Technical Stability of Very Slender Rectangular Columns Compressed by Ball-And-Socket Joints without Friction

Stability of load-bearing members, as known, is a challenging issue and several tools are available for designers. Disregarding the material properties in use, the avoidance of possible stability troubles is a mandatory and challenging step of the overall design process. In this study, a theoretical model is presented for the of loss of stability in elastic states of very slender rectangular shell elements axially compressed through ball-and-socket joints without friction. According to this theory, as shown, a loss of carrying capacity of very slender columns in elastic states occurs when the line of force leaves a critical transverse cross-section. The critical transverse cross-section, moreover, progressively moves because of the superposition of bending and pure compression. The theory allows to determine the governing differential equations of curved central lines and their slopes, as well as the critical stresses of columns, in the form of surface function in dependence on slenderness ratios and cross-sectional areas. The graphs for the elastic deflected central line y(x), slope dy/dx, dependence y_L/2(P), stresses and strains for a rectangular column made of steel and compressed by ball-and-socket joints without friction, as well as the corresponding surface graphs of critical stress, are presented in this study. The obtained surface graphs of critical stresses are then discussed and compared with Euler’s formulation.