8/12/2019 007 Flores

1/35

Performance of Existing

Reinforced Concrete ColumnsunderBidirectional Shear &

Axial Loading

Laura M. Flores

University of California, San DiegoREU Institution: University of California, Berkeley

REU Advisor: Dr. Jack P. Moehle

Pacif ic Earthquake Engin eering Research Center (PEER)

REU Symposium Kiawah Island Golf Resort - Kiawah, S.C. August 5-8, 2004

8/12/2019 007 Flores

2/35

Outline

Research Background & Project Objectives

Design of Test Setup

RC Column Specimen Material & GeometryCapacity Models

Flexural, Shear and Axial Capacity

MomentCurvature Response of Column

Deformation ComponentsLateral DeformationShear Failure

Axial Deformation

Residual Column Capacity & Damage Progression

Fabrication of RC Column SpecimensSensitivity Analysis

Ongoing

Acknowledgments

8/12/2019 007 Flores

3/35

Research Background

Mechanisms leading to the collapse of existing, pre-seismic codeRC frames are NOT well documented.

Shake table tests are currently being conducted at PEER-UCB toobserve & identify the failure components & load redistributionprocesses in RC bridge columns & in RC building frames under

seismic & gravity loading.Identifying mechanisms causing shear failure in RC columns canbe used to develop performance-based seismic design -strengthen future & existing structures against earthquake

loadingColumn shear failure & its effect on the degradation of axialcapacity in a pre-seismic code RC column is the focus of thisproject.

8/12/2019 007 Flores

4/35

8/12/2019 007 Flores

5/35

Simplified Model of RC Column

One-third scale of existing, pre-seismic ACI codedesigned RC Column

of RC column used in analysis

Free end of column idealized as hinge connectionwith a fixed end at base of column

8/12/2019 007 Flores

6/35

Simplified Model of RC Column (cont.)

RC

Coln

RC

Coln

M = 0

(hinge)

M(x)

M = MMAX(fixed)

8/12/2019 007 Flores

7/35

Design of Test Setup

RC

Coln

Gravity Load

= 10 kips

HINGEActuator / Seismic

Load = 8.3 kips

FIXED

8/12/2019 007 Flores

8/35

Design of Test Setup (cont.)

A

A

1'-5"

CONCRETE

FLOOR

9"x8" flanged beam 70lb/ft.

S=61.5 cu. in.

TEST APPARTUS

base plate 2 in. thickness

15 in.width and 3 ft. length

B

1'-158"2'-9

78"ACTUATOR

POSITION

FRONT VIEW

SIDE VIEW

(H-structure)safety frame

3"x2" angle iron

welded construction

1/2" concreteanchor bolts

( ??2 places??)

4'-778"

6"x3"channel beam

1/2" x 1/2" x 10"

hold-in-place

rods(check

height&spacing?)

4" x 5" x 1" pillow

block - pnt.load

4'-6"

lead ingot-14 bars

110 lb/bar

total wt. 1540 lb.

1'-4 3/8"

(platform

width?)

C

SECTION C-C

4" (add

spacing if

needed)

clamp??

42.25"

8/12/2019 007 Flores

9/35

RC Column Material & Geometry

8/12/2019 007 Flores

10/35

RC Column Material & Geometry (cont.)

8/12/2019 007 Flores

11/35

Capacity Models of RC Column

Specimen:Axial Capacity

Axial Capacity of undamaged RC column:

PN= 0.85*fC*(AgASL) + fYL*ASL

..where fC concrete compressive strength, Ag is the grossconcrete area, ASL is the longitudinal reinforcement area,

fYLis yield strength of longitudinal steel

PN = 0.85*(3ksi)*[36in2-0.884in2] +

(70ksi)*(0.884in2)

PN = 151.43 kips

8/12/2019 007 Flores

12/35

Capacity Models of RC Column

Specimen: Flexural Capacity!cu = .003

!s3

!s2h

!S1 = -00207

N.A.

