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2003 Course Mechanics of Composites

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Total No. of Questions : 12] [Total No. of Pages : 5 [3764]-364 P1566 B.E. (Polymer) MECHANICS OF COMPOSITES (2003 Course) Time : 3 Hours] [Max. Marks : 100 Instructions to candidates : 1) Answer any 3 questions from Section I and 3 questions from Section II. 2) Neat diagrams must be drawn wherever necessary. 3) Figures to the right indicate full marks. 4) Use of logarithmic tables slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed. 5) Assume suitable data, if necessary. SECTION - I Q1) a) Write in short about E and S type of glass fibres used in fibre reinforced composites. [3] b) Write Griffith s formula for strength of brittle fibres. [3] c) Give theoretical formulae for calculation of fibre content, density and void content. [4] d) Discuss resin transfer molding. Give schematic sketch of the process and discuss process variables. [8] OR Q2) a) Draw a schematic sketch of polar winding and give process variables for fibre met out. [6] b) Write in brief about hand lay up and spray technique and its applications. [6] c) Give Darcy s equation for resin flow and explain gel time test for determining Curing characteristics of resin catalyst combination. [6] Q3) a) A unidirectional glass epoxy lamina as shown below has following allowable stresses. i) Tensile failure strength in the longitudinal direction ii) Compressive failure strength in longitudinal direction LU = 610 MPa. iii) Tensile failure strength in transverse direction TU LU = 106 2MPa. = 31 a . P.T.O. iv) Compressive failure strength in transverse direction TU = 118 a . v) Shear strength LTU = 72 MPa. Determine if, according to maximum stress theory, the lamina will fail under applied stress. [6] Applied stresses are x = 50 MPa y = 25 MPa xy = 50 MPa b) State Tsai - Hill failure criteria for biaxial stress system. Explain how failure strength parameters are related to uniaxial failure strength. Reduce the criteria to unidirectional lamina. [8] c) Define coefficient of mutual influence of first kind by Lekhnitski. [2] OR Q4) a) Explain the concept of invariant form of stiffness and compliance. Give example of any one invariant in terms of stiffness. [5] b) Explain how you will determine the strength tensor of fourth order as defined in Tsai - Wu tensor theory. [6] c) Explain the limitation of maximum stress and minimum strain failure criteria for biaxial stress system. [5] [3764]-364 2 Q5) a) Derive an expression for longitudinal Young s modulus E11, in terms of fibre and matrix modulus. [8] b) Prove the rule of mixture for major Poisson s ratio 12 in terms Poisson s s ratio for fibre and Poisson s ratio for matrix using mechanics of materials approach. [8] OR Q6) a) Explain how you will calculate following elastic constants of a unidirectional discontinuous 0 lamina. [8] i) ii) iii) G12 b) E11 E22 iv) 12 For a sheet molding compound, data for the fibre and matrix is as follows for fibre. Ef = 68 GPa; f = 2 . 5 4 kg/mm3; lf = fibre length = 25 mm; df = fibre diameter 2.5 mm. for matrix Em = 3.45 GPa; m = 1.1 kg/mm3 [8] Calculate tensile modulus, shear modulus and Poisson s ratio. SECTION - II Q7) a) For a laminate with following configuration calculate extensional stiffness [A], coupling stiffness [B] and bending stiffness [D] matrices. Each lamina is 1 mm thick and has 50.% fibre. Following properties of the lamina are known. [12] E11 = 100 GPa; E22 = 10 GPa; 12 = 0.2 G12 = 5 GPa b) [3764]-364 Give features of symmetric laminate with multiple generally orthotropic layers. Give features of symmetric angle ply laminate comment on elements of stiffness matrix. [6] 3 OR Q8) a) A two ply laminate is as shown below: [12] Both the laminae have identical [Q] matrix as given below: 20 0 . 7 0 0 GPa 0 . 7 2 0 0 0 . 7 i) Calculate [A] [B] & [D] matrix. ii) If force of Nx = 1000 N/mm is applied. Calculate stresses and strains in the individual plies. b) Give examples of symmetric laminate with multiple specially orthotropic lamina. Comment on elements of the [A], [B] & [D] matrix. [6] Q9) a) A sandwich molding is made up of were and inner / outer skin material. The [Q] matrix for were as well as skin material is given below: [12] 4 10 3 1.5 103 0 gN 3 4 10 3 0 2 [Q]were = 1.5 10 3 m 0 1.2 10 0 [Q]skin = 75 30 0 30 75 0 0 0 20 Each 1 mm thick, if moment of 400 N m/m is applied to this sandwich structure, find resulting curvatures and stresses and strains. Show stress - strain variation graphically. b) Explain the benefit of using sandwich structures in place of solid sections in structural applications of beam. [4] OR [3764]-364 4 Q10)a) Obtain the deflections of a beam clamped at both ends as shown below. Assume that the beam of length L has a symmetric lay up and carries a uniformly distributed lead P0. [8] b) Give stepwise design procedure for design of a torsional member like automotive shaft. [8] Q11)a) Give test configuration of 10 off axis test to measure in - plane shear properties. Explain the strain gauge rosette arrangement and how measured. b) is [8] 12 Give schematic arrangement for charpy, Izod and drop weight impact tests. [8] OR Q12)a) Give test arrangement for Celanese compression test. [6] b) Show schematically various failure modes in pin bearing test. [4] c) Give average strength and variance formulae for two parameter Weibull distribution. [6] Y [3764]-364 5

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