2-Steel Seismic Design-Moment Resisting Frames

8/12/2019 2-Steel Seismic Design-Moment Resisting Frames

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Design of Seismic-Resistant Steel

Building Structures

Moment Resisting Frames

Adapted from material developed by Prof. Michael D. Engelhardt, University of Texas at Austin with the support of the AmericanInstitute of Steel Construction.

CEE 258

Seismic Design of

Building Structures


Definition and Basic Behavior of Moment ResistingFrames

Beam-to-Column Connections: Before and AfterNorthridge

Panel-Zone Behavior

AISC Seismic Provisions for Special Moment Frames


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MOMENT RESISTING FRAME (MRF)

Advantages Architectural Versatility

High Ductility and SafetyDisadvantages

Low Elastic Stiffness

Beams and columns with moment resisting

connections; resist lateral forces by flexure andshear in beams and columns

Develop ductility by:- flexural yielding of beams- shear yielding of column panel zones- flexural yielding of columns

Moment Resisting Frame


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Achieving Ductile Behavior:

Choose frame elements ("fuses") that willyield in an earthquake, i.e, choose plastichinge locations.

Detail plastic hinge regions to sustainlarge inelastic rotations prior to the onsetof fracture or instability.

Design all other frame elements to bestronger than the plastic hinge regions.

Understand and Control Inelastic Behavior:


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Behavior of an MRF Under Lateral Load:Internal Forces and Possible Plastic Hinge Locations


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M V

Possible Plastic Hinge Locations

Beam(Flexural Yielding)

Panel Zone(Shear Yielding)

Column(Flexural & Axial

Yielding)


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Plastic HingesIn Beams

Plastic HingesIn Column Panel Zones


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Plastic HingesIn Columns:

Potential for SoftStory Collapse

Critical Detailing Area for Moment Resisting Frames:

Beam-to-Column Connections

Design Requirement:Frame must develop large ductilitywithout failure of beam-to-columnconnection.


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Panel-Zone Behavior AISC Seismic Provisions for Special Moment Frames

Moment Connection Design Practice Prior to1994 Northridge Earthquake:

Welded flange-boltedweb moment connectionwidely used from early1970 s to 1994


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Pre-NorthridgeWelded Flange Bolted Web Moment Connection

Backup Bar

Beam Flange

Column FlangeStiffener

Weld Access Hole


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Experimental Data on Pre-Northridge Moment Connection

Typical ExperimentalSetup:


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Initial Tests on Large Scale Specimens:

Tests conducted at UC Berkeley ~1970

Tests on W18x50 and W24x76 beams Tests compared all-welded connections

with welded flange-bolted web connections


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All-Welded Detail


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Welded Flange Bolted Web Detail


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Observations from Initial UC Berkeley Tests:

Large ductility developed by all-weldedconnections.

Welded flange-bolted web connections developedless ductility, but were viewed as still acceptable.


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Subsequent Test Programs:

Welded flange-bolted web connections showedhighly variable performance.

Typical failure modes: fracture at or near beamflange groove welds.

A large number of laboratory tested connectionsdid not develop adequate ductility in the beamprior to connection failure.


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-5000

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04

Drift Angle (rad)

B e n

d i n g

M o m e n

t ( k N - m

)

Brittle Fracture at BottomFlange Weld

Mp

Mp

Pre-Northridge Connection


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Summary of Testing Prior to

Northridge Earthquake

Welded flange bolted web connection showedhighly variable performance

Many connections failed in laboratory with littleor no ductility

1994 Northridge Earthquake

Widespread failure ofwelded flange - boltedweb momentconnections


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1994 Northridge Earthquake January 17, 1994 Magnitude = 6.8 Epicenter at Northridge - San Fernando Valley

(Los Angeles area)

Fatalities: 58 Estimated Damage Cost: $20 Billion

Northridge - Ground Accelerations

Sylmar: 0.91g H 0.60g V Sherman Oaks: 0.46g H 0.18g V Granada Hills: 0.62g H 0.40g V Santa Monica: 0.93g H 0.25g V

North Hollywood: 0.33g H 0.15g V


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Damage to Steel Buildings in theNorthridge Earthquake

Large number of modern steel buildingssustained severe damage at beam-to-columnconnections.

