The stiffness method for dynamic analysis of frames presented in Chapter 15 for plane frames and in Chapter 16 for grids 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 translations along the x, y, z axes and three rotations 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.
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