# Frontiers of Structural and Civil Engineering

 Front Struc Civil Eng    2012, Vol. 6 Issue (3) : 297-307     https://doi.org/10.1007/s11709-012-0162-x
 RESEARCH ARTICLE
Finite element analysis of creep for plane steel frames in fire
Hui ZHU1, Yuching WU2()
1. Chinese Architecture Shanghai Design Institute Co. Ltd., Shanghai 200092, China; 2. Department of Building Engineering College of Civil Engineering, Tongji University, Shanghai 200092, China
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 Abstract Steel is widely used for the construction of bridges, buildings, towers, and other structures because of its great strength, light weight, ductility, and ease of fabrication, but the cost of fireproofing is a major disadvantage. Therefore, the resistance of a steel structure to fire is a significant subject for modern society. In the past, for simplification, creep behavior was not taken into account in research on the resistance of a steel structure to fire. However, it was demonstrated that the effect of creep is considerable at temperatures that commonly reach 600°C and should not be neglected in this context. In this paper, a co-rotational total Lagrangian finite element formulation is derived, and the corresponding numerical model is developed to study the creep behavior of plane steel frames in fire conditions. The geometric nonlinearity, material nonlinearity, high temperature creep, and temperature rate of change are taken into account. To verify the accuracy and efficiency of the numerical model, four prototypical numerical examples are analyzed using this model, and the results show very good agreement with the solutions in the literature. Next, the numerical model is used to analyze the creep behavior of the plane steel frames under decreasing temperatures. The results indicate that the effect of creep is negligible at temperatures lower than 500°C and is considerable at temperatures higher than 500°C. In addition, the heating rate is a critical factor in the failure point of the steel frames. Furthermore, it is demonstrated that the deflection at the midpoint of the steel beam, considering creep behavior, is approximately 13% larger than for the situation in which creep is ignored. At temperatures higher than 500°C, the deformed steel member may recover approximately 20% of the total deflection. The application of the numerical model proposed in this paper is greatly beneficial to the steel industry for creep analysis, and the numerical results make a significant contribution to the understanding of resistance and protection for steel structures against disastrous fires. Corresponding Author(s): WU Yuching,Email:ycwu@tongji.edu.cn Issue Date: 05 September 2012
 Cite this article: Yuching WU,Hui ZHU. Finite element analysis of creep for plane steel frames in fire[J]. Front Struc Civil Eng, 2012, 6(3): 297-307. URL: http://journal.hep.com.cn/fsce/EN/10.1007/s11709-012-0162-x http://journal.hep.com.cn/fsce/EN/Y2012/V6/I3/297
 Fig.1  Configuration of the plane steel frame and its cross-section. Fig.2  Horizontal displacements at the two top points of the columns at different temperatures. Fig.3  Configuration of the simple beam and its cross-section. Fig.4  Comparison between results from the present study and solutions from the literature at a heating rate of (a) 20°C/min, (b) 5°C/min, and (c) 2°C/min. Tab.1  Cross-sections of beams and columns Tab.2  Material properties of steel Fig.5  One-story two-span steel frame under loading. Fig.6  Temperature-time relationships of measurement points at (a) span A and (b) span B. Fig.7  Relationship between the time and the displacement at the midpoint of (a) span A and (b) span B. Fig.8  Configuration and cross-section of the simple beam Fig.9  Relationship between the displacement of the midpoint of the simple beam and time Fig.10  Comparison between the displacements of the midpoint of the beam with and without consideration of creep Fig.11  Configuration of the plane steel frame and cross-sections of the beam and column Fig.12  Comparison between the displacements of the midpoint of the beams with and without consideration of creep
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