Assignment4 - Density (Mg m-3 ) Young’s modulus (GN m-2 )...

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1 Assignment #4 ME264 Materials Science for Mechanical Engineering Spring 2009 Due Date: 18 March 2009 (4 pts) 1. (2pts) A composite material consists of parallel fibers of Young’s modulus E f in a matrix of Young’s modulus E m . The volume fraction of fibers in V f . Derive an expression for E c , Young’s modulus of the composite along the direction of the fibers, in terms of E f , E m and V f . Obtain an analogues expression for the density of composite ρ c . Using material parameters given below, find ρ c and E c for the flowing composites: (a) Carbon fiber-epoxy resin ( V f = 0.5) (b) Glass fiber-polyester resin ( V f = 0.5) (c) Steel-concrete ( V f = 0.02). Material
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Unformatted text preview: Density (Mg m-3 ) Young’s modulus (GN m-2 ) Carbon fiber 1.90 390 Glass fiber 2.55 72 Epoxy resin Polyester resin 1.15 3 Steel 7.90 200 Concrete 2.40 45 2. (2pts) A uniform, rectangular-section beam of fixed width w , unspecified depth d , and fixed length l rests horizontally on two simple supports at either end of the beam. A concentrated force F acts vertically downward through the center of the beam. The deflection, δ , of the loaded point is 3 3 4 c Fl E wd δ = ignoring the deflection due to self weight. Which of the three composites in question 1will give the lightest beam for a given force and deflection?...
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This note was uploaded on 11/17/2009 for the course MECHANICAL ME 264 taught by Professor during the Spring '09 term at Yeditepe Üniversitesi.

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