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Strength of Materials

Composite Shafts in Torsion

Two shafts AB...

Question

Two shafts AB and BC, of equal length and diameters d and 2d, are made of the same material. They are joined at B through a shaft coupling, while the ends A and C are built-in(cantilevered). A twisting moment T is applied to the coupling. If $T_{A}$ and $T_{C}$ represent the twisting moments at the ends A and C, respectively, then

A

T_{C} = T_{A}

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B

T_{C} = 8 T_{A}

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C

T_{C} = 16 T_{A}

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D

T_{A} = 16 T_{C}

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Solution

The correct option is C $T_{C} = 16 T_{A}$
Angular deflection in both shafts are same

$∴ θ_{A B} = θ_{B C}$

$\frac{T_{A} \times L}{G \times \frac{π}{32} \times d^{4}} = \frac{T_{C} \times L}{G \times \frac{π}{32} \times (2 d)^{4}}$

$T_{A} = \frac{T_{C}}{16}$

$∴ T_{C} = 16 T_{A}$

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