7 - Static Analysis of Plane Trusses

Abstract

A truss is an assembly of slender members that are pin-connected together at their ends, and it is used to support roofs and bridges. The joints where members are interconnected are called nodes and the external loads are only applied to the nodes. A truss member only undergoes longitudinal deformation (tension or compression) along its axis. The chapter analyzes trusses lying and deforming in a plane. A member is modeled as a longitudinal bar that is subjected to external loads only at its two ends. The longitudinal displacement of the bar is governed by a given differential equation. The three types of static disturbances are external forces—concentrated (pointwise) external forces applied to nodes; settlement of supports—deflections of supports in the directions of reactions; and fabrication errors and thermal effects—an increase or decrease of member length because of fabrication errors and thermal changes. A fundamental problem for a plane truss is determining its static response—displacements at nodes, internal forces of members, and reactions at supports—subjected to external loads, support settlement, fabrication errors, and thermal changes. The chapter provides a toolbox of MATLAB functions for obtaining the solution of the problem.