Stresses in Thin Cylinders

Q. A thin walled cylindrical pressure vessel having a radius of 0.5 m and wall thickness of 25 mm is subjected to an internal pressure of 700 kPa. The hoop stress developed is

1. 14 MPa
2. 1.4 MPa
3. 0.14 MPa
4. 0.014 MPa

Q. The variation of the hoop stress across the thickness of a thick cylinder is

1. linear
2. uniform
3. parabolic
4. hyperbolic

Q. A cast iron pipe of $1m$ diameter is required to withstand a $200m$ head of water. If the limiting tensile stress of the pipe material is $20MPa$, then the thickness of the pipe will be

1. $25mm$
2. $50mm$
3. $75mm$
4. $100mm$

Q. A thin-walled long cylindrical tank of inside radius r is subjected simultaneously to internal gas pressure p and axial compressive force F at its ends. In order to produce 'pure shear' state of stress in the wall of the cylinder, F should be equal to

1. $\pi P{r}^2$
2. $2\pi P{r}^2$
3. $3\pi P{r}^2$
4. $4\pi P{r}^2$

Q. A thin cylinder of unit length, thickness ${}^{\prime }{t}^{\prime }$ and radius ${}^{\prime }{r}^{\prime }$ is subjected to internal pressure ${}^{\prime }{p}^{\prime }$. What is the circumferential stress?

1. $pr/2Et$
2. $pr/2t$
3. $pr/t$
4. $2pr/t$

Q. A cylindrical shell of $100cm$ diameter made of mild steel plate is to be subjected to an internal pressure of $10kg/c{m}^2$. If the material yields at a stress of $200kg/c{m}^2$, assuming factor of safety as $4$ and using maximum principal stress theory, the requisite thickness of the plate will be

1. $8mm$
2. $10mm$
3. $12mm$
4. $15mm$

Q. A thin cylindrical shell made of mild steel plate is $1000mm$ in diameter. It is to be subjected to an internal pressure of $2N/m{m}^2$. If the material yields at $200N/m{m}^2$, the thickness of the plate in mm on the basis of Rankine's theory of failure with assuming a factor of safety of $3$ would be

1. 10
2. 12
3. $15$
4. $18$

Q. A thin cylindrical tube with closed ends is subjected to:
1. Longitudinal stress ${\sigma }_1=14N/m{m}^2$
2. Hoop stress ${\sigma }_2=2N/m{m}^2$
3. Shearing stress $\tau =8N/m{m}^2$
Then the maximum shearing stress is

1. $14N/m{m}^2$
2. $12N/m{m}^2$
3. $10N/m{m}^2$
4. $8N/m{m}^2$

Q. A thin hollow cylinder of diameter ${}^{\prime }{d}^{\prime }$, length $L$ and thickness ${}^{\prime }{t}^{\prime }$ is subjected to an internal pressure ${}^{\prime }{p}^{\prime }$. The hoop stress in the cylinder is

1. $\frac{pd}{8t}$
2. $\frac{pd}{4t}$
3. $\frac{pd}{2t}$
4. $\frac{pd}{8t}$

Q. A thick cylindrical pressure vessel of inner diameter $D_i$ and outer diameter $D_o$ is subjected to an internal fluid pressure of intensity ${}^{\prime }{p}^{\prime }$. The variation of the circumferential tensile stress '$p_y$' in the thickness of the shell will be

1. 
2. 
3. 
4. 

Q. Two closed thin vessels, one cylindrical and the other spherical with equal internal diameter and wall thickness are subjected to equal internal fluid pressure. The ratio of hoop stresses in the cylindrical to that of spherical vessel is

1. 4.0
2. 2.0
3. 1.0
4. 0.5

Q. A thin cylindrical vessel of mean diameter D and of length 'L' closed at both ends is subjected to a water pressure 'p'. The value of hoop stress and longitudinal stress in the shell shall be respectively

1. $\frac{pD}{2t},\frac{pD}{4t}$
2. $\frac{pD}{2t},\frac{pD}{8t}$
3. $\frac{pD}{8t},\frac{pD}{8t}$
4. $\frac{pD}{t},\frac{pD}{2t}$

Q. A thin cylindrical steel pressure vessel of diameter $6cm$ and wall thickness $3mm$ is subjected to an internal fluid pressure of intensity ${}^{\prime }{p}^{\prime }$. If the ultimate strength of steel $3600kg/c{m}^2$, the bursting pressure will be

1. $18kg/c{m}^2$
2. $36kg/c{m}^2$
3. $180kg/c{m}^2$
4. $360kg/c{m}^2$

Q. For the analysis of thick cylinders, the theory applicable is

1. Lame's theory
2. Rankine's theory
3. Poisson's theory
4. Courbon's theory

Q. The ratio of tensile stress developed in the wall of a boiler in the longitudinal direction to the tensile stress in the circumferential direction due to an internal pressure is

1. $4$
2. $2$
3. $1/4$
4. $1/2$

Q. A water main $160cm$ dia. contains water at a pressure head of $200m$. Take weight of water to be $1000kg/m^3$. The thickness of the metal shell required for the water main, given that the maximum permissible stress in the metal is $400kg/c{m}^2$, will be

1. $1cm$
2. $2cm$
3. $3cm$
4. $4cm$

Q. Assertion (A): The intensity of the longitudinal stress is one half of the intensity of hoop-stress or circumferential stress in a thin cylindrical shell
subjected to internal pressure.
Reason (R): The stresses in the longitudinal and circumferential directions develop when a thin cylindrical shell is subjected to internal force which tries to burst the cylinder

1. both A and R are true and R is the correct explanation of A
2. both A and R are true but R is not a correct explanation of A
3. A is true but R is false
4. A is false but R is true

Q. A cylindrical tank of radius r and wall thickness t has flat end closures. The tank is subjected to an internal pressure P. The longitudinal (${\sigma }_l$) and the circumferential (${\sigma }_h$) stresses respectively are given by:

1. Pr/t, 0
2. Pr/2t, Pr/t
3. Pr/4t, Pr/3t
4. Pr/6t, Pr/t