Stability Analysis of Compression Member on Elastic Supports

Abstract

Part of the large parametric study focused on the stability behavior of compression single members and the member structures with various loadings and boundary conditions is presented here. The presented part relates to the stability analysis of the compression member on elastic springs and elastic foundation. The span of the member L = nℓ, where ℓ is the length of the field which equals to the distance between the neighboring elastic springs. The members under investigation have seven various numbers of the fields n = 2, 3, 4, 5, 6, 7 and ∞. The members have uniform bending rigidity EI, uniform normal force N and (n – 1) elastic springs with equal spring stiffness Cw. The results are presented in the form of 4 diagrams. The curves of diagrams were replaced by the straight lines to be able derived approximate formulae for calculation of the critical force. It is shown that approximate formulae give the values of the critical forces Fcr.a which differ from exact diagram values Fcr less than 3.3 %, being slightly on the safe side. The exact values of the critical forces Fcr obtained from the solution of the stability equation are verified by comparisons with results Fcr.IQ of the computer program IQ 100. Excellent agreement is achieved between Fcr.IQ and Fcr. The presented solution of the compression member on elastic springs may be used also for the calculation of the critical force of the compression member on elastic foundation. The solution given in the paper creates scientific background needed in the design of the semi-through bridge trusses. Stability of the beams on elastic foundation is solved for three different boundary conditions too.