Nonlinear Elastic In-Plane Buckling of Shallow Truss Arches

Abstract

The available analytical methods for determining the buckling resistance of trusses typically focus on the local load capacity of individual elements and ignore global in-plane buckling behavior. In addition, theoretical expressions that describe the in-plane critical buckling load of shallow arches do not account for trusses or nonsolid cross sections. This paper investigates the nonlinear elastic in-plane buckling behavior of shallow truss arches subjected to a uniformly distributed gravity load. Adapted methods for calculating the equivalent moment of inertia and equivalent area of truss cross sections are presented first. Using these equivalent geometric properties and existing analytical expressions, a novel methodology is then presented for generating an equivalent arch model that accurately predicts the critical nonlinear elastic in-plane buckling behavior of shallow truss arches. This methodology is validated by obtaining close agreement between the nonlinear elastic critical buckling factors of the truss arches and their accompanying equivalent arch models. Approximation equations, using the equivalent moment of inertia, are also generated for estimating the nonlinear elastic critical buckling factor for fixed- and pin-connected shallow truss arches. A simple strategy is presented to augment the existing nonlinear elastic in-plane arch buckling equations by efficiently identifying the approximate central axis location of the truss cross section at midspan.