Primary Damage: Fracture in and around beamflange groove welds

Damage was largely unexpected by engineeringprofession


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Damage Observations:

Steel MomentConnections

Backup Bar

Beam Flange

Column FlangeStiffener

Weld Access Hole

Pre-Northridge

Welded Flange Bolted Web Moment Connection


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Damage Observations

A large number of steel moment frame buildingssuffered connection damage

No steel moment frame buildings collapsed Typical Damage:

fracture of groove weld

divot

fracture within column flange

fracture across column flange and web

Observations from Studies of FracturedConnections

Many connections failed by brittle fracture with little orno ductility

Brittle fractures typically initiated in beam flangegroove welds


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Response to Northridge Moment Connection

Damage

Nearly immediate elimination of welded flange -bolted web connection from US building codes anddesign practice

Intensive research and testing efforts to understandcauses of damage and to develop improvedconnections AISC, NIST, NSF, etc. SAC Program (FEMA)

Causes of Moment ConnectionDamage in Northridge

Welding

Connection Design

Materials


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Causes of Northridge Moment ConnectionDamage:

Welding Factors

Low Fracture Toughness of Weld Metal Poor Quality Effect of Backing Bars and Weld Tabs

Weld Metal Toughness

Most common Pre-Northridge welding electrode(E70T-4) had very low fracture toughness.

Typical Charpy V-Notch: < 5 ft.-lbs at 70 0F(7 J at 21 0C)


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Welding Quality

Many failed connections showed evidence of poorweld quality

Many fractures initiated at root defects in bottomflange weld, in vicinity of weld access hole


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Weld Backing Bars and Weld Tabs

Backing Bars: Can create notch effect Increases difficulty of inspection

Weld Tabs: Weld runoff regions at weld tabs contain

numerous discontinuities that can potentially

initiate fracture


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Design Factors:

Stress/Strain Too High at Beam Flange Groove Weld

Inadequate Participation of Beam Web Connection inTransferring Moment and Shear

Effect of Weld Access Hole Effect of Column Flange Bending

Other Factors

Causes of Northridge Moment ConnectionDamage:

Mp

Increase in Flange Stress Due toInadequate Moment Transfer Through Web Connection

F l a n g e

S t r e s s

Fy

Fu


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Vflange

Increase in Flange Stress Due to Shear in Flange

StressConcentrations: Weld access

hole

Shear in flange

Inadequateflexuralparticipation ofweb connection


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Causes of Moment Connection Damage inNorthridge:

Material Factors (Structural Steel)

Actual yield stress of A36 beams oftensignificantly higher than minimumspecified


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Strategies for Improved Performanceof Moment Connections

Welding

Materials

Connection Design and Detailing

Strategies for Improved Performance of MomentConnections:

WELDING

Required minimum toughness for weld metal: Required CVN for all welds in SLRS:

20 ft.-lbs at 0 0 F

Required CVN for Demand Critical welds:20 ft.-lbs at -20 0 F and 40 ft.-lbs at 70 0 F


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WELDING

Improved practices for backing bars and weld tabsTypical improved practice:

Remove bottom flange backing bar Seal weld top flange backing bar Remove weld tabs at top and bottom flange welds

Greater emphasis on quality and quality control (AISCSeismic Provisions - Appendix Q and W)



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Strategies for Improved Performance of Moment

Connections:Materials (Structural Steel)

Introduction of expected yield stress into designcodes

Fy = minimum specified yield strength

Ry = 1.5 for ASTM A36

= 1.1 for A572 Gr. 50 and A992(See AISC Seismic Provisions - Section 6 for other values of R y )

Expected Yield Stress = R y Fy


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Materials (Structural Steel)

