Modeling of Deep Girders Supporting Shear Walls
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This document summarizes a master's thesis presentation on modeling deep girders supporting shear walls. The presentation introduces various analysis techniques for deep beams, including the strut-and-tie method, finite element analysis using VecTor2, and two parameter kinematic theory. Seven test beams with varying sizes, loading eccentricities are described to compare the predictions of failure load between VecTor2 and the other methods. The results show that VecTor2 predictions match well but the other methods are unconservative. Adjusting parameters in the two parameter kinematic theory improves predictions. Size effects are demonstrated through a scaled model analysis.
![• Analysis Techniques for deep beams
Two Parameter Kinematic Theory: Predicts the response of a
concentrically loaded deep beam with only two degrees of freedom .[7]
Modeling of Deep Girders Supporting Shear
Walls
Shear Strength components of a deep
beam (Mihaylov, et al., 2013)
Introduction
Key Shear strength
Providing component](https://image.slidesharecdn.com/db52a428-6ff7-47d3-919d-f676f7565622-150612153155-lva1-app6891/85/Modeling-of-Deep-Girders-Supporting-Shear-Walls-4-320.jpg)
![References
[1]ACI 318-08, 2008. Building Code Requirements for Structural Concrete (ACI 318-08) and
Commentary, Farmington Hills, MI 48331: American Concrete Institute.
[2]Hooke, . R., 1678. Lectures de Potentia Restitutiva (Spring Explaining the Power of
Springing Bodies), s.l.: John Martyn Printer.
[3]Mihaylov, B. I., Bentz, E. C. & Collins, M. P., 2010. Behavior of Large Deep Beams
Subjected to Monotonic. ACI STRUCTURAL JOURNAL, Volume 107, pp. 726-734.
[4]Bentz, E. C., Vecchio, F. J. & Collins, M. P., 2006. Simplified Modified Compression Field
Theory for Calculating Shear Strength of Reinforced Concrete Elements. ACI STRUCTURAL
JOURNAL, 103(5), pp. 614-624.
[5]Vecchio, . F., 2000. Disturbed Stress Field Model for Reinforced Concrete: Formulation.
Journal of Structural Engineering, Volume 126 , pp. 1070-1077.
[6]Mihaylov, B. I., Bentz, E. C. & Collins, M. P., 2013. Two-Parameter Kinematic Theory for
Shear Behavior of. ACI STRUCTURAL JOURNAL, Volume 110, pp. 447-445.
Modeling of Deep Girders Supporting Shear
Walls](https://image.slidesharecdn.com/db52a428-6ff7-47d3-919d-f676f7565622-150612153155-lva1-app6891/85/Modeling-of-Deep-Girders-Supporting-Shear-Walls-17-320.jpg)
Modeling of Deep Girders Supporting Shear Walls
- 1. Modeling of Deep Girders Supporting Shear Walls Master’s Thesis Defense Presentation By Syed Karar Hussain Members of the Jury Prof. Boyan Mihaylov, ULg (Promoter) Prof. Jean-François Demonceau, ULg Prof. Jean-Marc Franssen, ULg Luc Demortier, GREISCH Yves Duchêne, GREISCH
- 2. Introduction Significance of the study Modeling of Deep Girders Supporting Shear Walls Transfer Girder Shear wall Simply supported deep beam with applied load and moment
- 3. • Analysis Techniques for deep beams Strut-and-Tie Method: An easy way to analyze and design deep beams. Widely used by different design codes (ACI, EC etc). Finite Element Analysis: Relatively complex but accurate method for analyzing RC members(deep beams). VecTor2-Takes its basis from Modified Compression Field Theory(Bentz 2006) and Distributed Stress Field Model(Collins,1986). Modeling of Deep Girders Supporting Shear Walls Introduction Compatibility of strains Equilibrium of stresses Stress-strain relationship FE analysis by VecTor2-Flow of stresses STM for the same deep beam
