

88 Member Design


this case the column axial allowable stress in compression is taken to be1.7 Fa


instead of Fa (UBC 2213.5.1, 2213.4.2).

• In Seismic Zones 3 and 4, the I-shaped beams, I-shaped columns, and Boxshaped columns are additionally checked for compactness criteria as describedin Table V-1 (UBC 2213.7.3). Compact I-shaped beam sections are addition-ally checked for b tf f2 to be less than 52 Fy . Compact I-shaped column

sections are additionally checked for b tf f2 to be less than the numbers givenfor plastic sections in Table V-1. Compact box shaped column sections are ad-ditionally checked for b t f and d tw to be less than 110 Fy . If this crite-

ria is satisfied the section is reported as SEISMIC as described earlier undersection classifications. If this criteria is not satisfied the user must modify thesection property.

• In Seismic Zones 3 and 4, the program checks the laterally unsupported lengthof beams to be less than 96ry . If the check is not satisfied, it is noted in the out-put (UBC 2213.7.8).

Braced Frames

For this framing system, the following additional requirements are checked or re-ported:





instead of Fa (UBC 2213.5.1, 2213.4.2).

• In Seismic Zones 3 and 4, the program checks the laterally unsupported lengthof beams to be less than 96ry . If the check is not satisfied, it is noted in the out-put (UBC 2213.8.1, 2213.7.8).

Member Design 89


• In Seismic Zones 3 and 4, the maximum l r ratio of the braces is checked not toexceed 720 Fy . If this check is not met, it is noted in the output (UBC

2213.8.2.1).

• In Seismic Zones 3 and 4, the Angle, Double-angle, Box, and Pipe shapedbraces are additionally checked for compactness criteria as described in TableV-1 (UBC 2213.8.2.5). For angles and double-angles b t is limited to52 Fy , for box sections b t f and d tw is limited to 110 Fy , for

pipe sections D t is limited to 1300 Fy . If this criteria is satisfied the sec-tion is reported as SEISMIC as described earlier under section classifications.If this criteria is not satisfied the user must modify the section property.

• In Seismic Zones 3 and 4, the allowable compressive stress for braces is re-duced by a factor, B, where

BKl r

C c

1

12

(UBC 2213.8.2.2)

In Seismic Zones 1 and 2, the allowable compressive stress for braces is re-duced by the same factor, B, where

B 0.8 (UBC 2214.6.2.1)

• In Seismic Zones 3 and 4, Chevron braces are designed for 1.5 times the speci-fied loading combinations (UBC 2213.8.4.1).

Eccentrically Braced Frames

For this framing system, the program looks for and recognizes the eccentricallybraced frame configurations shown in Figure V-1. The following additional re-quirements are checked or reported for the beams, columns and braces associatedwith these configurations. Special seismic design of eccentrically braced frames inSeismic Zones 1 and 2 is the same as those in Seismic Zones 3 and 4 (UBC 2214.8).

• In all Seismic Zones except Zone 0, the I-shaped beam sections are additionallychecked for compactness criteria as described in Table V-1. Compact I-shapedbeam sections are additionally checked for b tf f2 to be less than 52 Fy .

If this criteria is satisfied the section is reported as SEISMIC as described ear-lier under section classifications. If this criteria is not satisfied the user mustmodify the section property (UBC 2213.10.2). Other sections meeting this cri-teria are also reported as SEISMIC.

90 Member Design


• In all Seismic Zones except Zone 0, the link beam strength in shearV F dts y w0.55 and moment M Z Fs y are calculated. If V M es s2.0 , thelink beam strength is assumed to be governed by shear and is so reported. If theabove condition is not satisfied, the link beam strength is assumed to be gov-erned by flexure and is so reported. When link beam strength is governed byshear, the axial and flexural properties (area, A and section modulus, S ) for usein the interaction equations are calculated based on the beam flanges only(UBC 2213.10.3).

• In all Seismic Zones except Zone 0, if the link beam is connected to the column,the link beam length, e, is checked not to exceed the following (UBC2213.10.12):

eM

Vp

p

1.6 (UBC 2213.10.12)

If the check is not satisfied, it is noted in the output.

• In all Seismic Zones except Zone 0, the link beam rotation, , of the individualbay relative to the rest of the beam is calculated as the story drift M times baylength divided by the total lengths of link beams in the bay divided by height ofthe story. The link beam rotation, , is checked to be less than the followingvalues (UBC 2213.10.4).

0.090 , where link beam clear length, e M Vs s1.6 ,

0.030 , where link beam clear length, e M Vs s3.0 , and

value interpolated between 0.090 and 0.030 as the link beam clearlength varies from 1.6 M Vs s to 3.0 M Vs s .

• In all Seismic Zones except Zone 0, the link beam shear under the specifiedloading combinations is checked not to exceed 0.8Vs (UBC 2213.10.5).

• In all Seismic Zones except Zone 0, the brace strength is checked to be at least1.5 times the axial force corresponding to the controlling link beam strength(UBC 2213.10.13). The controlling link beam strength is either the shearstrength, Vs as V F dts y w0.55 , or the reduced flexural strength, M rs , which-ever produces the lower brace force. The value of M rs is taken asM Z F frs y a( ) (UBC 2213.10.3), where f a is the lower of the axial stressin the link beam corresponding to yielding of the link beam web in shear or thelink beam flanges in flexure. The correspondence between brace force and linkbeam force is obtained from the associated load cases, whichever has the high-est link beam force of interest.

Member Design 91


• In all Seismic Zones except Zone 0, the column is checked not to become in-elastic for gravity loads plus 1.25 times the column forces corresponding to thecontrolling link beam strength (UBC 2213.10.14). The controlling link beamstrength and the corresponding forces are as obtained by the process describedabove. If this condition governs, the column axial allowable stress in compres-sion is taken to be1.7 Fa instead of Fa and the column axial allowable stress intension is taken to be Fy instead of Fa .

92 Member Design


Figure V-1Eccentrically Braced Frame Configurations

• In all Seismic Zones except Zone 0, axial forces in the beams are included inchecking of the beams (UBC 2211.10.17). The user is reminded that using arigid diaphragm model will result in zero axial forces in the beams. The usermust disconnect some of the column lines from the diaphragm to allow beamsto carry axial loads. It is recommended that only one column line per eccentri-cally braced frame be connected to the rigid diaphragm or a flexible diaphragmmodel be used.

• In all Seismic Zones except Zone 0, the beam laterally unsupported length ischecked to be less than 76 b Ff y . If not satisfied it is so noted as a warning

in the output file (UBC 2213.10.18).

Note: The beam strength in flexure, of the beam outside the link, is NOT currentlychecked to be at least 1.5 times the moment corresponding to the controlling linkbeam strength (UBC 2213.10.13). Users need to check for this requirement.

Special Concentrically Braced Frames

Special seismic design of special concentrically braced frames in Seismic Zones 1and 2 is the same as those in Seismic Zones 3 and 4 (UBC 2214.7). For this framingsystem, the following additional requirements are checked or reported:

• In all Seismic Zones except Zone 0, whenever the axial stress, f a , in columnsdue to the prescribed loading combinations exceeds Fy , the Special SeismicLoad Combinations as described below are checked with respect to the columnaxial load capacity only (UBC 2213.9.5, 2213.5.1).




instead of Fa (UBC 2213.5.1, 2213.4.2).

• In all Seismic Zones except Zone 0, the I-shaped and Box shaped columns areadditionally checked for compactness criteria as described in Table V-1. Com-pact I-shaped column sections are additionally checked for b tf f2 to be lessthan the numbers given for plastic sections in Table V-1. Compact box shapedcolumn sections are additionally checked for b t f and d tw to be less than110 Fy . If this criteria is satisfied the section is reported as SEISMIC as

Member Design 93


described earlier under section classifications. If this criteria is not satisfied theuser must modify the section property (UBC 2213.9.5, 2213.7.3).

• In all Seismic Zones except Zone 0, bracing members are checked to be com-pact and are so reported. The Angle, Box, and Pipe sections used as braces areadditionally checked for compactness criteria as described in Table V-1. Forangles b t is limited to 52 Fy , for box sections b t f and d tw is limited

to110 Fy , for pipe sections D t is limited to 1300 Fy . If this criteria is

satisfied the section is reported as SEISMIC. If this criteria is not satisfied theuser must modify the section property (UBC 2213.9.2.4).

• In all Seismic Zones except Zone 0, the maximum Kl r ratio of the braces ischecked not to exceed 1000 Fy . If this check is not met, it is noted in the

output (UBC 2213.9.2.1).

Note: Beams intersected by Chevron braces are NOT currently checked tohave a strength to support loads represented by the following loading combina-tions (UBC 2213.9.4.1):

1.2DL + 0.5LL Pb (UBC 2213.9.4.1)

0.9DL Pb (UBC 2213.9.4.1)

where Pb is given by the difference of F Ay for the tension brace and 0.3 times1.7 F Aa for the compression brace. Users need to check for this requirement(UBC 2213.9.4.1, 2213.4.2).

Joint DesignWhen using UBC-ASD97 design code, the structural joints are checked and/ordesigned for the following:

• Check for the requirement of continuity plate and determination of its area

• Check for the requirement of doubler plate and determination of its thickness

• Check for the ratio of beam flexural strength to column flexural strength

• Reporting the beam connection shear

• Reporting the brace connection force

94 Joint Design


Design of Continuity Plates

In a plan view of a beam/column connection, a steel beam can frame into a columnin the following ways:





For connection conditions described in the last two steps above, the thickness ofsuch plates is usually set equal to the flange thickness of the corresponding beam.However, for the connection condition described by the first step above, where thebeam frames into the flange of the column, such continuity plates are not alwaysneeded. The requirement depends upon the magnitude of the beam-flange force andthe properties of the column. This is the condition that the program investigates.Columns of I-sections only are investigated. The program evaluates the continuityplate requirements for each of the beams that frame into the column flange (i.e. par-allel to the column major direction) and reports the maximum continuity plate areathat is needed for each beam flange. The continuity plate requirements are evalu-ated for moment frames only. No check is made for braced frames.

The continuity plate area required for a particular beam framing into a column isgiven by:

A =P

Ft t + 5kcp

bf

yc

wc fb c( ) (ASD K1-9)

If Acp 0, no continuity plates are required provided the following two conditionsare also satisfied:

• The depth of the column clear of the fillets, i.e. d kc c2 , is less than or equalto:

Joint Design 95


4100 t F

P

wc3

yc

bf

(ASD K1-8)

• The thickness of the column flange, t fc , is greater than or equal to:

0.4P

Fbf

yc

, where (ASD K1-1)

P f Abf b bf .

f b is the bending stress calculated from the larger of 5/3 of loading combinationswith gravity loads only 5 3 M d t Af fb and 4/3 of the loading combina-

tions with lateral loads 4 3 M d t Af fb (ASD K1.2). For special seismic

design, f b is specified to be beam flange strength.

If continuity plates are required, they must satisfy a minimum area specification de-fined as follows:

• The thickness of the stiffeners is at least 0.5 t fb , or

t = tcpmin

fb0.5 (ASD K1.8.2)

• The width of the continuity plate on each side plus 1/2 the thickness of the col-umn web shall not be less than 1/3 of the beam flange width, or

b = 2b

3

t

2cpmin fb wc (ASD K1.8.1)

• So that the minimum area is given by:

A = t bcpmin

cpmin

cpmin

Therefore, the continuity plate area provided by the program is either zero or thegreater of Acp and Acp

min .

Where

Abf = Area of beam flangeAcp = Required continuity plate areaFyb = Yield stress of beam materialFyc = Yield stress of the column and continuity plate material

96 Joint Design


t fb = Beam flange thicknesstwc = Column web thicknesskc = Distance between outer face of the column flange and

web toe of its filletd c = Column depthd b = Beam depthf b = Beam flange widthtcp = Continuity plate thicknessbcp = Continuity plate widthf b = Bending stress calculated from the larger of 5/3 of loading

combinations with gravity loads only 5 3 M d t Af fb

and 4/3 of the loading combinations with lateral loads4 3 M d t Af fb (ASD K1.2).

The special seismic requirements additionally checked by the program are depend-ent on the type of framing used and are described below for each type of framing.The requirements checked are based on UBC Section 2213 for frames in SeismicZones 3 and 4 and on UBC Section 2214 for frames in Seismic Zones 1 and 2 (UBC2204.2, 2205.2, 2213, 2214). No special requirement is checked for frames in Seis-mic Zone 0.

• In all Seismic Zones except Zone 0, for Ordinary Moment Frames the continu-ity plates are checked and designed for a beam flange force, Pbf .

P f Abf yb bf (UBC 2213.6.1, 2213.7.1.1, 2214.4.1, 2214.5.1.1)

• In Seismic Zones 3 and 4, for Special Moment-Resisting Frames, for determin-ing the need for continuity plates at joints due to tension transfer from the beamflanges, the force Pbf is taken as 1.8 f Ayb bf (UBC 2213.7.4). For design of thecontinuity plate the beam flange force is taken as f Ayb bf (UBC 2213.7.1.1).

In Seismic Zones 1 and 2, for Special Moment-Resisting Frames, for determin-ing the need for continuity plates at joints due to tension transfer from the beamflanges, the force Pbf is taken as f Ayb bf . For design of the continuity plate thebeam flange force is taken as f Ayb bf (UBC 2214.5.1.1).

• In all Seismic Zones except Zone 0, for Eccentrically Braced Frames, the conti-nuity plates are checked and designed for a beam flange force, Pbf .

P f Abf yb bf (UBC 2213.10.12, 2213.10.19)

Joint Design 97


Design of Doubler Plates

One aspect of the design of a steel framing system is an evaluation of the shearforces that exist in the region of the beam column intersection known as the panelzone.

Shear stresses seldom control the design of a beam or column member. However,in a Moment-Resisting frame, the shear stress in the beam-column joint can be criti-cal, especially in framing systems when the column is subjected to major directionbending and the joint shear forces are resisted by the web of the column. In minordirection bending, the joint shear is carried by the column flanges, in which case theshear stresses are seldom critical, and this condition is therefore not investigated bythe program.

Shear stresses in the panel zone, due to major direction bending in the column, mayrequire additional plates to be welded onto the column web, depending upon theloading and the geometry of the steel beams that frame into the column, either alongthe column major direction, or at an angle so that the beams have components alongthe column major direction. See Figure II-5. The program investigates such situa-tions and reports the thickness of any required doubler plates. Only columns withI-shapes are investigated for doubler plate requirements. Also doubler plate re-quirements are evaluated for moment frames only. No check is made for bracedframes.

The shear force in the panel zone, is given by

V = P - Vp c , or

V =M

d – t- Vp

n =

nbn n

n f

c

b

n1

cos

The required web thickness to resist the shear force,V p , is given by

t =V

F d

h

Fr

p

v c yc380(ASD F4)

The extra thickness, or thickness of the doubler plate is given by

t = t - tdp r wc , where,

Fv = 0.40 Fyc (ASD F4)Fyc = Yield stress of the column and doubler plate materialtr = Required column web thickness

98 Joint Design


tdp = Required doubler plate thicknesst fn = Thickness of flange of the n-th beam connecting to columntwc = Column web thicknessV p = Panel zone shearVc = Column shear in column aboveP = Beam flange forcesnb = Number of beams connecting to columnd n = Depth of n-th beam connecting to columnh = d tc fc2 if welded, d kc c2 if rolled,

n = Angle between n-th beam and column major directiond c = Depth of columnM bn = Calculated factored beam moment from the corresponding

loading combination

The largest calculated value of V p calculated for any of the load combinationsbased upon the factored beam moments is used to calculate doubler plate areas.

The special seismic requirements checked by the program for calculating doublerplate areas are dependent on the type of framing used and are described below foreach type of framing. The requirements checked are based on UBC Section 2213for frames in Seismic Zones 3 and 4 and on UBC Section 2214 for frames in Seis-mic Zones 1 and 2 (UBC 2204.2, 2205.2, 2213, 2214). No special requirement ischecked for frames in Seismic Zones 0, 1 and 2.

• In Seismic Zones 3 and 4, for Special Moment-Resisting Frames, the panelzone doubler plate requirements that are reported will develop the lesser ofbeam moments equal to 0.8 of the plastic moment capacity of the beam0.8 M pb , or beam moments due to gravity loads plus 1.85 times the seis-

mic load (UBC 2213.7.2.1).

The capacity of the panel zone in resisting this shear is taken as (UBC2213.7.2.1):

V = F d t +b t

d d tp yc c r

c cf

b c r

0.55 13 2

(UBC 2213.7.2.1)

giving the required panel zone thickness as

t =V

F d

b t

d d

h

Fr

p

yc c

c cf

b c yc0.55

3

380

2

(UBC 2213.7.2.1, ASD F4)

Joint Design 99


and the required doubler plate thickness as

t = t - tdp r wc

where

bc = width of column flange,h = d tc fc2 if welded, d kc c2 if rolled,tcf = thickness of column flange, andd b = depth of deepest beam framing into the major direction of

the column.

• In Seismic Zones 3 and 4, for Special Moment-Resisting Frames, the panelzone column web thickness requirement the program checks the following:

td t d t

wc

c fc b fb( ) ( )2 2

90(UBC 2213.7.2.2)


• In Seismic Zones 3 and 4, for Eccentrically Braced Frames, the doubler platerequirements are checked similar to the doubler plate checks for special Mo-ment-Resisting frames as discussed earlier (UBC 2213.10.19).

Beam/Column Plastic Moment Capacity Ratio

In Seismic Zones 3 and 4, for Special Moment-Resisting Frames, the code requiresthat the sum of beam flexure strengths at a joint should be less than the sum of col-umn flexure strengths (UBC 2213.7.5). The column flexure strength should reflectthe presence of axial force present in the column. To facilitate the review of thestrong column weak beam criterion, the program will report a beam/column plasticmoment capacity ratio for every joint in the structure.

