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PEER 2002 PEER Annual Meeting PEER 2002 Annual Meeting Ian Robertson University of Hawaii

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Objective Development of a load-deformation hysteretic model for slab-column connections of varying dimensions, reinforcement arrangements, gravity loads, and lateral loading routines. Specific reference to non-ductile specimens with discontinuous slab reinforcement.

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RC Floor Systems

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Punching Shear Failure No Continuity Reinforcement

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Approach Task 1: Assemble Web Database Task 2: Fabricate and test 6 non-ductile interior connections Task 3: Develop backbone curve parameters Task 4: Develop hysteretic model Task 5: Validate hysteretic model

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Non-Ductile Specimen tests Six specimens fabricated Three tested with varying gravity load levels V g /V o = 0.2, 0.28, 0.47 Three with varying slab reinforcement ratios = 0.3, 0.5 & 0.8% top reinforcement One specimen with bent-up bars

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Test Setup

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Varying gravity shear ratio TOP BOTTOM

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ND1: Non-ductile V g /V o = 0.2 SLAB PUNCH

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ND1: V g /V o = 0.2 SLAB PUNCH

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ND4: Non-ductile, V g /V o = 0.28 ZERO RESIDUAL STRENGTH PUNCHING FAILURE

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ND4: V g /V o = 0.28

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ND5: Non-ductile, V g /V o =0.47 PUNCHING FAILURE ZERO RESIDUAL STRENGTH

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ND5: V g /V o =0.47 TRANSVERSE BOTTOM REINF.

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Varying Gravity Shear Ratio

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Low reinforcement ratio BOTTOMTOP

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Low reinforcement ratio PUNCHING FAILURE ZERO RESIDUAL STRENGTH

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High reinforcement ratio TOPBOTTOM

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High reinforcement ratio PUNCHING FAILURE

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Reinforcement ratio comparison

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Bent-up bars TOP BOTTOM

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Bent-up bars PUNCHING FAILURE RESIDUAL STRENGTH

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Comparison

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Bent-up Bars

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Critical Limit States for Flat Slab Response

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FEMA 273 Backbone Curve

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Limit States Significant Cracking No Repair Required Repairable Cracking Major Reconstruction Punching Failure

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FEMA 273 Backbone

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Typical Interior Connection

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Backbone Curve Parameters

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Initial Stiffness

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FEMA 273: –Based on gross section modulus of one third slab width (uncracked). Proposed: –Based on cracked section modulus of one third slab width. for width

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Peak Lateral Load Capacity

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FEMA 273: –Based on flexural capacity, M n, of c 2 +5h slab width, divided by f where c 2 is the column width perpendicular to the applied lateral load h is the overall slab thickness f is the portion of unbalanced moment transferred by flexure according to the ACI 318 design approach.

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Peak Lateral Load Capacity Proposed: –Based on flexural capacity of c 2 +5h slab width using 1.25f y, divided by f –Overestimated for heavily reinforced slabs –Neglect reinforcement in excess of = 0.0065 –Discontinuous bottom reinforcement included proportional to development length beyond face of column.

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FEMA 356 Modification

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Peak Lateral Load Capacity

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Stiffness Degradation

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Stiffness Model

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Stiffness Degradation

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Drift Capacity FEMA 273: –Specify Plastic Rotation Angle beyond Yield point, a

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Drift Capacity FEMA 273: –Plastic Rotation Angle, a, depends on V g /V o V g = Gravity shear acting on slab critical section as defined by ACI 318 V o = direct punching shear strength as defined by ACI 318

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Maximum Drift Level Proposed Model: –Based on proposal by Hueste and Wight –Maximum drift level related to V g /V o –Based on prior test results for connections failing in punching shear Slab Shear Reinforcement –Connections with adequate shear reinforcement will not experience shear failure –Gradual strength decay after peak lateral load

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Prior test data

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Drift < 0.5%

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Pan and Moehle

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Maximum Drift Level

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Hueste and Wight

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Recent data points

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Proposed Model

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Residual Strength FEMA: –20% of peak lateral load strength Proposed: –20% of peak lateral load strength for connections with continuity reinforcement –0 for connections without continuity reinforcement

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Example Backbone Output

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Example Hysteretic Output

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Model Verification Comparison with data from tests performed at other universities Comparison with data from PEER non- ductile tests Verification of the models predicted energy dissipation to the measured energy dissipation

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Robertson and Durrani Specimen

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Test Setup

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Backbone Comparison

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Hysteretic Comparison

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Hwang-Moehle Specimen

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Hwang-Moehle Specimen - Plan N-S E-W

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Hwang-Moehle Specimen - Elev.

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Typical Interior Connection

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Summary Pre-1970 non-ductile specimens more appropriately referred to as non-continuity connections. Propose conservatism in estimating drift limit for punching shear of such connections. High gravity shear ratio produces non-ductile response. Develop backbone and hysteretic model for interior and exterior connections, both perpendicular and parallel to edge, including various connection parameters. Propose revised limit states for FEMA 273 (356) slab- column connection response.

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