Characteristics of Columns with Uncertain End Restraint
Publication: Journal of Structural Engineering
Volume 116, Issue 6
Abstract
This paper develops exact and approximate probabilistic characteristics of the buckling strength of end‐restrained metal columns. The exact probability density function of the strength is developed from the transcendental equation that governs the buckling condition by nonlinear transformation of random variables. It can only be evaluated by numerics. On the other hand, closed‐form solutions can be obtained if the transcendental equation is approximated by a smooth and differentiable analytic function. A simple analysis procedure based on this approximation is proposed to predict the strength of metal columns with uncertain end restraints. The procedure uses the conventional effective length factor for columns and incorporates the mean and standard deviation of the end restraint in formulation. The end restraint is modeled with two identical rotational springs at the ends of the column. The spring constant for these springs is assumed to be a Weibull‐distributed random variable with known parameters. Results in this work show that the characteristics of the column strength, such as the mean and standard deviation, vary significantly with the degree of uncertainty of the end restraint. It is assumed in this work that the column is slender and free of imperfections and residual stresses.
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References
1.
Bjorhovde, J. (1972). “Deterministic and probabilistic approaches to the strength of steel columns,” thesis presented to Lehigh University, at Bethlehem, Pa., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
2.
Bjorhovde, R. (1984). “Effect of end restraint on column strength—practical applications.” Engrg. J., 21(1), 1–13.
3.
Bjorhovde, R. (1988). “Column: From theory to practice.” Engrg. J., 23(1), 21–34.
4.
Chapuis, J., and Galambos, T. V. (1982). “Restrained crooked aluminium columns.” J. Struct. Div., ASCE, 108(3), 511–524.
5.
Chen, W. F. (1980). “End restraint and column stability,” J. Struct. Div., ASCE, 106(11), 2279–2295.
6.
Chen, W. F., and Lui, E. M. (1983). “End restraint and column design using LRFD.” Engrg. J., 20(1), 29–39.
7.
Chen, W. F., and Lui, E. M. (1984). “Simplified approach to the analysis and design of columns with imperfections.” Engrg. J., 21(1), 99–117.
8.
Chen, W. F., and Lui, E. M. (1985). “Columns with end restraint and bending in load and resistance design factor.” Engrg. J., 22(3), 105–132.
9.
Defalco, F., and Marino, F. J. (1966). “Column stability in type 2 construction.” Engrg. J., 3(2), 67–71.
10.
Galambos, T. V., ed. (1988). SSRC guide to stability design criteria for metal structures. 4th Ed., John Wiley and Sons, New York, N.Y.
11.
Huber, A. W., and Beedle, L. S. (1954). “Residual stresses and compressive strength of steel.” Welding J., 33(12), 589–614.
12.
Jones, W. S., Kirby, P. A., and Nethercot, D. A. (1982). “Columns with semirigid joints.” J. Struct. Div., ASCE, 108(2), 361–372.
13.
Madsen, H. O., Krenk, S., and Lind, N. C. (1986). Methods of structural safety. Prentice‐Hall, Inc., Englewood Cliffs, N.J.
14.
Mann, N. R., Shafer, R. E., and Singpurwalla, N. D. (1974). Methods of statistical analysis of reliability and life data. John Wiley and Sons, New York, N.Y.
15.
Munse, W. H., Bell, W. G., and Chesson, E. (1959). “Behavior of riveted and bolted beam‐to‐column connections.” J. Struct. Div., ASCE, 85(3), 29–50.
16.
Papoulis, A. (1984). Probability, random variables, and stochastic processes. McGraw‐Hill Inc., New York, N.Y.
17.
Razzaq, Z. (1983). “End restraint effect on steel column strength.” J. Struct. Engrg., ASCE, 109(2), 314–334.
18.
Ronald, J., and Maquoi, R. (1979). “Single equation for SSRC column strength curves.” J. Struct. Div., ASCE, 105(1), 247–250.
19.
Sugimoto, H., and Chen, W. F. (1982). “Small end restraint effects on strength of H‐columns.” J. Struct. Div., ASCE, 108(3), 661–681.
20.
Weibull, W. (1939). “A statistical theory of the strength of materials.” Proc., Royal Swedish Institute of Engineering Research, Stockholm, Sweden, 151, 873–876.
21.
Weibull, W. (1951). “A statistical distribution function of wide applicability.” J. Appl. Mech., 18(3), 293–297.
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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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