Shafts of Varying Cross Sections in Torsion

Q. A stepped circular shaft is fixed at A and C as shown in the below figure. The diameter of the shaft along BC is twice that of as along AB. The torsional rigidity of AB is GJ. The torque required for unit twist at B is

1. $\frac{2GJ}{l}$
2. $\frac{5GJ}{l}$
3. $\frac{9GJ}{l}$
4. $\frac{17GJ}{l}$

Q. A torque of 10 Nm is transmitted through a stepped shaft as shown in figure. The torsional stiffness of individual sections of lengths MN, NO and OP are 20 Nm/rad 30 Nm/rad and 60 Nm/rad respectively. The angular deflection between the ends M and P of the shaft is

1. 0.5 rad
2. 1.0 rad
3. 5.0 rad
4. 10 rad

Q. A section of a solid circular shaft with diameter D is subjected to bending moment M and torque T. The expression for maximum principal stress at the section is

1. $\frac{2M+T}{\pi D^3}$
2. $\frac{16\pi }{D^3}(M+\sqrt{M^2+T^2})$
3. $\frac{16\pi }{D^3}\left(\sqrt{M^2+T^2}\right)$
4. $\frac{16}{\pi D^3}(M+\sqrt{M^2+T^2})$

Q. Consider a stepped shaft subjected to a twisting moment applied at B as shown in the figure. Assume shear modulus, G = 77 GPa. The angle of twist at C (in degree) is

1. 0.2368

Q. Two thin-walled tubular members made of the same material have the same length, same wall thickness and same total weight and are both subjected to the same torque of magnitude T. If the individual cross-section are circular and square, respectively, as in the figures, then the ratios of the shear stresses reckoned for the circular member in relation to the square member will be

1. 0.785
2. 0.905
3. 0.616
4. 0.513

Q. A torque T is applied at the free end of circular cross-sections as shown in the figure. The shear modulus of the material of the rod is G. The expression for d to produce an angular twist $\theta$ at the free end is

1. ${\left(\frac{32TL}{\pi \theta G}\right)}^{\frac{1}{4}}$
2. ${\left(\frac{18TL}{\pi \theta G}\right)}^{\frac{1}{4}}$
3. ${\left(\frac{16TL}{\pi \theta G}\right)}^{\frac{1}{4}}$
4. ${\left(\frac{2TL}{\pi \theta G}\right)}^{\frac{1}{4}}$