Lateral Torsional Stability of Porous Thin-Walled I-Beams With Nonuniform Porosity Distributions Subjected to a Uniformly Distributed Load

Abstract

Existing pores play a significant role in structural materials used in structural members such as plates, shells, and beams. Numerous qualities expected from structural materials involving the lightweight, high stiffness-to-weight ratio, high strength-to-weight ratio, resistance to mechanical and thermal shocks, and thermal insulation can be satisfied by setting porosity distribution from one surface to another. The porosity distribution affects the Young's modulus, shear modulus, and mass density of the material. However, there is a lack of study on the lateral-torsional buckling (LTB) behavior of porous orthotropic thin-walled beams with I-sections. To remedy this lack, this paper aims to analyze the lateral-torsional buckling (LTB) behavior of porous orthotropic thin-walled beams with I-sections subjected to a uniformly distributed load. Young's modulus, shear modulus, and mass density are assumed to be varied in the height direction according to four different porosity distribution patterns. The governing differential equation system of the LTB problem, including the equation of the warping effect, is developed using the Virtual work principle based on classical beam theory. Galerkin's method and an auxiliary function of simply supported boundary conditions are employed to obtain critical LTB load formulation. Additionally, the formulation is confirmed via comparing with existing literature. A parametric study is applied to investigate the influences of porosity coefficients, porosity distribution patterns, orthotropy, slenderness ratio, and geometrical characteristics on the LTB characteristics of porous beams. Parametric study indicates that critical LTB loads of orthotropic I-beams reduce as the web depth and porosity coefficients increase, and they increase with an increase in the orthotropy ratio, flange slenderness ratio, flange-to-web thickness ratio, and span of the beam. The buckling loads of the beam with the D1 pattern are higher than its perfect (D4) counterpart, so the D1 porosity pattern is the best choice to improve the bearing capacity of orthotropic I-beams. Also, the nonuniform porosity distributions (D1 and D3) increasing from origin to flanges enhance the lateral stability of I-beams because the flange has the maximum Young's modulus. The novelty of this study lies in its comprehensive LTB investigation of orthotropic thin-walled beams with I sections exposed to specific effects, such as porosity and warping. These effects on the structural performance are highlighted to significant insights into the porous material design to improve engineering structures' LTB resistance. This study enhances our understanding of composite materials and their application in structural stability analysis across various engineering fields.