A static boundary element solution for Bickford–Reddy beam

. Bickford–Reddy beam theory is a refined model in which it is assumed that axial displacements vary cubically across the height of the cross section. Consequently, quadratic distribution for transverse shear stresses is automatically satisfied instead of Timoshenko beam model which predicts a constant distribution for those stresses, requiring the incorporation of a shear correction factor into the model. This article shows a new static solution which is based on direct boundary element method (BEM) for Bickford–Reddy beam theory. Mathematical steps required by this BEM technique are adequately addressed, for instance, a) integral equations are derived using Betti’s reciprocal theorem, b) fundamental solutions are obtained from the fundamental problem which has direct relationship to the real Bickford–Reddy beam problem; c) explicit influence matrices and load vectors are derived from source collocation at boundary points, and then at domain points, and d) BEM solutions are obtained for structures containing domain discontinuities such as stepped beams and continuous beams. Numerical results are presented for uniform beams having rectangular and circular cross sections and for problems having domain discontinuities.