On the lateral deformation of an elastic beam with step change in cross-section and arbitrary transversal loading

The lateral deformation of an elastic beam is studied within the framework of the distribution theory. It is assumed that the beam can have step discontinuity in the cross-section and that it is loaded by concentrated axial forces and distributed transversal forces. The existence and properties of the solution is studied. The main characteristic of our approach is the use of a single second order differential equation valid in the whole interval of interest (including points of discontinuities). From this equation, called governing equation, the solution in any point of the beam interval, including jumps at the points of discontinuities, can be obtained.