Introduction of ASTM A992 steel for wide flangeshapes

ASTM A992

Minimum F y = 50 ksi

Maximum F y = 65 ksi

Minimum F u = 65 ksi

Maximum F y / F u = 0.85

Strategies for Improved Performance of Moment

Connections:

Connection Design

Improved Weld Access Hole Geometry


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Improved Weld AccessHole

See Figure 11-1 in the2005 AISC SeismicProvisions for dimensionsand finish requirements


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Connection Design

Development of Improved Connection Designsand Design Procedures

Reinforced Connections Proprietary Connections Reduced Beam Section (Dogbone)

Connections

Other SAC Investigated Connections


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SLOTTED WEBCONNECTION

Connections Investigated ThroughSAC-FEMA Research Program


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Reduced BeamSection

WeldedUnreinforcedFlange - BoltedWeb


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WeldedUnreinforcedFlange - WeldedWeb

Free FlangeConnection


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Welded FlangePlate Connection

Bolted UnstiffenedEnd Plate


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Bolted StiffenedEnd Plate

Bolted Flange

Plate


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Double Split Tee

Results of SAC-FEMA Research ProgramRecommended Seismic Design Criteriafor Steel Moment Frames

FEMA 350Recommended Seismic Design Criteria for New Steel Moment-Frame Buildings

FEMA 351Recommended Seismic Evaluation and Upgrade Criteria forExisting Welded Steel Moment-Frame Buildings

FEMA 352Recommended Postearthquake Evaluation and Repair Criteriafor Welded Steel Moment-Frame Buildings

FEMA 353Recommended Specifications and Quality AssuranceGuidelines for Steel Moment-Frame Construction for Seismic

Applications


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Column Panel Zone

Column Panel Zone:- subject to high shear- shear yielding and large

shear deformations possible

(forms shear hinge )- provides alternate yielding

mechanism in a steel momentframe

Joint deformationdue to panel zoneshear yielding


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Plastic Shear HingesIn Column Panel Zones


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"kink" at corners ofpanel zone


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-400

-300

-200

-100

0

100

200

300

400

-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08

Story Drift Angle (rad)

C o

l u m n

T i p L o a

d ( k i p s

)

Composite RBS Specimen withWeak Panel Zone

-1200

-800

-400

0

400

800

1200

-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08

Panel Zone (rad)

P a n e

l Z o n e

S h e a r

F o r c e

( k i p s

)

Composite RBS Specimen withWeak Panel Zone

!


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Observations on Panel Zone Behavior

Very high ductility is possible. Localized deformations ( kinking ) at corners of

panel zone may increase likelihood of fracture invicinity of beam flange groove welds.

Building code provisions have varied greatly on panelzone design.

Current AISC Seismic Provisions permits limitedyielding in panel zone.

Further research needed to better define acceptablelevel of panel zone yielding




Panel-Zone Behavior

AISC Seismic Provisions for Special Moment Frames


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2005 AISC Seismic Provisions

Section 9 Special Moment Frames (SMF)

Section 10 Intermediate Moment Frames (IMF)

Section 11 Ordinary Moment Frames (OMF)

Section 9Special Moment Frames (SMF)

9.1 Scope

9.2 Beam-to-Column Joints and Connections

9.3 Panel Zone of Beam-to-Column Connections

9.4 Beam and Column Limitations

9.5 Continuity Plates

9.6 Column-Beam Moment Ratio

9.7 Lateral Bracing of at Beam-to-Column Connections

9.8 Lateral Bracing of Beams

9.9 Column Splices


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AISC Seismic Provisions - SMF9.1 Scope

Special moment frames (SMF) are expected to withstandsignificant inelastic deformations when subjected to theforces resulting from the motions of the designearthquake.

