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

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

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

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 beam of rectangular cross-section of width b and depth d, is subjected to a shear force F, the maximum shear stress induced will be

A

$$\frac{{\text{F}}}{{{\text{bh}}}}$$

B

$$\frac{{{\text{3F}}}}{{{\text{2bh}}}}$$

C

$$\frac{{{\text{2F}}}}{{{\text{bh}}}}$$

D

$$\frac{{{\text{4F}}}}{{{\text{bh}}}}$$

The value of shear stress which is induced in the shaft due to the applied couple varies

A

From maximum at the center to zero at the circumference

B

From zero at the center to maximum at the circumference

C

From maximum at the center to minimum at the circumference

D

From minimum at the center to maximum at the circumference

Shear stress induced in a shaft subjected to tension will be

A

Maximum at periphery and zero at center

B

Maximum at center

C

Uniform throughout

D

None of the above

When a machine member is subjected to torsion, the torsional shear stress set up in the member is

A

Zero at both the centroidal axis and outer surface of the member

B

Maximum at both the centroidal axis and outer surface of the member

C

Zero at the centroidal axis and maximum at the outer surface of the member

D

Maximum at the centroidal axis and zero at the outer surface of the member

The stress induced in a body will be shear stress, when it is subjected to

A

Longitudinal vibrations

B

Transverse vibrations

C

Torsional vibrations

D

None of these

When an open coiled helical compression spring is subjected to an axial compressive load, the maximum shear stress induced in the wire is (where D = Mean diameter of the spring coil, d = Diameter of the spring wire, K = Wahl's stress factor and W = Axial compressive load on the spring)

A

$$\frac{{{\text{WD}}}}{{\pi {{\text{d}}^3}}} \times {\text{K}}$$

B

$$\frac{{2{\text{WD}}}}{{\pi {{\text{d}}^3}}} \times {\text{K}}$$

C

$$\frac{{4{\text{WD}}}}{{\pi {{\text{d}}^3}}} \times {\text{K}}$$

D

$$\frac{{8{\text{WD}}}}{{\pi {{\text{d}}^3}}} \times {\text{K}}$$

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

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