presentaion-aisc seismic design-module2-moment resisting frames
TRANSCRIPT
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Design of Seismic-Resistant Steel
Building Structures
Prepared by:
Michael D. EngelhardtUniversity of Texas at Austin
with the support of the American Institute of Steel Construction.
Version 1 - March 2007
2. Moment Resisting Frames
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2 - Moment Resisting Frames
• Definition and Basic Behavior of Moment Resisting
Frames
• Beam-to-Column Connections: Before and After
Northridge
• Panel-Zone Behavior
• AISC Seismic Provisions for Special Moment Frames
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Moment Resisting Frames
• Definition and Basic Behavior of Moment Resisting
Frames
• Beam-to-Column Connections: Before and After
Northridge
• Panel-Zone Behavior
• AISC Seismic Provisions for Special Moment Frames
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MOMENT RESISTING FRAME (MRF)
Advantages
• Architectural Versatility• High Ductility and Safety
Disadvantages
• Low Elastic Stiffness
Beams and columns with moment resistingconnections; 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
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Moment Resisting Frame
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Achieving Ductile Behavior:
• Choose frame elements ("fuses") that willyield in an earthquake, i.e, choose plastic
hinge locations.• Detail plastic hinge regions to sustain
large 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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Possible Plastic Hinge Locations
Beam(Flexural Yielding)
Panel Zone(Shear Yielding)
Column(Flexural & Axial
Yielding)
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Plastic HingesIn Beams
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Plastic HingesIn Column Panel Zones
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Plastic HingesIn Columns:
Potential for SoftStory Collapse
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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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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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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 beam
prior 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 toNorthridge Earthquake
• Welded flange – bolted web connection showedhighly variable performance
• Many connections failed in laboratory with littleor no ductility
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1994 Northridge Earthquake
Widespread failure of welded 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
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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 Observations:Steel MomentConnections
Pre-Northridge
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Backup Bar
Beam Flange
Column FlangeStiffener
Weld Access Hole
Pre-NorthridgeWelded 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
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Response to Northridge Moment ConnectionDamage
• 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)
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Causes of Moment ConnectionDamage in Northridge
• Welding
• Connection Design
• Materials
Causes of Northridge Moment Connection
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Damage:
Welding Factors
• Low Fracture Toughness of Weld Metal
• Poor Quality• Effect of Backing Bars and Weld Tabs
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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 poor weld quality
• Many fractures initiated at root defects in bottomflange weld, in vicinity of weld access hole
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Causes of Northridge Moment ConnectionD
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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
Damage:
s s
Fu
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Mp
Increase in Flange Stress Due toInadequate Moment Transfer Through Web Connection
F l a n g e
S t r e s
Fy
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Vflange
Increase in Flange Stress Due to Shear in Flange
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Strategies for Improved Performanceof Moment Connections
• Welding
• Materials
• Connection Design and Detailing
Strategies for Improved Performance of Moment
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Connections:
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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Strategies for Improved Performance of MomentConnections:
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Materials (Structural Steel)
• Introduction of “expected yield stress” into designcodes
Fy = minimum specified yield strength
R y = 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
Strategies for Improved Performance of MomentConnections:
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Materials (Structural Steel)
• Introduction of ASTM A992 steel for wide flangeshapes
ASTM A992Minimum F y = 50 ksi
Maximum F y = 65 ksi
Minimum F u = 65 ksi
Maximum F y / Fu = 0.85
Strategies for Improved Performance of MomentConnections:
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Connections:
Connection Design
• Improved Weld Access Hole Geometry
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Improved Weld AccessHole
See Figure 11-1 in the2005 AISC Seismic Provisions for dimensionsand finish requirements
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Strategies for Improved Performance of MomentConnections:
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Connections:
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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Proprietary Connections
SIDE PLATE
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SIDE PLATECONNECTION
SLOTTED WEB
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SLOTTED WEBCONNECTION
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Connections Investigated ThroughSAC-FEMA Research Program
Reduced BeamSection
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Section
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WeldedUnreinforcedFlange - BoltedWeb
WeldedUnreinforced
