Mechanics of Composite Materials Tutorial 10 Autumn Semester 2014 Hand-out: 08.12.2014 Tutorial 10: Beam with Shear-Compliant Core Introduction As schematically shown in Figure 1, it may be distinguished between transverse and in-plane deformations induced by shear. These are assumed to act exclusively in the core (GD = ∞) as well as being linear (EK << ED ), which results in constant shear strains and stresses in the core. Figure 1: Shear deformations of a sandwich element. Figure 2: Cross-section of a sandwich beam. ETH Zurich Laboratory of Composite Materials and Adaptive Structures I. Kuder 1 Mechanics of Composite Materials Tutorial 10 Autumn Semester 2014 dws · d = (γ − γ0 ) · tk dx dws tk γtk γ0 tk = (γ − γ0 ) = − = dx d d d Z ws = x ( 0 τk Gk t k d − γ0 tk τk dtk γ0 tk Q γ0 tk = − = − d Gk d2 d S d Q γ0 tk MB γ0 t k − ) dx = − x + const S d S d The two unknowns arise from the boundary conditions. The aim of the following two exercises is to show that a shear loading may induce unexpected displacements of a shear-compliant core. Exercise 1 Consider a sandwich beam symmetrically loaded by a force P, as shown in Figure 3, and characterised by cross-sectional dimensions found in Figure 2. Assuming that the constituent pure bending deflection is much smaller than the pure shear displacement (wb ws ) and hence negligible (w ≈ ws ), determine the deflection of the beam using the above general formula describing the displacement arising from the shear deformation of the core. Figure 3: Symmetrically loaded sandwich beam with a shear-compliant core. ETH Zurich Laboratory of Composite Materials and Adaptive Structures I. Kuder 2 Mechanics of Composite Materials Autumn Semester 2014 Tutorial 10 Exercise 2: Consider an unsymmetrically loaded beam presented in Figure 4, with the same cross-sectional configuration as before (Figure 2). Determine the shearinduced constituent deflection, assuming negligibility of bending displacement. Provide a qualitative plot of the deformed structure. Figure 4: Unsymmetrically loaded sandwich beam with a shear-compliant core. ETH Zurich Laboratory of Composite Materials and Adaptive Structures I. Kuder 3
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