Evaluation of Elasto-Plastic Buckling Strength of Two-Way Grid Shells Using Continuum Analogy

Abstract

The present paper aims to propose a method to evaluate elasto-plastic buckling strength of two-way grid shells, using mathematical formulas for linear buckling derived based on the continuum shell analogy. The paper is organised from two principal points of view. In the first discussion, we derive two formulas for linear buckling of two-way grid shells by substituting the equivalent continuum rigidity into the buckling formulas for orthotropic shells. The applicability of the formulas is verified using several structural examples by comparison with the other proposed formulas and FEM results. In the second discussion, based on the concept of column buckling, an effective approach to estimate elasto-plastic buckling strength of two-way grid shells is demonstrated. In the estimation procedure, the buckling formulas derived in the first discussion are effectively applied to obtain the generalised slenderness.

Analysis based evaluation for buckling loads of two-way elliptic paraboloidal single layer lattice domes

“…In the case of two-way elliptic paraboloidal single layer lattice domes, the effects of geometrical imperfections are also large, as discussed in the studies [1,2]. The present study assumes a distribution, W imp (x, y), for geometrical imperfections, where the maximum imperfection is denoted as w i0 .…”

“…2. For a typical example, one value of 1/3 for β is adopted here, since the effects of β are expected not to be so big according to the study [1,2].…”

“…Secondly, an appropriate kind of strength interaction between design stresses is adopted for member proportioning. The following may be possible for the circular tube members used in the present study, with an assumption that the effects due to twisting moments will be small as discussed in the study [1,2].…”

“…Especially, the two-way elliptic paraboloidal single layer lattice dome has been often adopted for roof structures. However, the buckling characteristics have not been sufficiently investigated so far except for the studies [1,2]. In the design of such structures, one of the important tasks is to secure sufficient safety against buckling.…”

“…In this study, it is also proved that the column buckling concept is efficient in estimating elasto-plastic buckling loads of twoway elliptic paraboloidal single layer lattice domes if shelllike imperfection sensitivity is reflected using an appropriate knock down factor. The knock down factor for the two-way single layer lattice dome was not intensively investigated in the previous studies except for the researches [2][3][4] and the value is briefly discussed in this study. Following the studies for the column buckling strength curve considering shell-like imperfection sensitivity, this paper also suggests a systematic member proportioning procedure for design of such a twoway lattice dome.…”