A thin spherical shell of internal diameter d is subjected to an internal pressure p. If $${\sigma _{\text{t}}}$$ is the tensile stress for the shell material, then thickness of shell is equal to

A $$\frac{{{\text{pd}}}}{{{\sigma _{\text{t}}}}}$$
B $$\frac{{{\text{pd}}}}{{2{\sigma _{\text{t}}}}}$$
C $$\frac{{{\text{pd}}}}{{3{\sigma _{\text{t}}}}}$$
D $$\frac{{{\text{pd}}}}{{4{\sigma _{\text{t}}}}}$$

Correct Answer: $$\frac{{{\text{pd}}}}{{4{\sigma _{\text{t}}}}}$$

Bissoy MCQ
#Mechanical Engineering #Machine Design

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A thin spherical shell of diameter (d) and thickness (t) is subjected to an internal pressure (p). The stress in the shell material is
A $$\frac{{{\text{pd}}}}{{\text{t}}}$$
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C $$\frac{{{\text{pd}}}}{{4{\text{t}}}}$$
D $$\frac{{{\text{pd}}}}{{8{\text{t}}}}$$
A thin spherical shell of internal diameter d is subjected to an internal pressure p. If V is the storage capacity of shell, then its diameter will be
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A $$\frac{{{\text{pd}}}}{{\text{t}}}$$
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A thin cylindrical shell of diameter (d) length ($$l$$) and thickness (t) is subjected to an internal pressure (p). The longitudinal stress in the shell is
A $$\frac{{{\text{pd}}}}{{\text{t}}}$$
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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 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 $$\frac{1}{2}\sqrt {{{\left( {{\sigma _{\text{x}}} + {\sigma _{\text{y}}}} \right)}^2} + 4\tau _{{\text{xy}}}^2} $$
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 thin cylindrical shell of diameter (d), length ($$l$$) and thickness (t) is subjected to an internal pressure (p). The ratio of longitudinal strain to hoop strain is
A $$\frac{{{\text{m}} - 2}}{{2{\text{m}} - 1}}$$
B $$\frac{{2{\text{m}} - 1}}{{{\text{m}} - 2}}$$
C $$\frac{{{\text{m}} - 2}}{{2{\text{m}} + 1}}$$
D $$\frac{{2{\text{m}} + 1}}{{{\text{m}} - 2}}$$
When a body is subjected to a direct tensile stress ($$\sigma $$) in one plane, then tangential or shear stress on an oblique section of the body inclined at an angle $$\theta $$ to the normal of the section is
A $$\sigma \sin 2\theta $$
B $$\sigma \cos 2\theta $$
C $$\frac{\sigma }{2}\sin 2\theta $$
D $$\frac{\sigma }{2}\cos 2\theta $$
When a body is subjected to a direct tensile stress ($$\sigma $$) in one plane, then normal stress on an oblique section of the body inclined at an angle $$\theta $$ to the normal of the section is
A $$\sigma \cos \theta $$
B $$\sigma {\cos ^2}\theta $$
C $$\sigma \sin\theta $$
D $$\sigma {\sin ^2}\theta $$

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