NEES-CABER Group Meeting Work Progress at UMR

1

NEES-CABER Group Meeting

Work Progress at UMR

Meeting Date: 9/18/2007

2

UMR – Progress Overview

Current Status Future PlanExperiments Tested 7 columns

Constructed 4 columns for further testing

Retrofitted 1 column with CFRP sheets

Testing of CFRP retrofitted column

Casting 3 more columns Testing of columns with M/V

ratio of 6

Data reduction, Analysis and Upload

Completed 6 columns Data reduction of 1 column is

being conducted

Decoupling strain components

Developing softening coefficient

Publication Published 1 conference paper Submitted abstracts to 4

conferences One journal paper is under

preparation

Two journal papers are planned to be written

Analytical Models

Analytical model for columns under pure torsion is being developed

Empirical models for combined loadings

Evaluation of design procedures in AASHTO & CSA for combined loadings

Development of Finite Element Model

Developed a 2D-Fiber element that can account for shear deformation.

2D-Fiber element to include torsional loadings

3D-Fiber element for biaxial loading

3

Experimental Work – Schedule & Deadline

Schedule DeadlineData Reduction & Analysis

• Data reduction of the specimen (T/M(0.2)-2.10/1.32)

Computing shear strains from the LVDT rosettes

Decouple the interaction of bending and torsion using strain gage readings and LVDT rosettes

Develop empirical models and validate the design procedures for combined loadings in AASHTO and CSA codes

September’ 07

• September’ 07

• October’ 07

• November’ 07

Experiments Testing 2 short columns under bending-shear (M/V=6) and pure torsion

Testing of 4 short columns (M/V=6) under combined bending and torsion

December’ 07

March-April’ 08

4

- Published “Seismic performance of RC bridge columns subjected to combined loadings including torsion", May 16-

19, 2007, ASCE Structures Congress 2007, Long Beach, California, USA .

- Conferences (Abstracts Submitted) “Torsion-Flexure-Shear Interaction on the Behavior of Reinforced Concrete Members”, AGS’ 08, Second

Euro Mediterranean Symposium On Advances in Geo-material and Structures -08, May 7-8, Tunisia.

“Behavior of RC Circular Bridge Columns under Combined Cyclic Bending and Torsion” AGS’ 08, Second Euro Mediterranean Symposium On Advances in Geo-material and Structures -08, May 7-8, Tunisia.

“Torsion-Flexure-Shear Interaction on the Behavior of Reinforced Concrete Members”, CBC’ 08, 2008 Concrete Bridge Conference, HPC – Safe, Affordable, and Efficient May 4-6, 2008, Hyatt Regency, St. Louis, Missouri.

“An Experimental Study on Behavior of RC Bridge Columns under Combined Cyclic Bending and Torsion”, CBC’ 08, 2008 Concrete Bridge Conference, HPC – Safe, Affordable, and Efficient May 4-6, 2008, Hyatt Regency, St. Louis, Missouri.

- Journals (In preparation) “Behavior of RC Circular Bridge Columns under Combined Cyclic Bending and Torsion”, Manuscript is

under preparation and will be submitted to ACI Structural Journal

Publications:

5

No Specimen Name

Applied Load

Transverse Reinforcement

RatioAxial*

(A)Shear

(V)Bending

(M)Torsion

(T)

Loading Ratio

M/V (ft) T/M

1 M/V(12)-T/M (0)- 2.1 /0.73 Yes Yes Yes No

12 0 0.73Bending and Shear

2 M/V(0)-T/M (∞)- 2.1 /0.73 Yes No No Yes

0 ∞ 0.73Pure Torsion w/Spiral

3 M/V(12)-T/M (0.1)- 2.1 /0.73 Yes Yes Yes Yes

12 0.1 0.73Combined Bending, Shear, and Torsion









Test Matrix - Completed

6

No Specimen Name

Applied Load

Transverse Reinforcement

RatioAxial*

(A)Shear

(V)Bending

(M)Torsion

(T)

