Dynamic Response of Softening Structures
Publication: Journal of Structural Engineering
Volume 113, Issue 6
Abstract
Computation of the full response of concrete frame structures to severe dynamic loads requires consideration of softening in addition to plasticity and hysteresis. Critical softening parameters and ground frequencies are determined for simple flexural structures. For unidirectional loads, the critical softening parameter depends on the severity of the applied load as represented by the ratio of maximum applied force to maximum resistance (or by energy of impulse to maximum elastic strain energy), on the plastic plateau length (ductility) on any limit to the softening region, and on the duration of load in the case of a rectangular load function. Conversely, for a given softening slope, a critical severity of load, critical plateau length, or critical duration of load may be identified. For the response to reversible loads, a stiffness matrix for flexural elements with finite softening lengths is used in the analysis. The softening of individual hinges is reflected in the overall hysteresis loop of a structure. Elastic‐softening structures perform well in absorbing energy at relatively high frequencies.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Al‐Sulaimani, G. J., and Roessett, J. M., “Design Spectra for Degrating Systems,” Journal of Structural Engineering, ASCE, Vol. 111, No. 12, Dec., 1985, pp. 2611–2623.
2.
Atalay, M. B., and Penzien, J., “The Seismic Behavior of Critical Regions of Reinforced Concrete Components as Influenced by Moment, Shear and Axial Force,” Report No. EERC 75‐19, Earthquake Engineering Research Center, University of California, Berkeley, Calif., 1975.
3.
Bathe, K.‐J., and Wilson, E. L., Numerical Methods in Finite Element Analysis, Prentice‐Hall, Englewood Cliffs, N.J., 1976, pp. 322–323.
4.
Biggs, J. M., Introduction of Structural Dynamics, McGraw‐Hill, New York, N.Y., 1964.
5.
Clough, R. W., “Effect of Stiffness Degradation on Earthquake Ductility Requirements,” Report 66‐16, Structural and Material Research, Structural Engineering Laboratory, University of California, Berkeley, Calif., 1966.
6.
Clough, R. W, and Penzien, J., Dynamics of Structures, McGraw‐Hill, New York, N.Y., 1975.
7.
Darvall, P. L., “Critical Softening of Hinges in Indeterminate Beams and Portal Frames,” Civil Engineering Transactions, I.E. Australia, Vol. CE 25, No. 3, Aug., 1983, pp. 199–210.
8.
Darvall, P. L., “Critical Softening of Hinges in Portal Frames,” Journal of Structural Engineering, ASCE, Vol. 110, No. 1, Jan., 1984, pp. 157–162.
9.
Darvall, P. L., “Shakedown with Softening in Reinforced Concrete Beams,” Materials and Structures, RILEM (Paris), Vol. 17, No. 102, Nov.–Dec., 1984, pp. 421–426.
10.
Darvall, P., “Stiffness Matrix for Elastic‐Softening Beams,” Journal of Structural Engineering, ASCE, Vol. 111, No. 2, Feb., 1985, pp. 469–473.
11.
Darvall, P. L., and Mendis, P. A., “Elastic‐Plastic‐Softening Analysis of Plane Frames,” Journal of Structural Engineering, ASCE, Vol. 111, No. 4, Apr., 1985, pp. 871–888.
12.
Mahin, S. A., and Bertero, V. V., “An Evaluation of Inelastic Seismic Design Spectra,” Journal of the Structural Division, ASCE, Vol. 107, No. ST9, Sept., 1981, pp. 1777–1795.
13.
Newmark, N. M., “A Method of Computation for Structural Dynamics,” Journal of the Engineering Mechanics Division, ASCE, Vol. 85, No. EM3, Jul., 1959, pp. 67–94.
14.
Recommended Lateral Force Requirements and Commentary, Seismology Committee, Structural Engineers' Association of California, San Francisco, Calif., 1973, p. 146.
15.
Sanjayan, G., and Darvall, P. L., “Dynamic Response of a Single Degree‐of‐Freedom Elastic‐Plastic‐Softening Structure,” Research Report 8/1984, Dept. of Civil Engineering, Monash University, Victoria, Australia, 1984.
16.
Sanjayan, G., and Darvall, P. L., “Dynamic Response of Elastic‐Plastic‐Softening Structures to Reversible Loads,” Research Report 6/1985, Dept. of Civil Engineering, Monash University, Victoria, Australia, 1985.
17.
17. Takayanagi, T., and Schnobrich, W. C., “Computed Behaviour of Reinforced Concrete Coupled Shear Walls,” Structural Research Series, No. 434, University of Illinois, Urbana, Ill., 1976.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 113 • Issue 6 • June 1987
Pages: 1203 - 1220
Copyright
Copyright © 1987 ASCE.
History
Published online: Jun 1, 1987
Published in print: Jun 1987
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.