A solid steel shaft of diameter 50 mm is to be designed using an allowable shear stress - allow - 50MPa and allowable angle of twist per unit length - - 1o per meter- The maximum permissible torque in Nm T that may be applied to the shaft is - assuming G - 100GPa-

Torque based on allowable shear stress. TJ = τr T = τ(d/2)×π32d^4 = τ×π16d^3 T = (50× 10^6)×π16× (0.05)^3=1227Nm Torque based on allowable angle of twist. ...

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Standard XII

Physics

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A solid steel...

Question

A solid steel shaft of diameter 50 mm is to be designed using an allowable shear stress $τ_{a l l o w} = 50 M P a$ and allowable angle of twist per unit length $θ = 1^{o}$ per meter. The maximum permissible torque (in Nm) T that may be applied to the shaft is ? (assuming G = 100GPa).

1227

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1070

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2454

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2140

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Solution

The correct option is B 1070
Torque based on allowable shear stress.

$\frac{T}{J} = \frac{τ}{r}$

$T = \frac{τ}{(d / 2)} \times \frac{π}{32} d^{4}$

$= τ \times \frac{π}{16} d^{3}$

$T = (50 \times 10^{6}) \times \frac{π}{16} \times (0.05)^{3} = 1227 N m$

Torque based on allowable angle of twist.

$\frac{T}{J} = \frac{G θ}{l}$

$T = (100 \times 10^{9}) \times (1 \times \frac{π}{180}) \times \frac{π}{32} \times (0.05)^{4} = 1070 N m$

So max. permissible torque, T = 1070 Nm

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A solid steel shaft of diameter 50 mm is to be designed using an allowable shear stress τallow=50MPa and allowable angle of twist per unit length θ=1o per meter. The maximum permissible torque (in Nm) T that may be applied to the shaft is ? (assuming G = 100GPa).

The correct option is B 1070Torque based on allowable shear stress. TJ=τr T=τ(d/2)×π32d4 =τ×π16d3 T=(50×106)×π16×(0.05)3=1227Nm Torque based on allowable angle of twist. TJ=Gθl T=(100×109)×(1×π180)×π32×(0.05)4=1070Nm So max. permissible torque, T = 1070 Nm

A solid steel shaft of diameter 50 mm is to be designed using an allowable shear stress $τ_{a l l o w} = 50 M P a$ and allowable angle of twist per unit length $θ = 1^{o}$ per meter. The maximum permissible torque (in Nm) T that may be applied to the shaft is ? (assuming G = 100GPa).