The ratio of shear stress and shear strain of an elastic material, is

Three elastic constants for a completely anisotropic elastic material which follows the Hooke's law are young's modulus, elastic limit stress and yield stress. Which of the following properties is most sensitive to increase in strain rate ?

A

Tensile strength

B

Elastic limit

C

Proportional limit

D

Yield strength

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

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

A cylinderical rod subjected to a tensile strain within the elastic limit undergoes a volume change. If the volume strain is equal to half the tensile strain, then the Poisson's ratio of the rod is

A

0

B

0.33

C

0.44

D

0.25

The design stress, which is more than the damaging stress, is the least unit stress that will render a member unfit for service before the end of its normal life. The design stress factor or factor of safety indicates the margin between design stress and the __________ stress.

A

Working

B

Damaging

C

Allowable

D

None of these

According to maximum shear stress failure criterion, yielding in material occurs, when the maximum shear stress is equal to __________ times the yield stress.

A

0.5

B

2

C

$$\sqrt 2 $$

D

$$\sqrt {\frac{3}{2}} $$

Which of the following relationships is correct for relating the three elastic constants of an isotropic elastic material (where, E = Young's modulus, G = Modulus of rigidity or shear modulus v = Poisson's ratio)?

A

E = 2G (1 + v)

B

E = G (1 + v)

C

$${\text{E}} = \frac{{{\text{G}}\left( {1 + {\text{v}}} \right)}}{2}$$

D

E = 2G (1 + 2v)

Poisson's ratio of a material is the ratio of unit lateral strain to the unit axial elongation within its elastic limit. The value of Poisson's ratio for structural and pressure vessel steel may be taken as

A

0.01

B

0.3

C

0.75

D

0.95

Every direct stress is always accompanied by a strain in its own direction and an opposite kind of strain in every direction, at right angles to it. Such a strain is known as

A

Linear strain

B

Lateral strain

C

Volumetric strain

D

Shear strain

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

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

The ratio of shear stress and shear strain of an elastic material, is

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