This is an attempt to outline in a single paper the bases of structural analysis when stresses do not exceed the limit of proportionality. The fundamental theorems are stated and the general problems in the analysis of just-stiff and redundant frameworks are discussed. The solution of a just-stiff frame is obtained when a compatible system of stresses is determined, but this is insufficient if the structure be redundant; the strains must then also be compatible. Passing reference is made to the best known methods of stressing just-stiff frames; the stress diagram and method of sections, but the method of tension coefficients is described in rather more detail with reference to the elementary space frame. The classical methods of dealing with redundant frames are next outlined. After a reference to slope-deflexion analysis, of which an early example was Clapeyron's treatment of the continuous beam (the theorem of three moments), the work of Castigliano is considered and in illustration his second theorem is used to obtain the stresses in a flywheel due to the heating of the rim by a brake. A most important contribution to the treatment of redundant structures was made in 1930 when Professor Hardy Cross described his moment distribution method. This is illustrated by an example and reference is made to the powerful relaxation methods developed by Professor R. V. Southwell. The paper concludes with a short description of an experimental method for obtaining influence lines and of another for the solution of certain problems of plane stress analysis.
