Example 3.2 A 60mm diameter solid shaft has a strain gauge mounted at 65° to the axis of the shaft. In service a torque is applied to the shaft and the strain gauge reads 200 x 10-6. Calculate the value of the torque if the shaft is made from steel with E = 207 GPa and v = 0.3. (BC&A question 11.18) Strain Transformations ● Mechanical Engineering Mechanics of Materials 2 Solution 3.2 Applied torque alone will produce only shear stress/strain in the directions parallel and perpendicular to the torque. The strain gauge is punted at 65° to the axis of the shaft. Strain Transformations Mechanical Engineering Mechanics of Materials 2 Strain gauge E 65⁰ 33 Dr PJ Martin Lecture Notes 34 Dr PJ Martin Lecture Notes

Example 3.2 A 60mm diameter solid shaft has a strain gauge mounted at 65° to the axis of the shaft. In service a torque is applied to the shaft and the strain gauge reads 200 x 10-6. Calculate the value of the torque if the shaft is made from steel with E = 207 GPa and v = 0.3. (BC&A question 11.18) Strain Transformations ● Mechanical Engineering Mechanics of Materials 2 Solution 3.2 Applied torque alone will produce only shear stress/strain in the directions parallel and perpendicular to the torque. The strain gauge is punted at 65° to the axis of the shaft. Strain Transformations Mechanical Engineering Mechanics of Materials 2 Strain gauge E 65⁰ 33 Dr PJ Martin Lecture Notes 34 Dr PJ Martin Lecture Notes

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Concept explainers

Strain energy

The term strain indicates the variation in an object's length, area, and volume when the object is subjected to an external force. The external force may be of normal, shear, moment, torque, etc. The strain in an object depends on the types of external force and cross-section of the object. Mathematically, the evaluation of strain can be obtained with the help of elastic constants.

Question

●
Example 3.2
A 60mm diameter solid shaft has a strain gauge mounted at
65° to the axis of the shaft. In service a torque is applied to
the shaft and the strain gauge reads 200 x 10-6. Calculate
the value of the torque if the shaft is made from steel with E
= 207 GPa and v = 0.3.
(BC&A question 11.18)
Strain Transformations
Mechanical Engineering
Mechanics of Materials 2
Solution 3.2
Applied torque alone will produce only shear stress/strain
in the directions parallel and perpendicular to the torque.
The strain gauge is mounted at 65° to the axis of the shaft.
Strain Transformations
Mechanical Engineering
Mechanics of Materials 2
Now
Strain
gauge
From the strain circle
65⁰
Strain Transformations
Note that for circular shaft
4
D
J = ² (2) ²*
33
Dr PJ Martin
Lecture Notes
34
Dr PJ Martin
Lecture Notes
35

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