Quartic Formulation for Elastic Beam-Columns Subject to Thermal Effects
Publication: Journal of Engineering Mechanics
Volume 122, Issue 9
Abstract
This paper presents an advanced elastic formulation intended for modeling imperfect beam-columns subject to thermal loading using only one element per member. The new formulation is derived in a local Eulerian (convected) system, where the effects of large displacements and rotations in three-dimensional space are accounted for through transformations between the local and global systems. In the Eulerian system, the proposed formulation utilizes quartic shape functions for the transverse displacements and linear shape functions for the rotational twist, whereas no shape functions are required for the axial displacement since the constant axial force criterion is used. The paper proceeds with the formulation details, where particular emphasis is placed on the modeling of thermal effects. This is followed by a discussion on the modeling of distributed element loads which require special treatment in the context of the large-displacement Eulerian approach. Finally, verification of the new formulation is undertaken using the nonlinear analysis program ADAPTIC, where several examples are presented to illustrate the accuracy and efficiency of the quartic formulation.
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References
1.
Al-Bermani, F. G. A., and Kitipornchai, S.(1990). “Nonlinear analysis of thin-walled structures using least element/member.”J. Struct. Engrg., ASCE, 116(1), 215–234.
2.
Cooke, G. M. E. (1988). “An introduction to the mechanical properties of structural steel at elevated temperatures.”Fire Safety J., 13, 45–54.
3.
European Committee for Standardisation. (1993). “Eurocode 3—design of steel structures: Part 1.2 structural fire design.”EC3, British Standards Instn., London, England.
4.
Izzuddin, B. A. (1991). “Nonlinear dynamic analysis of framed structures,” PhD thesis, Dept. of Civ. Engrg., Imperial Coll., London, England.
5.
Izzuddin, B. A., and Elnashai, A. S. (1992). “ADAPTIC: a program for the adaptive dynamic analysis of space frames.”User manual, Imperial Coll., London, England.
6.
Izzuddin, B. A., and Elnashai, A. S.(1993a). “Adaptive space frame analysis: Part II, a distributed plasticity approach.”Struct. and Build. J., Proc. Instn. Civ. Engrs., London, England, 99(3), 317–326.
7.
Izzuddin, B. A., and Elnashai, A. S.(1993b). “Eulerian formulation for large displacement analysis of space frames.”J. Engrg. Mech., ASCE, 119(3), 549–569.
8.
Izzuddin, B. A., and Elnashai, A. S.(1994). “Discussion of `Buckling and geometrically nonlinear analysis of frames using only one element member,' by A. K. W. So and S. L. Chan.”J. Constructional Steel Res., 28, 321–322.
9.
Izzuddin, B. A., Karayannis, C. G., and Elnashai, A. S.(1994). “Advanced nonlinear formulation for reinforced concrete beam-columns.”J. Struct. Engrg., ASCE, 120(10), 2913–2934.
10.
Izzuddin, B. A., Song, L., and Elnashai, A. S. (1995). “Adaptive analysis of steel frames subject to fire loading.”Computing in civil and building engineering, (ICCCBE'95), P. J. Pahl and H. Werner, eds., A. A. Balkema, Rotterdam, The Netherlands, 643–649.
11.
Karayannis, C. G., Izzuddin, B. A., and Elnashai, A. S.(1994). “Application of adaptive analysis to reinforced concrete frames.”J. Struct. Engrg., ASCE, 120(10), 2935–2957.
12.
Kassimali, A., and Abbasnia, R.(1990). “Large deformation analysis of elastic space frames.”J. Struct. Engrg., ASCE, 117(7), 2069–2087.
13.
Kondoh, K., Tanaka, K., and Atluri, S. N.(1986). “An explicit expression for the tangent-stiffness of a finitely deformed 3-D beam and its use in the analysis of space frames.”Comp. and Struct., 24(2), 253–271.
14.
Oran, C.(1973). “Tangent stiffness in space frames.”J. Struct. Div., ASCE, 99(6), 987–1001.
15.
Oran, C., and Kassimali, A.(1976). “Large deformation of framed structures under static and dynamic loads.”Comp. and Struct., 6, 539–547.
16.
So, A. K. W., and Chan, S. L.(1991). “Buckling and geometrically nonlinear analysis of frames using one element/member.”J. Constructional Steel Res., 20, 271–289.
17.
Soreide, T. H., Amdahl, J., and Rembar, H. (1987). “The idealized structural unit method on space tubular frames.”Aluminium structures: advances, design and construction, R. Narayanan, ed., Elsevier Applied Science, London, England, 674–688.
18.
Wen, R. K., and Rahimzadeh, J.(1983). “Nonlinear elastic frame analysis by finite element.”J. Struct. Engrg., ASCE, 109(8), 1952–1971.
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Copyright © 1996 American Society of Civil Engineers.
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Published online: Sep 1, 1996
Published in print: Sep 1996
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