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Mechanical Engineering

Write the Shear strain max formula for Torsion?

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter3: Torsion

Section: Chapter Questions

Problem 3.11.10P: Compare the angle of twist 1 for a thin-walled circular tube (see figure) calculated from the...

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Concept explainers

Torsion

In mechanical engineering, torque, torsion, and twisting moment are three of the most important concepts which have different meanings. Torque is the consequence of a moment of a force that produces an angular acceleration in a body or induces rotational kinetic energy in a body. For instance, in an automobile, the power transmission shaft is a body that is always under rotation due to the external torque acting on it, this torque is created by the engine.

Question

Write the Shear strain max formula for Torsion?

Expert Solution

Step 1

To calculate the maximum shear strain value for torsion we must take into account the torsion equation of the shaft which can be given as:

$\frac{T}{J} = \frac{τ}{r} = \frac{Gθ}{L} where T = twisting moment J = polar moment of inertia τ = torsional shear stress r = radius of the shaft G = modulus of rigidity θ = angle of twist in radians L = length of shaft For calculating maximum shear stress we have to consider maximum torsional shear stress Maximum torsional shear stress will occur at the maximum distance from the center of the shaft i . e r_{\max} = R$

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