A displacement solution for transverse shear loading of beams using the boundary element method

In this paper the boundary element method is employed to develop a displacement solution for the general transverse shear loading problem of prismatic beams of arbitrary simply or multiply connected cross section. The analysis of the beam is accomplished with respect to a coordinate system that has its origin at the centroid of the cross section, while its axes are not necessarily the principal ones. The transverse shear loading is applied at the shear center of the cross section, avoiding in this way the induction of a twisting moment. A boundary value problem is formulated with respect to a warping function and solved employing a pure BEM approach requiring only a boundary discretization. The evaluation of the transverse shear stresses at any interior point is accomplished by direct differentiation of this function, while the coordinates of the shear center are obtained from this function using only boundary integration. The shear deformation coefficients are obtained from the solution of two boundary value problems with respect to warping functions appropriately arising from the aforementioned one, using again only boundary integration. Numerical examples are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method. The accuracy of both the thin tube theory and the engineering beam theory is examined through examples of practical interest.