Structural Analysis Based Upon Principles Pertaining to Unloaded Models

When the stresses in a structure are investigated by the use of unloaded models, known deformations are produced at a section at which the stresses are desired, and the corresponding displacements are measured at the point at which the load is applied in the actual structure. The ratios between the latter and the former deformations give the required stresses for a unit load, and when the original deformation is taken as unity, the model forms the influence line of stress. To obtain a moment, a known or unit rotation is produced at the section at which the stress is required; a normal displacement is produced to obtain a shear or a reaction; and an axial displacement is produced to obtain a direct tension or compression. The geometrical analysis of these operations without the actual use of models leads to fundamental simplifications, and it is the purpose of this paper to establish the few simple equations necessary for the use of this method of analyzing statically indeterminate structures.