For the major direction of any column (top end) the beam to column strength ratio isobtained as

R =

M

M + Mmajn =

n

pbn n

pcax pcbx

b

1

cos

(UBC 2213.7.5)

100 Joint Design


For the minor direction of any column the beam to column strength ratio is obtainedas

R =

M

M + Mn =

n

pbn n

pcay pcby

b

min1

sin, (UBC 2213.7.5)

where,

Rmaj min, = Plastic moment capacity ratios, in the major andminor directions of the column, respectively,

M pbn = Plastic moment capacity of n-th beam connectingto column,

n = Angle between the n-th beam and the columnmajor direction,

M pcax y, = Major and minor plastic moment capacities, reduced foraxial force effects, of column above story level.Currently, it is being taken equal to M pcbx y, if there is acolumn above the joint assuming that the column spliceis done far away from the joint. If there is no columnabove the joint, M pcax y, is taken as zero,

M pcbx y, = Major and minor plastic moment capacities, reduced foraxial force effects, of column below story level, and

nb = Number of beams connecting to the column.

The plastic moment capacities of the columns are reduced for axial force effectsand are taken as

M = Z F - fpc c yc a( ) , (UBC 2213.7.5)

where,

Zc = Plastic modulus of column,Fyc = Yield stress of column material, andf a = Maximum axial stress in the column.

For the above calculations the section of the column above is taken to be the sameas the section of the column below assuming that the column splice will be locatedsome distance above the story level.

Joint Design 101


Evaluation of Beam Connection Shears

For each steel beam in the structure the program will report the maximum majorshears at each end of the beam for the design of the beam shear connections. Thebeam connection shears reported are the maxima of the factored shears obtainedfrom the loading combinations.

For special seismic design, the beam connection shears are not taken less than thefollowing special values for different types of framing. The requirements checkedare based on UBC Section 2213 for frames in Seismic Zones 3 and 4 and on UBCSection 2214 for frames in Seismic Zones 1 and 2 (UBC 2204.2, 2205.2, 2213,2214). No special requirement is checked for frames in Seismic Zones 0.

• In all Seismic Zones except Zone 0, for Ordinary Moment Frames, the beamconnection shears reported are the maximum of the specified loading combina-tions and the following additional loading combination (UBC 2213.6.2,2214.4.2):

1.0 DL + 1.0 LL 0 EL (UBC 2213.6.2, 2214.4.2)

• In all Seismic Zones except Zone 0, for Special Moment-Resisting Frames, thebeam connection shears that are reported allow for the development of the fullplastic moment capacity of the beam (UBC 2213.7.1, 2214.5.1.1). Thus:

V =C M

L+ Vpb

DL LL+(UBC 2213.7.1.1, 2214.5.1.1)

where,

V = Shear force corresponding to END I or END J of beam,C = 0 if beam ends are pinned, or for cantilever beam,

= 1 if one end of the beam is pinned,= 2 if no ends of the beam are pinned,

M pb = Plastic moment capacity of the beam, Z Fy ,L = Clear length of the beam, andVDL LL+

= Absolute maximum of the calculated factored beamshears at the corresponding beam ends from the deadload and live load combinations only.

• In all Seismic Zones except Zone 0, for Eccentrically Braced Frames, the beamconnection shears reported are the maximum of the specified loading combina-tions and the following additional loading combination:

1.0 DL + 1.0 LL 0 EL

102 Joint Design


Evaluation of Brace Connection Forces

For each steel brace in the structure the program reports the maximum axial force ateach end of the brace for the design of the brace to beam connections. The braceconnection forces reported are the maxima of the factored brace axial forces ob-tained from the loading combinations.

For special seismic design, the brace connection forces are not taken less than thefollowing special values for different types of framing. The requirements checkedare based on UBC Section 2213 for frames in Seismic Zones 3 and 4 and on UBCSection 2214 for frames in Seismic Zones 1 and 2 (UBC 2204.2, 2205.2, 2213,2214). No special requirement is checked for frames in Seismic Zones 0.

• In all Seismic Zones except Zone 0, for ordinary Braced Frames, the bracingconnection force is reported at least as the smaller of the tensile strength of thebrace (F Ay ) and the following special loading combination (UBC 2213.8.3.1,2214.6.3.1):

1.0 DL + 1.0 LL 0 EL (UBC 2213.8.3.1, 2214.6.3.1)

• In all Seismic Zones except Zone 0, for Special Concentrically Braced Frames,the bracing connection force is reported at least as the smaller of the tensilestrength of the brace (F Ay ) and the following special loading combination(UBC 2213.9.3.1, 2214.7):

1.0 DL + 1.0 LL 0 EL (UBC 2213.9.3.1, 2214.7)

• In all Seismic Zones except Zone 0, for Eccentrically Braced Frames, the brac-ing connection force is reported as at least the brace strength in compressionwhich is computed as1.7 F Aa (UBC 2213.10.6, 2214.8). 1.7 F Aa is limited notto exceed F Ay .

Joint Design 103


C h a p t e r VI

Check/Design for UBC-LRFD97

This chapter describes the details of the structural steel design and stress check al-gorithms that are used by ETABS when the user selects the UBC-LRFD97 designcode. The UBC-LRFD97 design code in ETABS implements the InternationalConference of Building Officials’ 1997 Uniform Building Code: Volume 2: Struc-tural Engineering Design Provisions, Chapter 22, Division II, “Design Standardfor Load and Resistance Factor Design Specification for Structural Steel Build-ings” (ICBO 1997).

Chapter 22, Division III, of UBC adopted the American Institute of Steel Construc-tion’s Load and Resistance Factor Design Specification for Structural Steel Build-ings (AISC 1993), which has been implemented in the AISC-LRFD93 code inETABS. The ETABS implementation of UBC-LRFD97 is described in Chapter IV“Check/Design for AISC-LRFD93” of this manual. The current chapter frequentlyrefers to Chapter IV. It is suggested that the user read Chapter IV before continuingto read this chapter.

For referring to pertinent sections and equations of the UBC code, a unique prefix“UBC” is assigned. For referring to pertinent sections and equations of theUBC-LRFD code, a unique prefix “LRFD” is assigned. However, all references tothe “Specifications for Load and Resistance Factored Design of Single-AngleMembers” (AISC 1994) carry the prefix of “LRFD SAM”. Moreover, all sectionsof the “Seismic Provisions for Structural Steel Buildings June 15, 1992” (AISC

105

1994) are referred to as Section 2211.4 of the UBC code. In this manual, all sectionsand subsections referenced by “UBC 2211.4” or “UBC 2211.4.x” refer to theLRFD Seismic Provisions after UBC amendments through UBC Section 2210.Various notations used in this chapter are described in Table IV-1.

When using the UBC-LRFD97 option, the following Framing Systems are recog-nized (UBC 1627, 2210):

• Ordinary Moment Frame (OMF)

• Special Moment-Resisting Frame (SMRF)

• Concentrically Braced Frame (CBF)

• Eccentrically Braced Frame (EBF)

• Special Concentrically Braced Frame (SCBF)

By default the frame type is taken as Special Moment-Resisting Frame (SMRF) inthe program. However, the frame type can be overwritten in the Preference form tochange the default and in the Overwrites form on a member by member basis. If anymember is assigned with a frame type, the change of the frame type in the Prefer-ence will not modify the frame type of the individual member for which it is as-signed.

When using the UBC-LRFD97 option, a frame is assigned to one of the followingfive Seismic Zones (UBC 2210):

• Zone 0

• Zone 1

• Zone 2

• Zone 3

• Zone 4

By default the Seismic Zone is taken as Zone 4 in the program. However, the frametype can be overwritten in the Preference form to change the default.



106


Design Loading CombinationsThe design load combinations are the various combinations of the load cases forwhich the structural members and joints needs to be designed or checked. For theUBC-LRFD97 code, if a structure is subjected to dead load (DL), live load (LL),wind load (WL), and earthquake induced load (EL), and considering that wind andearthquake forces are reversible, then the following load combinations may have tobe defined (UBC 2204.1, 2206, 2207.3, 2210.3, 1612.2.1):

1.4 DL (UBC 1612.2.1 12-1)1.2 DL + 1.4 LL (UBC 1612.2.1 12-2)

1.2 DL 0.8 WL (UBC 1612.2.1 12-3)0.9 DL 1.3 WL (UBC 1612.2.1 12-6)1.2 DL + 0.5 LL 1.3 WL (UBC 1612.2.1 12-4)

1.2 DL 1.0 EL (UBC 1612.2.1 12-5)0.9 DL 1.0 EL (UBC 1612.2.1 12-6)1.2 DL + 0.5 LL 1.0 EL (UBC 1612.2.1 12-5)

These are also the default design load combinations in ETABS whenever theUBC-LRFD97 code is used. The user should use other appropriate loading combi-nations if roof live load is separately treated, if other types of loads are present, or ifpattern live loads are to be considered.


When using the UBC-LRFD97 code, ETABS design assumes that a P- analysishas been performed so that moment magnification factors for moments causingsidesway can be taken as unity. It is recommended that the P- analysis be done atthe factored load level of 1.2 DL plus 0.5 LL (White and Hajjar 1991).

It is noted here that whenever special seismic loading combinations are requiredby the code for special circumstances, the program automatically generates thoseload combinations internally. The following additional seismic load combinationsare frequently checked for specific types of members and special circumstances.

0.9 DL 0 EL (UBC 2210.3, 2211.4.3.1)1.2 DL + 0.5 LL 0 EL (UBC 2210.3, 2211.4.3.1)

where, 0 is the seismic force amplification factor which is required to account forstructural overstrength. The default value of 0 is taken as 2.8 in the program.

Design Loading Combinations 107

Chapter VI Check/Design for UBC-LRFD97

However, 0 can be overwritten in the Preference form to change the default andin the Overwrites form on a member by member basis. If any member is assigned avalue for 0 , the change of 0 in the Preference form will not modify the 0 ofthe individual member for which 0 is assigned. The guideline for selecting a rea-sonable value can be found in UBC 1630.3.1 and UBC Table 16-N. There are othersimilar special loading combinations which are described latter in this chapter.

These above combinations are internal to the program. The user does NOT need tocreate additional load combinations for these load combinations. The special cir-cumstances for which these load combinations are additionally checked are de-scribed later in this chapter as appropriate. The special loading combination factorsare applied directly to the ETABS load cases. It is assumed that any required scal-ing (such as may be required to scale response spectra results) has already been ap-plied to the ETABS load cases.

Member DesignA member is recognized in the program as either a beam, column, or brace. In theevaluation of the axial force/biaxial moment capacity ratios at a station along thelength of the member, first the actual member force/moment components and thecorresponding capacities are calculated for each load combination. Then the capac-ity ratios are evaluated at each station under the influence of all load combinationsusing the corresponding equations that are defined in this chapter. The controllingcapacity ratio is then obtained. A capacity ratio greater than 1.0 indicates over-stress. Similarly, a shear capacity ratio is also calculated separately.

Classification of Sections

The nominal strengths for axial compression and flexure are dependent on the clas-sification of the section as Compact, Noncompact, Slender or Too Slender. Thesections are classified in UBC-LRFD97 as either Compact, Noncompact, Slenderor Too Slender in the same way as described in section “Classification of Sections”of Chapter IV with some exceptions as described in the next paragraph. ETABSclassifies individual members according to the limiting width/thickness ratiosgiven in Table IV-2 and Table IV-3 (UBC 2204.1, 2205, 2206, and 2210; LRFDB5.1, A-G1, and Table A-F1.1). The definition of the section properties required inthese tables is given in Figure IV-1 and Table IV-1 of Chapter IV. The same limita-tions apply.

In general the design sections need not necessarily be Compact to satisfyUBC-LRFD97 codes (UBC 2213.2). However, for certain special seismic cases

108 Member Design


Member Design 109



Width-Thickness

Ratio

SEISMIC(Special requirements

in seismic design )( p )

Section References

I-SHAPE

b tf f2 Fy52 UBC 2211.4.8.4.b (SMRF)UBC 2211.4 Table 8-1 (SMRF)

h tc w

For P Pu b y ,520

1F

-P

Py

u

b y

For P Pu b y

191 253

F-

P

P Fy

u

b y y

UBC 2211.4.8.4.b (SMRF)UBC 2211.4 Table 8-1 (SMRF)

BOX

b tf

orh tc w

Fy110 (Beam and

column in SMRF, column inSCBF, Braces in BF)

UBC 2210.8 (SMRF)UBC 2210.10.g (SCBF)UBC 2211.4.9.2.d (BF)

b tf

orh tc w

Fy100

(Braces in SCBF)UBC 2210.10.c (SCBF)

CHANNELb tf f

h tc w

Same as I-ShapesSame as I-Shapes

UBC 2211.4.8.4.b (SMRF)UBC 2211.4 Table 8-1 (SMRF)

ANGLE b tFy52

(Braces in SCBF)

UBC 2210.10.c (SCBF)UBC 2211.4.9.2.d (SCBF)

DOUBLE-ANGLE b tFy52

(Braces in SCBF)

UBC 2210.10.c (SCBF)UBC 2211.4.9.2.d (SCBF)

PIPE D t FyUBC 2210.10.c (Braces in SCBF)UBC 2211.4.9.2.d (Braces in BF)

T-SHAPEb tf f2d tw


ROUND BAR No special requirement

RECTANGULAR No special requirement

GENERAL No special requirement

Table VI-1Limiting Width-Thickness Ratios for Classification of Sections when Special Seismic

Conditions Apply as per UBC-LRFD

they have to be Compact and have to satisfy special slenderness requirements. Seesubsection “Seismic Requirements” later in this section. The sections which do sat-isfy these additional requirements are classified and reported as “SEISMIC” inETABS. These special requirements for classifying the sections as “SEISMIC” inETABS (“Compact” in UBC) are given in Table VI-1 (UBC 2210.8, 2210.10c,2211.4.8.4.b, 2211.9.2.d, 2210.10g, 2211.4.10.6.e). If these criteria are not satis-fied, when the code requires them to be satisfied, the user must modify the sectionproperty. In this case ETABS gives a warning message in the output file.

Calculation of Factored Forces

The factored member loads that are calculated for each load combination are Pu ,M u33 , M u22 , Vu2 and Vu3 corresponding to factored values of the axial load, themajor moment, the minor moment, the major direction shear force and the minor di-rection shear force, respectively. These factored loads are calculated at each of thepreviously defined stations for each load combination. They are calculated in thesame way as described in section “Calculation of Factored Forces” of Chapter IVwithout any exception (UBC 2204.1 2205.2, 2205.3, 2206, 2210).

The bending moments are obtained along the principal directions. For I, Box,Channel, T, Double-angle, Pipe, Circular and Rectangular sections, the principalaxes coincide with the geometric axes. For the Angle sections, the principal axesare determined and all computations related to bending moment are based on that.For general sections it is assumed that all section properties are given in terms of theprincipal directions and consequently no effort is made to determine the principaldirections.

The shear forces for Single-angle sections are obtained for directions along the geo-metric axes. For all other sections the shear stresses are calculated along the geo-metric/principle axes.

For loading combinations that cause compression in the member, the factored mo-ment M u (M u33 and M u22 in the corresponding directions) is magnified to considersecond order effects. The magnified moment in a particular direction is given by:

M = B M + B Mu nt lt1 2 , (LRFD C1-1, SAM 6)

where M nt , M lt , B1 and B2 are defined in Chapter IV. B1 and B2 are moment mag-nification factors. B1 is calculated in the same way as in Chapter IV. Similarly toAISC-LRFD93, ETABS design assumes the analysis includes P- effects in thiscode too, therefore B2 is taken as unity for bending in both directions. If the pro-gram assumptions are not satisfactory for a particular structural model or member,

110 Member Design


the user has a choice of explicitly specifying the values of B1 and B2 for any mem-ber.

When using the UBC-LRFD97 code, ETABS design assumes that a P- analysishas been performed so that moment magnification factors for moments causingsidesway can be taken as unity. It is recommended that the P- analysis be done atthe factored load level of 1.2 DL plus 0.5 LL (White and Hajjar 1991).

The same conditions and limitations as AISC-LRFD93 apply.

Calculation of Nominal Strengths

The nominal strengths in compression, tension, bending, and shear for Seismic,Compact, Noncompact, and Slender sections according to the UBC-LRFD97 arecalculated in the same way as described in section “Calculation of NominalStrengths” of Chapter IV without any exception (UBC 2204.1 2205.2, 2205.3,2206, 2210.2, 2210.3). The nominal strengths for Seismic sections are calculated inthe same way as for Compact sections.

The nominal flexural strengths for all shapes of sections including Single-anglesections are calculated based on their principal axes of bending. For the I, Box,Channel, Circular, Pipe, T, Double-angle and Rectangular sections, the principalaxes coincide with their geometric axes. For the Angle sections, the principal axesare determined and all computations related to flexural strengths are based on that.

The nominal shear strengths are calculated along the geometric axes for all sec-tions. For I, Box, Channel, T, Double angle, Pipe, Circular and Rectangular sec-tions, the principal axes coincide with their geometric axes. For Single-angle sec-tions, principal axes do not coincide with the geometric axes.

If the user specifies nonzero factored strengths for one or more elements in the“Capacity Overwrites” form, these values will override the above mentioned cal-culated values for those elements. The specified factored strengths should bebased on the principal axes of bending.

The strength reduction factor, , is taken as follows (LRFD A5.3):

t = Resistance factor for tension, 0.9 (LRFD D1, H1, SAM 2, 6)

c = Resistance factor for compression, 0.85 (LRFD E2, E3, H1)

c = Resistance factor for compression in angles, 0.90 (LRFD SAM 4, 6)

b = Resistance factor for bending, 0.9 (LRFD F1, H1, A-F1, A-G2, SAM 5)

v = Resistance factor for shear, 0.9 (LRFD F2, A-F2, A-G3, SAM 3)

Member Design 111


All limitations and warnings related to nominal strengths calculation inAISC-LRFD93 also apply in this code.

Calculation of Capacity Ratios

The capacity ratios in UBC-LRFD97 are calculated in the same way as described insection “Calculation of Capacity Ratios” of Chapter IV with some modifications asdescribed below.

In the calculation of the axial force/biaxial moment capacity ratios, first, for eachstation along the length of the member, the actual member force/moment compo-nents are calculated for each load combination. Then the corresponding capacitiesare calculated. Then, the capacity ratios are calculated at each station for each mem-ber under the influence of each of the design load combinations. The controlling ca-pacity ratio is then obtained, along with the associated station and load combina-tion. A capacity ratio greater than 1.0 indicates exceeding a limit state.

During the design, the effect of the presence of bolts or welds is not considered.


The interaction ratio is determined based on the ratioP

Pu

n

. If Pu is tensile, Pn is the

nominal axial tensile strength and t ; and if Pu is compressive, Pn isthe nominal axial compressive strength and c , except for angle sec-tions c (LRFD SAM 6). In addition, the resistance factor for bend-ing, b .