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Flange - WeldedWeb
Free Flange
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Free FlangeConnection
Welded FlangePlate Connection
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Plate Connection
Bolted UnstiffenedEnd Plate
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End Plate
Bolted StiffenedEnd Plate
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Bolted FlangePlate
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Double Split Tee
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Double Split Tee
Results of SAC-FEMA Research ProgramR d d S i i D i C it i
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Recommended Seismic Design Criteriafor Steel Moment Frames
• FEMA 350Recommended Seismic Design Criteria for New Steel Moment-Frame Buildings
• FEMA 351Recommended Seismic Evaluation and Upgrade Criteria for Existing 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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FEMA 350
Moment Resisting Frames
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• Definition and Basic Behavior of Moment ResistingFrames
• Beam-to-Column Connections: Before and After
Northridge
• Panel-Zone Behavior
• AISC Seismic Provisions for Special Moment Frames
Column Panel Zone
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Colum n Panel Zon e: - subject to high shear - shear yielding and large
shear deformations possible(forms “shear hinge”)
- provides alternate yieldingmechanism in a steel momentframe
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Joint deformationdue to panel zoneshear yielding
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Plastic Shear HingesIn Column Panel Zones
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"kink" at corners of panel zone
400C i RBS S i i h
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-400
-300
-200
-100
0
100
200
300
-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
1200Composite RBS Specimen with
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-1200
-800
-400
0
400
800
-0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08
Panel Zone g (rad)
P a n e
l Z o n e
S h e a r
F o r c e
( k i p s )
Weak Panel Zone
g
Observations on Panel Zone Behavior
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Observations on Panel Zone Behavior
• Very high ductility is possible.
• Localized deformations (“kinking”) at corners of panelzone may increase likelihood of fracture in vicinity of beam flange groove welds.
• Building code provisions have varied greatly on panelzone design.
• Current AISC Seismic Provisions permits limited
yielding in panel zone.• Further research needed to better define acceptable
level of panel zone yielding
Moment Resisting Frames
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• Definition and Basic Behavior of Moment ResistingFrames
• Beam-to-Column Connections: Before and After
Northridge
• 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)
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p ( )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
AISC Seismic Provisions - SMF 9.1 Scope
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Special moment frames (SMF) are expected to withstandsignificant inelastic deformations when subjected to theforces resulting from the motions of the designearthquake.
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AISC Seismic Provisions - SMF - Beam-to-Column Connections9.2a Requirements
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Beam-to-column connections shall satisfy the following three
requirements:
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, shall
equal 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 three
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requirements (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
Required Shear Strength of Beam-to-Column Connection
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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 ] / L h + V gravity
V u V u
AISC Seismic Provisions - SMF - Beam-to-Column Connections9.2b Conformance Demonstration
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Demonstrate conformance with requirements of Sect. 9.2a by one of
the 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 other
documented test programs), where the test specimens arerepresentative of project conditions.
9.2b Conformance Demonstration
Demonstrate conformance with requirements of Sect 9 2a by one of
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Demonstrate conformance with requirements of Sect. 9.2a by one of the 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.
9.2b Conformance Demonstration - by Testing
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Test connectionin accordancewith Appendix S
Appendix SQualifying Cyclic Tests of Beam-to-Column
and Link-to-Column Connections
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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 depth of prototype beam- wt. per ft. of test beam ≥ 0.75 wt. per ft. of prototype beam
- depth of test column ≥ 0.90 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):
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• Lateral bracing in test specimen should be similar to prototype.• Connection configuration used for test specimen must match
prototype.
• Welding processes, procedures, electrodes, etc. used for test
specimen must be representative of prototype.
See Ap pendix S for o th er requirements .
Typical Test Subassemblages
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Exterior Subassemblage Interior Subassemblage
Typical Exterior Subassemblage
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Δ
Lbeam
Interstory Drift Angle = Δ Lbeam
Typical Exterior Subassemblage
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Δ Typical Interior Subassemblage
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Hcolumn
Interstory Drift Angle = Δ
Hcolumn
Typical Interior Subassemblage
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Appendix S
Testing Requirements - Loading History
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Apply the following loading history:6 cycles at = 0.00375 rad.
6 cycles at = 0.005 rad.
6 cycles at = 0.0075 rad.
4 cycles at = 0.01 rad.
2 cycles at = 0.015 rad.
2 cycles at = 0.02 rad.
