Shakedown of Grids under Combined Bending and Torsion
Publication: Journal of Structural Engineering
Volume 115, Issue 11
Abstract
The shakedown analysis of plane elastoplastic grillage structures for which plasticity is affected by the combined action of bending moment and torsion is formulated using the static or lower bound Bleich‐Melan theorem. Discretization of the structure into finite elements and the nonlinear yield surface into a piecewise linear one, converts the formulation into a linear programming problem that can be solved efficiently using standard packages. How the necessary requirements of equilibrium and yield conformity are satisfied, and how the elastic locus is calculated are also mentioned. A method of identifying whether incremental collapse or alternating plasticity is the governing mode of failure is given. Based on the formulation presented, a FORTRAN computer program named SGRID was written to carry out the shakedown analysis of general planar grillages. Finally, several examples of typical bridge grillages are presented primarily to demonstrate the effect of including torsion in the analyses and also to indicate how easy it is to perform such analyses for practical engineering applications.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Carskaddan, P. S., and Haaijer, G. (1978). “Bridge design by the autostress method.” Transp. Res. Rec., 664, 255–262.
2.
Draft bridge design specification (in limited state format). (1987). National Association of Australian State Road Authorities (NAASRA), Sydney, Australia.
3.
Eyre, D. G., and Galambos, T. V. (1973). “Shakedown of grids.” J. Struct. Engrg., ASCE, 99, 2049–2060.
4.
Grundy, P. (1976). “Bridge design criteria.” Proc. Metal Struct. Conf., Adelaide, Australia, 73–77.
5.
Grundy, P. (1981). “The application of shakedown theory to the design of bridge superstructures.” Proc. 9th Australas. Conf. Mech. Struct. Mater., Sydney, Australia, 179–184.
6.
Grundy, P., and Spencer, W. J. (1975). “Shakedown of elastoplastic grids.” Proc., 5th Australas. Conf. Mech. Struct. Mater., Melbourne, Australia, 219–236.
7.
Haaijer, G., Schilling, C. G., and Carskaddan, P. S. (1983). “Limit‐state criteria for load‐factor design of steel bridges.” Engrg. Struct., 5, 191–195.
8.
Hill, R., and Siebel, M. P. L. (1953). “On the plastic distortion of solid bars by combined bending and twisting.” J. Mech. Phys. Solids, 1, 207–214.
9.
Koiter, W. T. (1960). “General theorems for elastic‐plastic solids.” Progress in Solid Mechanics, North Holland, Amsterdam, The Netherlands, 165–221.
10.
König, J. A. (1987). Shakedown of elastic‐plastic structures, Elsevier, Amsterdam, The Netherlands.
11.
König, J. A., and Maier, G. (1981). “Shakedown analysis of structures: A review of recent developments.” Nucl. Engrg. Des., 66, 81–95.
12.
Maier, G. (1969). “Shakedown theory in perfect elastoplasticity with associated and nonassociated flow‐laws: A finite element, linear programming approach.” Meccanica, 6, 250–260.
13.
Maier, G. (1973). “A shakedown matrix theory allowing for workhardening and second‐order effects.” Proc., Int. Symp. Foundations of Plasticity, A. Sawczuk, ed., Noordhoff, Leyden, The Netherlands, 417–433.
14.
Maier, G. (1977). “Shakedown analysis.” Engineering Plasticity and Mathematical Programming, NATO‐ASI, Pergamon, Chap. 6.
15.
Maier, G., and Munro, J. (1982). “Mathematical programming applications to engineering plastic analysis.” AMR, 35, 1631–1643.
16.
Morris, G. A., and Fenves, S. J. (1969). “Approximate field surface equations.” J. Engrg. Mech., ASCE, 97, 937–954.
17.
Ontario highway bridge design code. (1983). 2nd Ed., Ontario Ministry of Transp. and Communications, Downsview, Ontario, Canada.
18.
Przemieniecki, J. S. (1968). Theory of matrix structural analysis. McGraw‐Hill, New York, N.Y.
19.
SCICONIC/VM user guide. (1986). Version 1.40, Scicon Limited, England.
20.
Standard specifications for highway bridges. (1983). 13th Ed., Amer. Assoc. of State Highways and Transp. Officials (AASHTO), Washington, D.C.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 115 • Issue 11 • November 1989
Pages: 2930 - 2943
Copyright
Copyright © 1989 ASCE.
History
Published online: Nov 1, 1989
Published in print: Nov 1989
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.