Download - PEER 2002 PEER Annual Meeting PEER 2002 Annual Meeting Ian Robertson University of Hawaii
PPEEEERR
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
Vg/Vo = 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” Vg/Vo = 0.2
-10
-8
-6
-4
-2
0
2
4
6
8
10
-10 -8 -6 -4 -2 0 2 4 6 8 10
Drift (%)
Lateral Load (kips)
ND1C Vg/Vo = 0.20
SLAB PUNCH
ND1: Vg/Vo = 0.2
SLAB PUNCH
ND4: “Non-ductile”, Vg/Vo = 0.28
-10
-8
-6
-4
-2
0
2
4
6
8
10
-10 -8 -6 -4 -2 0 2 4 6 8 10
Drift (%)
Lateral Load (kips)
ND4LL Vg/Vo = 0.28
ZERO RESIDUAL
STRENGTH
PUNCHINGFAILURE
ND4: Vg/Vo = 0.28
ND4: Vg/Vo = 0.28
ND5: “Non-ductile”, Vg/Vo=0.47
-10
-8
-6
-4
-2
0
2
4
6
8
10
-10 -8 -6 -4 -2 0 2 4 6 8 10
Drift (%)
Lateral Load (kips)
ND5XL Vg/Vo = 0.47
PUNCHINGFAILURE
ZERO RESIDUAL STRENGTH
ND5: Vg/Vo=0.47
TRANSVERSE BOTTOM REINF.
Varying Gravity Shear Ratio
-10
-8
-6
-4
-2
0
2
4
6
8
10
-10 -8 -6 -4 -2 0 2 4 6 8 10
Drift (%)
Lateral Load (kips)ND1C Vg/Vo = 0.20
ND4LL Vg/Vo = 0.28
ND5XL Vg/Vo = 0.47
Bent-up bars
TOP BOTTOM
Bent-up bars
-10
-8
-6
-4
-2
0
2
4
6
8
10
-10 -8 -6 -4 -2 0 2 4 6 8 10
Drift (%)
Lateral Load (kips)
ND1C Control
ND8B Bent-up Bars
PUNCHINGFAILURE
RESIDUAL STRENGTH
Bent-up Bars
Critical Limit Statesfor
Flat Slab Response
FEMA 273 Backbone Curve
Joint Rotation, θ
/P P
ce
1.0a
b
Limit States
Joint Rotation, ?
/P P
ce
Significant Cracking
No Repair Required
Repairable Cracking
Major Reconstruction
Punching Failure
FEMA 273 Backbone
-10
-8
-6
-4
-2
0
2
4
6
8
10
-6 -4 -2 0 2 4 6
Drift (%)
Lateral Load (kips) Hysteretic Response
Backbone Curve
FEMA 273 Backbone
Center Connection
FEMA 273 Backbone
-10
-8
-6
-4
-2
0
2
4
6
8
10
-6 -4 -2 0 2 4 6
Drift (%)
Load (kips)
Hysteretic Response
Backbone Curve
FEMA 273 Backbone
Typical Interior Connection
Drift (%)
Lateral Load
Peak Lateral Load
Punching Shear
Failure
Peak Lateral Load
Backbone Curve Parameters
Drift (%)
Lateral Load
Backbone Envelope
Backbone Envelope
Drift (%)
Lateral Load
Initial Stiffness
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
12
)3/( 32 dl
I =
crII = 3/2l
Peak Lateral Load Capacity
Drift (%)
Lateral Load
Peak Lateral Load Capacity
• FEMA 273:– Based on flexural capacity, Mn, of c2+5h slab
width, divided by f
• where c2 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 c2+5h slab width
using 1.25fy, 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.
FEMA 356 Modification
Joint Rotation, ?
/Q Q
y
1.0
a
b
Peak Lateral Load Capacity
Estimated Peak Load vs. Observed Peak Load (P est/Pu)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Specimen
Pest
/Pu
Johnson 2000
Lee 1999
Robertson 1992
Hwang 1990
Average = 0.96
Stiffness Degradation
Drift (%)
Lateral Load
Stiffness Model
Stiffness Degradation
Interior Connection - Normalized EI vs. %Drift
y = -0.22Ln(x) + 0.673
R2 = 0.9955
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Drift (%)
Normalized EI
Lee 2CS
Lee 3SL
Lee 4HS
Lee Ave
Drift Capacity
• FEMA 273:– Specify Plastic Rotation Angle beyond “Yield point”, a
Joint Rotation, θ
/P P
ce
1.0a
b
Drift Capacity
• FEMA 273:– Plastic Rotation Angle, a, depends on Vg/Vo
0
0.2
0.4
0 0.02
Plastic Rotation, a (Radians)
Gravity Shear Ratio, V
g/Vo• Vg = Gravity shear acting on slab
critical section as defined by ACI 318
• Vo = 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 Vg/Vo
– 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
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0 0.5 1 1.5 2 2.5 3 3.5 4
Drift Capacity (%)
Gravity Shear Ratio (V
g/Vo)
Dilger and Cao
Durrani and Du
Farhey et al.
Ghali et al.
Hanson and Hanson
Hawkins et al.