.85fC

a TS3

TS2

TS1

TS2

TS1

TS3

CC

TS2

TS1

TS3MN

CC

PN

Mh/2 = 0 @Balanced Failure (Z=-1)-TS3*[(h/2)-dS3] - CC*[(h/2)-(a/2)] + MN - TS1*[dS1-(h/2)]

MN

= TS3

*[(h/2)-dS3

] + CC

*[(h/2)-(a/2)] +

TS1*[dS1-(h/2)]

..so, MN =153.3 kip-in

8/12/2019 007 Flores

13/35

Capacity Models of RC Column

Specimen: ShearCapacityTotal shear capacity of an RC column depends on the shearcapacity of the concrete, VC and the shear capacity carried bythe transverse reinforcement, VST in the column

VN= (VC+ VST) = 2*[1+(P/2000*Ag)]*!fC*bW*d +

[(4*AST*fYT*d)/s]

..where AST is the transverse reinforcement area, fYTis yield strength of transverse reinforcement,

d is distance from compression fiber to farthest tensile reinforcement, s is transverse

reinforcement spacing, bW is the width of column x-section, P is axial load

VN = 2*[1+(10,000lb/(2000*35.12in2))]*!(3000psi)*(6in)(5.145in) +

(0.01228in2

)(70,000psi)(5.145in)

VN = 8.283 kips

8/12/2019 007 Flores

14/35

Interaction Diagram of RC Column Specimen

-40

-20

0

20

40

60

80

100

120

0 20 40 60 80 100 120 140 160

(nominal) Moment Capacity, Mn (kip-in)

(nom

inal)A

xialLoadCapacity,

Pn

(kips)

Maximum

Axial Load

Zero stress in tensile

reinforcement, Z=0

Balanced

Failure, Z= -1

TENSION

COMPRESSION

The flexural and axial capacity model for RC columns is used to derive aninteraction diagram which relates the axial load column capacity with itsmoment capacity at any given time

Moment Curvature Response ofShear Critical RC

8/12/2019 007 Flores

15/35

Moment-Curvature Response of Shear-Critical RC

Column under Axial & Lateral (Shear) Loading

The flexural and axial capacity model for RC columns is used to derive an interactiondiagram which relates the axial load column capacity with its moment capacity at anygiven time

0

20

40

60

80

100

120

140

160

-7.E-22

1.E-

04

3.E-

04

4.E-

04

5.E-

04

7.E-

04

8.E-

04

9.E-

04

1.E-

03

1.E-

03

1.E-

03

1.E-

03

2.E-

03

2.E-

03

2.E-

03

2.E-

03

2.E-

03

2.E-

03

2.E-

03

3.E-

03

3.E-

03

3.E-

03

3.E-

03

3.E-

03

3.E-

03

3.E-

03

3.E-

03

4.E-

03

4.E-

03

Curvature, !(1/in)

Moment,M(

kip-in)

MY=VY*l

D f ti C t

8/12/2019 007 Flores

16/35

Deformation Components:

Lateral DeflectionFlexure

M

M !FL = [(39in)2/6]*(7.6*10-4in-1)= 0.19266 in

DeformationComponents:

8/12/2019 007 Flores

17/35

Deformation Components:

Lateral DeflectionFlexure

D f ti C t

8/12/2019 007 Flores

18/35

Deformation Components:

Lateral DeflectionBar (Bond) Slip

M

M !SL = [(39in)(0.375in)(70,000psi)(7.6*10-4

in-1

)] /[8*6*!3000psi]

= 0.2959 in

D f ti C t

8/12/2019 007 Flores

19/35

Deformation Components:

Lateral DeflectionShear

V

V !SH = [2(113,000lb-in)] / (1.53*106)(29.26in2)

= 0.005048 in.

DeformationComponents:

8/12/2019 007 Flores

20/35

Deformation Components:

Lateral DeflectionShear

L t lYi ldD f ti fRC l

8/12/2019 007 Flores

21/35

Lateral Yield Deformation of RC column:

Lateral yield deformation (prior to shear failure) of longitudinalreinforcement in RC column results from 3 componentsacting in series:

Flexure, Bar (Bond) Slip, Shear

("LAT)Y="Y= ("FL+"SL + "SH)

("LAT)Y ="Y= (0.19266 in) + (0.2959 in) + (0.005048 in)

=0.49365 in.

Flexural

displacement ,

"FL

Slip

displacement,

"SL

Shear

displacement ,

"SH

Yield

displacement ,

"Y

0.19266 in 0.295941 in 0.005048 in 0.49365 in

D f ti C t

8/12/2019 007 Flores

22/35

Deformation Components:

Shear "Axial Failure

! After yielding of longitudinalreinforcement, columnsustains gravity and lateral(shear) loads until sheardemand on column exceedsultimate??? shear capacity of

column (V>VU)shear failureoccurs

! After shear failure occurs incolumn, gravity loads are

supported by shear-frictionforces along shear failureplane("LAT)AXoccurs

#

Shear

Failure

Plane

8/12/2019 007 Flores

23/35

Deformation Components:

Shear"

Axial Failure (cont.)

