The Timoshenko beam model in presence of internal singularities causing deflection and rotation discontinuities and resting on external concentrated supports along the span is studied in a static context. The internal singularities are modelled as concentrated reductions in the flexural and the shear stiffness by making use 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. The so-called static Green’s functions are also obtained by the proposed procedure and their explicit expressions are provided.

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

CALIO', Ivo Domenico;CADDEMI, Salvatore;CANNIZZARO F.
2013-01-01

Abstract

The Timoshenko beam model in presence of internal singularities causing deflection and rotation discontinuities and resting on external concentrated supports along the span is studied in a static context. The internal singularities are modelled as concentrated reductions in the flexural and the shear stiffness by making use 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. The so-called static Green’s functions are also obtained by the proposed procedure and their explicit expressions are provided.
2013
Closed-form solutions; Discontinuous beams; Singularities; Static Green's functions; Timoshenko beam
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/36041
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