Dynamic Analysis of Three-Dimensional Frames

Abstract

The stiffness method for dynamic analysis of frames presented in Chap. 11for plane frames and in Chap. 12for grid frames can readily be expanded for the analysis of three-dimensional space frames. Although for the plane frame or for the grid there were only three nodal coordinates at each joint, the three-dimensional frame has a total of six possible nodal displacements at each unconstrained joint: three translation components along the x, y, z axes and three rotational components about these axes. Consequently, a beam element of a three-dimensional frame or a space frame has for its two joints a total of 12 nodal coordinates; hence the resulting element matrices will be of dimension 12 × 12.