Overall stability of compressed compound bars in variable cross section

Abstract

The article provides the solution to the resistance problem of centrally compressed compound bars of variable section with power-law hardening. The assumed model of S. Timoshenko's theory is valid for calculating and analyzing the general resistance of tower-type bar systems (towers, masts, trestle supports) under certain conditions of stiffening behavior. Unlike the traditional way, the plastic design of lateral shear is made on the basis of independent equilibrium equations. The article describes the condition under which the traditional approach accepted in the technical rod theory and based on the inner forces correlation is valid. Boundary value problem is formulated on the basis of the resolving quadratic equation (traditional approach) and the equation of fourth order (more general, suggested in the paper, adequate definition). For this purpose the technique associated with the increase of the resolving equation’s degree is used. In the first case it is possible to examine only symmetric forms of resistance loss. In the second case both symmetric and asymmetric forms of resistance loss are possible to be examined. Transcendental equation of resistance for different cases of bar's fixing is obtained. The coeffcients of the given length are analyzed depending upon the ways of fixing the end sections. The article points out that unlike the situation with the bars of solid cross-section it is necessary to take into account the shear strain of the grid in the compound bars of variable stiffness while examining their general buckling resistance.

Keywords

• overall stability
• bifurcation
• lattice bar
• shift deformation
• various types of fixation
• non-autonomous differential equations
• degree increment
• accurate solution
• effective length factor