ForP

Pu

n


P

P+

M

M+

M

Mu

n

u

b n

u

b n

8

933

33

22

22

. (LRFD H1-1a, SAM 6-1a)

ForP

P<u

n


P

P+

M

M+

M

Mu

n

u

b n

u

b n233

33

22

22

. (LRFD H1-1b, SAM 6-1a)

112 Member Design


For circular sections an SRSS (Square Root of Sum of Squares) combination is firstmade of the two bending components before adding the axial load component in-stead of the simple algebraic addition implied by the above formulas.

For Single-angle sections, the combined stress ratio is calculated based on the prop-erties about the principal axes (LRFD SAM 5.3, 6). For I, Box, Channel, T, Doubleangle, Pipe, Circular and Rectangular sections, the principal axes coincide withtheir geometric axes. For Single-angle sections, principal axes are determined inETABS. For general sections it is assumed that all section properties are given interms of the principal directions and consequently no effort is made to determinethe principal directions.

Shear Stresses

Similarly to the normal stresses, from the factored shear force values and the nomi-nal shear strength values at each station for each of the load combinations, shear ca-pacity ratios for major and minor directions are calculated as follows:

V

Vu

v n

2

2

, and

V

Vu

v n

3

3

,

where v .


Member Design 113


Seismic Requirements

The special seismic requirements checked by the program for member design aredependent on the type of framing used and are described below for each type offraming (UBC 2204.1, 2205.2, 2205.3). The requirements checked are based onUBC Section 2211.4.2.1 for frames in Seismic Zones 0 and 1 and Zone 2 with Im-portance factor equal to 1 (UBC 2210.2, UBC 2211.4.2.1), on UBC Section2211.4.2.2 for frames in Seismic Zone 2 with Importance factor greater than 1(UBC 2210.2, UBC 2211.4.2.2), and on UBC Section 2211.4.2.3 for frames inSeismic Zones 3 and 4 (UBC 2210.2, UBC 2211.4.2.3). No special requirement ischecked for frames in Seismic Zones 0 and 1 and in Seismic Zone 2 with Impor-tance factor equal to 1 (UBC 2210.2, UBC 2211.4.2.1).

Ordinary Moment Frames

For this framing system, the following additional requirements are checked and re-ported (UBC 2210.2, 2211.4.2.2.c, 2211.4.2.3.c):

• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, whenever P Pu n 0.5 in columns due to the prescribed loading com-binations, the Special Seismic Load Combinations as described below arechecked (UBC 2210.2, 2211.4.2.2.b, 2211.4.2.3.b, 2210.5, 2211.4.6.1).


Special Moment-Resisting Frames

For this framing system, the following additional requirements are checked or re-ported (UBC 2210.2, 2211.4.2.2.d, 2211.4.2.3.d):

• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, whenever P Pu n 0.5 in columns due to the prescribed loading com-binations, the Special Seismic Load Combinations as described below arechecked (UBC 2210.2, 2211.4.2.2.d, 2211.4.2.3.d, 2210.5, 2211.4.6.1).


• In Seismic Zones 3 and 4, the I-shaped beams or columns, Channel-shapedbeams or columns, and Box shaped columns are additionally checked for com-pactness criteria as described in Table VI-1 (UBC 2210.8, 2211.4.8.4.b, Table2211.4.8-1). Compact I-shaped beam and column sections are additionally

114 Member Design


checked for b tf f2 to be less than 52 Fy . Compact Channel-shaped

beam and column sections are additionally checked for b tf f to be less than52 Fy . Compact I-shaped and Channel-shaped column sections are addi-

tionally checked for web-slenderness h tw to be less than the numbers given inTable VI-1. Compact box shaped column sections are additionally checked forb t f and d tw to be less than 110 Fy . If this criteria is satisfied the sec-

tion is reported as SEISMIC as described earlier under section classifications.If this criteria is not satisfied the user must modify the section property.

• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, the program checks the laterally unsupported length of beams to be lessthan 2500 F ry y . If the check is not satisfied, it is noted in the output (UBC2211.4.8.8).

Braced Frames

For this framing system, the following additional requirements are checked or re-ported (UBC 2210.2, 2211.4.2.2.e, 2211.4.2.3.e):

• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, whenever P Pu n 0.5 in columns due to the prescribed loading com-binations, the Special Seismic Load Combinations as described below arechecked (UBC 2210.2, 2211.4.2.2.e, 2211.4.2.3.e, 2210.5, 2211.4.6.1).


• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, the maximum l r ratio of the braces is checked not to exceed720 Fy . If this check is not met, it is noted in the output (UBC

2211.4.9.2.a).

• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, the compressive strength for braces is reduced as 0.8 c nP (UBC2211.4.9.2.b).

P Pu c n0.8 (UBC 2211.4.9.2.b)

• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, all braces are checked to be either Compact or Noncompact according toTable IV-2 (UBC 2211.4.9.2.d). The Box and Pipe shaped braces are addition-ally checked for compactness criteria as described in Table VI-1 (UBC

Member Design 115


2211.4.9.2.d). For box sections b t f and d tw is limited to 110 Fy , for

pipe sections D t is limited to 1300 Fy . If this criteria is satisfied the sec-tion is reported as SEISMIC as described earlier under section classifications.If this criteria is not satisfied the user must modify the section property.

• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, Chevron braces are designed for 1.5 times the specified loading combi-nations (UBC 2211.4.9.4.a.1).

Eccentrically Braced Frames

For this framing system, the program looks for and recognizes the eccentricallybraced frame configurations shown in Figure VI-1. The following additional re-quirements are checked or reported for the beams, columns and braces associatedwith these configurations (UBC 2210.2, 2211.4.2.2.e, 2211.4.2.3.e).

• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, whenever P Pu n 0.5 in columns due to the prescribed loading com-binations, the Special Seismic Load Combinations as described below arechecked (UBC 2210.2, 2211.4.2.2.b, 2211.4.2.3.b, 2210.5, 2211.4.6.1).


• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, the I-shaped and Channel-shaped beams are additionally checked forcompactness criteria as described in Table VI-1 (UBC 2211.4.10.2.a, 2210.8,2211.4.8.4.b, Table 2211.4.8-1). Compact I-shaped and Channel-shaped beamsections are additionally checked for b tf f2 to be less than 52 Fy . If this

criteria is satisfied the section is reported as SEISMIC as described earlier un-der section classifications. If this criteria is not satisfied the user must modifythe section property.

• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, the link beam yield strength, Fy , is checked not to exceed the following(UBC 2211.4.10.2.b):

Fy 50 ksi (UBC 2211.4.10.2.b)


• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, the shear strength for link beams is taken as follows (UBC 2210.10.b,2211.4.12.2.d):

116 Member Design


V Vu v n , (UBC 2211.4.10.2.d)

where,

V V M en pa pamin , 2 , (UBC 2211.4.10.2.d)

V VP

Ppa p

u

y

1

2

, (UBC 2211.4.10.2.f)

M MP

Ppa p

u

y

1.18 1 , (UBC 2211.4.10.2.f)

V F d t tp y f w0.6 ( )2 , (UBC 2211.4.10.2.d)

M Z Fp y , (UBC 2211.4.10.2.d)

v (default is 0.9) , (UBC 2211.4.10.2.d, 2211.4.10.2.f)

P A Fy g y . (UBC 2211.4.10.2.e)

• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, if P A Fu g y0.15 , the link beam length, e, is checked not to exceed thefollowing (UBC2211.4.10.2.f):

e

A

A

M

Vif

A

Aw

g

p

p

w

g

1.15 0.5 1.6 0.3 ,

1.6M

Vif

A

Ap

p

w

g

0.3 ,

(UBC 2211.4.10.2.f)

where,

A d t tw f w( )2 , and (UBC 2211.4.10.2.f)

P Vu u . (UBC 2211.4.10.2.f)


• The link beam rotation, , of the individual bay relative to the rest of the beamis calculated as the story drift M times bay length divided by the total lengthsof link beams in the bay. In Seismic Zones 3 and 4 and in Seismic Zone 2 withImportance factor greater than 1, the link beam rotation, , is checked asfollows (UBC 2211.4.10.2.g).

Member Design 117


0.090 , where link beam clear length, e M Vs s1.6 ,

0.030 , where link beam clear length, e M Vs s2.6 , and

value interpolated between 0.090 and 0.030 as the link beam clearlength varies from 1.6 M Vs s to 2.6 M Vs s .

• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, the brace strength is checked to be at least 1.25 times the axial force cor-responding to the controlling link beam strength (UBC 2211.4.10.6.a). Thecontrolling link beam strength is taken as follows:

min ,v pa v paV M e2 , (UBC 2211.4.10.2.d)

The values of V pa and M pa are calculated following the procedure describedabove. The correspondence between brace force and link beam force is ob-tained from the associated load cases, whichever has the highest link beamforce of interest.

• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, the column strength is checked for 1.25 times the column forces corre-sponding to the controlling link beam strength (UBC 2211.4.10.8). The con-trolling link beam strength and the corresponding forces are as obtained by theprocess described above.

• Axial forces in the beams are included in checking the beams. The user is re-minded that using a rigid diaphragm model will result in zero axial forces in thebeams. The user must disconnect some of the column lines from the diaphragmto allow beams to carry axial loads. It is recommended that only one columnline per eccentrically braced frame be connected to the rigid diaphragm or aflexible diaphragm model be used.

• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, the beam laterally unsupported length is checked to be less than76 b Ff y . If not satisfied it is so noted as a warning in the output file (UBC

2210.11, 2211.4.10.5).

Note: The beam strength in flexure of the beam outside the link, is NOT currentlychecked to be at least 1.25 times the moment corresponding to the controlling linkbeam strength (UBC 2211.4.10.6.b). Users need to check for this requirement.

118 Member Design


Special Concentrically Braced Frames

For this framing system, the following additional requirements are checked or re-ported (UBC 2210.2, 2211.4.2.2.e, 2211.4.2.3.e):

• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, whenever P Pu n 0.5 in columns due to the prescribed loading com-binations, the Special Seismic Load Combinations as described below arechecked (UBC 2210.2, 2211.4.2.2.e, 2211.4.2.3.e, 2210.5, 2211.4.6.1).

Member Design 119


Figure VI-1Eccentrically Braced Frame Configurations


• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, all columns are checked to be Compact according to Table IV-2. Com-pact box shaped column sections are additionally checked for b t f and d tw tobe less than 110 Fy as described in Table VI-1 (UBC 2211.4.12.5.a). If

this criteria is satisfied the section is reported as SEISMIC as described earlierunder section classifications. If this criteria is not satisfied the user must modifythe section property (UBC 2210.10.g, 2211.4.12.5.a).

• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, all braces are checked to be Compact according to Table IV-2 (UBC2210.10.c, 2211.4.12.2.d). The Angle, Double-angle, Box and Pipe shapedbraces are additionally checked for compactness criteria as described in TableVI-1 (UBC 2210.10.c, 2211.4.12.2.d). For box sections b t f and d tw is lim-ited to 100 Fy , for pipe sections D t is limited to 1300 Fy . If this cri-

teria is satisfied the section is reported as SEISMIC as described earlier undersection classifications. If this criteria is not satisfied the user must modify thesection property.

• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, the compressive strength for braces is taken as c nP (UBC 2210.10.b,2211.4.12.2.b). Unlike Braced Frames, no reduction is required.

P Pu c n (UBC 2211.4.12.2.b)

• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, the maximum l r ratio of the braces is checked not to exceed1,000 Fy . If this check is not met, it is noted in the output (UBC 2210.10.a,

2211.4.12.2.a).

Note: Beams intersected by Chevron braces are NOT currently checked tohave a strength to support loads represented by the following loading combina-tions (UBC 2213.9.4.1):

1.0DL + 0.7 LL Pb (UBC 2210.10.e, 2211.4.12.4.a.3)0.9DL Pb (UBC 2210.10.e, 2211.4.12.4.a.3)

where Pb is given by the difference of F Ay for the tension brace and 0.3 c nPfor the compression brace. Users need to check for this requirement.

120 Member Design


Joint DesignWhen using UBC-LRFD97 design code, the structural joints are checked and/or de-signed for the following:

• Check for the requirement of continuity plate and determination of its area

• Check for the requirement of doubler plate and determination of its thickness

• Check for the ratio of beam flexural strength to column flexural strength

• Reporting the beam connection shear

• Reporting the brace connection force

Design of Continuity Plates

In a plan view of a beam/column connection, a steel beam can frame into a columnin the following ways:





For connection conditions described in the last two steps above, the thickness ofsuch plates is usually set equal to the flange thickness of the corresponding beam.However, for the connection condition described by the first step above, where thebeam frames into the flange of the column, such continuity plates are not alwaysneeded. The requirement depends upon the magnitude of the beam-flange force andthe properties of the column. This is the condition that the program investigates.Columns of I-sections only are investigated. The program evaluates the continuityplate requirements for each of the beams that frame into the column flange (i.e. par-allel to the column major direction) and reports the maximum continuity plate areathat is needed for each beam flange. The continuity plate requirements are evalu-ated for moment frames only. No check is made for braced frames.

Joint Design 121


The program first evaluates the need for continuity plates. Continuity plates will berequired if any of the following four conditions are not satisfied:

• The column flange design strength in bending must be larger than the beamflange force, i.e.,

R = t F Pn fc yc bf(0.9)6.25 2 (LRFD K1-1)

• The design strength of the column web against local yielding at the toe of thefillet must be larger than the beam flange force, i.e.,

R k +t F t Pn c fb yc wc bf= (1.0) (5.0 ) (LRFD K1-2)

• The design strength of the column web against crippling must be larger than thebeam flange force, i.e.,

R t +t

d

t

tn wc

fb

c

wc

fc

= (0.75) 68 2 1 3

1.5

Ft

tPyc

fc

wcbf (LRFD K1-5a)

• The design compressive strength of the column web against buckling must belarger than the beam flange force, i.e.,

Rt F

dPn

wc yc

cbf= (0.9)

4100 3

(LRFD K1-8)

If any of the conditions above are not met the program calculates the required conti-nuity plate area as,

A =P

Ftcp

bf

yc

wc(0.85)(0.9 )

12 2 (LRFD K1.9, E2)

If Acp 0, no continuity plates are required.

The formula above assumes the continuity plate plus a width of web equal to12 twc

act as a compression member to resist the applied load (LRFD K1.9). The formulaalso assumes 0.85 and F Fcr yc0.9 . This corresponds to an assumption of

0.5 in the column formulas (LRFD E2-2). The user should choose the continu-ity plate cross-section such that this is satisfied. As an example when using Fyc 50ksi and assuming the effective length of the stiffener as a column to be 0.75h(LRFD K1.9) the required minimum radius of gyration of the stiffener cross-sec-tion would be r h0.02 to obtain 0.5 (LRFD E2-4).

122 Joint Design


If continuity plates are required, they must satisfy a minimum area specification de-fined as follows:

• The minimum thickness of the stiffeners is taken in ETABS as follows:

t = t bcpmin

fb fb0.5max ,Fy

95(LRFD K1.9.2)

• The minimum width of the continuity plate on each side plus 1/2 the thicknessof the column web shall not be less than 1/3 of the beam flange width, or

b = 2b

3

t

2cpmin fp wc (LRFD K1.9.1)

• So that the minimum area is given by:

A = t bcpmin

cpmin

cpmin (LRFD K1.9.1)

Therefore, the continuity plate area provided by the program is either zero or thegreater of Acp and Acp

min .

In the equations above,

Acp = Required continuity plate areaFyc = Yield stress of the column and continuity plate materiald b = Beam depthd c = Column depthh = Clear distance between flanges of column

less fillets for rolled shapeskc = Distance between outer face of the

column flange and web toe of its fillet.M u = Factored beam momentPbf = Beam flange force, assumed as M d tu b fb

Rn = Nominal strengtht fb = Beam flange thicknesst fc = Column flange thicknesstwc = Column web thickness

= Resistance factor

The special seismic requirements additionally checked by the program are depend-ent on the type of framing used and are described below for each type of framing.The requirements checked are based on UBC Section 2211.4.2.1 for frames in Seis-

Joint Design 123


mic Zones 0 and 1 and Zone 2 with Importance factor equal to 1 (UBC 2210.2,UBC 2211.4.2.1), on UBC Section 2211.4.2.2 for frames in Seismic Zone 2 withImportance factor greater than 1 (UBC 2210.2, UBC 2211.4.2.2), and on UBC Sec-tion 2211.4.2.3 for frames in Seismic Zones 3 and 4 (UBC 2210.2, UBC2211.4.2.3). No special requirement is checked for frames in Seismic Zones 0 and 1and in Seismic Zone 2 with Importance factor equal to 1 (UBC 2210.2, UBC2211.4.2.1).

• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, for Ordinary Moment Frames the continuity plates are checked and de-signed for a beam flange force, P M d tbf pb b fb (UBC 2211.4.7.2.a,

2211.4.8.2.a.1).

P M d tbf pb b fb (UBC 2211.4.7.2.a, 2211.4.8.2.a.1)

• In Seismic Zones 3 and 4, for Special Moment-Resisting Frames, for determin-ing the need for continuity plates at joints due to tension transfer from the beamflanges, the force Pbf is taken as f Ayb bf for all four checks described above(LRFD K1-1, K1-2, K1-5a, K1-8), except for checking column flange designstrength in bending Pbf is taken as 1.8 f Ayb bf (UBC 2211.4.8.5, LRFD K1-1).In Seismic Zone 2 with Importance factor greater than 1, for Special Mo-ment-Resisting Frames, for determining the need for continuity plates at jointsdue to tension transfer from the beam flanges, the force Pbf is taken as f Ayb bf

(UBC 2211.4.8.2.a.1).

P f Abf yb bf1.8 (Zone 3 and 4) (UBC 2211.4.8.5)

P f Abf yb bf (Zone 2 with I >1) (UBC 2211.4.8.2.a.1)

For design of the continuity plate the beam flange force is taken asP M d tbf pb b fb (UBC 2211.4.8.2.a.1).

P M d tbf pb b fb (UBC 2211.4.8.2.a.1)

• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, for Eccentrically Braced Frames, the continuity plate requirements arechecked and designed for a beam flange force of P f Abf yb bf .

