Parallel Connecting Beams for Equivalent Structures

Abstract

In this paper two equivalent systems are presented to replace in the analysis nonprismatic members with or without standard end conditions. While for a symmetrical nonprismatic member only a single prismatic beam with shear effect included is adequate, in the case of asymmetrical members, two or three equivalent prismatic beams are required. The characteristics of these beams are determined in terms of the real member characteristics by equating the strain energy stored in the real member and in the equivalent system. Improved versions of the stiffness matrix of the real beams are considered into the strain‐energy expression. The equivalent system characteristics are derived for both the general case and some particular cases. Two numerical examples are given to illustrate the procedure: One demonstrates that in the deck‐grillage analogy applied to the analysis of bridge decks the equivalent system presented in the paper can lead to very good results; the second shows that in the analysis of skeletal structures, the results obtained with the equivalent systems are practically the same as the “exact” solutions.