Hwang and Moehle
Islam and Park
Luo and Durrani
Megally and Ghali
Pan and Moehle
Robertson and Durrani
Symonds et al.
Wey and Durrani
Zee and Moehle
Drift < 0.5%
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0 0.5 1 1.5 2 2.5 3 3.5 4
Drift Capacity (%)
Gravity Shear Ratio (V
g/Vo)
Dilger and Cao
Durrani and Du
Farhey et al.
Ghali et al.
Hanson and Hanson
Hawkins et al.
Hwang and Moehle
Islam and Park
Luo and Durrani
Megally and Ghali
Pan and Moehle
Robertson and Durrani
Symonds et al.
Wey and Durrani
Zee and Moehle
Pan and Moehle
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0 0.5 1 1.5 2 2.5 3 3.5 4
Drift Capacity (%)
Gravity Shear Ratio (V
g/Vo)
Dilger and Cao
Durrani and Du
Farhey et al.
Ghali et al.
Hanson and Hanson
Hawkins et al.
Hwang and Moehle
Islam and Park
Luo and Durrani
Megally and Ghali
Pan and Moehle
Robertson and Durrani
Symonds et al.
Wey and Durrani
Zee and Moehle
Pan and Moehle
Maximum Drift Level
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0 0.5 1 1.5 2 2.5 3 3.5 4
Drift Capacity (%)
Gravity Shear Ratio (V
g/Vo)
Dilger and Cao
Durrani and Du
Farhey et al.
Ghali et al.
Hanson and Hanson
Hawkins et al.
Hwang and Moehle
Islam and Park
Luo and Durrani
Megally and Ghali
Pan and Moehle
Robertson and Durrani
Symonds et al.
Wey and Durrani
Zee and Moehle
Hueste and Wight
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0 0.5 1 1.5 2 2.5 3 3.5 4
Drift Capacity (%)
Gravity Shear Ratio (V
g/Vo)
Dilger and Cao
Durrani and Du
Farhey et al.
Ghali et al.
Hanson and Hanson
Hawkins et al.
Hwang and Moehle
Islam and Park
Luo and Durrani
Megally and Ghali
Pan and Moehle
Robertson and Durrani
Symonds et al.
Wey and Durrani
Zee and Moehle
Hueste and Wight
Recent data points
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0 0.5 1 1.5 2 2.5 3 3.5 4
Drift Capacity (%)
Gravity Shear Ratio (V
g/Vo)
Prior Research
Lee and Robertson
Johnson and Robertson
Hueste and Wight
Proposed Model
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0 0.5 1 1.5 2 2.5 3 3.5 4
Drift Capacity (%)
Gravity Shear Ratio (V
g/Vo)
Prior Research
Lee and Robertson
Johnson and Robertson
Hueste and Wight Model
for connections with continuity reinforcement
Proposed Model for
connections without continuity reinforcement
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 OutputLee-UH (Specimen 4HS)
Isolated Interior Connection
-12
-8
-4
0
4
8
12
-10 -8 -6 -4 -2 0 2 4 6 8 10
Drift (%)
Lateral Load (kips)Actual Hysteretic Response
Actual Backbone
Predicted Backbone
Example Hysteretic Output
Lee-UH (Specimen 4HS)Isolated Interior Connection
-12
-8
-4
0
4
8
12
-10 -8 -6 -4 -2 0 2 4 6 8 10
Drift (%)
Lateral Load (kips)Actual Hysteretic Response
Actual Backbone
Predicted Backbone
Predicted Hysteretic Response
Model Verification
• Comparison with data from tests performed at other universities
• Comparison with data from PEER “non-ductile” tests
• Verification of the model’s predicted energy dissipation to the measured energy dissipation
Robertson and Durrani Specimen
Test Setup
Backbone ComparisonRobertson and Durrani (Specimen 5SO)
Interior Connection
-12
-8
-4
0
4
8
12
-10 -8 -6 -4 -2 0 2 4 6 8 10
Drift (%)
Lateral Load (kips)Actual Hysteretic Response
Actual Backbone
Predicted Backbone
Hysteretic ComparisonRobertson and Durrani (Specimen 5SO)
Interior Connection
-12
-8
-4
0
4
8
12
-10 -8 -6 -4 -2 0 2 4 6 8 10
Drift (%)
Lateral Load (kips)Actual Hysteretic Response
Actual Backbone
Predicted Backbone
Predicted Hysteretic Response
Hwang-Moehle Specimen
Hwang-Moehle Specimen - Plan
N-S
E-W
Typical Interior Connection
Hwang-Berkeley (Specimen B3EW)Interior Connection
-6
-4
-2
0
2
4
6
-6 -4 -2 0 2 4 6
Drift (%)
Lateral Load (kips)Actual Hysteretic Response
Actual Backbone
Predicted Backbone
Predicted Hysteretic Response
Typical Interior ConnectionHwang-Berkeley (Specimen B3NS)
Interior Connection
-6
-4
-2
0
2
4
6
-6 -4 -2 0 2 4 6
Drift (%)
Lateral Load (kips)Actual Hysteretic Response
Actual Backbone
Predicted Backbone
Predicted Hysteretic Response
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.