124 Joint Design


Design of Doubler Plates

One aspect of the design of a steel framing system is an evaluation of the shearforces that exist in the region of the beam column intersection known as the panelzone.

Shear stresses seldom control the design of a beam or column member. However,in a Moment-Resisting frame, the shear stress in the beam-column joint can be criti-cal, especially in framing systems when the column is subjected to major directionbending and the joint shear forces are resisted by the web of the column. In minordirection bending, the joint shear is carried by the column flanges, in which case theshear stresses are seldom critical, and this condition is therefore not investigated bythe program.

Shear stresses in the panel zone, due to major direction bending in the column, mayrequire additional plates to be welded onto the column web, depending upon theloading and the geometry of the steel beams that frame into the column, either alongthe column major direction, or at an angle so that the beams have components alongthe column major direction. See Figure II-5. The program investigates such situa-tions and reports the thickness of any required doubler plates. Only columns withI-shapes are investigated for doubler plate requirements. Also doubler plate re-quirements are evaluated for moment frames only. No check is made for bracedframes.

The program calculates the required thickness of doubler plates (see Figure II-5) forAISC-LRFD93 similar to the procedure described in Section “Design of DoublerPlates” in Chapter II except that the following algorithms are used. The shear forcein the panel zone, is given by

V =M

d - tVp

n =

nbn n

n fn

c

b

1

cos

The nominal panel shear strength is given by

R = F d t P Pv y c r u y0.6 for 0.4, or if Pu is tensile, and (LRFD K1-9)

R = F d tP

PP >v y c r

u

y

u0.6 1.4 , for 0.4Py . (LRFD K1-10)

By using V Rp v , with 0.9, the required column web thickness tr can befound.

The extra thickness, or thickness of the doubler plate is given by

Joint Design 125


t = t th

Fdp r w

y418, (LRFD F2-1)

where,

Fy = Column and doubler plate yield stresstr = Required column web thicknesstdp = Required doubler plate thicknesstw = Column web thicknessh = d tc fc2 if welded, d kc c2 if rolled,V p = Panel zone shearVc = Column shear in column aboveFy = Beam flange forcesnb = Number of beams connecting to columnd n = Depth of n-th beam connecting to column

n = Angle between n-th beam and column major directiond c = Depth of column clear of fillets, equals d k2M bn = Calculated factored beam moment from

the corresponding loading combinationRv = Nominal shear strength of panelPu = Column factored axial loadPy = Column axial yield strength, F Ay

The largest calculated value of tdp calculated for any of the load combinationsbased upon the factored beam moments and factored column axial loads is re-ported.

The special seismic requirements checked by the program for calculating doublerplate areas are dependent on the type of framing used and are described below foreach type of framing. The requirements checked are based on UBC Section2211.4.2.1 for frames in Seismic Zones 0 and 1 and Zone 2 with Importance factorequal to 1 (UBC 2210.2, UBC 2211.4.2.1), on UBC Section 2211.4.2.2 for framesin Seismic Zone 2 with Importance factor greater than 1 (UBC 2210.2, UBC2211.4.2.2), and on UBC Section 2211.4.2.3 for frames in Seismic Zones 3 and 4(UBC 2210.2, UBC 2211.4.2.3). No special requirement is checked for frames inSeismic Zones 0 and 1 and in Seismic Zone 2 with Importance factor equal to 1(UBC 2210.2, UBC 2211.4.2.1).

• In Seismic Zones 3 and 4, for Special Moment-Resisting Frames, the panelzone doubler plate requirements that are reported will develop the lesser ofbeam moments equal to 0.9 of the plastic moment capacity of the beam

126 Joint Design


0.9 b pbM , or beam moments due to specified load combinations

involving seismic load (UBC 2211.4.8.3.a).

The capacity of the panel zone in resisting this shear is taken as (UBC2211.8.3.a):

v n v y c pcf cf

b c p

V = F d t +b t

d d t0.60 1

3 2

(UBC 2211.4.8.3.a)

giving the required panel zone thickness as

tV

F d

b t

d d

h

Fp

p

v y c

cf cf

b c y0.6

3

418

2

, (UBC 2211.4.8.3, LRFD F2-1)

and the required doubler plate thickness as

t = t - tdp p wc

where,

v = 0.75,bcf = width of column flange,tcf = thickness of column flange,t p = required column web thickness,h = d tc fc2 if welded, d kc c2 if rolled, andd b = depth of deepest beam framing into the major direction of

the column.

• In Seismic Zones 3 and 4, for Special Moment-Resisting Frames, the panelzone column web thickness requirement the program checks the following:

td t d t

wc

c fc b fb( ) ( )2 2

90(UBC 2211.4.8.3.b)


• In Seismic Zones 3 and 4, for Eccentrically Braced Frames, the doubler platerequirements are checked similar to the doubler plate checks for special Mo-ment-Resisting frames as discussed above (UBC 2211.4.10.7).

Joint Design 127


Weak Beam Strong Column Measure

In Seismic Zones 3 and 4, for Special Moment-Resisting Frames, the code requiresthat the sum of beam flexure strengths at a joint should be less than the sum of col-umn flexure strengths (UBC 2211.4.8.6). The column flexure strength should re-flect the presence of axial force present in the column. To facilitate the review of thestrong column weak beam criterion, the program will report a beam/column plasticmoment capacity ratio for every joint in the structure.

For the major direction of any column (top end) the beam to column strength ratio isobtained as

R =

M

M + Mmajn =

n

pbn n

pcax pcbx

b

1

cos(UBC 2211.4.8.6 8-3)

For the minor direction of any column the beam to column strength ratio is obtainedas

R =

M

M + Mn =

n

pbn n

pcay pcby

b

min1

sin, (UBC 2211.4.8.6 8-3)

where,

Rmaj min, = Plastic moment capacity ratios, in the major andminor directions of the column, respectively

M pbn = Plastic moment capacity of n-th beam connectingto column

n = Angle between the n-th beam and the columnmajor direction

M pcax y, = Major and minor plastic moment capacities, reduced foraxial force effects, of column above story level

M pcbx y, = Major and minor plastic moment capacities, reduced foraxial force effects, of column below story level

nb = Number of beams connecting to the column

The plastic moment capacities of the columns are reduced for axial force effectsand are taken as

M = Z F - P Apc c yc uc gc , (UBC 2211.4.8.6 8-3)

128 Joint Design


where,

Zc = Plastic modulus of column,Fyc = Yield stress of column material,Puc = Maximum axial strength in the column in compression, Puc 0 , andAgc = Gross area of column.

For the above calculations the section of the column above is taken to be the sameas the section of the column below assuming that the column splice will be locatedsome distance above the story level.

Evaluation of Beam Connection Shears

For each steel beam in the structure the program will report the maximum majorshears at each end of the beam for the design of the beam shear connections. Thebeam connection shears reported are the maxima of the factored shears obtainedfrom the loading combinations.

For special seismic design, the beam connection shears are not taken less than thefollowing special values for different types of framing. The requirements checkedare based on UBC Section 2211.4.2.1 for frames in Seismic Zones 0 and 1 and Zone2 with Importance factor equal to 1 (UBC 2210.2, UBC 2211.4.2.1), on UBC Sec-tion 2211.4.2.2 for frames in Seismic Zone 2 with Importance factor greater than 1(UBC 2210.2, UBC 2211.4.2.2), and on UBC Section 2211.4.2.3 for frames inSeismic Zones 3 and 4 (UBC 2210.2, UBC 2211.4.2.3). No special requirement ischecked for frames in Seismic Zones 0 and 1 and in Seismic Zone 2 with Impor-tance factor equal to 1 (UBC 2210.2, UBC 2211.4.2.1).

• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, for Ordinary Moment Frames, the beam connection shears reported arethe maximum of the specified loading combinations and the following addi-tional loading combinations (UBC 2211.4.7.2.a, 2211.4.8.2.b):


• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, for Special Moment-Resisting Frames, the beam connection shears thatare reported allow for the development of the full plastic moment capacity ofthe beam. Thus:

V =C M

L+ V Vu

pb

DL LL1.2 0.5 (UBC 2211.4.8.2.b)

Joint Design 129


where

V = Shear force corresponding to END I or END J of beam,C = 0 if beam ends are pinned, or for cantilever beam,

= 1 if one end of the beam is pinned,= 2 if no ends of the beam are pinned,

M pb = Plastic moment capacity of the beam, Z Fy ,L = Clear length of the beam,VDL = Absolute maximum of the calculated factored beam

shears at the corresponding beam ends from thedead load only, and

VLL = Absolute maximum of the calculated factored beamshears at the corresponding beam ends from thelive load only.

• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, for Eccentrically Braced Frames, the link beam connection shear is re-ported as equal to the link beam web shear capacity (UBC 2211.4.10.7).

Evaluation of Brace Connection Forces

For each steel brace in the structure the program reports the maximum axial force ateach end of the brace for the design of the brace to beam connections. The braceconnection forces reported are the maxima of the factored brace axial forces ob-tained from the loading combinations.

For special seismic design, the brace connection forces are not taken less than thefollowing special values for different types of framing. The requirements checkedare based on UBC Section 2211.4.2.1 for frames in Seismic Zones 0 and 1 and Zone2 with Importance factor equal to 1 (UBC 2210.2, UBC 2211.4.2.1), on UBC Sec-tion 2211.4.2.2 for frames in Seismic Zone 2 with Importance factor greater than 1(UBC 2210.2, UBC 2211.4.2.2), and on UBC Section 2211.4.2.3 for frames inSeismic Zones 3 and 4 (UBC 2210.2, UBC 2211.4.2.3). No special requirement ischecked for frames in Seismic Zones 0 and 1 and in Seismic Zone 2 with Impor-tance factor equal to 1 (UBC 2210.2, UBC 2211.4.2.1).

• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, for ordinary Braced Frames, the bracing connection force is reported atleast as the smaller of the tensile strength of the brace (F Ay ) (UBC2211.4.9.3.a.1) and the following special loading combinations (UBC2211.4.9.3.a.2):

130 Joint Design



• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, for Eccentrically Braced Frames, the bracing connection force is re-ported as at least the nominal strength of the brace (UBC 2211.4.10.6.d).

• In Seismic Zones 3 and 4 and in Seismic Zone 2 with Importance factor greaterthan 1, for Special Concentrically Braced Frames, the bracing connection forceis reported at least as the smaller of the tensile strength of the brace (F Ay ) (UBC2210.10, 2211.4.12.3.a.1) and the following special loading combinations(UBC 2211.10, 2211.4.12.3.a.2):


Joint Design 131


C h a p t e r VII

Check/Design for CISC94

This chapter describes the details of the structural steel design and stress check al-gorithms that are used by ETABS when the user selects the CAN/CSA-S16.1-94design code (CISC 1995). Various notations used in this chapter are described inTable VII-1.


In the evaluation of the axial force/biaxial moment capacity ratios at a station alongthe length of the member, first the actual member force/moment components andthe corresponding capacities are calculated for each load combination. Then the ca-pacity ratios are evaluated at each station under the influence of all load combina-tions using the corresponding equations that are defined in this section. The con-trolling capacity ratio is then obtained. A capacity ratio greater than 1.0 indicatesexceeding a limit state. Similarly, a shear capacity ratio is also calculated sepa-rately.

English as well as SI and MKS metric units can be used for input. But the code isbased on Newton-Millimeter-Second units. For simplicity, all equations and de-scriptions presented in this chapter correspond to Newton-Millimeter-Secondunits unless otherwise noted.

133

134


A = Cross-sectional area, mm2

Ag = Gross cross-sectional area, mm2

A Av v2 3, = Major and minor shear areas, mm2

Aw = Shear area, mm2

Ce = Euler buckling strength, N

C f = Factored compressive axial load, N

Cr = Factored compressive axial strength, N

Cw = Warping constant, mm6

C y = Compressive axial load at yield stress, A Fg y , N

D = Outside diameter of pipes, mm

E = Modulus of elasticity, MPa

Fy = Specified minimum yield stress, MPa

G = Shear modulus, MPa

I 33 , I 22 = Major and minor moment of inertia, mm4

J = Torsional constant for the section, mm4


K K33 22, = Effective length K-factors in the major and minor directions(assumed as 1.0 unless overwritten by user)

L = Laterally unbraced length of member, mm

M Mf f33 22, = Factored major and minor bending loads, N-mm

M Mp p33 22, = Major and minor plastic moments, N-mm

M Mr r33 22, = Factored major and minor bending strengths, N-mm

M u = Critical elastic moment, N-mm

M My y33 22, = Major and minor yield moments, N-mm

S S33 22, = Major and minor section moduli, mm3

Tf = Factored tensile axial load, N

Tr = Factored tensile axial strength, N

U1 = Moment magnification factor to account for deformationof member between ends

U 2 = Moment magnification factor ( on sidesway moments)to account for P-

V Vf f2 3, = Factored major and minor shear loads, N

V Vr r2 3, = Factored major and minor shear strengths, N

Z Z33 22, = Major and minor plastic moduli, mm3

Table VII-1CISC 94 Notations

135

Chapter VII Check/Design for CISC94

b = Nominal dimension of longer leg of angles

( )b tf w2 for welded

( )b tf f3 for rolled box sections, mm

b f = Flange width, mm

d = Overall depth of member, mm

h = Clear distance between flanges , taken as ( )d t f2 , mm

k = Web plate buckling coefficient, assumed as 5.34 (no stiffeners)

k = Distance from outer face of flange to web toe of fillet , mm

l = Unbraced length of member, mm

l l33 22, = Major and minor direction unbraced member lengths, mm

r = Radius of gyration, mm

r r33 22, = Radii of gyration in the major and minor directions, mm

rz = Minimum Radius of gyration for angles, mm

t = Thickness, mm

t f = Flange thickness, mm

t w = Web thickness, mm


= Resistance factor, taken as 0.9

1 = Moment Coefficient

13 12, = Major and minor direction moment coefficients

2 = Bending coefficient

Table VII-1CISC 94 Notations (cont.)

Design Loading CombinationsThe design load combinations are the various combinations of the load cases forwhich the structure needs to be checked. For the CAN/CSA-S16.1-94 code, if astructure is subjected to dead load (DL), live load (LL), wind load (WL), and earth-quake induced load (EL), and considering that wind and earthquake forces are re-versible, then the following load combinations may have to be defined (CISC 7.2):

1.25 DL1.25 DL + 1.50 LL (CISC 7.2.2)

1.25 DL 1.50 WL0.85 DL 1.50 WL1.25 DL + 0.7 (1.50 LL 1.50 WL) (CISC 7.2.2)

1.00 DL 1.00 EL1.00 DL + 0.50 LL 1.00 EL (CISC 7.2.6)

These are also the default design load combinations whenever the CISC Code isused. In generating the above default loading combinations, the importance factoris taken as 1.

The user should use other appropriate loading combinations if roof live load isseparately treated, other types of loads are present, or if pattern live loads are to beconsidered.


When using the CISC code, ETABS design assumes that a P- analysis has beenperformed so that moment magnification factors for moments causing sideswaycan be taken as unity. It is suggested that the P- analysis be done at the factoredload level of 1.25 DL plus 1.05 LL. See also White and Hajjar (1991).

For the gravity load case only, the code (CISC 8.6.2) requires that notional lateralloads be applied at each story, equal to 0.005 times the factored gravity loads actingat each story. If extra load cases are used for such analysis, they should be includedin the loading combinations with due consideration to the fact that the notionallateral forces can be positive or negative.



Classification of SectionsFor the determination of the nominal strengths for axial compression and flexure,the sections are classified as either Class 1 (Plastic), Class 2 (Compact), Class 3(Noncompact), or Class 4 (Slender). The program classifies the individual sectionsaccording to Table VII-2 (CISC 11.2). According to this table, a section is classi-fied as either Class 1, Class 2, or Class 3 as applicable.

If a section fails to satisfy the limits for Class 3 sections, the section is classified asClass 4. Currently ETABS does not check stresses for Class 4 sections.

Calculation of Factored ForcesThe factored member forces for each load combination are calculated at each of thepreviously defined stations. These member forces are T f or C f , M f 33 , M f 22 ,V f 2

and V f 3 corresponding to factored values of the tensile or compressive axial load,the major moment, the minor moment, the major direction shear, and the minor di-rection shear, respectively.

Because ETABS design assumes that the analysis includes P- effects, any magni-fication of sidesway moments due to the second order effects are already included,therefore U 2 for both directions of bending is taken as unity. It is suggested that theP- analysis be done at the factored load level of 1.25 DL plus 1.05 LL. See alsoWhite and Hajjar (1991).

However, the user can overwrite the values of U 2 for both major and minor direc-tion bending. In this case M f in a particular direction is taken as:

M M U Mf fg ft2 , where (CISC 8.6.1)

U 2 = Moment magnification factor for sidesway moments,M fg = Factored moments not causing translation, andM ft = Factored moments causing sidesway.






RatioChecked

Class 1(Plastic)

Class 2(Compact)

Class 3(Noncompact)

I-SHAPE

b tf f2 145 yF 170 yF 200 yF

h tw

11001 0 39

F- .

C

Cy

f

y

17001 0 61

F- .

C

Cy

f

y

19001 0 65

F- .

C

Cy

f

y

BOX

b tf420 yF (rolled)

525 yF (welded)525 yF 670 yF

h tw As for I-shapes As for I-shapes As for I-shapes

CHANNELb tf f

h tw

Not applicableNot applicable


200 yF

As for I-shapes

T-SHAPEb tf f2d tw



200 yF

340 yF

DOUBLEANGLE

b t Not applicable Not applicable 200 yF

ANGLE b t Not applicable Not applicable 200 yF

PIPE(Flexure)

D t 13000 yF 18000 yF 66000 yF

PIPE (Axial) D t 23000 yF

ROUND BAR Assumed Class 2

RECTAN-GULAR

Assumed Class 2

GENERAL Assumed Class 3

Table VII-2Limiting Width-Thickness Ratios for

Classification of Sections based on CISC 94



Figure VII-1CISC 94 Definition of Geometric Properties

Calculation of Factored StrengthsThe factored strengths in compression, tension, bending, and shear are computedfor Class 1, 2, and 3 sections in ETABS. The strength reduction factor, , is taken

as 0.9 (CISC 13.1).