AISC Seismic Provisions - SMF

9.2 Beam-to-Column Connections

9.2a Requirements

9.2b Conformance Demonstration

9.2c Welds

9.2d Protected Zones


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AISC Seismic Provisions - SMF - Beam-to-Column Connections9.2a Requirements

Beam-to-column connections shall satisfy the following threerequirements:

1. The connection shall be capable of sustaining aninterstory drift angle of at least 0.04 radians.

2. The measured flexural resistance of theconnection, determined at the column face, shallequal at least 0.80 M p of the connected beam atan interstory drift angle of 0.04 radians.

9.2a Requirements

Beam-to-column connections shall satisfy the following threerequirements (cont):

3. The required shear strength of the connectionshall be determined using the following quantityfor the earthquake load effect E :

E = 2 [ 1.1R y M p ] / Lh (9-1)

where:

R y = ratio of the expected yield strength to theminimum specified yield strength

M p = nominal plastic flexural strength

Lh = distance between plastic hinge locations


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Lh

(1.2 + 0.2S DS ) D + 0.5 L or (0.9-0.2S DS ) D1.1 R y M p 1.1 R y M p

V u = 2 [ 1.1 R y M p ] / Lh + V gravity

V u V u

Required Shear Strength of Beam-to-Column Connection

AISC Seismic Provisions - SMF - Beam-to-Column Connections

9.2b Conformance DemonstrationDemonstrate conformance with requirements of Sect. 9.2a by one ofthe following methods:

I. Conduct qualifying cyclic tests in accordance with Appendix S.

Tests conducted specifically for the project, with test specimens thatare representative of project conditions.

or

Tests reported in the literature (research literature or otherdocumented test programs), where the test specimens arerepresentative of project conditions.


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Demonstrate conformance with requirements of Sect. 9.2a by one ofthe following methods (cont):

II. Use connections prequalified for SMF in accordance with Appendix P

Use connections prequalified by the AISC ConnectionPrequalification Review Panel (CPRP) and documented in StandardANSI/AISC 358 -"Prequalified Connections for Special and IntermediateSteel Moment Frames for Seismic Applications"

or

Use connection prequalified by an alternative review panel that isapproved by the Authority Having Jurisdiction.

Test connectionin accordancewith Appendix S

9.2b Conformance Demonstration - by Testing


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Appendix SQualifying Cyclic Tests of Beam-to-Column

and Link-to-Column Connections

Testing Requirements:

Test specimens should be representative of prototype(Prototype = actual building)

Beams and columns in test specimens must be nearly full-scalerepresentation of prototype members:

- depth of test beam ! 0.90 x depth of prototype beam- wt. per ft. of test beam ! 0.75 x wt. per ft. of prototype beam- depth of test column ! 0.90 x depth of prototype column

Sources of inelastic deformation (beam, panel zone, connectionplates, etc) in the test specimen must similar to prototype.

Appendix S

Testing Requirements (cont):

Lateral bracing in test specimen should be similar to prototype.

Connection configuration used for test specimen must matchprototype.

Welding processes, procedures, electrodes, etc. used for testspecimen must be representative of prototype.

See Appendix S for other requirements.


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Typical Test Subassemblages

Exterior Subassemblage Interior Subassemblage

Typical Exterior Subassemblage

"

Lbeam

!

Interstory Drift Angle ! = "

Lbeam


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Typical Exterior Subassemblage

"

Hcolumn

!

Typical Interior Subassemblage

Interstory Drift Angle ! = "

Hcolumn


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Typical Interior Subassemblage

Typical Interior Subassemblage (with concrete floor slab)


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Appendix S

Testing Requirements - Loading History

Apply the following loading history:

6 cycles at # = 0.00375 rad.

6 cycles at # = 0.005 rad.







continue at increments of 0.01 rad, withtwo cycles of loading at each step

Appendix S

Testing Requirements - Loading History

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

I n t e r s

t o r y

D r i

f t A n g

l e !

