1. Ömer O. Erbay & Ahmet Çıtıpıtıoğlu 25 April 2008
Progressive Collapse Resistance Competition entry by, Simpson Gumpertz & Heger
Ömer O. Erbay & Ahmet Çıtıpıtıoğlu
25 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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4. Reinforcement Detail (Full-scale Frame)
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5. Reinforcement Detail (Test Frame)
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Test Frame
Glass Column
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7. 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
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
Concrete
2D Solid Elements
Reinforcement
Truss Elements
Detailed Continuum Model
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11. Modeling Concrete Behavior (1)
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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12. Modeling Concrete Behavior (2)
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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13. Modeling Concrete Behavior (3)
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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14. Parametric Frame Model
Distance from column centerline to the location of plastic hinge, dp
Rigid plastic hinges (M-qp)
Effective length of plastic hinge, lp
Rigid
offsets
Elastic beam elements
Spring for stabilization
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15. Modeling and Model Parameters (Cont.)
Beam Section Parameters
Effective depth to top or bottom
reinforcement, deff
Plastic Hinge Parameters (lumped plastic hinge model) M M M k2
k3/lp k1 f fp qp
Moment – Curvature
From section analysis using RESPONSE2000
Moment – Plastic Curvature
Derived from
Moment – Curvature
Moment – Plastic Rotation
Derived from
Moment – Plastic Curvature
relationship
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Uncertain Parameters
Plastic hinge locations, dp
Uniform
1.25”-6.25” where there is extra #7 (f 0.110”) rebar at the connection 1.25”-2.5” where there is no extra #7 (f 0.110”) rebar at the connection
Plastic hinge length, lp
0.5db – 0.75db
Yield and ultimate moment capacities, My & Mu
times the nominal values
Initial and post yield stiffness, ki, ky
times the nominal values
Elastic modulus of concrete, Ec
times the experimentally tested values
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Loading Sequence
0.2
Apply gravity (self weight of frame and attached masses)
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)
5.0
If frame not collapsed  switch to static analysis
6.0
Unload attached masses
8.0
Pull down on center column
7.0
Load magnitude
Time, s
Dynamic Analysis
Static Analysis
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Dynamic Test
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19. Dynamic Displacement Time-History of the Center Column
Calculated Displacement Time-History
Measured Displacement Time-History
Peak Dynamic Displacement
Calculated (Mean) Measured
0.4 in. (10 mm) in. (5.6 mm)
Peak Static Displacement
Calculated (Mean) Measured
0.3 in. (7.6 mm) in. (5.1 mm)
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20. Analytically Calculated Crack Locations after Column Removal
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21. Cracking at Beam-Column Joint
Model able to determine location and pattern of first cracking
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22. Most Probable Failure Sequence
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23. Most Probable Failure Sequence12 11 9 6 1 2 10 7 3 4 5 8 A B C D E
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24. Location of First Visually Observed Crack
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25. Pull Down Test (at 3.5 in. Displacement)
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26. Pull Down Force-Displacement Curve (Frame Model)
Calculated Pull-Down Force-Displacement Curve
Measured Pull-Down Force-Displacement
Ultimate Pull-Down Force
Measured
1800 lb
Calculated (Mean)
2000 lb (frame model)
1700 lb (continuum model)
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27. 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 lb
Where will be the first rebar rupture?
Measured: Grid D Calculated: Grid B-2 or D-2
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Concluding Remarks
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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Thank You
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