Closed-form analytical solution procedure for element design in D regions

Document Type : Research

Authors

1 Formerly PhD student , Department of civil and enviromental engineering, Imperial College London ,UK.

2 Department of civil and enviromental engineering, Imperial College London ,UK

Abstract

This paper presents a novel procedure for solving the equations system of the rotating crack model used for reinforced concrete. It is implemented in the programme NonOPt where it is used to optimise the reinforcement design of D regions. The procedure is based on solving explicit closed-form relations without the need to incrementally increase the applied loads. The solution procedure is based on a secant modulus approach and is developed initially on the basis that the stress-strain response of the steel and concrete is linearly elastic. Subsequently the effect of material nonlinearities is included and the solution procedure is adapted accordingly. A reinforcement design procedure for membrane elements is described along with some case studies. The design procedure minimises the amount of reinforcement required to satisfy predefined design constraints. Material nonlinearities are taken into account, stress and strain compatibilities are satisfied and the design considers both the ultimate and serviceability limit states through the application of appropriate design constraints.

Keywords

References

1. Amini Najafian, H., 2011. Nonlinear Optimisation of Reinforcement Design for Reinforced Concrete Structures Loaded in Plane Stress. PhD Thesis, Department of Civil and Environmental Engineering, Imperial College London, 354pp.
2. Amini Najafian, H. and Vollum, R.L. 2013a. Design of planar reinforced concrete D regions with nonlinear finite element analysis. Engineering Structures, 51 (6), 211-225. [DOI:10.1016/j.engstruct.2013.01.022]
3. Amini Najafian, H. and Vollum, R.L. 2013b. Automated nonlinear design of reinforced concrete D regions. Structural Engineering and Mechanics 46 (1), 91-110. [DOI:10.12989/sem.2013.46.1.091]
4. Amini Najafian, H. and Vollum, R.L. 2013c. Optimising reinforcement deign in D regions using nonlinear finite element analysis. Magazine of Concrete Research, 65 (4), 234-247. [DOI:10.1680/macr.12.00063]
5. Amini Najafian, H., Vollum, R.L. and Fang, L. 2013. Comparative assessment of finite element and strut and tie based design methods for deep beams. Magazine of Concrete Research, 65 (16), 970-986. [DOI:10.1680/macr.13.00006]
6. Collins, M. P., Bentz, E. C., Sherwood, E. G. and Xie, L. 2008. An adequate theory for the shear strength of reinforced concrete structures. Magazine of Concrete Research, 60 (9): 635-650. [DOI:10.1680/macr.2008.60.9.635]
7. DIANA 2007, Finite Element Analysis User's Manual. Release 9.2. TNO DIANA BV, Delft, the Netherlands.
8. Fernández Ruiz, M., Muttoni, A. and Burdet, O. 2007. Computer-aided development of stress fields for the analysis of structural concrete. fib Symposium, Dubrovnik, Croatia, 591-598.
9. Fernández Ruiz, M. and Muttoni, A. 2007. On development of suitable stress fields. ACI Structural Journal, 104 (4) 495-502. [DOI:10.14359/18780]
10. Hognestad, E. 1951. A Study of Combined Bending and Axial Load in Reinforced Concrete Members. Bulletin Series, No. 399, University of Illinois, Engineering Experiment Station, Urbana-Champaign, USA, 128 pp.
11. Kao, C. 1998. Performance of several nonlinear programming software packages on microcomputers, Computers and Operations Research, 25 (10), 807-816. [DOI:10.1016/S0305-0548(98)00013-6]
12. Liang, Q. Q. and Steven, G. P. 2002. A performance-based optimization method for topology design of continuum structures with mean compliance constraints. Computer Methods in Applied Mechanics and Engineering, 191 (13-14), 1471- 1489. [DOI:10.1016/S0045-7825(01)00333-4]
13. Ozgur, Y. 2005. A comparative study on optimization methods for the constrained nonlinear programming problems. Mathematical Problems in Engineering. Issue 2, 165-173. [DOI:10.1155/MPE.2005.165]
14. Rogowsky, D.M., MacGregor, J.G. and Ong, S.Y. 1986. Tests on reinforced concrete deep beams, ACI Structural Journal, 83 (4): 614-623. [DOI:10.14359/10558]
15. Tabatabai, S.M.R. and Mosalam, K.M. 2001. Computational platform for non-linear analysis/ optimal design of reinforced concrete structures. Engineering Computations, 18 (5-6), 726 744. [DOI:10.1108/EUM0000000005785]
16. Tjhin, T. N. and Kuchma, D. A. 2002. Computer-based tools for design by strut-and-tie method: Advances and challenges. ACI Structural Journal, 99 (5), 586-594. [DOI:10.14359/12298]
17. Vecchio, F. J. and Collins, M. P. 1986. The modified compression field theory for reinforced concrete elements subjected to shear. American Concrete Institute Journal, 83 (2), 219-231. [DOI:10.14359/10416]
18. Yun, Y. M. 2000. Computer graphics for nonlinear strut-tie model approach. Journal of Computing in Civil Engineering, 14 (2), 127-133. [DOI:10.1061/(ASCE)0887-3801(2000)14:2(127)]
Numerical Methods in Civil Engineering
Volume 1, Issue 3
March 2017
Pages 1-15

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History

  • Receive Date: 23 April 2014
  • Revise Date: 14 September 2014
  • Accept Date: 23 December 2014

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