Loading Ratio

M/V (ft) T/M

1 M/V(6)-T/M (0)-2.1 /1.32 Yes Yes Yes No

6 0 1.32Bending and Shear

2 M/V(0)-T/M (∞)-2.1 /1.32 Yes No No Yes

0 ∞ 1.32Pure Torsion w/Spiral

3 M/V(6)-T/M (X)-2.1 /1.32 Yes Yes Yes Yes

6 X 1.32Combined Bending, Shear, and Torsion







7 M/V(6)-T/M (X)-X /X Test parameters will be determined based on the previous test results

Test Matrix – To Be Tested

7

Bending-Shear

Combination of Bending-Shear-Torsion

Shear-Torsion

Bending Shear Torsion Interaction Surface – Problem Definitions

- Target of this Research Project

M-V-T Interaction Surface

Test Points of this research project

Tested

To be Tested

8

T/M(0.1) = 50.4 k

T/M(0.4) = 39.8 k

T/M(0.2) = 43.2 k

Spiral Unlocking Side

Spiral Locking Side

Ultimate Torque

T/M(0.1) = 51.9 k

T/M(0.4) = 45.6 k

T/M(0) = 52.3 k

T/M (0) = 53.3 k

The difference of ultimate strength between locking and unlocking sides becomes larger with increasing T/M ratio.

TEST RESULTS – Combined Bending, Shear and Torsion

- Hysteresis Curve

T/M(0.2) = 48.8 k-60

-30

0

30

60

-15 -10 -5 0 5 10 15

Displacement (in)

Lo

ad (

k)

M/V(12)-T/M(0)M/V(12)-T/M(0.1)M/V(12)-T/M(0.2)M/V(12)-T/M(0.4)

9

TEST RESULTS – Combined Bending, Shear and Torsion

- Hysteresis Curve

T/M(0.4) = 150.4 k-ft

T/M(0.1) = 64.8 k-ft

T/M(0.2) = 99.1 k-ft

Spiral Unlocking Side

Spiral Locking Side

Ultimate Torque

T/M(0.4) = 169.8 k-ft

T/M(0.1) = 63.8 k-ft

T/M(0.2) = 114.8 k-ft

The difference of ultimate strength between locking and unlocking sides becomes larger with increasing T/M ratio.

-250

-125

0

125

250

-20 -15 -10 -5 0 5 10 15 20

Twist (Deg)

To

rqu

e (

k-f

t)

Pure Torsion (M/V( )-T/M( )

Combined (M/V(12)-T/M(0.4))



T/M((∞) = 187.2 k-ft

T/M(∞) = 212.0 k-ft

0

10

Test Results – Moment-Torsion Interaction Diagram-At Peak Torque

* The numbers in the figure are Torsion to Moment Ratio

0

50

100

150

200

250

300

0 100 200 300 400 500 600 700

M (k-ft)

T (

k-ft

)Peak Torque-#3

Peak Torque-#4

Unlocking Case

T/M= 0.40

T/M=0.20

11

Long. Yield

Spiral Yield

Peak Torque

Peak Moment

Test Results – Long Columns with 3# spirals

0

500

1000

1500

2000

2500

3000

0 2000 4000 6000 8000

Moment (k-in)

To

rqu

e (k

-in

)

T/M-0.4

T/M-0.2

T/M-0.1

T/M-0

T/M-0/0

12

Long. Yield

Spiral Yield

Peak Torque

Peak Moment

0

500

1000

1500

2000

2500

0 1000 2000 3000 4000 5000 6000 7000 8000

Moment (k-in)

Tor

que

(k-in

)

#4(T/M 0.4)

#3(T/M 0.4)

#4(T/M 0.2)

#3(T/M 0.2)

With Increasing spiral ratio, torsional and bending strength is improved and helps to limit the spalling zone

Test Results – Effect of Change in Transverse Steel Reinforcement RatioLong Columns with #3 and #4 spirals

13

Analytical Models- Modification of RA-STM

RA-STM

Improvement of RA-STM in Circular Section

Estimation of proper ‘Td’-Shear flow zone

: no warping effect , satisfying Navier’s principle

Considering tension stiffening effect

: continuous prediction before and after cracking

Apparent truss action at the cracking point

: estimation of cracking torque and twist

Including the Poisson’s Effect

: prediction after the peak point

► To minimize other parameters like confinement effect or locking and unlocking effect, comparison is carried out with the results of column with hoop reinforcement tested under pure torsion

td

14

0

500

1000

1500

2000

2500

3000

0.0000 0.0010 0.0020 0.0030 0.0040

ANGLE OF TWIST PER UNIT LENTH, θ, (rad/in)

TO

RQ

UE

,T, (

in-k

ips)

POSITIVE

NEGATIVE

ANALYSIS

Tcr

(in-kip)θcr (rad/in)

Tpeak

(in-kip)

