HW2 (1).pdf - Problem 1 Deflection in torsion of a...

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Problem 1 Deflection in torsion of a nonuniform bar A bar in torsion has a circular cross section and includes a tapered portion of length l , as shown. The angle of twist of the tapered portion is given as: 2 2 1 1 2 2 3 3 1 2 32 3 Tl d d d d Gd d The polar second moment of area for circular cross section is: 4 32 J d Assume T = 1500 lbf·in and G = 11.5 Mpsi, determine the angle of twist in degrees for each portion if d 1 = 0.5 in, d 2 = 0.75 in, l = l 1 = l 2 = 2.0 in. Problem 2 Failures resulting from static loading A ductile hot-rolled steel bar has a minimum yield strength in tension and compression of 50 kpsi. Using the distortion-energy (DE) and maximum-shear-stress (MSS) theories determine the
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