Acceptance Criteria for SMF Beam-to-Column Connections: After completing at least one loading cycle at 0.04 radian, the measured flexuralresistance of the connection, measured at the face of the column, must be at least0.80 M p of the connected beam


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Example of Successful Conformance Demonstration Testper Appendix S:

-40000

-30000

-20000

-10000

0

10000

20000

30000

40000

-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08

Interstory Drift Angle (rad)

B e a m

M o m e n

t a

t F a c e o

f C o

l u m n

( i n - k

i p s

)

0.8 M p

- 0.8 M p

M0.04 0.8 M p

M0.04 0.8 M p

A Prequalified connection is one that has undergone sufficient

testing (per Appendix S)

analysis

evaluation and review

so that a high level of confidence exists that the connection canfulfill the performance requirements specified in Section 9.2a forSpecial Moment Frame Connections


........by use of Prequalified Connection


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Requirements for Prequalification of Connections:

Appendix P - Prequalification of Beam-to-Columnand Link-to-Column Connections

9.2b Conformance Demonstration .....by use of Prequalified Connection

Authority to Prequalify of Connections:

AISCConnection Prequalification Review Panel (CPRP)

Information on Prequalified Connections:Standard ANSI/AISC 358 - "Prequalified Connections forSpecial and Intermediate Steel Moment Frames for Seismic Applications "


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ANSI/AISC 358 - "Prequalified Connections for Special andIntermediate Steel Moment Frames for Seismic Applications "

Connections Prequalified in ANSI/AISC 358 (1st Ed - 2005)

Reduced Beam Section (RBS) Connection

Bolted Unstiffened and Stiffened Extended End-Plate Connection

RBS Concept: Trim Beam Flanges Near

Connection

Reduce Moment atConnection

Force Plastic Hinge Awayfrom Connection

Reduced Beam Section (RBS) Moment Connection


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Example of laboratory performance of an RBS connection:

Whitewashed connection prior to testing:


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Connection at ! ! 0.02 radian......



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-3000

-2000

-1000

0

1000

2000

3000

4000

5000

-0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05

Drift Angle (radian)

B e n

d i n g

M o m e n

t ( k N - m

)

RBS Connection

Mp

Mp


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ANSI/AISC 358:

Prequalification Requirements for RBS in SMF

Beam depth: up to W36

Beam weight: up to 300 lb/ft

Column depth: up to W36 for wide-flangeup to 24-inches for box columns

Beam connected to column flange(connections to column web not prequalified)

RBS shape: circular

RBS dimensions: per specified design procedure

ANSI/AISC 358:

Prequalification Requirements for RBS in SMFcont......

Beam flange welds: - CJP groove welds- Treat welds asDemand Critical - Remove bottom flange backing and provide

reinforcing fillet weld- Leave top flange backing in-place; fillet weld

backing to column flange- Remove weld tabs at top and bottom flanges

Beam web to column connection:- Use fully welded web connection (CJP weldbetween beam web and column

flange)

See ANSI/AISC 358 for additional requirements (continuity plates, beamlateral bracing, RBS cut finish req'ts., etc.)


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RBS with welded webconnection:

ANSI/AISC 358:

Prequalification Requirements for RBS in SMF

cont.......

Protected Zone


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Lateral brace at center of RBS - violates Protected Zone

Examples of RBS Connections.....


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AISC Seismic Provisions - SMF9.3 Panel Zone of Beam-to-Column Connections

9.3a Shear Strength

9.3b Panel Zone Thickness

9.3c Panel Zone Doubler Plates

AISC Seismic Provisions - SMF - Panel Zone Requirements

9.3a Shear Strength

The minimum required shear strength,R u , of the panel zone shall betaken as the shear generated in the panel zone when plastic hinges formin the beams.

To compute panel zone shear.....

Determine moment at beam plastic hinge locations(1.1 R

y M

p or as specified in ANSI/AISC 358)

Project moment at plastic hinge locations to the faceof the column (based on beam moment gradient)

Compute panel zone shear force.


