The strain energy stored in a hollow circular shaft of outer diameter (D) and inner diameter (d) subjected to shear stress is

The strain energy stored in a body due to shear stress, is (where $$\tau $$ = Shear stress, C = Shear modulus and V = Volume of the body)

A

$$\frac{{\tau {\text{V}}}}{{2{\text{C}}}}$$

B

$$\frac{{2{\text{C}}}}{{\tau {\text{V}}}}$$

C

$$\frac{{{\tau ^2}{\text{V}}}}{{2{\text{C}}}}$$

D

$$\frac{{2{\text{C}}}}{{{\tau ^2}{\text{V}}}}$$

The polar moment of inertia of a hollow shaft of outer diameter (D) and inner diameter (d) is

A

$$\frac{\pi }{{16}}\left( {{{\text{D}}^3} - {{\text{d}}^3}} \right)$$

B

$$\frac{\pi }{{16}}\left( {{{\text{D}}^4} - {{\text{d}}^4}} \right)$$

C

$$\frac{\pi }{{32}}\left( {{{\text{D}}^4} - {{\text{d}}^4}} \right)$$

D

$$\frac{\pi }{{64}}\left( {{{\text{D}}^4} - {{\text{d}}^4}} \right)$$

The torque transmitted by a hollow shaft of outer diameter (D) and inner diameter (d) is

A

$$\frac{\pi }{4} \times \tau \left( {\frac{{{{\text{D}}^2} - {{\text{d}}^2}}}{{\text{D}}}} \right)$$

B

$$\frac{\pi }{{16}} \times \tau \left( {\frac{{{{\text{D}}^3} - {{\text{d}}^3}}}{{\text{D}}}} \right)$$

C

$$\frac{\pi }{{16}} \times \tau \left( {\frac{{{{\text{D}}^4} - {{\text{d}}^4}}}{{\text{D}}}} \right)$$

D

$$\frac{\pi }{{32}} \times \tau \left( {\frac{{{{\text{D}}^4} - {{\text{d}}^4}}}{{\text{D}}}} \right)$$

The polar modulus for a hollow shaft of outer diameter (D) and inner diameter (d) is

A

$$\frac{\pi }{4}\left( {\frac{{{{\text{D}}^2} - {{\text{d}}^2}}}{{\text{D}}}} \right)$$

B

$$\frac{\pi }{{16}}\left( {\frac{{{{\text{D}}^3} - {{\text{d}}^3}}}{{\text{D}}}} \right)$$

C

$$\frac{\pi }{{16}}\left( {\frac{{{{\text{D}}^4} - {{\text{d}}^4}}}{{\text{D}}}} \right)$$

D

$$\frac{\pi }{{32}}\left( {\frac{{{{\text{D}}^4} - {{\text{d}}^4}}}{{\text{D}}}} \right)$$

A shaft is subjected to bending moment M and a torque T simultaneously. The ratio of the maximum bending stress to maximum shear stress developed in the shaft, is

A

$$\frac{{\text{M}}}{{\text{T}}}$$

B

$$\frac{{\text{T}}}{{\text{M}}}$$

C

$$\frac{{2{\text{M}}}}{{\text{T}}}$$

D

$$\frac{{2{\text{T}}}}{{\text{M}}}$$

When a body is subjected to biaxial stress i.e. direct stresses ($${\sigma _{\text{x}}}$$) and ($${\sigma _{\text{y}}}$$) in two mutually perpendicular planes accompanied by a simple shear stress ($${\tau _{{\text{xy}}}}$$ ), then maximum shear stress is

A

$$\frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} - {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$

B

$$\frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$

C

$$\sqrt {{{\left( {{\sigma _{\text{x}}} - {\sigma _{\text{y}}}} \right)}^2} + \tau _{{\text{xy}}}^2} $$

D

$$\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + \tau _{{\text{xy}}}^2} $$

When a body is subjected to a direct tensile stress ($${\sigma _{\text{x}}}$$) in one plane accompanied by a simple shear stress ($${\tau _{{\text{xy}}}}$$ ), the maximum shear stress is

A

$$\frac{{{\sigma _{\text{x}}}}}{2} + \frac{1}{2}\sqrt {\sigma _{\text{x}}^2 + 4\tau _{{\text{xy}}}^2} $$

B

$$\frac{{{\sigma _{\text{x}}}}}{2} - \frac{1}{2}\sqrt {\sigma _{\text{x}}^2 + 4\tau _{{\text{xy}}}^2} $$

C

$$\frac{{{\sigma _{\text{x}}}}}{2} + \frac{1}{2}\sqrt {\sigma _{\text{x}}^2 - 4\tau _{{\text{xy}}}^2} $$

D

$$\frac{1}{2}\sqrt {\sigma _{\text{x}}^2 + 4\tau _{{\text{xy}}}^2} $$

A shaft of diameter D is subjected to a twisting moment (T) and a bending moment (M). If the maximum bending stress is equal to maximum shear stress developed, then M is equal to

A

$$\frac{{\text{T}}}{2}$$

B

T

C

2T

D

4T

When a circular beam of diameter d is subjected to a shear force F, the maximum shear stress induced will be

A

$$\frac{{4{\text{F}}}}{{\pi {{\text{d}}^2}}}$$

B

$$\frac{{{\text{6F}}}}{{\pi {{\text{d}}^2}}}$$

C

$$\frac{{{\text{8F}}}}{{\pi {{\text{d}}^2}}}$$

D

$$\frac{{{\text{16F}}}}{{3\pi {{\text{d}}^2}}}$$

When a shaft, is subjected to torsion, the shear stress induced in the shaft varies from

A

Minimum at the center to maximum at the circumference

B

Maximum at the center to minimum at the circumference

C

Zero at the center to maximum at the circumference

D

Maximum at the center to zero at the circumference

The strain energy stored in a hollow circular shaft of outer diameter (D) and inner diameter (d) subjected to shear stress is

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