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2. The tapered cylindrical bar in Fig. 2 is subjected to opposing torques T on its free ends. For the tapered section only, the angle of twist 0 can be expressed as: 32 TI(d? + d,d2 + dž) Gd d? 37n (a) Derive an expression for the effective spring constant keff for the entire bar, treating each segment as a torsional spring in series. Fig. 2 (b) For the bar shown, let; I, = 12 = 12 in., 1= 24 in., d1= 0.25 in., d2= 1 in., T = 1000 lbf-in., and G = 13.5 x 103 kpsi. Calculate the angle twist 0 for the entire bar using the expression for kef determined in (a). Verify that this value is the sum the angles of twist for each individual %3D %3D segment.

Mechanical Engineering. Please help to solve, will upvote after.  What is the change in length of a 5-m tin rod if the temperature changes from 11 to245°C?

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