STIFFNESS-MATRIX FORMULATION OF BEAMS WITH SHEAR EFFECT ON ELASTIC-FOUNDATION

A stiffness matrix for a beam element with shear effect on an elastic foundation is developed using the differential-equation approach for p lane-frame analysis. Small-displacement theory and linear-elastic mate rial are assumed. The contribution of the shear stresses to the deflec tion of the beam in addition to the bending stresses is considered. Sh ear effect is represented by a second-order term of the derivative of beam deflection in the differential equation. This fact is also taken into account in the boundary conditions of the beam element. The compl ex variables are used in the solution of the differential equation. St iffness and loading matrices for a beam element resting on Winkler fou ndation are derived by means of a computer program coded in FORTRAN la nguage. Using this element, the effects of the shear forces on deflect ions and internal forces in the beams on an elastic foundation are inv estigated. The results of this finite-element analysis are exact for t he Winkler assumption. It is shown that the deflections due to shear e ffect are influenced particularly with the modulus of the foundation a nd for the beams that have small span to height ratio. Also, numerical examples are given to demonstrate this fact.