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

© 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential 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. © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

© 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential 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 © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Reinforcement Detail (Full-scale Frame) © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Reinforcement Detail (Test Frame) © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

© 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential Test Frame Glass Column © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

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? © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

© 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential 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 © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

© 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential 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 © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

© 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential 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 © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

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 © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

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 © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

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 © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

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 © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

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 © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

© 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential 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 0.90-1.15 times the nominal values Initial and post yield stiffness, ki, ky 0.90-1.10 times the nominal values Elastic modulus of concrete, Ec 0.95-1.05 times the experimentally tested values © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

© 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential 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 © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

© 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential Dynamic Test © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

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) 0.22 in. (5.6 mm) Peak Static Displacement Calculated (Mean) Measured 0.3 in. (7.6 mm) 0.20 in. (5.1 mm) © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Analytically Calculated Crack Locations after Column Removal © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Cracking at Beam-Column Joint Model able to determine location and pattern of first cracking © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Most Probable Failure Sequence © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Most Probable Failure Sequence 12 11 9 6 1 2 10 7 3 4 5 8 A B C D E © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Location of First Visually Observed Crack © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

Pull Down Test (at 3.5 in. Displacement) © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

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) © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

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 © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

© 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential 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. © 2007 Simpson Gumpertz & Heger Inc. Proprietary and Confidential

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