Determine which of the shafts in Figure 3 experiences the...

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HOMEWORK PROBLEMS Week 8: Due Friday 13 March 1. Determine which of the shafts in Figure 3 experiences the greatest shear stress and find the magnitude of that stress. diameter = 40 mm 50 mm 45 mm B C D A 4 00 N m 55 0 N m 25 0 N m Figure 3
Solution C T CD B C D AB D D 4 00 N m 250 N m 550 N m 55 0 N m 250 N m 250 N m Figure 1.1 Figure 1.1 shows appropriate free-body diagrams to expose the torques in the three seg- ments. We obtain T CD = - 250 N m ; T BC = 300 N m ; T AB = - 100 N m . The maximum shear stress in a shaft of diameter d is τ max = Tr max J = T ( d/ 2) πd 4 / 32 = 16 T πd 3 , so τ max CD = 16 × 250 × 10 3 π × 45 3 = 13 . 95 MPa ; τ max BC = 16 × 300 × 10 3 π × 50 3 = 12 . 2 MPa τ max AB = 16 × 100 × 10 3 π × 40 3 = 7 . 95 MPa . Thus, τ max = 13 . 95 MPa, in shaft CD .
2. The system shown in Figure 2 is built in at A and loaded by external moments at B, C, D . Find the angle through which the wheel at D rotates if the shafts are all made of steel with G = 80 GPa and the lengths of the segments are L AB = 300 mm, L BC = 400 mm, L CD = 400 mm. diameter = 40 mm 50 mm 45 mm B C D A 4 00 N m 55 0 N m 25 0 N m Figure 2
Solution C T CD B C D AB D D 4 00 N m 250 N m 550 N m 55 0 N m 250 N m 250 N m

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