Torsional Stresses

Q. The maximum and minimum shear stresses in a hollow circular shaft of outer diameter 20 mm and thickness 2 mm, subjected to a torque of 92.7 N.m will be

1. 59 MPa and 47.2 MPa
2. 100 MPa and 80 MPa
3. 118 MPa and 160 MPa
4. 200 MPa and 160 MPa

Q.

What is angle of twist?

Q. The ratio of the torsional moments of resistance of a solid circular shaft of diameter D, and a hollow circular shaft having external diameter D and internal diameter 'd' is given by

1. $\frac{D^4}{D^4-d^4}$
2. $\frac{D^4-d^4}{D^4}$
3. $\frac{D^3-d^3}{D^3}$
4. $\frac{D^3}{D^3-d^3}$

Q. A hollow steel shaft of external diameter 100 mm and internal diameter 50 mm is to be replaced by a solid alloy shaft. Assuming the same value of polar modulus for both, the diameter of the solid alloy shaft will be

1. $10\times 3\sqrt{9375}mm$
2. $10\times 2\sqrt{9375}mm$
3. $10\times 3\sqrt{\left(\frac{9375}{10}\right)}mm$
4. $3\sqrt{9375}mm$

Q. The failure surface of a standard cast iron torsion specimen, subjected to a torque is along

1. the surface helicoidal at ${45}^o$ to the axis of the specimen
2. the curved surface at the grips
3. the plane surface perpendicular to the axis of the specimen
4. the curved surface perpendicular to the axis of the specimen

Q. A hollow shaft of 16 mm outside diameter and 12 mm inside diameter is subjected to a torque of 40 N-m. The shear stresses at the outside and inside of the material of the shaft are respectively

1. $65.75N/m{m}^{2}and50.00N/m{m}^2$
2. $72.75N/m{m}^{2}and54.54N/m{m}^2$
3. $79.75N/m{m}^{2}and59.54N/m{m}^2$
4. $80.00N/m{m}^{2}and40.00N/m{m}^2$

Q. A long shaft of diameter d is subjected to twisting moment T at its ends. The maximum normal stress acting at its cross-section is equal to

1. Zero
2. $\frac{16T}{\pi d^3}$
3. $\frac{32T}{\pi d^3}$
4. $\frac{64T}{\pi d^3}$

Q. The polar modulus of a circular shaft of diameter d is

1. $\frac{\pi }{16}.d^3$
2. $\frac{\pi }{32}.d^3$
3. $\frac{\pi }{64}.d^3$
4. $\frac{\pi }{32}.d^2$

Q. Consider a circular shaft of radius 'R' having the maximum shear stress '$f_s$' developed by an applied torque.

Assertion (A) : The shear stress 'q' at a point on the section having coordinate (0, y) is $\frac{f_{s}y}{R}$

Reason(R) : In the shaft, the shear stress 'q' at a point of coordinate (x, y) is $\frac{f_s}{R}\sqrt{x^2+y^2}$

1. both A and R are true and R is the correct explanation of A
2. both A and R are true but R is not a correct explanation of A
3. A is true but R is false
4. A is false but R is true

Q. A solid circular shaft, ABC, has a total length of '3a'. A gear wheel positioned at B, at distance 'a' from the left hand end A, exerts a torque T. If the ends A and C are instantaneosuly locked in position by brakes just before the torque is applied, the torsional moments induced in both segments $T_1\left(AB\right)and{T}_2\left(BC\right)$ are in the ratio

1. 3 : 1
2. 2 : 3
3. 1 : 2
4. 2 : 1

Q. Consider the following statements :

1. The shear stress distribution across the section of a circular shaft subjected to twisting varies parabolically.
2. The shear stress at the Centre of a circular shaft under twisting moment is zero.
3. The shear stress at the extreme fibers of a circular shaft under twisting moment is maximum.

Which of the above statements is/are correct?

1. 1, 2 and 3
2. 1 only
3. 2 only
4. 3 only

Q. Which of the following terms represents the torque that produces a twist of one radian in a shaft of unit length?

1. Torisonal stress
2. Torsional rigidity
3. Flexural rigidity
4. Moment of resistance

Q. A hollow circular shaft has the diameters 50 cm and 30 cm and is subjected to a torque. If the realized maximum shear stress is $30N/m{m}^2$, what is the applied torque to nearest units?

1. 640884.9 Nm
2. 610000.0 Nm
3. 540889.5 Nm
4. 640000.0 Nm

Q. If
A = Cross-sectional area
E = Young's modulus of elasticity
G = Modulus of rigidity
I = Moment of inertia
J = Polar moment of inertia

then torsional rigidity is given by

1. AE
2. GE
3. EI
4. GJ