Stiffness Matrices for Linear and Buckling Analyses of Composite Beams with Partial Shear Connection

Abstract

AbstractThis paper is concerned with linear and buckling analyses of composite beams with partial shear connection (partial composite beams) using the finite element method. Two elements derived from different types of shape functions are proposed in this study. The first element, referred to as exact, is based on the exact shape functions obtained by solving the differential equations governing the transverse displacement and the slip of the shear connector layer of a partial composite beam. The second element, referred to as approximate, is based on the conventional linear and cubic shape functions used in conventional axial and beam elements. By making use of these two types of shape functions, the elastic and geometric stiffness matrices can be derived explicitly from the strain energy and the load potential, respectively. Both types of elements can be used to carry out linear static and buckling analyses. As expected, the exact element is more accurate than the approximate element if the same discretization is adopted. However, the approximate element has the advantage of easy implementation since the expressions of its elastic and geometric stiffness matrices are very simple. Also, the solutions obtained from the approximate element converge very fast; with reasonable discretization, say 8 elements per member, very accurate solutions can be obtained.