1. A circular shaft with a keyway can be approximated by the section shown in Fig. r=b r 0 r = 2acose Figure 1: Circular shaft with a keyway. The keyway is represented by the boundary equation r = b and the shaft is represented by the boundary equation r = 2a cos 0. Show that using a Prandtl stress function of the form b) = K (6² – 7²) (1 - 7²) (1 - 2a cos) will solve the problem of torsion on this shaft and find the constant K (assume an applied torque T). Compute the shear stress components Taz and Tyz. (Hint: start by converting the stress function to Cartesian coordinates).

1. A circular shaft with a keyway can be approximated by the section shown in Fig. r=b r 0 r = 2acose Figure 1: Circular shaft with a keyway. The keyway is represented by the boundary equation r = b and the shaft is represented by the boundary equation r = 2a cos 0. Show that using a Prandtl stress function of the form b) = K (6² – 7²) (1 - 7²) (1 - 2a cos) will solve the problem of torsion on this shaft and find the constant K (assume an applied torque T). Compute the shear stress components Taz and Tyz. (Hint: start by converting the stress function to Cartesian coordinates).

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter7: Analysis Of Stress And Strain

Section: Chapter Questions

Problem 7.7.8P

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