m06_ps02_spring04

m06_ps02_spring04 - Unified Engineering Spring 2004 Problem...

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r , (Mg/m 3 ) Density, Modulus, E, (GPa) CTE, a, x 10 -6 K -1 Price , p, ($/Mg) Tensile Strength, s f , (MPa) Unified Engineering Spring 2004 Unified Engineering Problem M6 This question is a first step towards designing a beam-like structure – e.g. a wing. You are asked to specify a material for a cantilever beam (i.e. a beam clamped at one end) which is to be of a specified length, L, and to be of the lowest possible mass to support a load, P, applied at its tip while minimizing the tip deflection, d , without failing. a) Assuming that the beam is constrained to have a solid square cross-section, side, h, express the mass of the beam, m, in terms of, L, the relevant material properties and the stiffness of the beam (P/ d). ( Note: The key to achieving this is to eliminate the cross-sectional dimension, h, from the expression). What is the figure of merit (combination of material properties) that must be minimized in order to achieve the lightest weight beam for a given desired stiffness?
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