performance of existing reinforced concrete columns under

Performance of Existing Reinforced Concrete Columns under Bidirectional Shear &

Axial Loading

Laura M. FloresUniversity of California, San Diego

REU Institution: University of California, BerkeleyREU Advisor: Dr. Jack P. Moehle

Pacific Earthquake Engineering Research Center (PEER)REU Symposium Kiawah Island Golf Resort - Kiawah, S.C. August 5-8, 2004

Outline

Research Background & Project ObjectivesDesign of Test SetupRC Column Specimen Material & GeometryCapacity Models

Flexural, Shear and Axial Capacity Moment � Curvature Response of Column

Deformation ComponentsLateral Deformation � Shear FailureAxial DeformationResidual Column Capacity & Damage Progression

Fabrication of RC Column SpecimensSensitivity Analysis

OngoingAcknowledgments

Research Background

Mechanisms leading to the collapse of existing, pre-seismic code RC frames are NOT well documented.Shake table tests are currently being conducted at PEER-UCB to observe & identify the failure components & load redistribution processes in RC bridge columns & in RC building frames under seismic & gravity loading.Identifying mechanisms causing shear failure in RC columns can be used to develop performance-based seismic design -strengthen future & existing structures against earthquake loading Column shear failure & its effect on the degradation of axial capacity in a pre-seismic code RC column is the focus of this project.

Project ObjectivesPERSONAL:

To independently conduct research & gain extensive laboratory experience in the field of structural � earthquake engineering

Opportunity to work with researchers on cutting-edge research and learn about ongoing studies in seismic design and retrofitting

Opportunity to learn and apply theories of seismic design & analysis to RC columns under seismic and gravity loads

RESEARCH:

Identify lateral & axial deformation components leading to RC column failure

Compute flexural, shear and axial capacity models of RC column

Design experimental setup allowing bidirectional loading of RC column for specific loading requirements & under budget

Fabricate RC column specimens based on design specs

Analyze the effect of bidirectional loading on the shear and axial failure of RC column and compare to predictive capacity models

Simplified Model of RC Column

One-third scale of existing, pre-seismic ACI code designed RC Column½ of RC column used in analysisFree end of column idealized as hinge connection with a fixed end at base of column

Simplified Model of RC Column (cont.)

RC Col�n

RC Col�n

M = 0 (hinge)

M(x)

M = MMAX(fixed)

Design of Test Setup

RC Col�n

Gravity Load = 10 kips

HINGEActuator / SeismicLoad = 8.3 kips

FIXED

Design of Test Setup (cont.)

A

A

1'-5"

CONCRETEFLOOR

9"x8" flanged beam 70lb/ft.S=61.5 cu. in.

TEST APPARTUS

base plate 2 in. thickness15 in.width and 3 ft. length

B

1'-158"2'-97

8"ACTUATORPOSITION

FRONT VIEW

SIDE VIEW

(H-structure) safety frame3"x2" angle ironwelded construction

1/2" concrete anchor 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 bars110 lb/bartotal wt. 1540 lb.

1'-4 3/8" (platform width?)

C

SECTION C-C

4" (add spacing if needed)

clamp??

42.25"

RC Column Material & Geometry

RC Column Material & Geometry (cont.)

Capacity Models of RC Column Specimen: Axial Capacity

Axial Capacity of undamaged RC column:

PN = 0.85*fC�*(Ag� ASL ) + fYL*ASL..where fC’ concrete compressive strength, Ag is the gross concrete 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

Capacity Models of RC Column Specimen: Flexural Capacity

εcu = .003

εs3

εs2h

εS1 = -00207

�

�

�

�N.A.

.85fC�

a TS3

TS2

TS1

TS2

TS1

TS3

CC

TS2

TS1

TS3MN

�

CC

PN

ΣMh/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

Capacity Models of RC Column Specimen: Shear Capacity

Total shear capacity of an RC column depends on the shear capacity of the concrete, VC and the shear capacity carried by the 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

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

) Axi

al L

oad

Cap

acity

, Pn

(kip

s)

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 an interaction diagram which relates the axial load column capacity with its moment capacity at any given time

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 interaction diagram which relates the axial load column capacity with its moment capacity at any given time

0

20

40

60

80

100

120

140

160

-7.E-2

21.E

-043.E

-044.E

-045.E

-047.E

-048.E

-049.E

-041.E

-031.E

-031.E

-031.E

-032.E

-032.E

-032.E

-032.E

-032.E

-032.E

-032.E

-033.E

-033.E

-033.E

-033.E

-033.E

-033.E

-033.E

-033.E

-034.E

-034.E

-03

Curvature, θ (1/in)

Mom

ent,

M (k

ip-in

)

MY=VY*l

Deformation Components:Lateral Deflection

Flexure

M

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


Flexure


Bar (Bond) SlipM

M ∆SL = [(39in)(0.375in)(70,000psi)(7.6*10-4in-1)] / [8*6*√3000psi]

= 0.2959 in


Shear

V

V ∆SH = [2(113,000lb-in)] / (1.53*106)(29.26in2)= 0.005048 in.


