Design of Shafts for Torsion

Q. A hollow shaft of 1 m length is designed to transmit a power of 30 kW at 700 rpm. The maximum permissible angle of twist in the shaft is $1^0$. The inner diameter of the shaft is 0.7 times the outer diameter. The modulus of rigidity is 80 GPa. The outside diameter (in mm) of the shaft is

1. 44.5212

Q. What is the diameter d of a solid circular shaft when subjected to a torque T with a corresponding maximum shear stress of magnitude $f_s$?

1. $\frac{16T}{\pi f_s}$
2. $\frac{\pi f_s}{16T}$
3. $\sqrt{\frac{16T}{\pi f_s}}$
4. $3\sqrt{\frac{16T}{\pi f_s}}$

Q. A solid circular shaft is subjected to a torque T(in Nm), which produces a maximum shear stress of $f_s\left(inN/m{m}^2\right)$ in the shaft. The required diameter of the shaft would be

1. $10{\left(\frac{16T}{\pi f_s}\right)}^{1/3}$
2. $10{\left(\frac{\pi f_s}{16T}\right)}^{1/3}$
3. $10{\left(\frac{16T}{\pi f_s}\right)}^{1/2}$
4. $10{\left(\frac{\pi f_s}{16T}\right)}^{1/2}$

Q. Torsion applied to a circular shaft results in a twist of $1^o$ over a length of 1 m. The maximum shear stress induced is $120N/m{m}^2$ and the modulus of rigidity of the shaft material is $0.8\times {10}^{5}N/m{m}^2$. What is the radius of the shaft?

1. $\frac{300}{\pi }$
2. $\frac{180}{\pi }$
3. $\frac{90}{\pi }$
4. $\frac{270}{\pi }$

Q. A solid circular shaft subjected to a torque T procduces maximum shear stress $f_s$, which is the maximum principal value in the material. The corresponding diameter of the shaft should be

1. $3\sqrt{\frac{\pi .f_s}{16.T}}$
2. $3\sqrt{\frac{32.T}{\pi .f_s}}$
3. $3\sqrt{\frac{\pi }{16.T.f_s}}$
4. $3\sqrt{\frac{32.T}{\pi .f_s}}$

Q. The two circular shafts made of same material, one solid(S) and one hollow(H), have the same length and polar moments of inertia. Both are subjected to same torque. Here ${\theta }_S$ is the twist and ${\tau }_S$ is the maximum shear stress in the solid shaft, whereas ${\theta }_H$ is the twist and ${\tau }_H$ is the maximum shear stress in the hollow shaft. Which one of the following is TRUE?

1. ${\theta }_S={\theta }_{H}and{\tau }_S={\tau }_H$
2. ${\theta }_S>{\theta }_{H}and{\tau }_S>{\tau }_H$
3. ${\theta }_S={\theta }_{H}and{\tau }_S<{\tau }_H$
4. ${\theta }_S={\theta }_{H}and{\tau }_S={\tau }_H$

Q. A hollow circular shaft of inner radius 10 mm outer radius 20 mm and length 1 m is to be used as a torsional spring. If the shear modulus of the material of the shaft is 150 GPa, the torsional stiffness of the shaft (in kN-m/rad) is _______ (correct to two decimal places).

1. 35.343