- 4. • Analysis Techniques for deep beams Two Parameter Kinematic Theory: Predicts the response of a concentrically loaded deep beam with only two degrees of freedom .[7] Modeling of Deep Girders Supporting Shear Walls Shear Strength components of a deep beam (Mihaylov, et al., 2013) Introduction Key Shear strength Providing component
- 5. • Comparison of shear strength predictions made by 2PKT and strut-and-tie method Modeling of Deep Girders Supporting Shear Walls Introduction 2PKT & CSA sectional Average=1.10, COV=13.7% (Mihaylov, et al., 2013) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0 a/d Vexp/Vpred ACI strut-and-tie & sectional Average=1.30, COV=29.0% (Mihaylov, et al., 2013) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0 a/d
- 6. 7 beams with different loading column/wall sizes and eccentricity cases Modeling of Deep Girders Supporting Shear Walls Description of beams to-be- investigated f y = 550 MPa f u = 594 MPa fc’ = 70 MPa Varying Eccentricity Varying column/wall size Name h(mm) e DB400CF 800 0 DB400E-0.2-F 0.25h DB400E-0.4-F 0.5h DB800CF 1600 0 DB800E-0.4-F 0.25h DB800E-0.8-F 0.5h DB1800CF 3600 0 DB1800E-0.9-F 0.25h DB1800E-1.8-F 0.5h DB2800CF 5600 0 DB2800E-1.4-F 0.25h DB2800E-2.8-F 0.5h DB3800CF 7600 0 DB3800E-1.9-F 0.25h DB3800E-3.8-F 0.5h DB4800CF 9600 0 DB4800E-2.4-F 0.25h DB4800E-4.8-F 0.5h DB5800CF 11600 0 DB5800E-2.9-F 0.25h DB5800E-5.8-F 0.5h Details of the variables
- 7. Modeling Details Modeling of Deep Girders Supporting Shear Walls Description of beams to-be- investigated Infinitely Rigid Layer Infinitely Rigid Layer DB2800E-2.8-F-Material Types DB2800E-2.8-F-Eccentric loading
- 8. Load-displacement response and failure load predictions from VecTor2 Modeling of Deep Girders Supporting Shear Walls Results & Discussion on Behavior of Deep Beams
- 9. Concentrically Loaded beams Modeling of Deep Girders Supporting Shear Walls Cracking Pattern-DB400CF Cracking Pattern-DB2800CF Cracking Pattern-DB5800CF Results & Discussion on Behavior of Deep Beams
- 10. Concentrically Loaded beams Modeling of Deep Girders Supporting Shear Walls Results & Discussion on Behavior of Deep Beams Principal compressive stresses-DB400CF Principal compressive stresses-DB2800CF Principal compressive stresses-DB5800CF f y(MPa) profile at the top of the loading column f y(MPa) profile at the junction
- 11. Eccentrically Loaded Beams Modeling of Deep Girders Supporting Shear Walls Results & Discussion on Behavior of Deep Beams Cracking pattern-DB2800E-2.8-F Principal compressive stresses-DB2800E-2.8-F f y(MPa) profile at the top of the loading column f y(MPa) profile at the junction
- 12. Comparison of results between VecTor2 and 2PKT predictions For deep beams loaded with very wide walls, the failure load predictions by 2PKT are unrealistic. Modeling of Deep Girders Supporting Shear Walls Comparison of Results V CLZ = k f avg b lb1e sin2 α c DOF t,avg DOF c kl =l0 V Pb1(V/P)l b1l c r t,min t,max A CLZ =0 b1el = d B t,avg x z h 1 v b2l slip w A 1 a+ d cott,avg x z x z c z B 2.5(h-d) kl =l0 d Kinematic Model of 2PKT 0 50000 100000 150000 200000 250000 0 2000 4000 6000 8000 10000 12000 14000 LoadP(KN) Width of the Column Lb1 (mm) Comparison of Failure loads obtained from VecTor2 and 2PKT C 0.25h 0.5h 2PKT VecTor2
