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

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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.

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Authors and Affiliations

  1. Dipartimento di Ingegneria Civile e Ambientale, Università degli Studi di Catania, Viale Andrea Doria 6, 95125, Catania, Italy

    S. Caddemi, I. Caliò & F. Cannizzaro

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  1. S. Caddemi
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  2. I. Caliò
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  3. F. Cannizzaro
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Correspondence to S. Caddemi.

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Caddemi, S., Caliò, I. & Cannizzaro, F. Closed-form solutions for stepped Timoshenko beams with internal singularities and along-axis external supports. Arch Appl Mech 83, 559–577 (2013). https://doi.org/10.1007/s00419-012-0704-7

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  • DOI: https://doi.org/10.1007/s00419-012-0704-7

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