For Class 4 (Slender) sections and any singly symmetric and unsymmetric sectionsrequiring consideration of local buckling, flexural-torsional and torsional buck-ling, or web buckling, reduced nominal strengths may be applicable. The user mustseparately investigate this reduction if such elements are used.

If the user specifies nonzero factored strengths for one or more elements in the“Capacity Overwrites” form, these values will override the above mentioned cal-culated values for those elements.

Compression Strength

The factored axial compressive strength value, C r , for Class 1, 2, or 3 sections de-pends on a factor, , which eventually depends on the slenderness ratio, Kl r,which is the larger of K l r33 33 33 and K l r22 22 22 , and is defined as

=Kl

r

F

Ey .

For single angles rZ is used in place of r r33 22and . For members in compression, ifKl r is greater than 200, a message is printed (CISC 10.2.1).

Then the factored axial strength is evaluated as follows (CISC 13.3.1):

C AFr yn n

-

1 21

, where (CISC 13.3.1)

n is an exponent and it takes three possible values to match the strengths relatedto three SSRC curves. The default n is 1.34 which is assigned to W-shapesrolled in Canada, fabricated boxes and I shapes, and cold-formed non-stress re-lieved (Class C) hollow structural sections (HSS) (CISC 13.3.1, CISC C13.3,Manual Page 4-12, Manual Table 6-2). The WWF sections produced in Canadafrom plate with flame-cut edges and hot-formed or cold-relieved (Class H)HSS are assigned to a favorable value of n (CISC 13.3.1, CISC C13.3,Manual Page 4-12). For heavy sections, a smaller value of n (n ) is con-sidered appropriate (CISC C13.3). ETABS assumes the value of n as follows:

140 Calculation of Factored Strengths


n

for WWF, HS (Class H) and HSS (Class H) sections,

for W, L, and 2L sections and normal HS and HSS sections,

for other sections with thickness less than 25.4 mm,

for other sections with thickness larger than or equal to 25.4 mm.

The HSS sections in the current Canadian Section Database of ETABS are pre-fixed as HS instead of HSS. Also, to consider any HSS section as Class H, it isexpected that the user would put a suffix to the HS or HSS section names.

Tension Strength

The factored axial tensile strength value, Tr , is taken as A Fg y (CISC13.2.(a).(i)). For members in tension, if l r is greater than 300, a message is printedaccordingly (CISC 10.2.2).

T A Fr g y (CISC 13.2)

Bending Strengths

The factored bending strength in the major and minor directions is based on thegeometric shape of the section, the section classification for compactness, and theunbraced length of the member. The bending strengths are evaluated according toCISC as follows (CISC 13.5 and 13.6):

For laterally supported members, the moment capacities are considered to be as fol-lows:

For Class 1 and 2, M ZFr y , and (CISC 13.5)

For Class 3, M SFr y . (CISC 13.5)

Special considerations are required for laterally unsupported members. The proce-dure for the determination of moment capacities for laterally unsupported members(CISC 13.6) is described in the following subsections.

If the capacities (M r 22 and M r 33 ) are overwritten by the user, they are used in theinteraction ratio calculation when strengths are required for actual unbracedlengths. None of these overwritten capacities are used for strengths in laterally sup-ported case.

Calculation of Factored Strengths 141


I-shapes and Boxes


For Class 1 and 2 sections of I-shapes and boxes bent about the major axis,

when M > Mu p33 ,

M = M -M

MMr p

p

up3 33

33331 , and (CISC 13.6)

when M Mu p33 ,

M r 33 = M u , where (CISC 13.6)

M r 33 = Factored major bending strength,M p33 = Major plastic moment, Z Fy33 ,M u = Critical elastic moment,

2

LEI GJ +

E

LI C w22

2

22 , (CISC 13.6)

L = Laterally unbraced length, l22 ,C w = Warping constant assumed as 0.0 for boxes, pipes,

rectangular and circular bars, and

2 = +M

M+

M

Ma

b

a

b

2

. (CISC 13.6)

M a and M b are end moments of the unbraced segment and M a is less than

M b ,M

Ma

b

being positive for double curvature bending and negative for sin-

gle curvature bending. If any moment within the segment is greater than M b ,

2 is taken as 1.0. The program defaults 2 to 1.0 if the unbraced length, l of themember is overwritten by the user (i.e. it is not equal to the length of the mem-ber). 2 should be taken as 1.0 for cantilevers. However, the program is unableto detect whether the member is a cantilever. The user can overwrite the valueof 2 for any member by specifying it.

For Class 3 sections of I-shapes, channels, boxes bent about the major axis,

when M Mu y 33 ,



M = MM

MMr y

y

uy33 33

33331 , and (CISC 13.6)

when M Mu y 33 ,

M Mr u33 , where (CISC 13.6)

M r 33 and M u are as defined earlier for Class 1 and 2 sections andM y 33 is the major yield moment, S Fy33 .


For Class 1 and 2 sections of I-shapes and boxes bent about their minor axis,

M = M = Z Fr p y22 22 22 .

For Class 3 sections of I-shapes and boxes bent about their minor axis,

M = M = S Fr y y22 22 22 .

Rectangular Bar


For Class 2 rectangular bars bent about their major axis,

when M > Mu p33 ,

M = M -M

MMr p

p

up33 33

33331 , and (CISC 13.6)

when M Mu p33 ,

M = Mr u33 . (CISC 13.6)


For Class 2 sections of rectangular bars bent about their minor axis,

M = M = Z Fr p y22 22 22 .

Pipes and Circular Rods

For pipes and circular rods bent about any axis



When M > Mu p33 ,

M = M -M

MMr p

p

up33 33

33331 , and (CISC 13.6)

when M Mu p33 ,

M = Mr u33 . (CISC 13.6)

Channel Sections


For Class 3 channel sections bent about their major axis,

when M Mu y 33 ,

M = MM

MMr y

y

uy33 33

33331 , and (CISC 13.6)

when M Mu y 33 ,

M = Mr u33 .


For Class 3 channel sections bent about their minor axis,

M = M = S Fr y y22 22 22 .

T-shapes and double angles


For Class 3 sections of T-shapes and double angles the factored major bendingstrength is assumed to be (CISC 13.6d),

M =EI GJ

LB + + B F Sr y33

22 23312 , where

B = d L I J22 .



The positive sign for B applies for tension in the stem of T-sections or the out-standing legs of double angles (positive moments) and the negative sign applies forcompression in stem or legs (negative moments).


For Class 3 sections of T-shapes and double angles the factored minor bendingstrength is assumed as,

M = F Sr y22 22 .

Single Angle and General Sections

For Class 3 single angles and for General sections, the factored major and minor di-rection bending strengths are assumed as,

M = F Sr y33 33 , and

M = F Sr y22 22 .

Shear Strengths

The factored shear strength,Vr 2 , for major direction shears in I-shapes, boxes andchannels is evaluated as follows (CISC 13.4.1.1):

• Forh

t

k

Fw

v

y

,

V = A Fr w y2 . (CISC 13.4.1.1)

• Fork

F<

h

t

k

Fv

y w

v

y

502 ,

V = Ak F

h tr w

v y

w2 290 . (CISC 13.4.1.1)

• For 502 621k

F<

h

t

k

Fv

y w

v

y

,

V = A F Fr w cri t2 , where (CISC 13.4.1.1)



F =k F

h tcri

v y

w

290 , and

F = F Fa/h

t y cri

1

1 2.

Assuming no stiffener is used, the value of Ft is taken as zero.

• Forh

t>

k

Fw

v

y

621 ,

V = A F Fr w cre t2 , where (CISC 13.4.1.1)

F =k

h/tcre

v

w

1800002( )

.

In the above equations, kv is the shear buckling coefficient, and it is defined as:

ka h

v 42( / )

, a h/ 1

ka h

v

42( / )

, a h/ 1

and the aspect ratio a h is the ratio of the distance between the stiffeners to webdepth. Assuming no stiffener is used, the value of kv is taken as 5.34.

The factored shear strength for minor direction shears in I-shapes, boxes and chan-nels is assumed as

V F Ar y v2 3 . (CISC 13.4.2)

The factored shear strength for major and minor direction shears for all other sec-tions is assumed as (CISC 13.4.2):

V F Ar y v2 2 , and (CISC 13.4.2)

V F Ar y v3 3 . (CISC 13.4.2)



Calculation of Capacity RatiosIn the calculation of the axial force/biaxial moment capacity ratios, first, for eachstation along the length of the member, for each load combination, the actual mem-ber force/moment components are calculated. Then the corresponding capacitiesare calculated. Then, the capacity ratios are calculated at each station for each mem-ber under the influence of each of the design load combinations. The controllingcompression and/or tension capacity ratio is then obtained, along with the associ-ated station and load combination. A capacity ratio greater than 1.0 indicates ex-ceeding a limit state.

If the axial, flexural, and shear strengths of a section are overwritten by the user, theoverwritten values are used in calculating the stress ratios. However, certainstrengths can not be overwritten. If the axial and bending capacities are overwrittenby the user, they are used in the interaction ratio calculation when strengths are re-quired for actual unbraced lengths. None of these overwritten capacities are usedfor strengths in laterally supported case. More specific information is given in thefollowing subsections as needed.



From the factored axial loads and bending moments at each station and the factoredstrengths for axial tension and compression and major and minor bending, an inter-action capacity ratio is produced for each of the load combinations as follows:

Compressive Axial Load

If the axial load is compressive, the capacity ratio is given by:

C

C+

U M

M+

U M

Mf

r

f

r

f

r

13 33

33

12 22

22

, for all but Class 1 I-shaped sections (13.8.1)

C

C+

U M

M+

U M

Mf

r

f

r

f

r

13 33

33

12 22

22

, for Class 1 I-shaped sections (13.8.2)

The above ratios are calculated for each of the following conditions and the largestratio is reported:



• Cross-sectional Strength:

– The axial compression capacity is based on 0 .

C A Fr y (CISC 13.3.1)

– The M Mr r33 22and are calculated assuming that the member is laterallyfully supported ( l22 0 and l33 0) irrespective of its actual lateral brac-ing length (CISC 13.5), and

– U 12 and U 13 are taken as 1.

U U13 12 . (CISC 13.8.1, 13.8.2)

If the capacities (C r , M r 22 and M r 33 ) are overwritten by the user, they are as-sumed not to apply to this case and are ignored.

• Overall Member Strength:

– The axial compression capacity is based on both major and minor direction

buckling using bothK l

r22 22

22

andK l

r33 33

33

as described in an earlier section

(CISC 13.3.1) .

– M Mr r33 22and are calculated assuming that the member is laterally fullysupported ( l22 0 and l33 0) irrespective of its actual lateral bracinglength (CISC 13.5), and

– U 12 and U 13 are calculated using the expression given below forU 1 . In thisequation specific values for major and minor directions are to be used tocalculate values of U 12 and U 13 (CISC 13.8.3).

If the capacities (C r , M r 22 , and M r 33 ) are overwritten by the user, the onlyoverwritten capacity used in this case is C r .

• Lateral-Torsional Buckling Strength:

– The axial compression capacity is based on weak-axis buckling only based

onK l

r22 22

22

(CISC 13.3.1),

– M Mr r33 22and are calculated based on actual unbraced length (CISC13.6), and



– U 12 and U 13 are calculated using the expression given below forU 1 . In thisequation specific values for major and minor directions are to be used tocalculate values of U 12 and U 13 (CISC 13.8.3). Moreover,

U 13 1 is enforced. (CISC 13.3.1, 13.8.2)

If the capacities (C r , M r 22 , and M r 33 ) are overwritten by the user, all threeoverwritten capacities are used in this case.

In addition, For Class 1 I-shapes, the following ratio is also checked:

M

M

M

Mf

r

f

r

33

33

22

22

. (CISC 13.8.2)

If the capacities (M r 22 and M r 33 ) are overwritten by the user, all these over-written capacities are used in this case.

In the above expressions,

U =- C /Cf e

11

1, (CISC 13.8.3)

CE I

Le

2

2,

1- M M .a b 0 4 , and

M Ma b is the ratio of the smaller to the larger moment at the ends of the member,M Ma b being positive for double curvature bending and negative for single cur-vature bending. 1 is assumed as 1.0 for beams with transverse load and when M b

is zero.

The program defaults1

to 1.0 if the unbraced length, l, of the member is redefinedby the user (i.e. it is not equal to the length of the member). The user can overwritethe value of

1for any member by specifying it. The factor U 1 must be a positive

number. Therefore C f must be less than C e . If this is not true, a failure conditionis declared.

Tensile Axial Load

If the axial load is tensile the capacity ratio is given by the larger of two ratios. In thefirst case, the ratio is calculated as



T

T+

M

M+

M

Mf

r

f

r

f

r

33

33

22

22

, (CISC 13.9)

assuming M Mr r33 22 are calculated based on fully supported member ( l22 0and l33 0). If the capacities (Tr , M r 22 and M r 33 ) are overwritten by the user, theonly overwritten capacity used in this case is Tr . M r 22 and M r 33 overwrites are as-sumed not to apply to this case and are ignored.

In the second case the ratio is calculated as

M

M+

M

M

T Z

M Af

r

f

r

f

r

33

33

22

22

33

33

(for Class 1 and 2), or (CISC 13.9)

M

M+

M

M

T S

M Af

r

f

r

f

r

33

33

22

22

33

33

(for Class 3). (CISC 13.9)

If the capacities (M r 22 and M r 33 ) are overwritten by the user, both of these over-written capacities are used in this case.

For circular sections an SRSS combination is first made of the two bending compo-nents before adding the axial load component instead of the simple algebraic addi-tion implied by the above interaction formulas.

Shear Stresses

From the factored shear force values and the factored shear strength values at eachstation, for each of the load combinations, shear capacity ratios for major and minordirections are produced as follows:

V

Vf

r

2

2

and

V

Vf

r

3

3

.



C h a p t e r VIII

Check/Design for BS 5950

This chapter describes the details of the structural steel design and stress check al-gorithms that are used by ETABS when the user selects the BS 5950 design code(BSI 1990). Various notations used in this chapter are described in Table VIII-1.


In the evaluation of the axial force/biaxial moment capacity ratios at a station alongthe length of the member, first the actual member force/moment components andthe corresponding capacities are calculated for each load combination. Then the ca-pacity ratios are evaluated at each station under the influence of all load combina-tions using the corresponding equations that are defined in this section. The con-trolling capacity ratio is then obtained. A capacity ratio greater than 1.0 indicatesexceeding a limit state. Similarly, a shear capacity ratio is also calculated sepa-rately.


151

152


A = Cross-sectional area, mm2

Ag = Gross cross-sectional area, mm2

A Av v2 3, = Major and minor shear areas, mm2

B = Breadth, mm

D = Depth of section, mmor outside diameter of pipes, mm


Fc = Axial compression, N

Ft = Axial tension, N

F Fv v2 3, = Major and minor shear loads, N


H = Warping constant, mm6

I 33 = Major moment of inertia, mm4

I 22 = Minor moment of inertia, mm4

J = Torsional constant for the section, mm4


K K33 22, = Major and minor effective length factors

M = Applied moment, N-mm

M 33 = Applied moment about major axis, N-mm

M 22 = Applied moment about minor axis, N-mm

M a 33 = Major maximum bending moment, N-mm

M a 22 = Minor maximum bending moment, N-mm

M b = Buckling resistance moment, N-mm

M c = Moment capacity, N-mm

M c33 = Major moment capacity, N-mm

M c22 = Minor moment capacity, N-mm

M E = Elastic critical moment, N-mm

Pc = Compression resistance, N

P Pc c33 22, = Major and minor compression resistance, N

Pt = Tension capacity, N

P Pv v2 3, = Major and minor shear capacities, N

S S33 22, = Major and minor plastic section moduli, mm3

T = Thickness of flange or leg, mm

Ys = Specified yield strength, MPa

Z Z33 22, = Major and minor elastic section moduli, mm3

Table VIII-1BS 5950 Notations

153

Chapter VIII Check/Design for BS 5950

a = Robertson constant

b = Outstand width, mm

d = Depth of web, mm

h = Story height, mm

k = Distance from outer face of flange to web toe of fillet , mm

l = Unbraced length of member, mm


l le e33 22, = Major and minor effective lengths, mm ( , )K l K l33 33 22 22

m = Equivalent uniform moment factor

n = Slenderness correction factor

qe = Elastic critical shear strength of web panel, MPa

qcr = Critical shear strength of web panel, MPa

r r33 22, = Major and minor radii of gyration, mm

rz = Minimum radius of gyration for angles, mm

t = Thickness, mm


t w = Thickness of web, mm

u = Buckling parameter

v = Slenderness factor

= Ratio of smaller to larger end moments

= Constant275

12

y


o = Limiting slenderness

LT = Equivalent slenderness

Lo = Limiting equivalent slenderness

= Perry factor

LT = Perry coefficient

c = Compressive strength, MPa

E = Euler strength, MPa

y = Yield strength, MPa

= Monosymmetry index

Table VIII-1BS 5950 Notations (cont.)

Design Loading CombinationsThe design load combinations are the various combinations of the load cases forwhich the structure needs to be checked. According to the BS 5950 code, if a struc-ture is subjected to dead load (DL), live load (LL), wind load (WL), and earthquakeload (EL), and considering that wind and earthquake forces are reversible, then thefollowing load combinations may have to be considered (BS 2.4):

1.4 DL1.4 DL + 1.6 LL (BS 2.4.1.1)

1.0 DL 1.4 WL1.4 DL 1.4 WL1.2 DL + 1.2 LL 1.2 WL (BS 2.4.1.1)

1.0 DL 1.4 EL1.4 DL 1.4 EL1.2 DL + 1.2 LL 1.2 EL

These are also the default design load combinations whenever BS 5950 Code isused. The user should use other appropriate loading combinations if roof live loadis separately treated, other types of loads are present, or if pattern live loads are tobe considered.


In addition to the above load combinations, the code requires that all buildingsshould be capable of resisting a notional design horizontal load applied at each flooror roof level. The notional load should be equal to the maximum of 0.01 times thefactored dead load and 0.005 times the factored dead plus live loads (BS 2.4.2.3).The notional forces should be assumed to act in any one direction at a time andshould be taken as acting simultaneously with the factored dead plus vertical im-posed live loads. They should not be combined with any other horizontal load cases(BS 5.1.2.3). It is recommended that the user should define additional load cases forconsidering the notional load in ETABS and define the appropriate design combi-nations.

