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School of Mechanical & Aerospace EngineeringMA4001 – Engineering DesignSolutions to Materials Selection Practice QuestionsProblems on the derivation of Material Performance index1.A thermal connecting rod of given length,l,and unknown cross-section (squarecross-section of side length,t),t x t,is set atT1andT2temperature at the twoextreme ends.We need to transfer less than a heat ofQ0from one end toanother end having minimum weight. Derive an expression for performanceindex.
2.You are required to design a light weight Crutch (a column with padded top,which goes under armpit, and loaded in compression) to support an appliedaxial compressive load of 80N. For design perspective, based on length eitherit shouldn’t crush or shouldn’t buckle (applied separately). The crutch is ofgiven length L, has a hollow circular cross-section of fixed wall thickness (t)and varying radius r. For this design (a) identify the function, objective,constraint, fixed and free variable. (b) Is this fully determined, overconstrained or underconstrained problem? And (c) Obtain material index tomaximize the performance of design.!
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(c) objective: minimum weight,m=ALρ=(2π)rtLρ---(1)We need to eliminate the free variableAor radiusrfrom the objective equation (1)Consider the constraint of uniaxial crushing:σ=PA≤σyA=Pσy(2)Substituting the expression for A from the constraint equation in (1) we get:m=ALρ=Pσy=(P) (L)ρσyMass can be minimized by maximizing the index:M=σyρ, which is specifc strength.Now, consider the constraint of buckling,P=π2EIL2≤PcPc=π2E(π r3t)L2(2)r=(PcL2π3Et)13(3)Now, substituting the expression for radius (r) from (3) in the objective equation we get:m=(2π)rtLρ=(2π)(PcL2π3Et)1/3tLρ=38Pc(L5t2)13ρ3EMass can be minimized by maximizing the index:M3.Currently a light weight cantilever beam of given length (L) in solid rectangular cross-sectionof prescribed width (w) and unspecifiedheight (h) is made of balsa (wood, perpendicular to=3Eρ

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Term
Fall
Professor
AngHockEng,NgHeongWah
Tags
Fracture mechanics, Cantilever, Closure
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