Shear

Lateral Yield Deformation of RC column:Lateral yield deformation (prior to shear failure) of longitudinal reinforcement in RC column results from 3 components acting 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

Deformation Components:Shear → Axial Failure

! After yielding of longitudinal reinforcement, column sustains gravity and lateral (shear) loads until shear demand on column exceeds ultimate??? shear capacity of column (V>VU) � shear failureoccurs

! After shear failure occurs in column, gravity loads are supported by shear-friction forces along shear failure plane � (∆LAT)AX occurs

θ

Shear Failure Plane

Deformation Components:Shear → Axial Failure (cont.)

θ

Shear Failure Plane


Residual Axial Capacity (after shear failure) of damaged RC column:

PN = tanθ*[(AST*fYT*dC)/s]*[(1+µtanθ)/(tanθ-µ)]..where fYT is yield strength of transverse reinforcement, dC is distance b/w extreme longitudinal reinforcement., s is transverse reinforcement spacing, θ is critical crack angle, µ 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 failure occurs in column (column loses ALL shear capacity) → total collapse of structure


Axial Failure of Column

Total Collapse of Column

Damage Progression in Column � Drift Capacity Model

Progression of damage in a shear-critical RC column can be quantified using an empirical drift capacity model based on the column�s lateral displacement (i.e. �drift�)

Drift Ratio at Yielding of Longitudinal Reinforcement

(∆/L)Y = 0.00494

Drift Ratio at Shear Failure

(∆/L)SH = 0.026248

L LDrift Ratio at Axial Failure

(∆/L)AX = 0.035183

Damage Progression in Column � EPP Backbone Model

Elastic-Perfectly-Plastic (EPP) backbone model approximates the shear load vs. lateral displacement behavior of shear-critical RC columns via. a �shear-failure surface�EPP backbone model utilizes the calculated column drift ratios at yielding, shear & axial failure, as well as the yield moment derived from the column moment-curvature response to generate the column�s �shear failure surface� under lateral and gravity loading

Shear-Critical RC column Shear Hysteretic (force-displacement) Response w/ EPP shear-drift backbone

EPP-predicted shear failure

surface

∆Y

∆SH

∆AX

Fabrication of RC Column SpecimensColumn Forms �plywood, 2x4�s

RC Col�n

6�

1�-1 5/8�

2�-4 5/8�

1�-10�

Fabrication of RC Column Specimens (cont.)

Steel Cages / Longitudinal & Transverse Reinforcement � 60 Grade #3 & #5 rebar, tie wires, 1/8�diameter stirrups

Fabrication of RC Column Specimens (cont.)

Casting of Column Specimens � fC� = 3 ksi

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' (ksi)

(nom

inal

) Mom

ent C

apac

ity, M

n (k

ip-in

)

fy constant

Fabrication of RC Column Specimens(cont.) � Sensitivity Analysis

Sensitivity 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)

(nom

inal

) Axi

al L

oad

Cap

acity

, Pn

(kip

s)

fy constant

-Ongoing-My Research Objectives to be completed:

" Fabrication of experimental setup" Testing of RC column specimens" Comparing observed RC column hysteretic response under axial & shear

loading w/ that response predicted by capacity models

Overall Research Objectives to be completed:

" Using results to calibrate existing OpenSees analytical model that is based on RC structure deformation components & capacity models

" Using revised OpenSees analytical model to predict hysteretic response of existing RC building structure (composed of several column-beam components) to seismic & gravity loading

" Fabrication & testing of large-scale RC building frame" Additional verification studies of OpenSees analytical model

Acknowledgments

Research conducted as part of the 2004 Pacific Earthquake Engineering Research Center (PEER) Research Experience for Undergraduates & funded by the National Science FoundationSpecial thanks to my PEER advisor, Professor Jack P. Moehle for his 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, Wassim Michael Ghannoum & Yoon Bong Shin for their assistance in every aspect of this projectThanks to Richmond Field Station � PEER headquarters lab personnel for their assistance in the design & fabrication of myexperimental setup

performance of existing reinforced concrete columns under

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