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M pr-2 M pr1

V beam-2

V beam-1

Beam 1 Beam 2

Plastic Hinge Location


s h s h

M f1 M f2

M pr = expected moment at plastic hinge = 1.1R y M p or as specified in ANSI/AISC 358V beam = beam shear (see Section 9.2a - beam required shear strength)

sh = distance from face of column to beam plastic hinge location (specified in ANSI/AISC 358)

Panel Zone Shear Strength (cont)

M pr-2 M pr1

V beam-2

V beam-1

Beam 1 Beam 2



s h s h

M f1 M f2


M f = moment at column face

M f = M pr + V beam ! s h


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Ru = M f !

d b " t f ( )" V cPanel Zone Required Shear Strength =


Panel Zone Design Requirement:

R u " " v R v where " v = 1.0

R v = nominal shear strength, basedon a limit state of shear yielding, ascomputed per Section J10.6 of the

AISC Specification


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To compute nominal shear strength, R v , of panel zone:

When P u $ 0.75 P y in column:

Rv = 0.6 F yd ct p 1 +3 bcf t cf

2

d bd ct p

!

"#

$

%&

(AISC Spec EQ J10-11)

Where: d c = column depth

d b = beam depth

bcf = column flange widtht cf = column flange thickness

F y = minimum specified yield stress of column web

t p = thickness of column web including doubler plate


To compute nominal shear strength, R v , of panel zone:

When P u > 0.75 P y in column (not recommended) :

Rv = 0.6 F yd ct p 1 +3bcf t cf

2

d bd ct p

!

"#

$

%& 1.9 '

1.2 PuP y

!

"#

$

%& (AISC Spec EQ J10-12)


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If shear strength of panel zone is inadequate:

- Choose column section with larger web area- Weld doubler plates to column

Options for Web Doubler Plates


9.4 Beam and Column LimitationsBeam and column sections must satisfy the width-thickness limitations given in Table I-8-1

b f 2 t f

! 0.30 E s

F y

Beam Flanges

Beam Web

ht w

! 2.45 E s

F y

b f

t f

h

t w


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Column Flanges b f 2 t f

! 0.30 E sF y

Column Web

Pu! P y

" 0.125 h

t w! 3.14 E s

F y1 " 1.54 Pu

# P y

$

%&

'

()

Pu! P y

> 0.125ht w

! 1.12 E sF y

2.33 " Pu# P y

$

%&

'

() > 1.49

E sF y

Note: Column flange and web slenderness limits can be taken as! p in AISCSpecification Table B4.1, if the ratio for Eq. 9-3 is greater than 2.0


Continuity Plates




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Continuity Plates



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AISC Seismic Provisions - SMF9.5 Continuity Plates

Continuity plates shall be consistent with therequirements of a prequalified connection as specified inANSI/AISC 358 (Prequalified Connections for Special andIntermediate Steel Moment Frames for Seismic Applications)

or

As determined in a program of qualification testing inaccordance with Appendix S

ANSI/AISC 358 -Continuity Plate Requirements

Continuity PlatesFor Wide-Flange Columns:

Continuity plates are required, unless:

t cf ! 0.4 1.8 bbf t bf R ybF yb R ycF yc

t cf !bbf 6

and

t cf = column flange thickness

bbf = beam flange width

t bf = beam flange thickness


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Continuity Plates

For Box Columns:

Continuity plates must be provided.


Required thickness of continuity plates

a) For one-sided (exterior) connections, continuity plate thickness shall beat least one-half of the thickness of the beam flange.

b) For two-sided (interior) connections, continuity plate thickness shall be atleast equal to the thicker of the two beam flanges on either side of thecolumn

For other design, detailing and welding requirements forcontinuity plates - See ANSI/AISC 358


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t cp

t bf t cp ! 1/2 % t bf


t cp

t bf-2 t bf-1

t cp ! larger of ( t bf-1 and t bf-2 )



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AISC Seismic Provisions - SMF9.6 Column-Beam Moment Ratio

Section 9.6 requires strong column - weak girder design for SMF (with a few exceptions)

Purpose of strong column -weak girder requirement:

Prevent Soft Story Collapse


9.6 Column-Beam Moment RatioThe following relationship shall be satisfied at beam-to-column connections:

M pc*!

