Mechanical and Finite Element Analysis for Circular RC Column

1. Mechanical and Finite Element Analysis for Circular RC Column 2 / 22 / 2008

2. PHASE I : Circular RC Column under Pure Torsion Finite Element Model PHASE II : Circular RC Column under Torsion + Axial Force • Considered Parameters • Softening Effect • Confinement Effect • Interface Behavior between Core and Cover Concrete • Spalling Effect • Poisson’s Effect PHASE III : Circular RC Column under Combined Action Mechanical Model (Modified RA-STM) PHASE IV : Circular RC Column under Cyclic Combined Action Experiment PHASE V : Simplified Analytical Model and Design Method SCHEMATIC OF ANALYSIS

3. PHASE I-1 : Mechanical Model Improvement of RA-STM in Circular Section • Estimation of proper td • : 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 Effect • : prediction after the peak point RA-STM td

4. τr τρ Sr Sρ σd σr Different Behavior between Rectangular and Circular Section COMMON BEHAVIOR εt εd εr εl

5. y x z x z Critical Issues in Circular Section td td 3 D Model (xyz plane) STM : 2 D Model (xy plane)

6. Governing Equations and Modification of RA-STM (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) σl = σt = 0 in Pure Torsion

7. t r Proper Estimation of Shear Flow Zone

8. confined fcon fc non-effected ζfc softened εd ζε0 ε0 The Relationship Between td and Concrete Property ε0 ζε0 εd center Strain Distribution c fcon fc A3 ζfc A2 SPALLING A1 Stress Distribution Intermediate region Am,3 k3fc Am,3 Am,2 k2fc td = constant Am,2 Average Stress Distribution (constant td) σd = constant Am,1 k1ζfc Am,1 td = 2c td = variable Am,3 Average Stress Distribution (constant σd) Am,2 Am,1 td = A/u

9. Apparent Truss Action (First Cracking) and Tension Stiffening Effect Effective thickness of td at cracking (initial value in the calculation with εcr)

10. 2 2 (a) Biaxial strain (b) Uniaxial strain 1 1 1 1 1 1 Poisson’s Effect

11. Calculate , fl Calculate , σd, σr Calculate , ft Flow Chart of Solution Procedure 1 Select εd (εr = εcr) Assume εl Assume εr (εd) Assume td (td0) NO Is σl close ? Calculate A0, p0, ρt, ρl Assume εt ( ρt< ρl ) [ Assume εl ( ρt> ρl )] NO Is td (td0)close ? Calculate υ12 Is εr (εd) close ? NO Is σt close ? NO Calculate α, τlt, γlt, T, θ End 1

12. Further Models Current Model MST Specimen PHASE I-2 : Simulation of Idealized Specimen • All conditions are exactly same with experimental specimens except for steel ratios and transverse type. • Same steel ratios on longitudinal and transverse steel ( ρl = ρt = 0.0117 → fl = ft ) • To minimize secondary effects, such as locking effect in spiral, hoop is used as the transverse steel • Although this condition is rare in real situation, it might provide a initial understanding for the further consideration for the mechanical model as well as FE models 12 - #6 #6 @ 7 in. (Hoop)

13. Analytical Cases FEM models including fixed end (Total No. = 13 x 2 = 26) Mechanical models with constant td (Total No. = 6) Final mechanical model (Total No. = 1)

14. FE Models 6 Nodes Edge Element in Core (HX24L in DIANA) Mechanical Models in DIANA • Rotational Smeared Crack Model • Softening Model • 1. Adopting Vecchio & Collins Model (1993) • 2. Resolve the dimensional problem (adoption 2D model to 3D model) by averaging two lateral stress as shown in the eqation. • Confinement Model • 1. Using Selby & Vecchio Model Rigid Material Property in Both Block 8 Nodes Brick Element in Whole Region (HX24L in DIANA)

15. PHASE I-3 : Results of Analyses Torque-Twist Relation by Mechanical Model (Series AI) Concrete Crush Both Steel Yield Crack

16. Torque-Twist Relation by FE Models SERIES FI_S SERIES FI_T2 SERIES FI_T3 SERIES FI_T5 SERIES FI_T6Y SERIES FI_T4

17. Comparison (FI-S series and AI-TS)

18. PHASE I-4 : Damage Zone (Effect of Boundary Condition) STEEL STRESSES VON MISES STRESSES FI – S2S FI – S2S - B

19. PHASE II : Circular Column under Torsion + Axial Force Analysis for circular column under torsion and axial force is exactly same with one under pure torsion except for σl = constant. Therefore, same procedure is applied in this analysis. Mechanical analysis is compared with FEM results and experimental results done by MST.

20. Validation of Modified RA-STM Apparent Truss Action & Tension Stiffening Post-peak behavior (Poisson effect) T-εt relation T-εl relation T-εt relation (near cracking)

21. Conclusion The thickness of shear flow zone, td, could be rationally predicted under some specified conditions. Therefore, it is necessary to develop the generalized methods for estimating td In addition, secondary effects like confinement and spalling should be considered in the estimation of td through micro levels investigation. It seems to be reasonable to adopt td0 suggested by Collins. By adopting this value as an initial estimate of td, it was possible to predict the exact cracking torque and twist angle as well as the behavior after cracking. The poisson effect plays a very important role in the prediction of behavior during the entire loading history as well as after the post-peak behavior. Based on this model, remaining phases will be carried out