When using the BS 5950 code, ETABS design assumes that a P- analysis has al-ready been performed, so that moment magnification factors for the moments caus-ing side-sway can be taken as unity. It is suggested that the P- analysis be done at



the factored load level corresponding to 1.2 dead load plus 1.2 live load. See alsoWhite and Hajjar (1991).

Classification of SectionsThe nominal strengths for axial compression and flexure are dependent on the clas-sification of the section as Plastic, Compact, Semi-compact, or Slender. ETABSchecks the sections according to Table VIII-2 (BS 3.5.2). The parameters R, c and

along with the slenderness ratios are the major factors in classification of section.

• R is the ratio of mean longitudinal stress in the web to y in a section. This im-plies that for a section in pure bending R is zero. In calculating R, compressionis taken as positive and tension is taken as negative. R is calculated as follows:

RP

Ag y

• is given as c d, where c is the distance from the plastic neutral axis to theedge of the web connected to the compression flange. For , the section istreated as having compression throughout.

c

d 2

cy

DT

P

t2 2, for I and Channel section

for Box and Double Channel sD

TP

ty2 4, ection

In calculating c , compression is taken as negative and tension is taken as posi-tive.

• is defined as follows:

2751 2

y

/

The section is classified as either Class 1 (Plastic), Class 2 (Compact), or Class 3(Semi-compact) as applicable. If a section fails to satisfy the limits for Class 3(Semi-compact) sections, the section is classified as Class 4 (Slender). Cur-rently ETABS does not check stresses for Slender sections.






RatioChecked

Class 1(Plastic)

Class 2(Compact)

Class 3(Semi-compact)

I-SHAPE

b T (Rolled)

b T (welded)

d twebs ( )

For R 0 :

Rand

41

R(welded)

1 + Rand

41

R(rolled)

For R 0 : , and

For R 0 :21 + R

and .

d twebs ( )

(rolled)

d twebs ( )

(welded)

BOX

b T (Rolled)

b T (welded)

d t As forI-shapes

As forI-shapes

As forI-shapes

CHANNELb Td t

As forI-shapes

As forI-shapes

As forI-shapes

T-SHAPEb Td t

DOUBLEANGLE

(separated)

d t

( )b + d t

Table VIII-2Limiting Width-Thickness Ratios for

Classification of Sections based on BS 5950

Calculation of Factored ForcesThe factored member loads that are calculated for each load combination are Ft orFc , M 33 , M 22 , Fv 2 , and Fv 3 corresponding to factored values of the tensile or com-pressive axial load, the major moment, the minor moment, the major directionshear load, and the minor direction shear load, respectively. These factored loadsare calculated at each of the previously defined stations.

The moment magnification for non-sidesway moments is included in the overallbuckling interaction equations.

M = M + Mg s

1

1 200s,max

, where (BS 5.6.3)

s,max= Maximum story-drift divided by the story-height,

M g = Factored moments not causing translation, andM s = Factored moments causing sidesway.




RatioChecked

Class 1(Plastic)

Class 2(Compact)

Class 3(Semi-compact)

ANGLEb t

( )b + d t

PIPE D t 2 2 2

SOLIDCIRCLE Assumed Compact

SOLIDRECTANGLE Assumed Compact

GENERAL Assumed Semi-compact

Table VIII-2 (cont.)Limiting Width-Thickness Ratios for

Classification of Sections based on BS 5950



Figure VIII-1BS 5950 Definition of Geometric Properties

The moment magnification factor for moments causing sidesway can be taken asunity if a P- analysis is carried out. ETABS design assumes a P- analysis hasbeen done and, therefore, s max, for both major and minor direction bending istaken as 0. It is suggested that the P- analysis be done at the factored load level of1.2 DL plus 1.2 LL. See also White and Hajjar (1991).

Calculation of Section CapacitiesThe strengths in compression, tension, bending, and shear are computed for Class1, 2, and 3 sections according to the following subsections. By default, ETABStakes the design strength, y , to be 1.0 times the minimum yield strength of steel,Ys , as specified by the user. In inputting values of the yield strength, the user shouldensure that the thickness and the ultimate strength limitations given in the code aresatisfied (BS 3.1.1).

y sY (BS 3.1.1)

For Class 4 (Slender) sections and any singly symmetric and unsymmetric sectionsrequiring special treatment, such as the consideration of local buckling, flexural-torsional and torsional buckling, or web buckling, reduced section capacities maybe applicable. The user must separately investigate this reduction if such elementsare used.

If the user specifies nonzero strengths for one or more elements in the “CapacityOverwrites” form, these values will override the above mentioned calculated val-ues for those elements.

Compression Resistance

The compression resistance for plastic, compact, or semi-compact sections isevaluated as follows:

P = Ac g c , (BS 4.7.4)

where c is the compressive strength given by

cE y

E y2 1

2

, where (BS C.1)

y E , (BS C.1)

Calculation of Section Capacities 159


E = Euler strength, 2 2E ,

= Perry factor,0

a ) 0 , (BS C.2)a = Robertson constant from Table VIII-3, (BS C2, BS Table 25)

0= Limiting slenderness,

212

E

y

, and (BS C.2)

= the slenderness ratio in either the major,33

l re 33 33 , orin the minor,

22l re 22 22 direction (BS 4.7.3.1).

The larger of the two values is used in the above equationsto calculate Pc .

160 Calculation of Section Capacities



Thickness (mm)Axis of Bending

Major Minor

I-SHAPE(rolled)

any 2.0 3.5

H-SHAPE(rolled)

4040

3.55.5

5.58.0

I-SHAPE(welded)

4040

3.53.5

5.58.0

BOX or Pipe(Rolled)

any 2.0 2.0

BOX(welded)

4040

3.55.5

3.55.5

CHANNEL,T-SHAPE, ANGLE

any 5.5 5.5

RECTANGULARor CIRCLE

4040

3.55.5

3.55.5

GENERAL any 5.5 5.5

Table VIII-3Robertson Constant in BS 5950

For single angles rz is used instead of r33 and r22 . For members in compres-sion, if is greater than 180, a message to that effect is printed (BS 4.7.3.2).

Tension Capacity

The tension capacity of a member is given by

P = At g y . (BS 4.6.1)

It should be noted that no net section checks are made. For main members in ten-sion, the slenderness, , should not be greater than 250 (BS 4.7.3.2). If is greaterthan 250, a message is displayed accordingly.

The user may have to separately investigate the members which are connected ec-centrically to the axis of the member, for example angle sections.

Moment Capacity

The moment capacities in the major and minor directions, M Mc c33 22and are basedon the design strength and the section modulus, the co-existent shear and the possi-bility of local buckling of the cross-section. Local buckling is avoided by applyinga limitation to the width/thickness ratios of elements of the cross-section. The mo-ment capacities are calculated as follows:

Plastic and Compact Sections

For plastic and compact sections, the moment capacities about the major and theminor axes of bending depend on the shear force, Fv , and the shear capacity, Pv .

For I, Box, Channel, and Double-Channel sections bending about the 3-3 axis themoment capacities considering the effects of shear force are computed as

M = S Z , F Pc y y v v , (BS 4.2.5)

M = S S Z , F Pc y v y v v( )1 , (BS 4.2.6)

where

S = Plastic modulus of the gross section about the relevant axis,

Z = Elastic modulus of the gross section about the relevant axis,



S v = Plastic modulus of the gross section about the relevant axisless the plastic modulus of that part of the section remainingafter deduction of shear area i.e. plastic modulus of shear area.For example, for rolled I-shapes S v 2 is taken to be tD 2 4 and

for welded I-shapes it is taken as td 2 4 ,

Pv = The shear capacity described later in this chapter,

1=

F

Pv

v

.

The combined effect of shear and axial forces is not being considered because prac-tical situations do not warrant this. In rare cases, however, the user may have to in-vestigate this independently, and if necessary, overwrite values of the sectionmoduli.

For all other cases, the reduction of moment capacities for the presence of shearforce is not considered. The user should investigate the reduced moment capacityseparately. The moment capacity for these cases is computed in ETABS as

M = S Zc y y . (BS 4.2.5)

Semi-compact Sections

Reduction of moment capacity due to coexistent shear does not apply for semi-compact sections.

M Zc y (BS 4.2.5)

Lateral-Torsional Buckling Moment Capacity

The lateral torsional buckling resistance moment, M b , of a member is calculatedfrom the following equations. The program assumes the members to be uniform (ofconstant properties) throughout their lengths. Furthermore members are assumed tobe symmetrical about at least one axis.

For I, Box, T, Channel, and Double-Channel sections M b is obtained from

M =S M

S Mb

y E

B B y E

33

331 22 ) /

, where (BS B2.1)



B

y LT ES M33 ,

M E = The elastic critical moment,S E

LT

33

2

2

, and (BS B2.3)

LT = The Perry coefficient.

The Perry coefficient, LT , for rolled and welded sections is taken as follows:

For rolled sections

LT b LT L 0 , and (BS B2.3)

for welded sections

LT b L2 0 , with b LT L LT b LT L( ) ( )0 02 .(BS B2.2)

In the above definition of LT , L 0 and LT are the limiting equivalent slendernessand the equivalent slenderness, respectively, and b is a constant. b is taken as0.007 (BS 2.3). For flanged members symmetrical about at least one axis and uni-form throughout their length, L 0 is defined as follows:

Ly

E0

2

, (BS B2.4)

For I, Channel, Double-Channel, and T sections LT is defined as

LT n u v , (BS B2.5)

and for Box sections LT is defined as

LT bn2.251 2

, where (BS B2.5)

• is the slenderness and is equivalent to l re 22 22 .

• n is the slenderness correction factor. For flanged members in general, notloaded between adjacent lateral restraints, and for cantilevers without interme-diate lateral restraints, n is taken as 1.0. For members with equal flanges loadedbetween adjacent lateral restraints, the value of n is conservatively taken asgiven by the following formula. This, however, can be overwritten by the userfor any member by specifying it (BS Table 13).

nC b

11.0 , where



C b =M

M + M + M + MA B C

max

max3 4 3

, and

Mmax

, M M MA B C, , and are absolute values of maximum moment, 1/4point, center of span and 3/4 point major moments respectively, in themember. The program also defaults C b to 1.0 if the unbraced length, l, ofthe member is redefined by the user (i.e. it is not equal to the length of themember). C b should be taken as 1.0 for cantilevers. However, the programis unable to detect whether the member is a cantilever. The user can over-write the value of C b for any member.

• u is the buckling parameter. It is conservatively taken as 0.9 for rolledI-shapes and channels. For any other section, u is taken as 1.0 (BS 4.3.7.5). ForI, Channel, and Double-Channel sections,

uS

A D T

4 332

2 2

1 4

( ), for I, Channel, and Double-Channel, (BS B2.5b)

uI S

A H22 33

2

2

1 4

, for T section, where (BS B2.5b)

1 22

33

I

I. (BS B2.5b)

• v is the slenderness factor. For I, Channel, Double-Channel, and T sections, itis given by the following formula.

v

N N +x

12

4 11

20

22( )

12

, where (BS B2.5d)

N

0.5 , for I, Channel, Double - Channel sections,

1.0 , for T sections with flange in compression,

0.0 , for T sections with flange in tension, and

(BS B2.5d)

0.0 , for I, Channel, Double - Channel sections,

0.8 , for T sections with flange in compression, and

-1.0 , for T sections with flange in tension.

(BS B2.5d)



• b is the buckling index for box section factor. It is given by the following for-mula. (BS B2.6.1).

b

S

A J332

2

1 2

, where (BS B2.6.1)

1 122

33 33

I

I

J

I2.6. (BS B2.6.1)

For all other sections, lateral torsional buckling is not considered. The user shouldinvestigate moment capacity considering lateral-torsional buckling separately.

Shear Capacities

The shear capacities for both the major and minor direction shears in I-shapes,boxes or channels are evaluated as follows:

P = Av y v2 2 , and (BS 4.2.3)

P = Av y v3 3 . (BS 4.2.3)

The shear areas Av 3 and Av 2 are given in Table VIII-4.

Moreover, the shear capacity computed above is valid only if d t 63 , strictlyspeaking. For d t 63 , the shear buckling of the thin members should be checkedindependently by the user in accordance with the code (BS 4.4.5).








ConditionAxis of Bending

Major Minor

I-SHAPERolledWelded

tDtd

0.9 4bT0.9 4bT

CHANNELRolledWelded

tDtd

0.9 2bT0.9 2bT

DOUBLE CHANNELRolledWelded

2.0 tD2.0 td

2.0 0.9* 2bT2.0 0.9* 2bT

BOX D

D BA

B

D BA

T-SHAPERolledWelded

tdt d T

0.9 2bT0.9 2bT

DOUBLE ANGLE 2td 2bt

ANGLE td bt

RECTANGULAR 0.9 A 0.9 A

CIRCLE 0.9 A 0.9 A

PIPE 0.6 A 0.6 A

GENERAL 0.9 A 0.9 A

Table VIII-4Shear Area in BS 5950

Local Capacity Check

For members under axial load and moments, local capacity ratios are calculated asfollows:

Under Axial Tension

A simplified approach allowed by the code is used to check the local capacity forplastic and compact sections.

F

A+

M

M+

M

Mt

g y c c

33

33

22

22

(BS 4.8.2)

Under Axial Compression

Similarly, the same simplified approach is used for axial compression.

F

A+

M

M+

M

Mc

g y c c

33

33

22

22

(BS 4.8.3.2)

Overall Buckling Check

In addition to local capacity checks, which are carried out at section level, a com-pression member with bending moments is also checked for overall buckling in ac-cordance with the following interaction ratio:

F

A

m M

M+

m M

Zc

g c b y

33 33 22 22

22

(BS 4.8.3.3.1)

The equivalent uniform moment factor, m, for members of uniform section andwith flanges, not loaded between adjacent lateral restraints, is defined as

m = + 2 . (BS Table 18)

For other members, the value of m is taken as 1.0. The program defaults m to 1.0 ifthe unbraced length, l, of the member is overwritten by the user (i.e. if it is not equalto the length of the member). The user can overwrite the value of m for any mem-ber by specifying it. is the ratio of the smaller end moment to the larger end mo-ment on a span equal to the unrestrained length, being positive for single curvaturebending and negative for double curvature bending.



Shear Capacity Check

From the factored shear force values and the shear capacity values at each station,shear capacity ratios for major and minor directions are produced for each of theload combinations as follows:

F

Pv

v

2

2

, and

F

Pv

v

3

3

.



C h a p t e r IX

Check/Design for EUROCODE 3

This chapter describes the details of the structural steel design and stress check al-gorithms that are used by ETABS when the user selects the Eurocode 3 design code(CEN 1992). The program investigates the limiting states of strength and stabilitybut does not address the serviceability limit states. Various notations used in thischapter are described in Table IX-1.


In the evaluation of the axial force/biaxial moment capacity ratios at a station alongthe length of the member, first the actual member force/moment components andthe corresponding capacities are calculated for each load combination. Then the ca-pacity ratios are evaluated at each station under the influence of all load combina-tions using the corresponding equations that are defined in this section. The con-trolling capacity ratio is then obtained. A capacity ratio greater than 1.0 indicatesexceeding a limit state. Similarly, a shear capacity ratio is calculated separately.


169

170


A = Gross cross-sectional area, mm2

A Av v2 3, = Areas for shear in the 2- and 3-directions, mm2

C1 = Bending coefficient



I t = Torsion constant, mm4

I w = Warping constant, mm6

I 33 = Major moment of inertia, mm4

I 22 = Minor moment of inertia, mm4


L = Length, span, mm

K K33 22, = Major and minor effective length factors

M b Rd. = Design buckling resistance moment, N-mm

M cr = Elastic critical moment for lateral-torsional buckling, N-mm

M g Sd. = Design moments not causing sidesway , N-mm

M s Sd. = Design moments causing sidesway, N-mm

MV Sd. = Design moment resistance after considering shear, N-mm

M Sd33. = Design value of moment about the major axis, N-mm

M Sd22. = Design value of moment about the minor axis, N-mm

M Rd33. = Design moment resistance about the major axis, N-mm

M Rd22. = Design moment resistance about the minor axis, N-mm

N b Rd. = Design buckling resistance of a compression member, N

N b Rd33. = Design buckling resistance of a compression memberabout the major axis, N

N b Rd22. = Design buckling resistance of a compression memberabout the minor axis, N

N c Sd. = Design value of compressive force, N

N c Rd. = Design compression resistance, N

N t Sd. = Design value of tensile force, N

N t Rd. = Design tension resistance, N

N pl Rd. = Design plastic shear resistance, N

V Sd2. = Design value of shear force in the major direction, N

V Sd3. = Design value of shear force in the minor direction, N

V Rd2. = Design shear resistance in the major direction, N

Table IX-1Eurocode 3 Notations

171

Chapter IX Check/Design for EUROCODE 3

V Rd3. = Design shear resistance in the minor direction, N

W Wel el. .,33 22 = Major and minor elastic section moduli, mm3

W Wpl pl. .,33 22 = Major and minor plastic section moduli, mm3

b = Width, mm

c = Distance, mm

d = Depth of web, mm

f y = Nominal yield strength of steel, MPa

h = Overall depth, mm


i i33 22, = Major and minor radii of gyration, mm

iz = Minimum radius of gyration for angles, mm

k k33 22, = Factors applied to the major and minor design moments inthe interaction equations

kLT = Factor applied to the major design moments in the interactionequation checking for failure due to lateral-torsional buckling

t = Thickness, mm


t w = Web thickness, mm

= Ratio used in classification of sections

M0 , M1 = Material partial safety factors

=f y

2351

2

( f y in MPa)

= Reduction factor

ba = Post-critical shear strength, MPa

33 22, = Reduction factors for buckling about the 3-3 and 2-2 axes

LT = Reduction factor for lateral-torsional buckling

= Ratio of smaller to larger end moment of unbraced segment

s = Amplification factor for sway moments

Table IX-1Eurocode 3 Notations (cont.)

Design Loading CombinationsThe design loading combinations define the various factored combinations of theload cases for which the structure is to be checked. The design loading combina-tions are obtained by multiplying the characteristic loads with appropriate partialfactors of safety. If a structure is subjected to dead load (DL) and live load (LL)only, the design will need only one loading combination, namely 1.35 DL + 1.5 LL.