M pb*!

> 1.0 Eqn. (9-3)


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M pc*!

M pb*! > 1.0

M pc*

=! the sum of the moments in the column above and below the joint atthe intersection of the beam and column centerlines." M * pc is determined by summing the projections of thenominalflexural strengths of the columns above and below the joint to thebeam centerline with a reduction for the axial force in the column.

It is permitted to take" M * pc = " Z c ( F yc - P uc /Ag )

M pb*

=

! the sum of the moments in the beams at the intersection of the beamand column centerlines." M * pb is determined by summing the projections of theexpectedflexural strengths of the beams at the plastic hinge locations to thecolumn centerline.

C ColumnL

C BeamL

M* pc-top

M* pc-bottomM* pb-left

M* pb-right

M pc*!

M pb*

! > 1.0

Note:

M* pc is based on minimum specified yieldstress of column

M* pb is based on expected yield stress of beamand includes allowance for strain hardening


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M pr-right M pr-left

V beam-right

V beam-left

Left Beam Right Beam



s h+d col /2

M pr = expected moment at plastic hinge = 1.1R y M p or as specified in ANSI/AISC 358

V beam

= beam shear (see Section 9.2a - beam required shear strength)

sh = distance from face of column to beam plastic hinge location (specified in ANSI/AISC 358)

M* pb-left M* pb-right

s h+d col /2

M* pb = M pr + V beam (s h + d col /2 )

Computing M* pb

Top Column

Bottom Column

M pc

= nominal plastic moment capacity of column, reduced for presence of axial force; cantake M pc = Z c (F yc - P uc / Ag ) [or use more exact moment-axial force interactionequations for a fully plastic cross-section]

V col = column shear - compute from statics, based on assumed location of column inflection points (usually midheight of column)

M* pc-bottom

M* pc = M pc + V col (d beam /2 )

Computing M* pc

M pc-bottom

M pc-topM* pc-top

d beam

V col-top

V col-bottom


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AISC Seismic Provisions - SMF9.8 Lateral Bracing of Beams

Must provide adequate lateral bracing of beams in SMFso that severe strength degradation due to lateraltorsional buckling is delayed until sufficient ductility isachieved

(Sufficient ductility = interstory drift angle of at least 0.04rad is achieved under Appendix S loading protocol)

Lateral Torsional BucklingLateral torsionalbuckling controlled by:

Lbr y

Lb = distance between beam lateral braces

r y = weak axis radius of gyration

Lb Lb

Beam lateral braces (top & bottom flanges)


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Lb ! 0.086 E F y

" # $

% & ' r y = 50 r y for F y = 50 ksi( )

AISC Seismic Provisions - SMF9.8 Lateral Bracing of Beams

Both flanges of beams shall be laterally braced, with a maximumspacing of Lb = 0.086r y E / F y

Note:

For typical SMF beam: r y 2 to 2.5 inches.and Lb 100 to 125 inches (approx. 8 to 10 ft)


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In addition to lateral braces provided as a maximum spacingof Lb = 0.086r y E / F y :

Lateral braces shall be placed near concentrated forces, changes in cross-section and other locations where analysis indicates that a plastic hingewill form.

The placement of lateral braces shall be consistent with that specified inANSI/AISC 358 for aPrequalified Connection , or as otherwise determinedby qualification testing.


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ANSI/AISC 358 -Lateral Bracing Requirements for the RBS

For beams with an RBS connection:

When a composite concrete floor slab is present, no additionallateral bracing is required at the RBS.

When a composite concrete floor slab is not present, provide anadditional lateral brace at the RBS. Attach brace just outside ofthe RBS cut, at the end farthest from the column face.


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Section 9Special Moment Frames (SMF)

9.1 Scope

9.2 Beam-to-Column Joints and Connections

9.3 Panel Zone of Beam-to-Column Connections




9.7 Lateral Bracing of at Beam-to-ColumnConnections


9.9 Column Splices

2-Steel Seismic Design-Moment Resisting Frames

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