Question

Problem 4. (15 pts) The cylindrical pressure vessel is made of an aluminum alloy [E 7° GPa; and a shear modulus of G-26.1 GPa]. The cylinder has an inside diameter of 625 mm and a wall thickness of 10 mm. Two strain gages are mounted on the exterior surface of the cylinder at right angles to each other; however the angle θ is not known. The strains measured by the two gages are ε.-640 με and 6-1160 με. a) Determine the pressure in the vessel given E b) Determine the elastic modulus (E). and Eb

Answer 1

E = 70 Gpa, G = 26.1 Gpa d = 625 mm, t = 10 mm Ea = 640 times 10^-6, E_b = 1160 times 10^- 6 E = 2 G(1 + mu) 70 = 2 times 261(1 + mu) 1 + mu = 70/2 times 26.1 = 1.341 mu = 0.341 almostequalto 0.34 E_1 = E_b = 1160 times 10^-6, E_2 = E_a = 640 times 10^- 6 sigma_1 = (E/1 - mu^2) (E_1 + mu E_2) = 70 times 10^3/1 - 0.34^2 [1160 times 10^- 6 + (0.34 times 640 times 10^- 6)] sigma_1 = 109.036 N/mm^2 sigma_1 almostequalto 109 N/mm^2 (a) sigma_1 = hoostress = [pr/t] = p times (625/2)/10 109.036 = p times 625/20 P = 3.49 N/mm^2 \r\n (b) elastic modulus (E) = 70 Gpa it is given in question