θpeak

(rad/in)ANALYSIS 1531 0.00003215 2443 0.001157

UNLOCKING 1603 0.00005275 2489 0.001147

LOCKING 1604 0.00003752 2390 0.001187

Unlocking/Analysis 1.05 1.64 1.02 0.99

Locking/Analysis 1.05 1.17 0.98 1.03

Peak point

Analytical Models- Results of RA-STM

15

Analytical Models- Further Study

I. Adopt material laws derived from sectional analysis

• Material laws considering softening and Poisson effect simultaneously

• 2D material laws → 3D material laws (illogical), however, this attempt can provide a possibility to extend an 2-D analytical model to 3-D model

II. Considering Confinement and Spalling Effect to Analytical Model

• Both of them are interdependent and strongly affected by one another

• Can STM model be modified for accounting these effects?

16

tdtd

x

z

y

x

z

STM : 2 D Model (xy plane) 3 D Model (xyz plane)

Analytical Models- Critical Issues in Circular Section

17

Axial LoadTorque

Bending

Confinement Effect

Spalling

Poisson’sEffect

Analytical Models- Spalling and Confinement Effect

18

u

u1 (x,y)

x

y

x

Y

y

u1u2

u3

1jd 2

jd3jd ij 1

id2id

3id

Curvature

Axial Displacement

SectionRotation

w out of plane deformation

u in plane deformation

Fiber Element Formulations- Shear Element

1

( , )1 111

1

2 222

2

1 2 1 212

2 1

, ( ) ( )

2 ( )

0 !

2 ( )

x yx

y

x xxy

u x y u x y x

u x w x

u u uy y

x x x x

u u

x y

u u u u wx

x x y x x

Shear Strain

Curvature

19

ysyc

x xy y

Concrete BeamStirrups

y

x

0yc c ys sA A

From Lateral Equilibrium:

Fiber Element Formulations- Model with Stirrups

20

X

Y

Z

xN

S V

M

iwjw

i j

*

x

Section

N

V

M

K

( )x xxy

wx

x

x

ui

uj

Fiber Element Formulations- Inclusion of Shear Deformation

21

Element in CartesianCoordinate System

Element in PrincipalCoordinate System

cracks

1

1

2

2

P

Stress/Strain ModelIn Principal Directions

0

'cf

1 P

1 P

0

ip ci c

ip ci

K f

K2

2

2 21

1 12

1 0.92 0.76

1 0.92 0.76

cc c

cc c

Kf f

Kf f

ci cK f

Equivalent Uniaxial Stress: Rotating Crack Model

22

UC San Diego Column R3- Monotonic

24”

16”

22, #6 bars

#2 hoops @ 5”

Length of the column = 96”

0

20

40

60

80

100

120

140

160

180

200

0 0.2 0.4 0.6 0.8 1 1.2

Lateral Displacement (in)

La

tera

l F

orc

e (

kip

)

UC San Diego_Shear ElementUC San Diego_No_Shear ElementUC San Diego_Experiment

Double curvature column

Fiber Element Formulations- Validation with Test Result

23

UC San Diego Column R3 – Cyclic

-200

-150

-100

-50

0

50

100

150

200

-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5


La

tera

l Fo

rce

(k

ip)

UC San Diego_Shear_Cyclic

UC San Diego_No_Shear_Cyclic


24

12' Long 2' Diameter Column

-60

-40

-20

0

20

40

60

-6 -4 -2 0 2 4 6 8


Lat

eral

Fo

rce

(kip

)

NEES_UMR_12'_Shear_Cyclic

NEES_UMR_12'_No_Shear_Cyclic

NEES UMR– Cyclic

Longitudinal Reinforcement 12, #8 barsTransverse Reinforcement #3 bars 2.75” SpacingLength of the column 12’

2.5” Dia.24” Dia.


25

6' Long 2' Diameter Column

-150

-100

-50

0

50

100

150

-3 -2 -1 0 1 2 3


La

tera

l F

orc

e (

kip

)

NEES_UMR_6'_Shear_Cyclic

Fiber Element Formulations- Prediction for Short Column

26

Schedule DeadlineFinite element Analysis

2-D Fiber section is ready with displacement formulation

Testing the 2-D Fiber element with displacement formulation

Dynamic test predictions

Element formulation for Combined loads including Torsion 1st Phase ( Pure Torsion)

September’ 07

October’ 07

December’ 07

Fiber Element Development- Schedule & Deadline

Documents

NEES-CABER Group Meeting Work Progress at UMR