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

Abstract

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 balland-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 yL/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.

Stability, Stress and Strain Analysis of Very Slender Pinned Thin-Walled Box Columns according to FEM, Euler and TSTh

“…In the paper (Murawski, 2020c), according to the TSTh as a theoretical example, was analyzed the rectangular column made of steel with dimensions: The shorter median side a = 20 mm, longer median side b = 28 mm, thickness t = 1 mm, length L = 2500 mm and slenderness ratio  = 314.8. From the stability analysis were obtained the graphs of the elastic line y(x), its slope dy/dx, the function yL/2(P) and compressive critical stresses cr.…”

“…The Linear Critical Buckling Load analysis was applied. The column was modelled as made of steel R35 (Murawski 2003a(Murawski , 2004b(Murawski , 2017a(Murawski , 2017b(Murawski , 2020a(Murawski , 2020b(Murawski , 2020c.…”

“…9-13 for a box-section column made of steel R35 with the Young's modulus E = 166 600 MPa and nominal dimensions a = 20 mm, b = 28 mm and t = 1 mm and length L = 2500 mm ( = 314.8 the slenderness, when the limiting slenderness el-lt = 102.7) and the column is compressed by ball-and-socket joints without friction. The same column was searched according to TSTh in the paper of (Murawski, 2020c).  a -0,000240 0,00 0,000240 0,000720 0,00120 0,00168…”

Liquid induced vibrations of partially liquid-filled elastic cylindrical-conical shells

“…The investigation [2] focused on examining the natural frequencies of toroidal and coaxial cylindrical shells, while [8] and [11] delved into the mitigation of liquid sloshing using rigid baffles. Furthermore, research involving the theoretical and experimental stability aspects of cylindrical shells and beams has been accomplished in [1], [12]. The design and manufacture of each new powerful launch vehicles necessitate the development of new fuel tanks.…”

Stability of Heterogeneous Beams with Three Supports—Solutions Using Integral Equations

“…When it comes to the stability of beams or columns, the number of available works is numerous. Notable articles [5][6][7][8] are subject to the elastic stability of axially loaded beams. Not only analytical but also numerical and experimental findings are available.…”