Matrix Stiffness Method for Composite and Prestressed Beam Analysis Using Linear Integral Operators

Abstract

In the paper, the analysis of composite and prestressed beams using the matrix stiffness method is presented. The stiffness matrix for the frame element with a moment release at one end and the vector of equivalent nodal forces for the frame element with and without a moment release are derived. In the presented method, concrete is assumed to behave as viscoelastic material and the relaxation of the prestressing steel is also considered. Therefore, the relations between the generalized element displacements and the generalized element forces are integral and, here, are presented using the mathematical operators. Applying the linear integral operators, the solution to the problem is derived without introducing additional mathematical approximations and simplifications, besides the inevitable approximations related to the rheological properties of constitute materials, i.e., steel, concrete, prestressing and reinforcement steel. The derived relations can be applied with any concrete creep functions and for the element with a variable cross section.