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.