Www.sgh.com DESIGN INVESTIGATE REHABILITATE Progressive Collapse Resistance Competition entry by, Simpson Gumpertz & Heger Ömer O. Erbay & Ahmet Çıtıpıtıoğlu.

www.sgh.com

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Progressive CollapseResistance Competition

entry by,

Simpson Gumpertz & Heger

Ömer O. Erbay & Ahmet Çıtıpıtıoğlu25 April 2008

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

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


Reinforcement Detail (Full-scale Frame)


Reinforcement Detail (Test Frame)


Test Frame


Glass Column

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?


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


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


Continuum Model


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

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



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



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

Elastic beam elements

Parametric Frame Model


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)

Modeling and Model Parameters (Cont.)


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

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

0.2

Apply gravity (self weight of frame and attached masses)

Loading Sequence


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

Dynamic Displacement Time-History of the Center Column


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

Analytically Calculated Crack Locations after Column Removal


Cracking at Beam-Column Joint


Model able to determine location and pattern of first cracking

Most Probable Failure Sequence


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

Most Probable Failure Sequence


A B C D E

1 2

3 4

5 8

10 7

9 6

1112

Location of First Visually Observed Crack


Pull Down Test (at 3.5 in. Displacement)


Pull Down Force-Displacement Curve (Frame Model)


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)

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


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.


Thank You

Www.sgh.com DESIGN INVESTIGATE REHABILITATE Progressive Collapse Resistance Competition entry by, Simpson Gumpertz & Heger Ömer O. Erbay & Ahmet Çıtıpıtıoğlu.

Documents

confidential slide

simpson gumpertz heger

concrete cracking

mass slide

test frame

exterior frame

fullscale frame

confidential smeared