Nonlinear Elastoplastic Analysis of Semirigid Steel Frames at Elevated Temperature: MP Approach
Publication: Journal of Structural Engineering
Volume 129, Issue 5
Abstract
An elastoplastic analysis of semirigid steel frames subjected to elevated temperature is presented. Within the discretized structural framework, an updated Lagrangian approach is used to incorporate the nonlinear geometric effects on the equilibrium and constitutive conditions. Modeling of elastoplastic behavior is based on the generalized plastic hinge concept for beam-column elements that obey piecewise linearized yield criteria. Under the proportional temperature variation, the analysis for finite temperature increment becomes the standard form of a nonlinear complementarity problem in mathematical programming (MP) formalism. An iterative predictor–corrector scheme coupled with an MP-based method is used in the analytical procedures. Numerical studies are carried out on rigid and semirigid frames. It is found that the benefits of using a full-strength rigid connection over the semirigid one are not unlimited, particularly on the frames with fire-unprotected columns.
Get full access to this article
View all available purchase options and get full access to this article.
References
Allam, A. M., Green, M. G., Burgess, I. W., and Plank, R. J.(1998). “Fire engineering design of steel-framed, structures-integration of design and research.” J. Constr. Steel Res., 46, 1–3, Paper No. 170.
Arora, J. S. (1989). Introduction to optimum design, McGraw-Hill, Singapore.
Chan, S. L., and Chan, B. H. M.(2001). “Refined plastic hinge analysis of steel frames under fire.” Steel Comp. Struct., 1(1), 111–130.
Comi, C., and Maier, G.(1990). “Extremum theorem and convergence criterion for an iterative solution to finite-step problem in elastoplasticity with mixed nonlinear hardening.” Eur. J. Mech. A/Solids, 9(6), 563–585.
De Freitas, J. A. T., and Smith, D. Lloyd (1984). “Existence, uniqueness and stability of elastoplastic solutions in the presence of large displacements.” S M Arch., 9.
De Freitas, J. A. T., and Smith, D. Lloyd(1985). “Elastoplastic analysis of planar structures for large displacements.” J. Struct. Mech., 12(4), 419–445.
El-Rimawi, J. A., Burgess, I. W., and Plank, R. J.(1995). “The analysis of semi-rigid frames in fire—a secant approach.” J. Constr. Steel Res., 33, 125–146.
Eurocode 3. “Design of steel structures: Part 1.2. General rules. Structural fire design.” (EC3-1.2) (1995). Draft ENV 1993-1-2, Commission of European Communities, Brussels, Belgium.
Furumura, F., and Shinohara, Y. (1978). “Inelastic behaviour of protected steel beams and frames in fire.” Rep. No. 3, Research Laboratory of Engineering Materials, Tokyo.
Kirby, B. R., and Preston, R. R.(1988). “High temperature properties of hot-rolled structural steels for use in fire engineering design studies.” Fire Saf. J., 13, 27–37.
Liu, T. C. H.(1998). “Three-dimensional modelling of steel/concrete composite connection behaviour in fire.” J. Constr. Steel Res., 46, 1–3, Paper No. 361.
Lui, E. M., and Chen, W. F.(1986). “Analysis and behaviour of flexibly-jointed frames.” Eng. Struct., 8(1), 107–118.
Lloyd Smith, D. (1986). “Additional forces in elasto-plastic structural analysis.” Proc., Steel Structures: Recent Research Advances and Their Applications to Design, M. N. Pavlovic, ed., Elsevier Applied Science, London, 53–70.
Lloyd Smith, D., ed. (1990). “Mathematical programming methods in structural plasticity.” CISM Courses and Lectures, Udine, 1986, Springer Verlag, New York.
Maier, G.(1970). “A matrix theory of piecewise linear elastoplasticity with interacting yield planes.” Meccanica, 5, 54–66.
Maier, G., and Lloyd Smith, D. (1986). “Update to mathematical programming applications to engineering plastic analysis.” Appl. Mech. Update, C. R. Steele and G. S. Springer, eds., ASME, New York, 377–383.
Maier, G., and Munro, J.(1982). “Mathematical programming application to engineering plasticity.” Appl. Mech. Rev., 35, 1631–1643.
Najjar, S. R., and Burgess, I. W.(1995). “A nonlinear analysis for three-dimensional steel frames in fire conditions.” Eng. Struct., 18(1), 77–89.
Ravindran, A. (1970). “A computer routine for quadratic and linear programming problems.” Collected Algorithms CACM, School of Industrial Engineering, Purdue Univ., Lafayette, 431, P1–P4.
Rubert, A., and Schaumann, P.(1986). “Structural steel and plane frame assemblies under fire actions.” Fire Saf. J., 10, 173–184.
Saab, H. A., and Nethercot, D. A.(1991). “Modelling of steel frame behaviour under fire conditions.” Eng. Struct., 13, 371–382.
Tang, C. Y., and Tan, K. H.(2001). “Basis and application of simple interaction formula for steel frames under fire conditions.” J. Struct. Eng., 127(10), 1214–1220.
Tin-Loi, F., and Misa, J. S.(1996). “Large displacement of elastoplastic analysis of semirigid steel frames.” Int. J. Numer. Methods Eng., 39, 741–762.
Tin-Loi, F., and Vimonsatit, V.(1996). “Nonlinear analysis of semirigid frames: a parametric complementarity approach.” Eng. Struct., 18(2), 115–124.
Toh, W. S., Fung, T. C., and Tan, K. H.(2001a). “Fire resistance of steel frames using classical and numerical methods.” J. Struct. Eng., 127(7), 829–838.
Toh, W. S., Tan, K. H., and Fung, T. C.(2001b). “Strength and stability of steel frames in fire: The Rankine approach.” J. Struct. Eng., 127(4), 461–469.
Vimonsatit, V., Tan, K. H., and Ting, S. K.(2003). “Plastic limit temperatures of flexibly connected steel frames: an LP problem.” J. Struct. Eng., 129(1), 79–86.
Wang, Y. C., and Moore, D. B.(1995). “Steel frames in fire: Analysis.” Eng. Struct., 17(6), 462–472.
Wong, M. B.(2001). “Plastic frame analysis under fire conditions.” J. Struct. Eng., 127(3), 290–295.
Wong, M. B., Ghojel, J. I., and Crozier, D. A.(1998). “Temperature-time analysis for steel structures under fire conditions.” Struct. Eng. Mech., 6(3), 275–289.
Information & Authors
Information
Published In
Copyright
Copyright © 2003 American Society of Civil Engineers.
History
Received: Dec 6, 2001
Accepted: Jul 29, 2002
Published online: Apr 15, 2003
Published in print: May 2003
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.