However, in addition to the dead load and live load, if the structure is subjected towind (WL) or earthquake induced forces (EL), and considering that wind and earth-quake forces are subject to reversals, the following load combinations may have tobe considered (EC3 2.3.3):

1.35 DL1.35 DL + 1.50 LL (EC3 2.3.3)

1.35 DL 1.50 WL1.00 DL 1.50 WL1.35 DL + 1.35 LL 1.35 WL (EC3 2.3.3)

1.00 DL 1.00 EL1.00 DL + 1.5*0.3 LL 1.0 EL (EC3 2.3.3)

In fact, these are the default load combinations which can be used or overwritten bythe user to produce other critical design conditions. These default loading combina-tions are produced for persistent and transient design situations (EC3 2.3.2.2) bycombining forces due to dead, live, wind, and earthquake loads for ultimate limitstates. See also section 9.4 of Eurocode 1 (CEN 1994) and Table 1, 3, and 4 and sec-tion 4 of United Kingdom National Application Document (NAD).

The default load combinations will usually suffice for most building design. Theuser should use other appropriate loading combinations if roof live load is sepa-rately treated, other types of loads are present, or if pattern live loads are to be con-sidered.


In addition to the loads described earlier, equivalent lateral load cases for geomet-ric imperfection should be considered by the user. This equivalent load is similar tothe notional load of the British code, and depends on the number of stories andnumber of columns in any floor (EC3 5.2.4.3). Additional load combinations arealso needed for these load cases.



When using Eurocode 3, ETABS design assumes that a P- analysis has been per-formed so that moment magnification factors for moments causing sidesway can betaken as unity. It is suggested that the P- analysis should be done at the factoredload level corresponding to 1.35 dead load plus 1.35 live load. See also White andHajjar (1991).

Classification of SectionsThe design strength of a cross-section subject to compression due to moment and/oraxial load depends on its classification as Class 1 (Plastic), Class 2 (Compact),Class 3 (Semi-compact), or Class 4 (Slender). According to Eurocode 3, the classi-fication of sections depends on the classification of flange and web elements. Theclassification also depends on whether the compression elements are in pure com-pression, pure bending, or under the influence of combined axial force and bending(EC3 5.3.2).

ETABS conservatively classifies the compression elements according to TableIX-2 and Table IX-3. Table IX-2 is used when the section is under the influence ofaxial compression force only or combined axial compression force and bending.Table IX-3 is used when the section is in pure bending or under the influence ofcombined axial tensile force and bending. The section dimensions used in the tablesare given in Figure IX-1. If the section dimensions satisfy the limits shown in the ta-bles, the section is classified as Class 1, Class 2, or Class 3 as applicable. Across-section is classified by reporting the highest (least favorable) class of its com-pression elements.

If a section fails to satisfy the limits for Class 3 sections, the section is classifiedas Class 4. Currently ETABS does not check stresses for Class 4 sections.

One of the major factors in determining the limiting width-thickness ratio is . Thisparameter is used to reflect the influence of yield stress on the section classification.

235

f y

(EC3 5.3.2)

In classifying I, Box, Channel, Double-Channel, and T sections, two other factors, are defined as follows:




ETABS Steel Design ManualSection Element Ratio Checked Class 1 Class 2 Class 3

I-SHAPE

web d tw

If 0.5 ,396

13 1,

else if 0.5,36

.

If 0.5,456

13 1,

else if 0.5,41.5

.

If 1,42

0.67 0.33,

else if 1,62 1

flangec tf (rolled) 10 11 15

c tf (welded) 9 10 14

BOX

web d twSame asI-Shape

Same asI-Shape

Same asI-Shape

flange

( )b t tf f3(rolled)

42 42 42

b tf (welded) 42 42 42

CHANNELweb d tw

Same asI-Shape

Same asI-Shape

Same asI-Shape

flange b tf 10 11 15

T-SHAPE

web d tw 33 38 42

flangeb tf2 (rolled) 10 11 15

b tf2 (welded) 9 10 14

DOUBLEANGLES

h t( ) max( , )b h t b2 Not applicable Not applicable

15ε11.5ε

ANGLE h t

( ) max( , )b h t b2 Not applicable Not applicable15ε

11.5ε

PIPE d t 50ε2 70ε2 90ε2

ROUND BAR None Assumed Class 1

RECTANGLE None Assumed Class 2

Table IX-2Limiting Width-Thickness Ratios for

Classification of Sections based on Eurocode 3 (Compression and Bending)



Section Element Ratio Checked Class 1 Class 2 Class 3

I-SHAPE

web d tw 72 83 124

flangec tf (rolled) 10 11 15

c tf (welded) 9 10 14

BOX

web d tw 72 83 124

flange( )b t tf f3 (rolled) 33 38 42

b tf (welded) 33 38 42

CHANNELweb

d tw (Major axis) 72 83 124

d tw (Minor axis) 33 38 42

flange b tf 10 11 15

T-SHAPE

web d tw 33 38 42

flangeb tf2 (rolled) 10 11 15

b tf2 (welded) 9 10 14

DOUBLEANGLES

h t( ) max ,b h t b2

Notapplicable

Notapplicable

15.0 ε11.5 ε

ANGLE h t

( ) max ,b h t b2Not

applicableNot

applicable15.0ε11.5ε

PIPE d t 50ε2 70ε2 90ε2

ROUND BAR None Assumed Class 1

RECTANGLE None Assumed Class 2

GENERAL None Assumed Class 3

Table IX-3Limiting Width-Thickness Ratios for

Classification of Sections based on Eurocode 3 (Bending Only)



Figure IX-1Eurocode 3 Definition of Geometric Properties

1

2

1

2

N

ht fc Sd

w f

, , for I, Channel, and T sections,

for Box and D1

2

1

2 2

N

ht fc Sd

w f

, , ouble - Channel sections, and

1 2N

Afc Sd

y

, ,

0 1.0 ,

-3.0 1.0 .

In the above expression, N c Sd, is taken as positive for tension and negative for com-pression. equals 0.0 for full tension, 0.5 for pure bending and 1.0 for full compres-sion. equals -3.0 for full tension, -1.0 for pure bending and 1.0 for full compres-sion.

Calculation of Factored ForcesThe internal design loads which are calculated for each load combination are N t Sd.

or N c Sd. , M Sd33. , M Sd22. ,V Sd2. and V Sd3. corresponding to design values of the ten-sile or compressive axial load, the major moment, the minor moment, the major di-rection shear and the minor direction shear respectively. These design loads are cal-culated at each of the previously defined stations of each frame element.

The design moments and forces need to be corrected for second order effects. Thiscorrection is different for the so called “sway” and “nonsway” components of themoments. The code requires that the additional sway moments introduced by thehorizontal deflection of the top of a story relative to the bottom must be taken intoaccount in the elastic analysis of the frame in one of the following ways (EC35.2.6.2):

• Directly by carrying out the global frame analysis using P- analysis. Mem-ber design can be carried out using in-plane buckling lengths for nonswaymode.

• Indirectly by modifying the results of a linear elastic analysis using an ap-proximate method which makes allowance for the second order effects. Thereare two alternative ways to do this “amplified sway moment method” or“sway mode in-plane buckling method”.



The advantage of the direct second order elastic analysis is that this method avoidsuncertainty in approximating the buckling length and also avoids splitting up mo-ments into their “sway” and “nonsway” components.

ETABS design assumes that P- effects are included in the analysis. Thereforeany magnification of sidesway moments due to second order effects is alreadyaccounted for, i. e. s in the following equation is taken as 1.0. It is suggested

that the P- analysis be done at the factored load level of 1.35 DL plus 1.35 LL. Seealso White and Hajjar (1991). However, the user can overwrite the values of s forboth major and minor direction bending in which case M Sd in a particular directionis taken as:

M = M + MSd g.Sd s s.Sd , where (EC3 5.2.6.2)

M g Sd. = Design moments not causing translation, andM s Sd. = Design moments causing sidesway.

Moment magnification for non-sidesway moments is included in the overall buck-ling interaction equations.

Sway moments are produced in a frame by the action of any load which results insway displacements. The horizontal loads can be expected always to produce swaymoments. However, they are also produced by vertical loads if either the load or theframe are unsymmetrical. In the case of a symmetrical frame with symmetrical ver-tical loads, the sway moments are simply the internal moments in the frames due tothe horizontal loads (EC3 5.2.6.2).

Calculation of Section ResistancesThe factored strengths in compression, tension, bending, and shear are computedfor Class 1, 2, and 3 sections according to the following subsections. The materialpartial safety factors used by the program are:

M 0 , and (EC3 5.1.1)

M 1 . (EC3 5.1.1)

For Class 4 (Slender) sections and any singly symmetric and unsymmetric sectionsrequiring special treatment, such as the consideration of local buckling, flexural-torsional and torsional buckling, or web buckling, reduced section capacities maybe applicable. The user must separately investigate this reduction if such elementsare used.

178 Calculation of Section Resistances


If the user specifies nonzero factored strengths for one or more elements in the“Capacity Overwrites” form, these values will override the above mentioned cal-culated values for those elements.

Tension Capacity

The design tension resistance for all classes of sections is evaluated in ETABS asfollows:

N = A ft.Rd y M 0 (EC3 5.4.3)

It should be noted that the design ultimate resistance of the net cross-section at theholes for fasteners is not computed and checked. The user is expected to investigatethis independently.

Compression Resistance

The design compressive resistance of the cross-section is taken as the smaller of thedesign plastic resistance of the gross cross-section (N pl Rd. ) and the design localbuckling resistance of the gross cross-section (N b Rd. ).

N N Nc Rd pl Rd b Rd. . , .min ( ) (EC3 5.4.4)

The plastic resistance of Class 1, Class 2, and Class 3 sections is given by

N = A fpl.Rd y M0. (EC3 5.4.4)

The design buckling resistance of a compression member is taken as

N = A fb.Rd y Mmin A 1 , where (EC3 5.5.1)

A = 1, for Class 1, 2 or 3 cross-sections.

χ is the reduction factor for the relevant buckling mode. This factor is calcu-lated below based on the assumption that all members are of uniform cross-section.

2 2 12

, in which (EC3 5.5.1.2)

2 ,

Calculation of Section Resistances 179




Section Limits α(major axis)

α(minor axis)

I-SHAPE (rolled)h b 1 2.

tf 40 mm 0.21 0.34

tf 40 mm 0.34 0.49

I-SHAPE (rolled)h b 1.2

tf 100 mm 0.34 0.49

tf 100 mm 0.76 0.76

I-SHAPE (welded)tf 40 mm 0.34 0.49

tf 40 mm 0.49 0.76

BOXRolled 0.21 0.21

welded 0.34 0.34

CHANNEL any 0.49 0.49

T-SHAPE any 0.49 0.49

DOUBLEANGLES

any 0.49 0.49

ANGLE any 0.49 0.49

PIPE any 0.21 0.21

ROUND BAR any 0.49 0.49

RECTANGLE any 0.49 0.49

GENERAL any 0.49 0.49

Table IX-4The factor for different sections and different axes of buckling

1

0.5

A ,

K l

i

K l

i33 33

33

22 22

22

. The two values of give3

and2.

minis

the lesser of the two.

Kl

L1. K is conservatively taken as 1 in ETABS design (EC3 5.5.1.5).

The user can, however, override this default option if it is deemed neces-sary. An accurate estimate of K can be obtained from the Annex E of thecode. See also EC3 5.2.6.2(2).

l is the buckling length,

L is the length of the column,

i is the radius of gyration about the neutral axis, and is determined usingthe properties of the gross cross-section,

1

12

E

f y

, and

is an imperfection factor and is obtained from Table IX-4. Values of thisfactor for different types of sections, axes of buckling, and thickness of ma-terials are obtained from Tables 5.5.1 and 5.5.3 of the code.

Angle, Channel, and T-sections in compression are subjected to an additional mo-ment due to the shift of the centroidal axis of the effective cross-section (EC35.4.4). ETABS does not currently considers this eccentricity. The user is expectedto investigate this issue separately.

Shear Capacity

The design shear resistance of a section is the minimum of the plastic shear capacityand the buckling shear capacity. For all types of sections, the plastic shear resis-tance is computed as

V = V =A f

Rd pl.Rd

v y

M3

0 , (EC3 5.4.6)



where Av is the effective shear area for the section and the appropriate axis of bend-ing.

The buckling shear capacities are only computed for the I, Box, and Channel sec-tions if the width-thickness ratio is large (d tw 69 ). The capacities are computedas

V = V = d tRd ba.Rd w ba M 1 , (ford

tw

69 ) (EC3 5.6.3)

where, ba is the simple post-critical shear strength which is determined as follows:

ba

ywf

3, for w , (EC3 5.6.3)

ba wywf

3, for w , and (EC3 5.6.3)

ba wywf

3, for w . (EC3 5.6.3)

in which w is the web slenderness ratio,

t

wwd t

k, and (EC3 5.6.3)

kt

is the buckling factor for shear. For webs with transverse stiffeners at the sup-ports but no intermediate transverse stiffeners,

kt

. (EC3 5.6.3)

Moment Resistance

The moment resistance in the major and minor directions is based on the sectionclassification. Moment capacity is also influenced by the presence of shear forceand axial force at the cross section. If the shear force is less than half of the shear ca-pacity, the moment capacity is almost unaffected by the presence of shear force. Ifthe shear force is greater than half of the shear capacity, additional factors need tobe considered.

If V VSd pl.Rd

• For Class 1 and Class 2 Sections

M M = W fc Rd pl Rd pl y. . M0. (EC3 5.4.5.2)



• For Class 3 Sections

M = M = W fc Rd el Rd el y. . M0. (EC3 5.4.5.2)

If V > VSd pl.Rd

• For I, Box, and Channel sections bending about the 3-3 axis the moment ca-pacities considering the effects of shear force are computed as

M = W -A

t

fMV Rd pl

v

w

y

M

c Rd. .

2

04, where (EC3 5.4.7)

2

21

V

V-Sd

pl.Rd

.

• For all other cases, the reduction of moment capacities for the presence of shearforce is not considered. The user should investigate the reduced moment capac-ity separately.

Lateral-torsional Buckling

For the determination of lateral-torsional buckling resistance, it is assumed that thesection is uniform, doubly symmetric, and loaded through its shear center. The lat-eral-torsional buckling resistance of I, Box, and Double Channel sections is evalu-ated as,

M = W fb.Rd LT w pl. y M33 1 , where (EC3 5.5.2)

w = , for Class 1 and Class 2 sections,

wel.

pl.

=W

W33

33

, for Class 3 sections,

LT

LT LT LT

12

2 2, in which

LT LT LT LT2 , where

LT , for rolled sections,

LT , for welded sections, and



LT

w pl. y

cr

.W f

M33

0 5

, where

M = CE I

L

I

I+

L G I

E Icr

w t

.

1

222

222

2

222

0 5

, (EC3 F1.1)

I t = The torsion constant,

I w = The warping constant,

L = Laterally unbraced length for buckling about the minor axis. It is takenas l22 ,

C = -12 , and

= The ratio of smaller to larger end moment of unbraced segment,M

Ma

b

.

varies between -1 and 1 ( 1 1). A negative value implies double curva-ture. M a and M b are end moments of the unbraced segment and M a is less

than M b ,M

Ma

b

being negative for double curvature bending and positive for

single curvature bending. If any moment within the segment is greater thanM b , C1 is taken as 1.0. The program defaults C1 to 1.0 if the unbraced length,l22 of the member is overwritten by the user (i.e. it is not equal to the length ofthe member). C1 should be taken as 1.0 for cantilevers. However, the programis unable to detect whether the member is a cantilever. The user can overwritethe value of C1 for any member by specifying it.

If LT , no special consideration for lateral torsional buckling is made inthe design.

The lateral-torsional buckling resistance of a Channel, T, Angle, Double-Angle andGeneral sections is evaluated as,

M =W fb.Rd el y M, 33 1 ,

and the lateral-torsional buckling resistance of Rectangle, Circle and Pipe sectionsis evaluated as,

M =W fb.Rd pl y M, 33 1 .



Currently ETABS does not consider other special considerations for comput-ing buckling resistance of Rectangle, Circle, Pipe, Channel, T, Angle, DoubleAngle and General sections.



Bending, Axial Compression, and Low Shear

When the design value of the coexisting shear, VSd , is less than half of the corre-sponding capacities for plastic resistance, V pl Rd. and buckling resistance, Vba Rd. , i.e.

V VSd pl Rd. , and (EC3 5.4.9)

V VSd ba Rd. , (EC3 5.4.9)

the capacity ratios are computed for different types of sections as follows:

For Class 1 and Class 2 sections, the capacity ratio is conservatively taken as

N

N+

M

M+

M

Mc.Sd

pl.Rd

.Sd

pl. Rd

.Sd

pl. Rd

33

33

22

22. .

. (EC3 5.4.8.1)

For Class 3 sections, the capacity ratio is conservatively taken as

N

Af+

M

W f+

M

W fc.Sd

yd

.Sd

el. yd

.Sd

el. yd

33

33

22

22

, where (EC3 5.4.8.1)

ff

yd

y

M 0

.



Bending, Axial Compression, and High Shear

When the design value of the coexisting shear, VSd , is more than half the corre-sponding capacities for plastic resistance, V pl Rd. or buckling resistance, Vba Rd. , theshear is considered to be high, i.e. the shear is high if

V VSd pl Rd. , or (EC3 5.4.9)

V VSd ba Rd. . (EC3 5.4.9)

Under these conditions, the capacity ratios are computed for different types of sec-tions as follows (EC3 5.4.9):

For Class 1, 2, and 3 sections, the capacity ratio is conservatively taken as

N

N+

M

M+

M

Mc.Sd

pl.Rd

.Sd

V. .Rd

.Sd

V. .Rd

33

33

22

22

, where (EC3 5.4.8.1)

M V. .Rd33 and M V. .Rd22 are the design moment resistances about the major and theminor axes, respectively, considering the effect of high shear (see page 182).

Bending, Compression, and Flexural Buckling

For all members of Class 1, 2, and 3 sections subject to axial compression, N Sd ,major axis bending, M Sd33. , and minor axis bending, M Sd22. , the capacity ratio isgiven by

N

N+

k M

M+

k Mc.Sd .Sd

c. .Rd

.Sd

b.min.Rd

33 33

33

22 22

M c. .Rd22

, where (EC3 5.5.4)

N N Nb min Rd b Rd b Rd. . . . . .min ,33 22 ,

M

M

0

1

,

k = -N

A fc.Sd

y33

33

33

1 ,

k = -N

A fc.Sd

y22

22

22

1 ,



33 33( )2 433

33 33

33

M.

pl. el.

el.

