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Unformatted text preview: Shear and Torsion 14:125:208 Introduction to Biomechanics Shearing Stress and Strain • When we apply a shear stress we get angular deformation • When you plot shear stress ( t ) vs. shear strain ( g ) you obtain ? ¡? = ¡? – Hooke’s Law for shearing stress and strain – G is the shear modulus or modulus of rigidity Shearing Stress and Strain • The same holds true for other shear stresses • Limits for G • Solve for shear stress Shear and Elastic Properties • Earlier we measured the effects of axial stresses on transverse faces – If a cube with sides of length 1 is subjected to axial strain, the lengths become • What if we turn the cube, those strains will change the angles and lead to shearing stresses Shear and Elastic Properties • After noting that ? occurs at 45° and using geometric identities – = 1 + ? ? • Using both Hooke’s Laws we can relate the shear and elastic moduli Shear in Bending • For any beam subjected to a shearing force, V, both ‘horizontal’ and ‘vertical’ shear stresses, t , are produced t Shear in Bending • Consider a cantilever beam made up of planks that are not bonded and subjected to transverse loading • Each individual plank will be subjected to slip at the interfaces • Plane sections before deformation do not remain plane after deformation • If the planks are bonded together, longitudinal shear...
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 Fall '11
 JosephFreeman
 Shear Stress, Shear, Elastic Properties

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