Stiffness Analysis of Thin‐Walled Girders

Abstract

For complex arrangements of thin‐walled girders a generalized method of analysis is required that is suitable for rapid solution by computer. A method of elastic analysis based on a stiffness approach, is proposed which is equally applicable to straight and curved girders of thin‐walled cross section. For straight girders, the member stiffness matrix is derived explicitly by inverting the appropriate member flexibility matrix and considering equilibrium of the member ends. The member stiffness matrix for curved girders is obtained by the same method but in numerical form due to the extreme complexity of the various terms. By transforming individual member stiffness matrices into system co‐ordinates, a system stiffness matrix is established, whose inversion leads directly to a global solution for the structure. In this type of analysis uniformly distributed flexural and torsional loads must be applied as fixed‐ends loads at the nodes. These are derived for both straight and curved girders. In addition, the distribution of bimoment is presented graphically for a variety of typical beam cross sections.