Abstract
The derivations and applications of one-dimensional elements, including truss, beam, and frame elements are presented. The differences between truss, beam, and frame elements are identified. The stiffness matrices of a space truss element in local and global coordinates are derived. The derivations of consistent load vectors due to initial (thermal) strains and body forces are presented. The stiffness matrix of a one-dimensional beam element and consistent load vectors are derived. The computational details in finding the stresses in a beam subjected to loads are also given. The derivation of the stiffness matrix of the space frame element is considered an assembly of the stiffness matrices of the member under axial forces, torsional forces, and bending loads in two mutually perpendicular (xy and xz) planes. The total 12×12 stiffness matrix of the space frame element, and the 12×12 coordinate transformation matrix are given. The special cases of the space frame element for use in planar frames and beams are also derived. Finally the general characteristics of stiffness matrices such as symmetry, positive diagonal elements, and singularity are discussed.
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