Buckling of Columns with Random Initial Displacements

by Michael C. Bernard, Assoc. Prof. of Engrg. Sci. and Mech.; Georgia Inst. of Tech. Atlanta, GA,
John L. Bogdanoff, Prof. of Aeronautical, Astronautical, and Engrg. Sci.; Purdue Univ., Lafayette, IN,

Serial Information: Journal of the Engineering Mechanics Division, 1971, Vol. 97, Issue 3, Pg. 755-771

Document Type: Journal Paper


Classical Bernoulli-Euler results for column buckling are compared with those obtained by considering a column that is initially, randomly bent and twisted instead of being ideally straight. The nonlinear column equations of Love are formulated in terms of the displacement components and the angle of twist; linearization proceeds on the assumption that the twist rate is large. A scheme is then developed whereby the statistical moments of these quantities may be calculated to any degree of accuracy. Computations show that the scatter in buckling data may be very large due to the initial geometrical eccentricities in the shape of the column which are generally neglected in obtaining classical buckling results. The addition of frequency components in the twist results in substantially larger increases in the scatter of the displacement components than the addition of the same components to the initial bending; further, the addition of higher frequency components results in smaller increases in the scatter than the addition of lower frequency components.

Subject Headings: Columns | Buckling | Displacement (mechanics) | Bents (structural) | Linear functions | Statistics | Computing in civil engineering | Geometrics

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