Incremental Collapse of Structures with Constant Plus Cyclically Varying Loads
Publication: Journal of Structural Engineering
Volume 117, Issue 6
Abstract
Energy methods previously developed for the shakedown analyses of framed structures are extended to include structures subjected to cyclically varying loads in the presence of constant, or bias, loads. This approach is based on the hypothesis that, if the total hysteresis energy absorbed by a structure during an indefinitely prolonged repetitive loading program is unbounded, then the structure must ultimately fail. This hypothesis leads to results that are entirely consistent with the classical shakedown theorems. Several illustrative examples demonstrate that the incremental collapse envelopes of framed structures subjected to cyclically varying patterns of loading can be drastically reduced when constant loads are present. These results are essentially due to inelastic interactions between the cyclic and constant loads that magnify the effects of hysteresis. In fact, the reduction in the safe loading ranges (as defined by the incremental collapse envelope) can be a sensitive function of the constant, or bias, load components.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Akiyama, H. (1985). Earthquake‐resistant limit‐state design of buildings. University of Tokyo Press, Tokyo, Japan.
2.
Bernstein, B., Erber, T., and Guralnick, S. A. (1991). “Thermodynamics of plastic hinges with damage.” J. Contin. Mech. Thermodyn. (in press).
3.
Bleich, H., (1932). “Ueber die Bemessung statisch unbestimmter Stahltragwerke unter Berucksichtigung des elastich‐plastischen Verhaltens des Baustoffes.” Bauingenieur, Berlin, Germany, 13 (19/20), 261–267(in German).
4.
Debordes, O., and Nayroles, B. (1976). “Sur la Theorie et le Calcul a L'Adaption des Structures Elastoplastiques.” J. de Mecanique, Paris, France, 15(1), 1–53(in French).
5.
Erber, T., Guralnick, S. A., and Latal, H. G. (1972). “A general phenomenology of hysteresis.” Ann. Phys., 69(1), 161–192.
6.
Erber, T., and Guralnick, S. A. (1988). “Hysteresis and incremental collapse: The iterative evolution of a complex system.” Ann. Phys., 181(1), 25–53.
7.
Gruening, M. (1926). Die tragfahigkeit statisch Unbestimmter Tragwerke aus Stahl bei beliebig haufig wiederholter Belastung. Julius Springer, Berlin, Germany (in German).
8.
Guralnick, S. A. (1973). “Incremental collapse under conditions of partial unloading.” Pub., Int. Assoc. for Bridge and Struct. Engrg., Zurich, Switzerland, 33(2), 69–84.
9.
Guralnick, S. A. (1975). “Incremental collapse model for metal fatigue.” Pub., Int. Assoc. for Bridge and Struct. Engrg., Zurich, Switzerland, 35(2), 83–99.
10.
Guralnick, S. A., Singh, S., and Erber, T. (1984). “Plastic collapse, shakedown and hysteresis.” J. Struct. Engrg., ASCE, 110(9), 2103–2110.
11.
Guralnick, S. A., Erber, T., Stefanis, J., and Soudan, O. (1986). “Plastic collapse shakedown and hysteresis of multistory steel structures.” J. Struct. Engrg., ASCE, 112(12), 2610–2627.
12.
Guralnick, S. A., Erber, T., Soudan, O., and Stefanis, J. (1988). “Energy method for incremental collapse analysis of framed structures.” J. Struct. Engrg., ASCE, 114(1), 31–49.
13.
Hodge, P. G., Jr. (1954). “Shakedown of elastic plastic structures.” Residual stresses in metals and metal construction, W. R. Osgood, ed., Reinhold, New York, N.Y.
14.
Horne, M. R. (1948). Discussion of“Theory of inelastic bending with reference to limit design.” by A. Hrennikoff, Trans., ASCE, 113, 250–258.
15.
Horne, M. R. (1954). “The effect of variable repeated loads on building structures designed by the plastic theory.” Proc., Int. Assoc. of Bridge and Struct. Engrg., Zurich, Switzerland, 14, 53–74.
16.
Koiter, W. T. (1960). “Energy theorems for elastic‐plastic solids.” Progress in solid mechanics, 1, Amsterdam, The Netherlands.
17.
Massonet, C. E., and Save, M. A. (1965). Plastic analysis and design. 1, Blaisdell Publishing Co., New York, N.Y.
18.
Melan, E. (1936). “Theorie statisch unbestimmter Systeme.” Prelim. Pub., Second Cong., Int. Assoc. of Bridge and Struct. Engrg., Berlin, Germany, 43‐64 (in German).
19.
Neal, B. G. (1951). “The behavior of framed structures under repeated loadings.” Q. J. Mech. Appl. Math., 4, 78–97.
20.
Neal, B. G. (1977). The plastic methods of structural analysis. Third Ed., Chapman and Hall, London, U.K.
21.
Singh, S. (1982). “Shakedown load and hysteresis phenomena of portal frames,” thesis presented to Ilinois Institute of Technology, at Chicago, Ill., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
22.
Skallerud, B., and Larsen, P. K. (1989). “Nonlinear effects of shakedown of side‐sway frames.” J. Struct. Engrg., ASCE, 115(1), 221–227.
23.
Soudan, O. (1987). “Incremental collapse analysis of multi‐bay, multi‐story structures,” thesis presented to Illinois Institute of Technology, at Chicago, Ill., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
24.
Stefanis, I. P. (1987). “Plastic collapse, shakedown and hysteresis of multi‐bay, multi‐story rigid frame structures,” thesis presented to Illinois Institute of Technology, at Chicago, Ill, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
25.
Symonds, P. S., (1952). Discussion of “Plastic design and the deformation of structures.” Yang, C. H., Beedle, L. S., and Johnston, B. G. Welding, 31 (1), 33–36.
26.
Symonds, P. S., and Neal, B. G. (1950). “The calculation of failure loads on plane frames under arbitrary loading programmes.” J. Inst. Civ. Engrs., London, England, 35(1), 41–61.
27.
Symonds, P. S., and Neal, B. G. (1951). “Recent progress in the plastic method of structural analysis.” J. Franklin Inst., 252(5), 383–407.
28.
Xiaofeng, Y. (1989). “Shakedown analysis in plastic design of steel structures.” J. Engrg. Mech., ASCE, 115(2), 304–314.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 117 • Issue 6 • June 1991
Pages: 1815 - 1833
Copyright
Copyright © 1991 ASCE.
History
Published online: Jun 1, 1991
Published in print: Jun 1991
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.