Closed-form solutions for stepped Timoshenko beams with internal singularities and along-axis external supports

The Timoshenko beam model in presence of internal singularities causing deflection and rotationdiscontinuities and resting on external concentrated supports along the span is studied in a static context. Theinternal singularities are modelled as concentrated reductions in the flexural and the shear stiffness by makinguse of the distribution theory. Along-axis supports are treated as unknown concentrated loads and moments.An exact integration procedure of the proposed model, not requiring continuity conditions at all, is presented.Closed-form solutions are provided for both cases of homogeneous and stepped Timoshenko beams. Theso-called static Green’s functions are also obtained by the proposed procedure and their explicit expressionsare provided.