- +W - W

W, (Class 1 and Class 2),

22 22 2222 22

22

2 4- +W - W

WM.

pl. el.

el.

( ) , (Class 1 and Class 2),

33 33 33 4M. - ) , (for Class 3 sections),

22 22 22 4-M. ) , (for Class 3 sections),

M.33 = Equivalent uniform moment factor for flexural buckling about the3-3 (major) axis between points braced in 2-2 direction, and

M.22 = Equivalent uniform moment factor for flexural buckling about the2-2 (minor) axis between points braced in 3-3 direction.

The equivalent uniform moment factors, M.33 and M.22 , are determined from

M

Q= +M

M, and

M Q = Absolute maximum moment due to lateral load only assumingsimple support at the ends,

ψ = Absolute value of the ratio of smaller to larger end moment.varies between -1 and 1 ( 1 1). A negative value implies

double curvature.

M = Absolute maximum value of moment for moment diagram withoutchange of sign, and

M = Sum of absolute maximum and absolute minimum value of momentsfor moment diagram with change of sign.

Bending, Compression, and Lateral-Torsional Buckling

For all members of Class 1, 2, and 3 sections subject to axial compression, N Sd , ma-jor axis bending, M Sd33. , and minor axis bending, M Sd22. , the capacity ratio is givenby

N

N+

k M

M+

k M

Mc.Sd

b. Rd

LT .Sd

b Rd

.Sd

c.22

33 22 22

22. . .Rd

, where (EC3 5.5.4)



k 22 and are as defined in the previous subsection “Bending, Compression,and Flexural Buckling”,

k = -N

A fLTLT c.Sd

y

1 122

, where

LT M.LT= -22 , and

M.LT = Equivalent uniform moment factor for lateral-torsional buckling. It isdetermined for bending about the y-y axis and between two pointsbraced in the y-y direction.

Bending, Axial Tension, and Low Shear

When the design value of the coexisting shear, VSd , is less than half of the corre-sponding capacities for plastic resistance, V pl Rd. and buckling resistance, Vba Rd. , i.e.

V VSd pl Rd. , and (EC3 5.4.9)

V VSd ba Rd. , (EC3 5.4.9)

the capacity ratios are computed for different types of sections as follows:

For Class 1 and Class 2 sections, the capacity ratio is conservatively taken as

N

N+

M

M+

M

Mt.Sd

t.Rd

.Sd

pl. Rd

.Sd

pl. Rd

33

33

22

22. .

. (EC3 5.4.8.1)

For Class 3 sections, the capacity ratio is conservatively taken as

N

Af+

M

W f+

M

W ft.Sd

yd

.Sd

el. yd

.Sd

el. yd

33

33

22

22

. (EC3 5.4.8.1)

Bending, Axial Tension, and High Shear

When the design values of the coexisting shear, VSd , is more than half the corre-sponding capacities for plastic resistance, V pl Rd. or buckling resistance, Vba Rd. , theshear is considered to be high, i.e. the shear is high if

V VSd pl Rd. , or (EC3 5.4.9)

V VSd ba Rd. . (EC3 5.4.9)



Under these conditions, the capacity ratios are computed for different types of sec-tions as follows (EC3 5.4.9):

For Class 1, 2, and 3 sections, the capacity ratio is conservatively taken as

N

N+

M

M+

M

Mt.Sd

t.Rd

.Sd

V. .Rd

.Sd

V. .Rd

33

33

22

22

. (EC3 5.4.8.1)

Bending, Axial Tension, and Lateral-Torsional Buckling

The axial tensile force has a beneficial effect for lateral-torsional buckling. In orderto check whether the member fails under lateral-torsional buckling, the effective in-ternal moment about the 3-3 axis is calculated as follows:

M MN W

Aeff Sd Sd vect Sd com

. . .. .

33 3333 , where (EC3 5.5.3)

vec (according to the EC3 box value), and

Wcom. 33 is the elastic section modulus for the extreme compression fiber.

For all members of Class 1, 2, and 3 sections subject to axial tension, N t Sd. , majoraxis bending, M Sd33. , and minor axis bending, M Sd22. , the capacity ratio is taken as

N

N+

k M

M+

k M

Mt.Sd

t.Rd

LT .Sd

b.Rd

.Sd

c. .Rd

33 22 22

22

vec LTt Sd com

b Rd

kN W

A M. .

.

33 , (EC3 5.5.4)

where kLT , k 22 and are as defined in the previous subsections.

Shear

From the design values of shear force at each station, for each of the load combina-tions and the shear resistance values, shear capacity ratios for major and minor di-rections are produced as follows:

V

V.Sd

.Rd

2

2

andV

V.Sd

.Rd

3

3

.



C h a p t e r X

Design Output

OverviewETABS creates design output in three different major formats: graphical display,tabular output, and member-specific detailed design information.

The graphical display of steel design output includes input and output design infor-mation. Input design information includes design section labels, K-factors, liveload reduction factors, and other design parameters. The output design informationincludes axial and bending interaction ratios and shear stress ratios. All graphicaloutput can be printed.

The tabular output can be saved in a file or printed directly. The tabular output in-cludes most of the information which can be displayed. This is generated for addedconvenience to the designer.

The member-specific detailed design information shows the details of the calcula-tion. It shows the design section dimensions, material properties, design and allow-able stresses or factored and nominal strengths, and some intermediate results forall the load combinations at all the design sections of a specific frame member.

In the following sections, some of the typical graphical display, tabular output, andmember-specific detailed design information are described. Some of the design in-

Overview 191

formation is specific to the chosen steel design codes which are available in the pro-gram. The AISC-ASD89 design code is described in the latter part of this chapter.For all other codes, the design outputs are similar.

Graphical Display of Design Input and OutputThe graphical output can be produced as screen display. Moreover, the activescreen display can be sent directly to the printer. The graphical display of designoutput includes input and output design information.

Input design information, for the AISC-ASD89 code, includes

• Design section labels,

• Framing type,

• Live Load Reduction Factors,

• Unbraced Length Ratios for major and minor directions of bending,

• K-factors for major and minor directions of buckling,

• C m -factors for major and minor directions,

• C b -factors,

• Axial allowable stresses,

• Allowable stresses in flexure, and

• Allowable stresses in shear.

The output design information which can be displayed is

• Color coded P-M interaction ratios with or without values, and

• Color coded shear stress ratios.

The graphical displays can be accessed from the Design menu. For example, thecolor coded P-M interaction ratios with values can be displayed by selecting theDesign menu > Steel Frame Design > Display Design Info command. This willpop up a dialog box called Display Design Results. Then the user should switch onthe Design Output option button (default) and select P-M Ratios Colors &Values in the drop-down box. Then clicking the OK button will show the interac-tion ratios in the active window.

The graphics can be displayed in either 3D or 2D mode. The ETABS standard viewtransformations are available for all steel design input and output displays. Forswitching between 3D or 2D view of graphical displays, there are several buttons

192 Graphical Display of Design Input and Output


on the main toolbar. Alternatively, the view can be set by choosing Set 3D View,Set Plan View, or Set Elevation View from the View menu.

The graphical display in an active window can be printed in gray scaled black andwhite from the ETABS program. To send the graphical output directly to theprinter, click on the Print Graphics button in the File menu. A screen capture ofthe active window can also be made by following the standard procedure providedby the Windows operating system.

Tabular Display of Design Input and OutputThe tabular design output can be sent directly either to a printer or to a file. Theprinted form of tabular output is the same as that produced for the file output withthe exception that for the printed output font size is adjusted.

The tabular design output includes input and output design information which de-pends on the design code of choice. For the AISC-ASD89 code, the tabular outputincludes the following. All tables have formal headings and are self-explanatory, sofurther description of these tables is not given.

Input design information includes the following:

• Material Analysis Property Data

– Material label,

– Modulus of elasticity,

– Poisson’s ratio,

– Coefficient of thermal expansion,

– Weight per unit volume, and

– Mass per unit volume.

• Material Design Property Data

– Material label,

– Governing design code (Steel or Concrete),

– Yield strength.

• Frame Section Property Data (Referenced sections only)

– Section label,

– Associated material label,

– Section name,

Tabular Display of Design Input and Output193

Chapter X Design Output

– Section geometric properties (depth, web thickness, top flange width, topflange thickness, bottom flange width, bottom flange thickness), and

– Section gross property (area, major and minor shear areas, major and minorshear moment of inertia, torsional inertia, major and minor section Moduli,major and minor plastic Moduli, major and minor radii of gyration).

• Load Combination Multipliers

– Combination name,

– Combination type,

– Load factors,

– Load types, and

– Combination title.

• Beam or Column Steel Stress Check Element Information (code dependent)

– Story level,

– Beam bay or Column line,

– Design Section ID,

– Framing type,

– Live Load Reduction Factors,

– Unbraced Length Ratios, and

– K-factors for major and minor direction of buckling.

The output design information includes the following:

• Beam or Column Steel Stress Check Output (code dependent)

– Story level,



– Controlling load combination ID for P-M interaction,

– Tension or compression indication ( “T” or “C”),

– Axial and bending interaction ratio with breakdown into axial, and majorand minor bending,

– Controlling load combination ID for major and minor shear forces, and

– Shear stress ratios, and

– Occasional warning messages.

194 Tabular Display of Design Input and Output


The tabular output can be accessed by selecting the File menu > Print Tables >Steel Frame Design command. This will pop up a dialog box. The design informa-tion has been grouped into four categories: Preferences, Input Summary, OutputSummary, and Detailed Output. The user can specify the design quantities forwhich the results are to be tabulated by checking the associated check boxes. By de-fault, the output will be sent to the printer. If the user wants the output stream to beredirected to a file, he/she can check the Print to File box. This will provide a de-fault filename. The default filename can be edited. Alternatively, a file list can beobtained by clicking the File Name button to chose a file from. If the user wants theoutput table to be appended to the existing text file, he/she should select the filefrom the file list and check the Append box. Then clicking the OK button will directthe tabular output to the requested file or to the requested printer.

For easy review of the file in which the tabular information has just been saved, theprogram provides an easy access to a text editor though the File > Display In-put/Output Text Files command.

Member Specific InformationThe member specific design information shows the details of the calculation. It pro-vides an access to the geometry and material input data, design section dimensions,design and allowable stresses, stress ratios, and some of the intermediate results fora member. The design detail information can be displayed for a specific load com-bination and for a specific station of a frame member.

The detailed design information can be accessed by right clicking on the desiredframe member. This will pop up a dialog box called Steel Stress Check Informa-tion which includes the following tabulated information for the specific member.

– Story level,


– Analysis Section ID,


– Load combination ID,

– Station location,

– Axial and bending interaction ratio, and

– Shear stress ratio along two axes.

Member Specific Information 195

Chapter X Design Output

Additional information can be accessed by clicking on the Overwrites and Detailsbuttons in the dialog box. Additional information that is available by clicking on theOverwrites button is as follows:

• Current Design Section ID,

• Element Framing Type,

• Live Load Reduction Factor,

• Horizontal Earthquake Factor,

• Design Parameters (code dependent)

– Unbraced Length Ratios for major and minor directions,

– Effective length factors, K , for major and minor directions of buckling,

– C m -factors for major and minor directions,

– C b -factors,

– s -factors for major and minor directions,

– b -factors for major and minor directions,

– Yield stress,

– 0 -factors,

– Compressive and tensile allowable stresses,

– Major and minor bending allowable stresses, and

– Major and minor shear allowable stresses.

Additional information that is available by clicking on the Details button is givenbelow.

• Design code name, Units,

• Story, Beam bay or Column line, Station, Section, and Element type,

• Section geometric information and graphical representation,

• Material properties of steel,

• Warning information,

• Load Combination ID,

• Moment and forces,

• Demand/Capacity ratios,

• Design and allowable stresses for axial force and biaxial moments, and

• Design and allowable stresses for shear.

196 Member Specific Information


References

AISC, 1989a

Specification for Structural Steel Buildings: Allowable Stress Design and Plas-tic Design, June 1, 1989 with Commentary, 2nd Impression, American Instituteof Steel Construction, Chicago, Illinois, 1989.

AISC, 1989b

Manual of Steel Construction, Allowable Stress Design, 9th Edition, AmericanInstitute of Steel Construction, Chicago, Illinois, 1989.

AISC, 1993

Load and Resistance Factor Design Specification for Structural Steel Building,American Institute of Steel Construction, Chicago, Illinois, 1993.

AISC, 1994

Manual of Steel Construction, Load & Resistance Factor Design, 2nd Edition,American Institute of Steel Construction, Chicago, Illinois, 1994.

BSI, 1990

Structural Use of Steelwork in Building, Part 1, Code of Practice for Design inSimple and Continuous Construction: Hot Rolled Sections, BS 5950 : Part 1 :1990, British Standards Institution, London, UK, 1990.

197

CEN, 1992

Design of Steel Structures, Part 1.1 : General Rules and Rules for Buildings,ENV 1993-1-1 : 1992, European Committee for Standardization, Brussels, Bel-gium, 1992.

CISC, 1995

Handbook of Steel Construction, CAN/CSA-S16.1-94, 6th Edition, CanadianInstitute of Steel Construction, Willowdale, Ontario, Canada, 1995.

CSI, 1999

ETABS User’s Manual, Vols. I and II, Computers and Structures, Inc., Berke-ley, California, 1999.

CSI, 2000

ETABS Quick Tutorial, Computers and Structures, Inc., Berkeley, California,2000.

ICBO, 1997

1997 Uniform Building Code Volume 2, Structural Engineering DesignProvisions, International Conference of Building Officials, Whittier, Califor-nia, 1997.

D. W. White and J. F. Hajjar, 1991

“Application of Second-Order Elastic Analysis in LRFD: Research to Prac-tice,” Engineering Journal, American Institute of Steel Construction, Inc., Vol.28, No. 4, 1991.

198


Index

Beam Connection ShearUBC-ASD, 102UBC-LRFD, 129

Beam-column capacity ratiosUBC-ASD, 100UBC-LRFD, 128

Bending strengthASD (allowable), 34BS, 161CISC, 141Eurocode, 182LRFD, 65

Brace Connection ForceUBC-ASD, 103UBC-LRFD, 130

Braced frames, 8BS, 159CISC, 137Eurocode, 177LRFD, 56UBC-ASD, 89UBC-LRFD, 115

Capacity ratio, 2, 8ASD, 19, 44BS, 151, 165

CISC, 133, 147Eurocode, 169, 185LRFD, 49, 77UBC-ASD, 80, 85UBC-LRFD, 106, 112

Check stations, 8

Classification of sectionsASD, 22BS, 155CISC, 137Eurocode, 173LRFD, 52UBC-ASD, 82UBC-LRFD, 108

Compact sectionSee Classification of sections

Compressive strengthASD, 27ASD (allowable), 27BS, 159CISC, 140Eurocode, 179LRFD, 58

Continuity Plates, 13UBC-ASD, 95

199

UBC-LRFD, 121

Design codes, 1See also "Supported design codes"

Design load combinations, 6

Design output, 191graphical, 192member specific, 195tabular, 193

Design stations, 8

Doubler Plates, 15UBC-ASD, 98UBC-LRFD, 125

EBFUBC-ASD, 90UBC-LRFD, 116

Effective length factor, 11

Euler buckling loadASD, 28BS, 159CISC, 140Eurocode, 179LRFD, 56UBC-LRFD, 110

Factored forces and momentsBS, 157CISC, 137Eurocode, 177LRFD, 56UBC-LRFD, 110

Flexural bucklingASD, 27BS, 159CISC, 140Eurocode, 179LRFD, 27, 58

Graphical output, 192

Interaction equationsSee Capacity ratio

Interactive environment, 1

Lateral drift effect, 9See also P-Delta analysis

Lateral-torsional bucklingASD, 34BS, 162CISC, 141Eurocode, 183LRFD, 65, 70, 73

Link Beam RotationUBC-ASD, 91UBC-LRFD, 117

Live load reduction factor, 7, 22, 52, 81,107, 136, 154, 172

Loading combinations, 2ASD, 22BS, 154CISC, 136Eurocode, 172LRFD, 52UBC-ASD, 81UBC-LRFD, 107

Member specific output, 195

Member stability effect, 9See also P-Delta analysis

Moment magnificationBS, 157CISC, 137Eurocode, 178LRFD, 56UBC-LRFD, 110

Noncompact sectionSee Classification of sections

200


Nonsway, 8BS, 159CISC, 137Eurocode, 177LRFD, 56

Notional loadBS, 154CISC, 136Eurocode, 172

OMFUBC-ASD, 88UBC-LRFD, 114

Output, 2details, 196graphical, 191tabular, 191

P-Delta analysis, 8BS, 154, 159CISC, 136 - 137Eurocode, 173, 178LRFD, 52, 57, 110UBC-LRFD, 107, 111

P-Delta effects, 8

Perry factor, 159

Plastic sectionSee Classification of sections

Redesign, 196

Robertson constant, 159

SCBFUBC-ASD, 93UBC-LRFD, 119

Second order effectsSee P-Delta effects

Shear strengthASD (allowable), 43BS, 165CISC, 145

Eurocode, 181LRFD, 76

Slender sectionSee Classification of sections

SMRFUBC-ASD, 88, 97UBC-LRFD, 114, 124

Strength reduction factorsBS (partial factors), 159CISC, 140Euro (partial factors), 178LRFD, 58UBC-LRFD, 111

Supported design codes, 1AASHTO, 5ASD, 5, 19BS, 6, 151CISC, 5, 133Eurocode, 6, 169LRFD, 5, 49UBC-ASD, 79UBC-LRFD, 105

Sway, 8BS, 159CISC, 137Eurocode, 177LRFD, 56

Tabular output, 193

Tensile strengthASD (allowable), 27BS, 161CISC, 141Eurocode, 179LRFD, 64

Unbraced frames, 8BS, 159CISC, 137Eurocode, 177

201

Index

LRFD, 56

Units, 3, 17ASD, 22BS, 151CISC, 133Eurocode, 169LRFD, 52UBC-ASD, 80UBC-LRFD, 106

Unsupported length, 9

202


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