2 cycles at = 0.03 rad.2 cycles at = 0.04 rad.
continue at increments of 0.01 rad, with twocycles of loading at each step
Appendix S Testing Requirements - Loading History
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-0.05
-0.04
-0.03
-0.02
-0.010
0.01
0.02
0.03
0.040.05
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
Example of Successful Conformance Demonstration Testper Appendix S:
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-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
9.2b Conformance Demonstration........by use of Prequalified Connection
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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 for
Special Moment Frame Connections
9.2b Conformance Demonstration .....by use of Prequalified Connection
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Requirements for Prequalification of Connections:Appendix P - Prequalification of Beam-to-Column
and Link-to-Column Connections
Authority to Prequalify of Connections:AISCConnection Prequalification Review Panel (CPRP)
Information on Prequalified Connections:Standard ANSI/AISC 358 - "Prequalified Connections for Special and Intermediate Steel Moment Frames for Seismic Applications "
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ANSI/AISC 358 - "Prequalified Connections for Special and I di S l M F f S i i A li i "
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Intermediate 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
Reduced Beam Section (RBS) Moment Connection
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RBS Concept:
• Trim Beam Flanges Near Connection
• Reduce Moment atConnection
• Force Plastic Hinge Awayfrom Connection
Example of laboratory performance of an RBS connection:
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Whitewashed connection prior to testing:
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Whitewashed connection prior to testing:
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Connection at 0.02 radian......
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Connection at 0.02 radian......
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Connection at 0.03 radian......
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Connection at 0.04 radian......
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3000
4000
5000
Mp
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-5000
-4000
-3000
-2000
-1000
0
1000
2000
3000
-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
ANSI/AISC 358:
Prequalification Requirements for RBS in SMF
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• Beam depth: up to W36• Beam weight: up to 300 lb/ft
• Column depth: up to W36 for wide-flange
up 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 SMF
cont......
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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 weldbacking 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.)
RBS with welded web
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RBS with welded web
connection:
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Examples of RBS Connections.....
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AISC Seismic Provisions - SMF - Panel Zone Requirements9.3a Shear Strength
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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.
Panel Zone Shear Strength (cont)
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M pr-2 M pr1
V beam-2
V beam-1
Beam 1 Beam 2
Plastic Hinge Location
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 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)
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Panel Zone Shear Strength (cont)
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c
f b
f u V
t d
M R Panel Zone Required Shear Strength =
Panel Zone Shear Strength (cont)
Panel Zone Design Requirement:
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Panel Zone Design Requirement:
R u v R v wh ere v = 1.0
R v = nominal shear strength, basedon a limit state of shear yielding, ascomputed per Section J10.6 of the
AISC Specification
Panel Zone Shear Strength (cont)
To compute nominal shear strength, R v , of panel zone:
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When P u 0.75 P y in column:
pc b
2 cf cf
pc y v
t d d
t b31t d F 6 .0 R
(AISC Spec EQ J10-11)
Where: d c = column depth
d b = beam depth
bcf = column flange width
t cf = column flange thickness
F y = minimum specified yield stress of column web
t p = thickness of column web including doubler plate
Panel Zone Shear Strength (cont)
To compute nominal shear strength, R v , of panel zone:
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When P u > 0.75 P y in column (not recommended) :
y
u
pc b
2 cf cf pc y v P
P 2 .19.1t d d t b31t d F 6 .0 R (AISC Spec EQ J10-12)
If shear strength of panel zone is inadequate:
- Choose column section with larger web area
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- Weld doubler plates to column
Options for Web Doubler Plates
AISC Seismic Provisions - SMF 9.4 Beam and Column Limitations
Beam and column sections must satisfy the width-
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y
thickness limitations given in Table I-8-1
y
s
f
f
F E 30 .0
t 2 b
Beam Flanges
Beam Web
y
s
w F E
45 .2 t h
≤
b f
t f
h
t w
Column Flanges sf E 30 .0
b ≤
9.4 Beam and Column Limitations
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y f F t 2
Column Web
125 .0 P
P
y
u ≤
y
u
y
s
w P
P 54.11
F
E 14.3
t
h
≤
125 .0
P
P
y
u
y
s
y
u
y
s
w F E
49.1P
P 33.2
F E
12 .1t h
Note: Column flange and web slenderness limits can be taken as p in AISCSpecificationTable B4.1, if the ratio for Eq. 9-3 is greater than 2.0
AISC Seismic Provisions - SMF 9.5 Continuity Plates
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Continuity Plates
9.5 Continuity Plates
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Continuity Plates
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AISC Seismic Provisions - SMF 9.5 Continuity Plates
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Continuity plates shall be consistent with therequirements of a prequalified connection as specified inANSI/AISC 358 (Prequalified Connections for Special and Intermediate 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:
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Continuity plates are required, unless:
yc yc
ybybbf bf cf F R
F R t b8 .14.0 t
6 b
t bf cf
and
t cf = column flange thickness
bbf = beam flange width
t bf = beam flange thickness
ANSI/AISC 358 -Continuity Plate Requirements
For Box Columns:
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Continuity Plates
For Box Columns:
Continuity plates must be provided.
