Limit Analysis of Curved Grids
Publication: Journal of Structural Engineering
Volume 116, Issue 6
Abstract
The limit analysis of a class of grillages consisting of essentially two main circular arc girders connected by a number of straight cross beams is formulated as a mathematical programming problem using the static or lower bound theorem of plasticity. Discretization of both the structure into finite elements and of the nonlinear bending‐torsion yield surface into a piecewise linear polygon converts the formulation into an easy‐to‐solve linear programming problem. Sufficient details on how to enforce the necessary requirements of equilibrium and yield conformity are given to allow a direct computer implementation. The use of a mathematical programming based formulation is shown to overcome various shortcomings of existing methods to solve the same problem, the main ones being lack of generality, need for prior knowledge of collapse modes, and computational difficulty. Finally, an example is presented primarily to illustrate the application of method, and also to show how useful design‐oriented charts can be developed through parametric studies.
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References
1.
Badawy, H. E. I., and Jordaan, I. J. (1977). “Plastic analysis of curved beams under point loads.” J. Struct. Div., ASCE, 103(7), 1429–1445.
2.
“BLP88—Linear programming with bounded variables fo the IBM PC.” (1987). User's Manual, Ver. 7.08, Eastern Software Products, Inc., Alexandria, Va.
3.
Boulton, N. S., and Boonsukha, B. (1959). “Plastic collapse of circular‐arc bow girders.” Proc., Institution of Civil Engineers, 13, June, 161–178.
4.
Charnes, A., and Greenberg, H. J. (1951). “Plastic collapse and linear programming.” Abstract No. 506, Amer. Math. Soc., Sep.
5.
Grierson, D. E., and Abdel‐Basset, S. B. (1977). “Plastic analysis under combined stresses.” J. Engrg. Mech. Div., ASCE, 103(5), 837–854.
6.
Heyman, J. (1951). “The limit design of space frames.” J. Appl. Mech., 18(2), 157–162.
7.
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(3), 207–214.
8.
Imai, F., and Ohta, T. (1983). “Plastic analysis of curved grillage girders.” Memoirs of the Fac. of Engrg., Kyushu Univ., 43(1), 1–8.
9.
Imegwu, E. O. (1964). “Ultimate strength of plane curved girders.” The Struct. Engr., 42(4), 129–134.
10.
Jackson, N. (1965). “The automatic calculation of collapse loads for circular‐arc beams.” The Struct. Engr., 43(12), 413–421.
11.
Jackson, N. (1966). “Collapse loads for circular‐arc beams.” J. Struct. Div., ASCE, 92(5), 1–12.
12.
Jordaan, I. J., and Khalifa, M. A., and McMullen, A. E. (1974). “Collapse of curved reinforced concrete beams.” J. Struct. Div., ASCE, 100(11), 2255–2269.
13.
Maier, G. (1970). “A matrix theory of piecewise linear elastoplasticity with interacting yield planes.” Meccanica, 5(1), 54–66.
14.
Maier, G., and Munro, J. (1982). “Mathematical programming applications to engineering plastic analysis.” Appl. Mech. Review, 35(12), 1631–1643.
15.
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., American Society of Mechanical Engineers, New York, N.Y., 377–383.
16.
Mikami, I., and Yonezawa, H. (1967). “On the plastic analysis of curved grillage girders. Third report: Curved bridges with multiple cross girders.” Proc., 17th Japan Nat. Congress of Appl. Mech., Japan National Committee for Theoretical and Applied Mechanics, 17, 64–69.
17.
Tin‐Loi, F. (1990). “A yield surface linearization procedure in limit analysis.” To be published in Mech. Struct. Mach., 18(1).
18.
Yonezawa, H., and Mikami, I. (1965). “On the plastic analysis of curved grillage girders.” Proc. 15th Japan Nat. Congress of Appl. Mech., Japan National Committee for Theoretical and Applied Mechanics, 15, 82–87.
19.
Yonezawa, H., and Mikami, I. (1966). “On the plastic analysis of curved grillage girders. Second report: Curved bridges under a load uniformly distributed over cross girder.” Proc. 16th Japan Nat. Congress of Appl. Mech., Japan National Committee for Theoretical and Applied Mechanics, 16, 67–73.
20.
Yoo, C. H., and Heins, C. P. (1972). “Plastic collapse of horizontally curved girders.” J. Struct. Div., ASCE, 98(4), 899–913.
21.
Zavelani‐Rossi, A. (1973). “A new linear programming approach to limit analysis.” Variational Methods in Engineering, Vol. 2, C. A. Brebbia and H. Tottenham, eds., Southampton University Press, Southampton, England.
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Copyright © 1990 ASCE.
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Published online: Jun 1, 1990
Published in print: Jun 1990
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