Browse > Article
http://dx.doi.org/10.7734/COSEIK.2018.31.1.9

Bending Moment Calculation Method and Optimum Element Size for Finite Element Analysis with Continuum Elements  

Heo, Ji-Hye (Department of Architecture, Konkuk Univ.)
Kim, Han-Soo (Department of Architecture, Konkuk Univ.)
Publication Information
Journal of the Computational Structural Engineering Institute of Korea / v.31, no.1, 2018 , pp. 9-16 More about this Journal
Abstract
When designing a reinforced concrete member using nonlinear finite element analysis results, the bending moment at the critical section should be calculated. In this paper, a bending moment calculation method using the results of reinforced concrete finite element analysis(FEA) using continuum elements is presented and the optimum element size according to the order of the displacement function of the finite element is proposed. The bending moments calculated by integrating the stresses from the FEA are compared with the bending moments calculated using the static equilibrium conditions. In the method of integrating the stress, both the stress due to the reinforcing bar and the stress of the concrete are considered. In addition, various factors affecting the accuracy of the stresses calculated by the FEA were analyzed and the influence of the displacement function and the element size was verified. If the purpose of the analysis is to roughly observe the behavior of the members, it is appropriate to use the first order displacement function and the element size should be about 25% of the section height of the analytical model. When the bending moment of a member with high accuracy is required, it is suggested that the secondary displacement function be used and the element size be 12.5%.
Keywords
reinforced concrete; nonlinear analysis; bending moment; nodal stress; element size;
Citations & Related Records
연도 인용수 순위
  • Reference
1 ABAQUS 6.14 Online Documentation (2014) Dassault Systemes Simulia Corp., Providence, RI, USA.
2 ACI Committee 318 (2008) Building Code Requirements for Structural Concrete (ACI 318M-08) and Commentary, American Concr. Inst., p.465.
3 Atkinson, K.E. (1989) An Introduction to Numerical Analysis 2d ed, John Wiley & Sons, p.218.
4 Carpinteri, A. (2011) Failure Mode Transitions in Reinforced Concrete Beams - Part2: Experimental Tests, ACI Struct. J., 108-S27, pp.286-293.
5 CEB-FIP (2010) fib Model Code for Concrete Structures 2010 Ernst & Sohn, p.292.
6 Chandrupatla, T.R., Belegundu, A.D. (2002) Introduction to Finite Elements in Engineering, Prentice Hall, Third ed, p.453.
7 Chaudhari, S.V., Chakrabarti, M.A. (2012) Modeling of Concrete for Nonlinear Analysis Using Finite Element Code ABAQUS, Int. J. Comput. Appl., 44, pp.15-18.
8 Cook, R.D. (1995) Finite Element Modeling For Stress Analysis, John Wiley & Sons, Inc, pp.330.
9 Cook, R.D., Malkus, D.S. (1989) Concepts and Applications of Finite Element Analysis 3rd ed, John Wiley & Sons, Inc, p.630.
10 Durand, R., Farias, M.M. (2014) A Local Extrapolation Method for Finite Elements, Adv. Eng. Softw., 67, pp.1-9.   DOI
11 Gere, J.M. (2003) Mechanics of Materials 6th ed, Thomson Brooks/Cole, p.960.
12 Gilbert, R.J., Warner, R.F. (1978) Tension Stiffening in Reinforced Concrete Slabs, American Soc. Civil Eng., 104, pp.1885-1900.
13 Hu, H.-T. (2004) Nonlinear Finite Element Analysis of Reinforced Concrete Beams Strengthened by Fiber-reinforced Plastics, Compos. Struct., 63, pp.271-281.   DOI
14 Jain, S.C., Kennedy, J.B. (1974) Yield Criterion for Reinforced Concrete Slabs, American Soc. Civil Eng., 100, pp.631-644.
15 Jie, Y.-X., Yuan, H.-N. (2013) Bending Moment Calculations for Piles Based on the Finite Element Method, J. Appl. Math., pp.1-19.
16 KCI (2012) Concrete Structure Code and Commentary, Korea Concr. Inst., p.342.
17 Logan, D.L. (2012) A First Course in The Finite Element Method, Cengage Learning, p.925.
18 Timoshenko, S., Goodier, J.N. (1951) Theory of Elasticity 2nd ed., Mcgraw-hill Book Company, Inc, p.506.
19 Yu, J. (2016) New Extended Finite Element Method for Pinching Effect in Reinforced Concrete Columns, ACI Struct. J., No. 113-S59 pp.689-699.
20 Hibbeler, R.C. (2012) Structural Analysis 8 edition in SI Units, Pearson, p.695.