Maximum Strength Design of Structural Frames
Publication: Journal of Structural Engineering
Volume 111, Issue 6
Abstract
A method of solving the minimum weight/maximum strength design problem of plane rigid frames under the influence of their self‐weight as well as externally applied forces is described. Each member of the frame attains the maximum allowable normal or shear stress, or both, for the material. Concepts from the differential game theory are used to reduce the corresponding mathematical optimization problem to a minimax variational one. In the first instance, analytical expressions for the optimum shape of typical plane frame members are obtained. These are then combined with a modified stiffness matrix analysis routine to obtain the optimum shape of the plane rigid frame as a whole. The unified method is applicable to a wide variety of plane rigid frames. Several examples are given to demonstrate its potential.
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References
1.
Banichuk, N. V., “On the Game Theory Approach to Problems of Optimization of Elastic Bodies,” Prikladnaya Matematika i Mekhanika(English Translation: PMM, Applied Mechanics & Mathematics), Vol. 37, No. 6, 1973, pp. 1098–1108.
2.
Banichuk, N. V., “Minimax Approach to Structural Optimization Problems,” Journal of Optimization Theory and Applications, Vol. 20, No. 1, 1976, pp. 111–127.
3.
Gallagher, R. H., and Zienkiewicz, O. C., Optimum Structural Design—Theory and Applications, John Wiley & Sons, London, England, 1973, p. 267.
4.
Haug, E. J., and Kirmser, P. G., “Minimum Weight Design of Beams with Inequality Constraints on Stress and Deflection,” Journal of Applied Mechanics, American Society of Mechanical Engineers, Series E, Vol. 34, No. 4, Dec., 1967, pp. 999–1004.
5.
Kanagasundaram, S., “Game Theory in the Maximum Strength Design of Statically Indeterminate Beams,” Proceedings of the Eighth Australasian Conference on the Mechanics of Structures and Materials, Newcastle, Australia, 1982, pp. 17.1–17.6.
6.
Kanagasundaram, S., and Karihaloo, B. L., “Optimal Strength and Stiffness Design of Beams,” Journal of the Structural Division, ASCE, Vol. 109, No. 1, Jan., 1983, pp. 221–237.
7.
Kanagasundaram, S., and Karihaloo, B. L., “Optimal Strength Design of Beam‐Columns,” International Journal of Solids and Structures, Vol. 19, 1983, pp. 937–953.
8.
Karihaloo, B. L., “Minimum Weight Design of Multi‐purpose Tie‐column of Solid Construction,” Engineering Optimization, Vol. 3, 1978, pp. 239–243.
9.
Karihaloo, B. L., “Optimal Design of Beam‐Columns,” International Journal of Solids and Structures, Vol. 15, 1979, pp. 103–109.
10.
Karihaloo, B. L., and Hemp, W. S., “Maximum Strength/Stiffness Design of Structural Members in Presence of Self‐Weight,” Proceedings Royal Society, London, Series A, Vol. 389, 1983, pp. 119–132.
11.
Karihaloo, B. L., and Parbery, R. D., “Optimal Design of Multi‐purpose Beam‐Columns,” Journal of Optimization Theory and Applications, Vol. 27, 1979, pp. 439–448.
12.
Keller, J. B., “The Shape of the Strongest Column,” Archives of Rational Mechanics and Analysis, Vol. 5, 1960, pp. 275–285.
13.
Keller, J. B., and Niordson, F. I., “The Tallest Column,” Journal of Mathematics and Mechanics, Vol. 16, 1966, pp. 443–444.
14.
Majid, K. I., and Okdeh, S., “Limit State Design of Sway Frames,” The Structural Engineer, Vol. 60B, 1982, pp. 76–82.
15.
Majid, K. I., Stojanovski, P., and Saka, M. P., “Minimum Cost Topological Design of Steel Sway Frames,” The Structural Engineer, Vol. 58B, 1980, pp. 14–20.
16.
Meek, J. L., Matrix Structural Analysis, McGraw‐Hill, New York, N.Y., 1971, p. 330.
17.
Olhoff, N., and Rasmussen, S. H., “On Single and Bimodal Optimum Buckling Loads of Clamped Columns,” International Journal of Solids and Structures, Vol. 13, 1977, pp. 605–614.
18.
Pedersen, P., and Jorgensen, L., “Minimum Mass Design of Elastic Frames Subjected to Multiple Load Cases,” Computers and Structures, Vol. 18, 1984, pp. 147–157.
19.
Tadjbakhsh, I., and Keller, J. B., “Strongest Column and Isoperimetric Inequalities for Eigenvalues,” Journal of Applied Mechanics, American Society of Mechanical Engineers, Series E, Vol. 29, No. 1, Mar., 1962, pp. 159–164.
20.
Taylor, J. E., “Maximum Strength Elastic Structural Design,” Journal of the Engineering Mechanics Division, ASCE, Vol. 95, No. EM3, June, 1969, pp. 653–663.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 111 • Issue 6 • June 1985
Pages: 1267 - 1287
Copyright
Copyright © 1985 ASCE.
History
Published online: Jun 1, 1985
Published in print: Jun 1985
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