2 A composite material consists of parallel fibers of Young’s modulus E in a matrix of Young’s modulus Em. The volume fraction of fibers is V. Derive an expression for E. Young’s modulus of the composite along the direction of the fibers, in terms of E, Em and V. Obtain an analogous expression for the density of the composite, pe Using material parameters given in the next table, find pe and E for the following composites: (a) carbon fiber-epoxy resin (V= 0.5), (b) glass fiber-polyester resin (V: = 0.5), (c) steel-concrete (V: = 0.02). Young’s modulus (GN m2 390 Density (Mg m) 1.90 2.55 1.15 Material Carbon fiber Glass fiber Epoxy resin Polyester resin Steel Concrete 72 3 } 7.90 2.40 200 45

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2 A composite material consists of parallel fibers of Youngs modulus E in a matrix of Youngs modulus Em. The volume fractio

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Ang) Since both the density and Yound Modulus follow the law of mixture Law Of Mixture weighted mean of property + fľky ke f
Page b) Glass fibey - Polyften Resin Vp=0.5 G-P VfL GF + (1-Up) Ser 0.5 (2.55) + (1 -0.5) (1.15) 1.85 mg/m3 Ege Vf EG-E + (1-