GATE ME 2022 Set 2 — Question 50
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Strength of Materials → Beams & Columns → Torsion of Shafts
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Question
A shaft of length is made of two materials, one in the inner core and the other in the outer rim, and the two are perfectly joined together (no slip at the interface) along the entire length of the shaft. The diameter of the inner core is and the external diameter of the rim is , as shown in the figure. The modulus of rigidity of the core and rim materials are and , respectively. It is given that and . When the shaft is twisted by application of a torque along the shaft axis, the maximum shear stress developed in the outer rim and the inner core turn out to be and , respectively. All the deformations are in the elastic range and stress-strain relations are linear. Then the ratio is ______ (round off to 2 decimal places).
Correct answer
1.48 to 1.52
Solution
For a shaft under torsion, the shear stress at a distance from the center is given by , where is the modulus of rigidity, is the angle of twist, and is the length of the shaft.Since the inner core and outer rim are perfectly joined, they share the same angle of twist and length .
1.Maximum shear stress in the inner core ():
This occurs at the outer radius of the core, .2.Maximum shear stress in the outer rim ():
This occurs at the outer radius of the rim, .3.Calculating the ratio:
Given and :Rounding to two decimal places, the ratio is .Continue learning with Success Tracker
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