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DESIG
NIN
VE
STIG
AT
ER
EH
AB
ILIT
AT
E
Progressive CollapseResistance Competition
entry by,
Simpson Gumpertz & Heger
Ömer O. Erbay & Ahmet Çıtıpıtıoğlu25 April 2008
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Objective
• The objective of this investigation was to predict the progressive collapse response of a 1/8th scale reinforced concrete frame, which was designed and tested by Northeastern University, using analytical methods.
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Frame Design
• The reinforced concrete frame is the exterior frame of a building located in Memphis, TN (Seismic Category D).
• Designed and detailed to satisfy ACI-318 integrity and special moment frame requirements.
• Loads:– LL = 70 psf– DL = 100 psf (including the partitions) – Exterior nonstructural walls: 100 plf– Total weight of the building
for seismic calculation = 2770 kips
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Reinforcement Detail (Full-scale Frame)
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Reinforcement Detail (Test Frame)
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Test Frame
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Glass Column
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Competition Questions
• What will be the maximum dynamic displacement after column removal?
• What will be the displacement after system becomes stationary after column removal?
• Will there be any rebar rupture after column removal?
• If the frame does not collapse after column removal, how much load can it sustain before failure?
• What will be the failure mode and failure sequence?
• Where will be the first rebar rupture?
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Challenges
• Cannot make conservative assumptions– Need to precisely estimate the response
• Unknown parameters:– Unknown bond characteristic between reinforcement and
concrete– Uncertain concrete properties– Uncertain construction quality
• Representing loading sequence; dynamic and then quasi-static pull down
• Developing a model that can always converge without user intervention
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Method of Approach
• Detailed Model: Continuum plane stress model to capture localize failure mechanisms, concrete cracking, rebar slippage, and shear failure
• Parametric Model: Lumped-plastic-hinge model with beam elements, used for parametric analyses to determine the distribution of response quantities
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Continuum Model
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Detailed Continuum Model
ReinforcementTruss Elements
Concrete2D Solid Elements
Concrete:– 2D Continuum Plane Stress
elements with Reduced Integration.
– Concrete damaged plasticity with tension stiffening to model post cracking rebar slippage.
Wire rebar:– Embedded Truss elements.– Rate independent metal
plasticity with calibrated hardening.
Self weight and point mass
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Modeling Concrete Behavior (1)
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Smeared Cracking” : cracks enters into these calculations by the way in which the cracks affect the stress and material stiffness associated with the integration point.
Cracking is assumed to occur when the stress reaches a failure surface that is called the “crack detection surface”
Image taken from ABAQUS manual
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Modeling Concrete Behavior (2)
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Concrete behavior is considered independent of the rebar Rebar/concrete interface, such as bond slip and dowel action,
are modeled by “tension stiffening” to simulate load transfer across cracks through the rebar
“Shear Interlock”: as concrete cracks, its shear stiffness is diminished.
Shear modulus is reduced as a function of the opening strain across the crack.
Images taken from “Reinforced Concrete Mechanics and Design” by MacGregor J. G. and Wight J. K. 2005
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Modeling Concrete Behavior (3)
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Concrete Stress Strain Relationship
-8
-7
-6
-5
-4
-3
-2
-1
0
1
-0.007 -0.006 -0.005 -0.004 -0.003 -0.002 -0.001 0 0.001 0.002 0.003
Strain (in/in)
Str
ess
(ksi
)
et*10
et*15
et*5
In the absence of data to calibrate bond slippage “tension stiffening” was modeled as strain softening after failure reducing the stress linearly to zero at a total strain of 5, 10, and 15 times the strain at cracking
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Elastic beam elements
Parametric Frame Model
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Rigid offsets
Distance from column centerline to the location of plastic hinge, dp
Effective length of plastic hinge, lp
Spring for stabilization
Rigid plastic hinges (M-p)
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Modeling and Model Parameters (Cont.)
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Effective depth to top or bottomreinforcement, deff
Beam Section Parameters
M
p
M
k2
k1123 k
1
k
1
k
1
p
M
Moment – CurvatureFrom section analysis
using RESPONSE2000
Moment – Plastic CurvatureDerived from
Moment – Curvature
Moment – Plastic RotationDerived from
Moment – Plastic Curvaturerelationship
Plastic Hinge Parameters (lumped plastic hinge model)
k3/lp
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Uncertain Parameters• Plastic hinge locations, dp
– Uniform
– 1.25”-6.25” where there is extra #7 (0.110”) rebar at the connection 1.25”-2.5” where there is no extra #7 (0.110”) rebar at the connection
• Plastic hinge length, lp
– Uniform
– 0.5db – 0.75db
• Yield and ultimate moment capacities, My & Mu
– Uniform
