Abstract
In this paper, the co-rotational total Lagrangian forms of finite element formulations are derived to perform elasto-plastic analysis for plane steel frames that either experience increasing external loading at ambient temperature or constant external loading at elevated temperatures. Geometric nonlinearities and thermal-expansion effects are considered. A series of programs were developed based on these formulations. To verify the accuracy and efficiency of the nonlinear finite element programs, numerical benchmark tests were performed, and the results from these tests are in a good agreement with the literature. The effects of the nonlinear terms of the stiffness matrices on the computational results were investigated in detail. It was also demonstrated that the influence of geometric nonlinearities on the incremental steps of the finite element analysis for plane steel frames in the presence of fire is limited.
Similar content being viewed by others
References
Bathe K J. Finite Element Procedures. New Jersey: Prentice Hall, Inc. 1996
Belytschko T, Liu WK. Nonlinear Finite Elements for Continua and Structures. London: Moran B. John Wiley & Sons, Ltd. 2000
Wang X. Finite Element Method. Beijing: Tsinghua University Press Inc. 2002
Mitchell G P, Owen D R J. Numerical solution for elastic-plastic problems. Engineering with Computers, 1988, 5: 274–284
Zhao J C. Application of the direct iteration method for non-linear analysis of steel frames in fire. Fire Safety Journal, 2000, 35(3): 241–255
Tang C Y, Tan K H, Ting S K. Basis and application of a simple interaction formula for steel columns under fire conditions. Journal of Structural Engineering, 2001, 127(10): 1206–1213
Toh W S, Tan K H, Fung T C. Strength and stability of steel frames in fire. Journal of Structural Engineering, 2001, 127(4): 461–469
Tan K H, Ting S K, Huang Z F. Visco-elasto-plastic analysis of steel frames in fire. Journal of Structural Engineering, 2002, 128(1): 105–114
Vimonsatit V, Tan K H, Ting S K. Nonlinear elastoplastic analysis of semirigid steel frames at elevated temperature: MP appraoch. Journal of Structural Engineering, 2003, 129(5): 661–671
Huang Z F, Tan K H. Effects of external bending moments and heating schemes on the responses of thermally restrained steel columns. Engineering Structures, 2004, 26(6): 769–780
Huang Z F, Tan K H. Fire resistance of compartments within a highrise steel frame: New sub-frame and isolated member models. Journal of Constructional Steel Research, 2006, 62(10): 974–986
Li G Q, Guo S X. Analysis of restrained heated steel beams during cooling phase. Steel and Composite Structures, 2009, 9(3): 191–208
Huang Z F, Tan K H, Ting S K. Heating rate and boundary restraint effects on fire resistance of steel columns with creep. Engineering Structures, 2006, 28(6): 805–817
Huang Z H, Burgess I W, Plank R J. Three-dimensional analysis of composite steel-framed buildings in fire. Journal of Structural Engineering, 2000, 126(3): 389–397
Li G Q, Wang P, Hou H. Post-buckling behaviours of axially restrained steel columns in fire. Steel and Composite Structures, 2009, 9(2): 89–101
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Xia, B., Wu, Y. & Huang, Z. Implementation of total Lagrangian formulation for the elasto-plastic analysis of plane steel frames exposed to fire. Front. Struct. Civ. Eng. 6, 257–266 (2012). https://doi.org/10.1007/s11709-012-0163-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11709-012-0163-9