5003 Lectures - Faculty of Engineering and Applied Science

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E5003 - Ship Structures I 64 © C.G. Daley To determine the stress/strain/deflection relationships, we convert the x-section to an equivalent section. The idea is to modify the section so that it is all made of one material, but retains the distribution of axial force (and bending stiffness). We do this by adjusting the width of one of the materials, in accordance with the ratio of Young’s Modulus. For example, Aluminum is converted to steel, but made thinner by Eal/Est. For the modified section, ITR is calculated in the usual way. The strains and deflections for any vertical bending moment will be correct. i.e. v ′ = M EI TR The only error will be the stresses in the transformed region. The stresses in the unmodified region will be correct, but the modified region will be wrong by the ratio of modulii. We can correct this as follows; My My σ ≠ ⇒ σ 1 = and 2 I I = σ TR TR E E 2 1 My I TR
E5003 - Ship Structures I 65 © C.G. Daley Topic 7: Problems 7.1. Find the moment of inertia of this compound section: dimensions in mm 7.2. A box steel hull is 4m x 1m with a shell thickness of 10mm. It is inclined at 15 degrees, and subject to a vertical bending moment of 2 MN-m. Find the bending stress at the emerged deck edge. 7.3. For a composite beam (Steel plate with Aluminum web/Flange) loaded as show below a) find the central deflection. b) find the maximum stress in the Aluminum 7.4. Consider a compound steel-aluminum beam, shown below. Calculate the deflection d (show steps) Ans: 0.112m
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5003 Lectures - Faculty of Engineering and Applied Science

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