– 0.90-1.15 times the nominal values
• Initial and post yield stiffness, ki, ky
– Uniform
– 0.90-1.10 times the nominal values
• Elastic modulus of concrete, Ec
– Uniform
– 0.95-1.05 times the experimentally tested values© 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential
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0.2
Apply gravity (self weight of frame and attached masses)
Loading Sequence
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Time, s
Lo
ad m
agn
itu
de
7.0
0.3
Continue analysis to damp-out dynamic effects
0.305
Remove center column in 0.05s
4.0
Continue analysis to damp-out dynamic effects(check whether the frame has collapsed or not)
Dynamic Analysis Static Analysis
5.0
If frame not collapsed switch to static analysis
6.0
Unload attached masses
8.0
Pull down on center column
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Dynamic Displacement Time-History of the Center Column
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Peak Dynamic Displacement Calculated (Mean) Measured0.4 in. (10 mm) 0.22 in. (5.6 mm)
Peak Static DisplacementCalculated (Mean) Measured0.3 in. (7.6 mm) 0.20 in. (5.1 mm)
Calculated Displacement Time-History
Measured Displacement Time-History
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Analytically Calculated Crack Locations after Column Removal
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Cracking at Beam-Column Joint
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Model able to determine location and pattern of first cracking
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Most Probable Failure Sequence
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Run Els_Stff_Pos Els_Stff_Neg UY_Col_Elas UY_Col_Dyn UY_Col_Sta UY_Col_Res Sprn_Force Frame_Stat UY_Col_Fail Force_Max DC_RatioId (lb/in.) (lb/in.) (in.) (in.) (in.) (in.) (lb) (in.) (lb)
36 52168 52164 -0.09 0.00 0.00 0.00 0 Failed 0.00 0 1.00071 48473 48470 -0.10 0.00 0.00 0.00 0 Failed 0.00 0 1.00088 49823 49820 -0.10 0.00 0.00 0.00 0 Failed 0.00 0 1.0001 47581 47577 -0.10 -0.45 -0.43 -0.33 61 Not_Failed -0.98 1845 0.9082 51423 51420 -0.09 -0.32 -0.29 -0.20 47 Not_Failed -0.90 2067 0.8153 48186 48183 -0.10 -0.42 -0.40 -0.30 60 Not_Failed -0.98 1944 0.8684 48612 48608 -0.10 -0.29 -0.26 -0.16 39 Not_Failed -0.92 2173 0.7675 47449 47445 -0.10 -0.33 -0.30 -0.20 44 Not_Failed -0.86 2075 0.7986 50289 50285 -0.10 -0.30 -0.26 -0.16 41 Not_Failed -0.87 2126 0.7857 46767 46764 -0.10 -0.33 -0.30 -0.20 45 Not_Failed -1.02 2146 0.7818 49404 49401 -0.10 -0.36 -0.34 -0.24 51 Not_Failed -0.98 1981 0.8449 46289 46285 -0.10 -0.34 -0.30 -0.20 45 Not_Failed -1.18 2209 0.757
10 48536 48532 -0.10 -0.35 -0.33 -0.23 48 Not_Failed -0.87 1937 0.856
Failure Sequence1_1 1_2 1_3 1_4 1_5 1_6 1_7 1_8 ** 2_1 2_2 2_3 2_4 2_5 2_6 2_7 2_8 ** 3_1 3_2 3_3 3_4 3_5 3_6 3_7 3_8
0 0 0 0 0 0 0 0 ** 0 0 0 0 0 0 0 0 ** 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 ** 0 0 0 0 0 0 0 0 ** 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 ** 0 0 0 0 0 0 0 0 ** 0 0 0 0 0 0 0 00 0 5 10 4 8 0 0 ** 0 0 6 12 11 2 0 0 ** 0 0 1 3 7 9 0 00 0 9 5 1 6 0 0 ** 0 0 3 7 4 2 0 0 ** 0 0 0 8 0 0 0 00 0 0 1 10 11 0 0 ** 0 0 7 4 2 3 0 0 ** 0 0 8 9 6 5 0 00 0 2 7 11 5 0 0 ** 0 0 1 8 6 4 0 0 ** 0 0 10 3 9 12 0 00 0 3 1 6 2 0 0 ** 0 0 9 4 7 5 0 0 ** 0 0 8 0 10 11 0 00 0 2 8 4 6 0 0 ** 0 0 5 7 3 1 0 0 ** 0 0 0 9 10 0 0 00 0 7 5 2 4 0 0 ** 0 0 9 11 3 6 0 0 ** 0 0 10 8 0 1 0 00 0 7 6 8 3 0 0 ** 0 0 5 10 4 9 0 0 ** 0 0 11 2 1 0 0 00 0 9 4 0 11 0 0 ** 0 0 8 2 10 6 0 0 ** 0 0 7 3 1 5 0 00 0 4 1 5 2 0 0 ** 0 0 3 7 12 8 0 0 ** 0 0 6 10 11 9 0 0
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Most Probable Failure Sequence
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A B C D E
1 2
3 4
5 8
10 7
9 6
1112
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Location of First Visually Observed Crack
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Pull Down Test (at 3.5 in. Displacement)
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Pull Down Force-Displacement Curve (Frame Model)
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Calculated Pull-Down Force-Displacement Curve
Measured Pull-Down Force-Displacement
Ultimate Pull-Down Force
Measured1800 lb
Calculated (Mean)2000 lb (frame model)1700 lb (continuum model)
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Summary of Results Comparison• What will be the maximum dynamic displacement after
column removal?Measured: 0.22 in. Calculated: 0.4 in.
• What will be the displacement after system becomes stationary after column removal?Measured: 0.20 in. Calculated: 0.3 in.
• Will there be any rebar rupture after column removal?Measured: No Calculated: No
• If the frame does not collapse after column removal, how much load can it sustain before failure?Measured: 1800 lb Calculated: 1700 lb - 2000 lb
• Where will be the first rebar rupture?Measured: Grid D-2 Calculated: Grid B-2 or D-2
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Concluding Remarks
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Analysis results are extremely sensitive to rebar bond slippage modeling.
Predicted excessive permanent displacements due to rebar slippage, compared to measured -0.2 inches :– -1.7 inches using 15 x et– -8.8 inches using 10 x et
Initial pilot test frame built with plain wire reinforcement (no ribs) resulted with displacements within captured range in the continuum model where rebar slippage was considered.
More detailed modeling possible, but requires more data for more parameters to be calibrated.
More data may introduce more uncertainty and the problem may become unmanageable. A sensitivity analysis can be used to eliminate parameters that do not significantly affect the response parameters.
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