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On the Derivation of Exact Solutions of a Tapered Cantilever Timoshenko Beam

Tjong, Wong Foek and GUNAWAN, JUNIUS and AGUSTA, KEVIN and HERRYANTO, and TANAYA, LEVIN SERGIO (2019) On the Derivation of Exact Solutions of a Tapered Cantilever Timoshenko Beam. Civil Engineering Dimension, 21 (2). pp. 89-96. ISSN 1401-9530 print/ 1979-570X online

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    Abstract

    A tapered beam is a beam that has a linearly varying cross section. This paper presents an analytical derivation of the solutions to bending of a symmetric tapered cantilever Timoshenko beam subjected to a bending moment and a concentrated force at the free end and a uniformly-distributed load along the beam. The governing differential equations of the Timoshenko beam of a variable cross section are firstly derived from the principle of minimum potential energy. The differential equations are then solved to obtain the exact deflections and rotations along the beam. Formulas for computing the beam deflections and rotations at the free end are presented. Examples of application are given for the cases of a relatively slender beam and a deep beam. The present solutions can be useful for practical applications as well as for evaluating the accuracy of a numerical method.

    Item Type: Article
    Uncontrolled Keywords: Timoshenko beam; tapered beam; the principle of minimum potential energy; slender beam; deep beam
    Subjects: T Technology > TA Engineering (General). Civil engineering (General)
    Q Science > QA Mathematics
    Divisions: Faculty of Civil Engineering and Planning > Civil Engineering Department
    Depositing User: Admin
    Date Deposited: 21 Oct 2019 17:26
    Last Modified: 30 Oct 2019 19:35
    URI: http://repository.petra.ac.id/id/eprint/18470

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