Question

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2. Two circular rods are loaded in tension along their longitudinal axis. Both rods have a diameter of 20 mm and a length of 150 mm. One bar is made of aluminum and the other is hot pressed silicon nitride (SigN). Both have an applied tensile load of 80 kN. Assume that both materials behave elastically under this loading condition (the aluminum does not plastically deform and the silicon nitride does not fracture), and given the following properties for these materials: Ea = 69 GPa and Esian4 = 304 GPa a.) What are the stress and strain in the aluminum (Al) bar? b.) What are the stress and strain in the silicon nitride (SIN) bar? c.) What is the final length of the Al bar? d.) What is the final length of the SizN4 bar?

Answer 1

Given Data for and Aluminium rod, ? Silicon Nitride rod diameter d = 20mm Length I = 150mm load Applied p = 80000 N youngs modulur EAL = 69 GPa E Signy = 304 GPa Assumptions Aluminium ir ductile material, Aluminium doesnot plastically deform ie Aluminium deformr in elastic zone so Hoofer law it Applicable Silicon nitride is brittle material. at does not fracture. It ie it also abeys hooler law. Now a - load stress in 'Al bar TAL = - 80000 1 (2002 strain in All bal = 254.64 Mpa Exlu = 254.64 69x103 a 0.00369 = load - 80000 6) stress in Sigtu bar 254.64 Mpa Strain in Sigfly Esigny 254.64 - 304x103

Esiinty = 0.000837 & final length of A bal sa de Ela = {xd = 0.00369 x 150 = 0.553 If = Iffl =150.553 mm d) final leyth of Sigtly' bal > E=ff Sel a 0.000837 x 150 - 0.125 mm la = 150 +0.125 = 150-125 mm