Time-dependent analysis of composite and prestressed beams using the slope deflection method

Abstract

The paper presents the viscoelastic analysis of composite and prestressed beams using the slope deflection method. For the fixed-end frame element, considering the viscoelastic behavior of concrete and relaxation of prestressing steel, the integral relation between the generalized element forces and the generalized element displacements, i.e., the element stiffness matrix, is derived and presented using the mathematical operators. From the element and system equilibrium equations, the integral equations of the problem with unknown displacements are formulated. Comparing to the analysis of homogeneous elastic structures, the governing equations of the problem are similar, but with integral equations instead of algebraic equations. In the presented method, the solution to the problem is derived using the linear integral operators without introducing any additional mathematical approximations, apart from the adopted rheological relations for constitute materials. In addition, the obtained expressions are general in a sense that any concrete creep functions can be used and the element can be with a variable cross section.