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

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.

RC Floor Systems

Punching Shear Failure No Continuity Reinforcement

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

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

Test Setup

Varying gravity shear ratio TOP BOTTOM

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

ND1: V g /V o = 0.2 SLAB PUNCH

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

ND4: V g /V o = 0.28

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

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

Varying Gravity Shear Ratio

Low reinforcement ratio BOTTOMTOP

Low reinforcement ratio PUNCHING FAILURE ZERO RESIDUAL STRENGTH

High reinforcement ratio TOPBOTTOM

High reinforcement ratio PUNCHING FAILURE

Reinforcement ratio comparison

Bent-up bars TOP BOTTOM

Bent-up bars PUNCHING FAILURE RESIDUAL STRENGTH

Comparison

Bent-up Bars

Critical Limit States for Flat Slab Response

FEMA 273 Backbone Curve

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

FEMA 273 Backbone

Typical Interior Connection

Backbone Curve Parameters

Initial Stiffness

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

Peak Lateral Load Capacity

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.

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 = –Discontinuous bottom reinforcement included proportional to development length beyond face of column.

FEMA 356 Modification

Peak Lateral Load Capacity

Stiffness Degradation

Stiffness Model

Stiffness Degradation

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

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

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

Prior test data

Drift < 0.5%

Pan and Moehle

Maximum Drift Level

Hueste and Wight

Recent data points

Proposed Model

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

Example Backbone Output

Example Hysteretic Output

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

Robertson and Durrani Specimen

Test Setup

Backbone Comparison

Hysteretic Comparison

Hwang-Moehle Specimen

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

Hwang-Moehle Specimen - Elev.

Typical Interior Connection

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.