Analysis of Rigid Frames by Successive Replacement

An analytical method is developed for the calculation of moments at the supports or joints of rigid frames by replacing a portion of a structure with a member of its equivalent in stiffness or in rigidity. The derivation of formulas in this pape is based on the concept that when a member continuous over several supports or rigid joints is cut at any of its supports or joints the equilibrium of the two portions of the member is unaltered if the slope at the section is preserved. Thus either its left or its right portion can be replaced by any such torsion or flexure member that fulfills this requirements. This facilitates the transformation of a complicated plane or space frame into a much simpler type of plane structures for analysis.