A cube subjected to three mutually perpendicular stress of equal intensity p expenses a volumetric strain

A $$\frac{{3{\text{p}}}}{{\text{E}}} \times \frac{2}{{{\text{m}} - 1}}$$
B $$\frac{{3{\text{p}}}}{{\text{E}}} \times \left( {2 - {\text{m}}} \right)$$
C $$\frac{{3{\text{p}}}}{{\text{E}}} \times \left( {1 - \frac{2}{{\text{m}}}} \right)$$
D $$\frac{{\text{E}}}{{3{\text{p}}}} \times \frac{2}{{{\text{m}} - 1}}$$

Correct Answer: $$\frac{{3{\text{p}}}}{{\text{E}}} \times \left( {1 - \frac{2}{{\text{m}}}} \right)$$

Bissoy MCQ
#Mechanical Engineering #Strength Of Materials In ME

Related Questions

The ratio of direct stress to volumetric strain in case of a body subjected to three mutually perpendicular stresses of equal intensity, is equal to
A Young's modulus
B Bulk modulus
C Modulus of rigidity
D Modulus of elasticity
When a body is subjected to three mutually perpendicular stresses, of equal intensity, the ratio of direct stress to the corresponding volumetric strain is known as
A Young's modulus
B Modulus of rigidity
C Bulk modulus
D Poisson's ratio
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 $$\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + \tau _{{\text{xy}}}^2} $$
A plate with an elliptical hole in the centre, with semi-major axis (a) perpendicular to the direction of loading and semi-minor axis (b) along the direction of loading, is subjected to a pull P. The maximum stress induced at the edge of the hole is equal to (where $$\sigma $$ = Stress for a plate with no hole i.e. nominal stress)
A $$\sigma \left( {1 + \frac{{\text{b}}}{{2{\text{a}}}}} \right)$$
B $$\sigma \left( {1 + \frac{{2{\text{a}}}}{{\text{b}}}} \right)$$
C $$\sigma \left( {1 + \frac{{\text{b}}}{{3{\text{a}}}}} \right)$$
D $$\sigma \left( {1 + \frac{{3{\text{a}}}}{{\text{b}}}} \right)$$
When a body is subjected to direct tensile stresses ($${\sigma _{\text{x}}}$$ and $${\sigma _{\text{y}}}$$) in two mutually perpendicular directions, accompanied by a simple shear stress $${\tau _{{\text{xy}}}}{\text{,}}$$  then in Mohr's circle method, the circle radius is taken as
A $$\frac{{{\sigma _{\text{x}}} - {\sigma _{\text{y}}}}}{2} + \tau $$
B $$\frac{{{\sigma _{\text{x}}} + {\sigma _{\text{y}}}}}{2} + \tau $$
C $$\frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} - {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$
D $$\frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$
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
If the length of a edge of cube X is thrice the length of an edge of cube Y, What is the ration of the volume of cube Y to the volume of cube X?
A 1/2
B 1/4
C 1/6
D 1/8
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
The strain energy due to volumetric strain
A Is directly proportional to the volume
B Is directly proportional to the square of exerted pressure
C Is inversely proportional to Bulk modulus
D All the above

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