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 + d?) Gd d? (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., d= 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 segment. %3D

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 + d?) Gd d? (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., d= 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 segment. %3D

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter2: Axially Loaded Members

Section: Chapter Questions

Problem 2.2.3P: The L-shaped arm ABCD shown in the figure lies in a vertical plane and pivots about a horizontal pin...

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