- 13. Iteration of L1e: The effective width of the loading column for the all the beams was iterated in a way that the failure load predictions by 2PKT and VecTor2 became same. Modeling of Deep Girders Supporting Shear Walls Extension for 2PKT Lb1e,a= Most Stressed Portion
- 14. Comparison of the shear strength contributions by all components obtained by initial(Lb1e) & adjusted(Lb1e,a) predictions. A suitable method for estimating Lb1e is required to be devised. Modeling of Deep Girders Supporting Shear Walls Extension for 2PKT 0.0 20000.0 40000.0 60000.0 80000.0 100000.0 120000.0 0.0 2000.0 4000.0 6000.0 8000.0 10000.0 12000.0 V-LeftSupport(KN) Column/Wall Size(Lb1)-mm Results with Lb1e V(clz) Vs Vci Vd V 0.0 5000.0 10000.0 15000.0 20000.0 25000.0 30000.0 35000.0 40000.0 0.0 2000.0 4000.0 6000.0 8000.0 10000.0 12000.0 V-LeftSupport(KN Column/Wall Size(Lb1)-mm Results with Lb1e,a VCLZ Vs Vci Vd V Vs Vd
- 15. Comparison of results between VecTor2 and strut-and-tie method Failure load predictions from STM are highly un-conservative as compared to VecTor2 predictions. Modeling of Deep Girders Supporting Shear Walls Comparison of Results 0 10000 20000 30000 40000 50000 60000 70000 80000 0 2000 4000 6000 8000 10000 12000 14000 LoadP(KN) Width of the Column Lb1 (mm) Failure load comparison of VecTor2 and Strut-and-Tie method predictions C 0.25h 0.5h 0.25h 0.25h 0.50h STM VecTor2
- 16. Possible reasons for deviation in predictions by VecTor2 and STM Size Effect in deep beams : A geometrically similar model of DB800CF on a scale of 1/5 was analyzed by all the approaches. If extrapolated, the predictions by STM will be more un-conservative as compared to STM and 2PKT. Modeling of Deep Girders Supporting Shear Walls Comparison of Results Size Effect demonstration for Zhang and Tin tests(Mihaylov et al,2013) STM doesn’t capture size effect of deep beams Comparison of DB800CF and its 1/5th scale model 0 1 2 3 4 5 6 7 0 1000 2000 3000 4000 5000 6000 Shearstress-V/bd-MPa Effective depth(d)-mm Demonstration of size effect for DB800CF and its scaled model VecTor2 2PKT Strut- and-tie method Scaled Model DB800CF Unsafe
- 17. References [1]ACI 318-08, 2008. Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary, Farmington Hills, MI 48331: American Concrete Institute. [2]Hooke, . R., 1678. Lectures de Potentia Restitutiva (Spring Explaining the Power of Springing Bodies), s.l.: John Martyn Printer. [3]Mihaylov, B. I., Bentz, E. C. & Collins, M. P., 2010. Behavior of Large Deep Beams Subjected to Monotonic. ACI STRUCTURAL JOURNAL, Volume 107, pp. 726-734. [4]Bentz, E. C., Vecchio, F. J. & Collins, M. P., 2006. Simplified Modified Compression Field Theory for Calculating Shear Strength of Reinforced Concrete Elements. ACI STRUCTURAL JOURNAL, 103(5), pp. 614-624. [5]Vecchio, . F., 2000. Disturbed Stress Field Model for Reinforced Concrete: Formulation. Journal of Structural Engineering, Volume 126 , pp. 1070-1077. [6]Mihaylov, B. I., Bentz, E. C. & Collins, M. P., 2013. Two-Parameter Kinematic Theory for Shear Behavior of. ACI STRUCTURAL JOURNAL, Volume 110, pp. 447-445. Modeling of Deep Girders Supporting Shear Walls
- 18. THANK YOU FOR YOUR PATIENCE Modeling of Deep Girders Supporting Shear Walls