#

Shear

FailurePlane

DeformationComponents:

8/12/2019 007 Flores

24/35

Deformation Components:

Shear "Axial Failure (cont.)

ResidualAxial Capacity (after shear failure) of damaged RCcolumn:

PN= tan#*[(AST*fYT*dC)/s]*[(1+tan#)/(tan#-)]

..where fYT is yield strength of transverse reinforcement, dC is distance b/wextreme longitudinal reinforcement., s is transverse reinforcement spacing, # is

critical crack angle, is effective friction coefficient, AST is transverse

reinforcement area

PN= [tan65(0.01228in2)(70ksi)(4.5417in) / (4in)]*[(1+(8.28kip/10kip)*tan65) /

(tan65-(8.28kip/10kip))]=4.4 kips

!When gravity loads exceed shear-friction forces, axial failureoccurs in

column (column loses ALL shear capacity)$ total collapse of structure

8/12/2019 007 Flores

25/35

Deformation Components:

Shear"

Axial Failure (cont.)

Axial Failure ofColumn

Total Collapse ofColumn

DamageProgression inColumn Drift

8/12/2019 007 Flores

26/35

Damage Progression in Column Drift

Capacity ModelProgression of damage in a shear-critical RC column can bequantified using an empirical drift capacity model based on thecolumns lateral displacement (i.e. drift)

Drift Ratio at Yielding ofLongitudinal Reinforcement

("/L)Y=0.00494

Drift Ratio at Shear Failure

("/L)SH=0.026248

L LDrif t Ratio at Axial Failure

("/L)AX=0.035183

DamageProgression inColumn EPP

8/12/2019 007 Flores

27/35

Damage Progression in Column EPP

Backbone ModelElastic-Perfectly-Plastic (EPP) backbone model approximates theshear load vs. lateral displacement behavior of shear-critical RCcolumns via. a shear-failure surface

EPP backbone model utilizes the calculated column drift ratiosatyielding, shear & axial failure, as well as the yield moment derivedfrom the column moment-curvature response to generate thecolumns shear failure surface under lateral and gravity loading

Shear-Critical RC column Shear Hysteretic (force-

8/12/2019 007 Flores

28/35

y (

displacement) Response w/ EPP shear-drift backbone

EPP-predicted

shear failure

surface

!Y

!SH

!AX

FabricationofRCColumnSpecimens

8/12/2019 007 Flores

29/35

Fabrication of RC Column Specimens

Column Formsplywood, 2x4s

RC

Coln

6

1-1 5/8

2-4 5/8

1-10

8/12/2019 007 Flores

30/35

Fabrication of RCColumn Specimens (cont )

8/12/2019 007 Flores

31/35

Fabrication of RC Column Specimens (cont.)

Casting ofColumn

SpecimensfC = 3 ksi

FabricationofRCColumnSpecimens

8/12/2019 007 Flores

32/35

Fabrication of RC Column Specimens(cont.)Sensitivity Analysis

Sensitivity of RC Column Moment Capacity to Increasing 28-day Compressive Strength of

Concrete.

0

20

40

60

80

100

120

140

160

180

200

1.5 2 2.5 3 3.5 4 4.5

Concrete Compressive Strength, fc' (ks i)

(nomin

al)MomentCapacity,Mn(kip-in)

fy constant

FabricationofRCColumnSpecimens

8/12/2019 007 Flores

33/35

Fabrication of RC Column Specimens

(cont.)Sensitivity AnalysisSensitivity of RC Column Axial Load Capacity to Increasing 28-day Compressive Strength of

Concrete.

0

10

20

30

40

50

60

70

1.5 2 2.5 3 3.5 4 4.5

Concrete Compressive Strength, fc' (ksi)

(nominal)AxialLoadCapacity,

Pn(kips)

fy constant

8/12/2019 007 Flores

34/35

Acknowledgments

8/12/2019 007 Flores

35/35

Acknowledgments

Research conducted as part of the 2004 Pacific Earthquake

Engineering Research Center (PEER) Research Experience forUndergraduates & funded by the National Science Foundation

Special thanks to my PEER advisor, Professor Jack P. Moehle forhis guidance in the direction of my project and working hard to

secure the funding which made this research experience possibleThanks to UC Berkeley graduate students, WassimMichaelGhannoum& Yoon Bong Shin for their assistance in every aspectof this project

Thanks to Richmond Field StationPEER headquarters labpersonnel for their assistance in the design & fabrication of myexperimental setup