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Unformatted text preview: A Beam Theory for Laminated Composites A Beam Theory for Laminated Composites nd Application to Torsion Problems nd Application to Torsion Problems and Application to Torsion Problems and Application to Torsion Problems Dr. Dr. Bhavani BhavaniV. V. Sankar Sankar Presented By: Sameer Luthra EAS 6939 Aerospace Structural Composites 1 troduction troduction Introduction Introduction Composite beams have become very common in applications like Automobile Suspensions, Hip Prosthesis etc. Unlike beams of Isotropic materials, Composite beams may exhibit strong coupling between: Extensional Flexural & Twisting modes of Deformation. There is a need for simple and efficient analysis procedures for Composite beam like structures. 2 Beam Theories Beam Theories EULERBERNOULLI BEAM THEORY ssumptions: Assumptions: 1. Crosssections which are plane & normal to the longitudinal axis remain plane and normal to it after deformation . 2. Shear Deformations are neglected . 3. Beam Deflections are small . EulerBernoulli eq. for bending of Isotropic beams of constant crosssection: where: w(x): deflection of the neutral axis q(x): the applied transverse load 3 Beam Theories Beam Theories TIMOSHENKO BEAM THEORY asic difference om Euler ernoulli beam theory is that Basic difference from Euler Bernoulli beam theory is that Timoshenko beam theory considers the effects of Shear and also of Rotational Inertia in the Beam Equation. So physically, imoshenkos theory effectively wers the stiffness f beam Timoshenkos theory effectively lowers the stiffness of beam and the result is a larger deflection . Timoshenkos eq. for bending of Isotropic beams of constant ti crosssection: where: A: Area of Crosssection G: Shear Modulus : Shear Correction Factor 4 Beam Theories Beam Theories TIMOSHENKO BEAM THEORY(Contd.) hear Correction Factor Shear Correction Factor...
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This note was uploaded on 03/27/2012 for the course EAS 4240c taught by Professor Staff during the Spring '11 term at University of Florida.
 Spring '11
 Staff

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