Analysis of Trusses, Beams, and Frames

This chapter discusses the derivation of element equations for one-dimensional structural elements. These elements are used for analysis of skeletal-type systems such as planar trusses, space trusses, beams, continuous beams, planar frames, grid systems, and space frames. Pin-jointed bar elements are used in the analysis of trusses. A truss element is a bar that resists only axial forces (compressive or tensile) and can be deformed only in the axial direction. In planar truss analysis, each of the two nodes can have components of displacement parallel to X and Y axes. In three-dimensional truss analysis, each node can have displacement components in X, Y, and Z directions. Rigidly jointed bar (beam) elements are used in the analysis of frames. Thus, a frame or a beam element is a bar that can resist not only axial forces but also transverse loads and bending moments. In the analysis of planar flames, each of the two nodes of an element has two translational displacement components (parallel to X and Y axes) and a rotational displacement (in the plane XY). For a space frame element, each of the two ends is assumed to have three translational displacement components (parallel to X, Y, and Z axes) and three rotational displacement components (one in each of the three planes XY, YZ, and ZX. The chapter also describes a computer program―called FRAME―for the displacement analysis of three dimensional frame structures.