A torque T is applied, as shown below, to a solid shaft with built-in ends. Prove that the resisting torques at the walls are TI = Tb/L and T2 = Ta/L. How would these values be changed if the shaft were hollow? (Practice at Home)

A torque T is applied, as shown below, to a solid shaft with built-in ends. Prove that the resisting torques at the walls are TI = Tb/L and T2 = Ta/L. How would these values be changed if the shaft were hollow? (Practice at Home)

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter1: Tension, Compression, And Shear

Section: Chapter Questions

Problem 1.3.17P: A stepped shaft ABC consisting of two solid, circular segments is subjected to torques T}and...

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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:
12.
A torque T is applied, as shown
below, to a solid shaft with built-in
ends. Prove that the resisting torques
at the walls are TI = Tb/L and T2 =
Ta/L. How would these values be
changed if the shaft were hollow?
(Practice at Home)
T₂
a
T
b
T₂

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