1. 1 NEES-CABER Group Meeting Work Progress at UMR Meeting Date: 9/18/2007

2. 2 UMR – Progress Overview Current StatusFuture Plan Experiments  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. 3 Experimental Work – Schedule & Deadline ScheduleDeadline Data Reduction & AnalysisData 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. 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. 5 NoSpecimen Name Applied Load Transverse Reinforcement Ratio Axial* (A) Shear (V) Bending (M) Torsion (T) Loading Ratio M/V (ft)T/M 1M/V(12)-T/M (0)- 2.1 /0.73 Yes No 1200.73 Bending and Shear 2M/V(0)-T/M (∞)- 2.1 /0.73 YesNo Yes 0∞0.73 Pure Torsion w/Spiral 3M/V(12)-T/M (0.1)- 2.1 /0.73 Yes 120.10.73 Combined Bending, Shear, and Torsion 4M/V(12)-T/M (0.2)- 2.1 /0.73 Yes 120.20.73 Combined Bending, Shear, and Torsion 5M/V(12)-T/M (0.4)- 2.1 /0.73 Yes 120.40.73 Combined Bending, Shear, and Torsion 6M/V(12)-T/M (0.2)- 2.1 /1.32 Yes 120.21.32 Combined Bending, Shear, and Torsion 7M/V(12)-T/M (0.4)- 2.1 /1.32 Yes 120.41.32 Combined Bending, Shear, and Torsion Test Matrix - Completed

6. 6 NoSpecimen Name Applied Load Transverse Reinforcement Ratio Axial* (A) Shear (V) Bending (M) Torsion (T) Loading Ratio M/V (ft)T/M 1M/V(6)-T/M (0)-2.1 /1.32 Yes No 601.32 Bending and Shear 2M/V(0)-T/M (∞)-2.1 /1.32 YesNo Yes 0∞1.32 Pure Torsion w/Spiral 3M/V(6)-T/M (X)-2.1 /1.32 Yes 6X1.32 Combined Bending, Shear, and Torsion 4M/V(6)-T/M (X)-2.1 /1.32 Yes 6X1.32 Combined Bending, Shear, and Torsion 5M/V(6)-T/M (X)-2.1 /1.32 Yes 6X1.32 Combined Bending, Shear, and Torsion 6M/V(6)-T/M (X)-2.1 /1.32 Yes 6X1.32 Combined Bending, Shear, and Torsion 7 M/V(6)-T/M (X)-X /XTest parameters will be determined based on the previous test results Test Matrix – To Be Tested

7. 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. 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

9. 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. T/M(( ∞ ) = 187.2 k-ft T/M( ∞ ) = 212.0 k-ft 0

10. 10 Test Results – Moment-Torsion Interaction Diagram-At Peak Torque * The numbers in the figure are Torsion to Moment Ratio

11. 11 Long. Yield Spiral Yield Peak Torque Peak Moment Test Results – Long Columns with 3# spirals 0 500 1000 1500 2000 2500 3000 02000400060008000 Moment (k-in) Torque (k-in) T/M-0.4 T/M-0.2 T/M-0.1 T/M-0 T/M-0/0

12. 12 Long. Yield Spiral Yield Peak Torque Peak Moment 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 Ratio Long Columns with #3 and #4 spirals

13. 13 Analytical Models- Modification of RA-STM RA-STM Improvement of RA-STM in Circular Section  Estimation of proper ‘T d ’-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 tdtd

14. 14 T cr (in-kip) θ cr (rad/in) T peak (in-kip) θ peak (rad/in) ANALYSIS15310.0000321524430.001157 UNLOCKING16030.0000527524890.001147 LOCKING16040.0000375223900.001187 Unlocking/Analysis1.051.641.020.99 Locking/Analysis1.051.170.981.03 Peak point Analytical Models- Results of RA-STM

15. 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. 16 tdtd 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. 17 Axial Load Torque Bending Confinement Effect Spalling Poisson’s Effect Analytical Models- Spalling and Confinement Effect

18. 18 u u 1 (x,y) x y Y u1u1 u2u2 u3u3 i j Axial Displacement Fiber Element Formulations- Shear Element Shear Strain Curvature

19. 19 s ys s yc exex g xy eyey Concrete Beam Stirrups eyey exex g From Lateral Equilibrium: Fiber Element Formulations- Model with Stirrups

20. 20 X Y Z uiui ujuj Fiber Element Formulations- Inclusion of Shear Deformation

21. 21 Element in Cartesian Coordinate System Element in Principal Coordinate System cracks s1s1 s1s1 s2s2 s2s2 P Stress/Strain Model In Principal Directions Equivalent Uniaxial Stress : Rotating Crack Model

22. 22 UC San Diego Column R3- Monotonic 24” 16” 22, #6 bars #2 hoops @ 5” Length of the column = 96” Double curvature column Fiber Element Formulations- Validation with Test Result

23. 23 UC San Diego Column R3 – Cyclic Fiber Element Formulations- Validation with Test Result

24. 24 NEES UMR– Cyclic Longitudinal Reinforcement 12, #8 bars Transverse Reinforcement #3 bars 2.75” Spacing Length of the column 12’ 2.5” Dia. 24” Dia. Fiber Element Formulations- Validation with Test Result

25. 25 Fiber Element Formulations- Prediction for Short Column

26. 26 ScheduleDeadline Finite 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