Example 7.8: (Application of equation(7.42) for a thin hollow circular bar) (a) Obtain the value of Prandtl stress function at the inner surface of a thin hollow circular bar (b) Find the torque transmitted and J-integral and (c) the shear stress along the wall. R

Example 7.8: (Application of equation(7.42) for a thin hollow circular bar) (a) Obtain the value of Prandtl stress function at the inner surface of a thin hollow circular bar (b) Find the torque transmitted and J-integral and (c) the shear stress along the wall. R

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter8: Applications Of Plane Stress (pressure Vessels, Beams, And Combined Loadings)

Section: Chapter Questions

Problem 8.5.13P: . A segment of a generator shaft with a hollow circular cross section is subjected to a torque T =...

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Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

Example 7.8: (Application of equation(7.42) for a thin hollow circular
bar) (a) Obtain the value of Prandtl stress function at the inner surface of a
thin hollow circular bar (b) Find the torque transmitted and J-integral and (c)
the shear stress along the wall.
R

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