ANSI/AISC 358 -Continuity Plate Requirements
Required thickness of continuity plates
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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 the
column
For other design, detailing and welding requirements for continuity plates - See ANSI/AISC 358
t
ANSI/AISC 358 -Continuity Plate Requirements
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t cp
t bf t cp ≥ 1/2 t bf
t cp
ANSI/AISC 358 -Continuity Plate Requirements
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p
t bf-2 t bf-1
t cp ≥ larger of ( t bf-1 and t bf-2 )
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AISC Seismic Provisions - SMF 9.6 Column-Beam Moment Ratio
Section 9.6 requires strong column - weak girder design for SMF (with a few exceptions)
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design for SMF (with a few exceptions)
Purpose of strong column -weak girder requirement:
Prevent Soft Story Collapse
AISC Seismic Provisions - SMF 9.6 Column-Beam Moment Ratio
The following relationship shall be satisfied at beam-to-l ti
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column connections:
0 .1M
M * pb
* pc Eqn. (9-3)
9.6 Column-Beam Moment Ratio
0 .1M
M * pb
* pc
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pb
* pc M the sum of the moments in the column above and below the joint at
the intersection of the beam and column centerlines.∑M *
pc is determined by summing the projections of thenominal
flexural strengths of the columnsabove 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 )
* pbM 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 theexpected
flexural strengths of the beamsat the plastic hinge locations to thecolumn centerline.
C ColumnL0 .1M M
* pb
* pc
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C BeamL
M* pc-top
M* pc-bottom M* pb-left
M* pb-right
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
V beam-right
Left Beam Right Beam
Plastic Hinge Location
Computing M* pb
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M pr-right M pr-left
beam right
V beam-left Plastic Hinge Location
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-r ight
s h+d col /2
M* pb = M pr + V beam (s h + d col /2 )
Top Column
Computing M* pc M pc- top
M* pc- top
V col-top
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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 interaction
equations for a fully plastic cross-section]V col = column shear - compute from statics, based on assumed location of column inflectio
points (usually midheight of column)
M* pc-bot tom
M* pc = M pc + V col (d beam /2 )
M pc-bot tom
d beam
V col-bottom
AISC Seismic Provisions - SMF 9.8 Lateral Bracing of Beams
Must provide adequate lateral bracing of beams in SMF
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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: b
r
L
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y r
L b = dis tanc e betw een beam lateral br aces
r y = w eak axis radius o f gyrat ion
L b L b
Beam lateral braces (top & bottom flanges)
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Effect of Lateral Torsional Buckling on Flexural Strength and Ductility:
M
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M
M p
Increasing L b / r y
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AISC Seismic Provisions - SMF 9.8 Lateral Bracing of Beams
In addition to lateral braces provided as a maximum spacing
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of 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 hinge
will form.
The placement of lateral braces shall be consistent with that specified inANSI/AISC 358 for aPrequalified Connection , or as otherwise determined
by qualification testing.
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ANSI/AISC 358 -Lateral Bracing Requirements for the RBS
For beams with an RBS connection:
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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 of the RBS cut, at the end farthest from the column face.
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Section 9Special Moment Frames (SMF)
9.1 Scope
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9.2 Beam-to-Column Joints and Connections9.3 Panel Zone of Beam-to-Column Connections
9.4 Beam and Column Limitations
9.5 Continuity Plates9.6 Column-Beam Moment Ratio
9.7 Lateral Bracing of at Beam-to-Column