Problems for Practice

PROBLEMS FOR PRACTICE

1. A thin cylindrical shell has an internal diameter 350 mm, and is 3.5 mm thick. It is subjected to an internal pressure of 2 N/mm2. Calculate the circumferential and longitudinal stresses.

2. A cylinder of internal diameter 3 m and of thickness 20 mm contains a fluid. If the tensile stress in the material is not to exceed 75 N/mm2, estimate the internal pressure of the gas.

3. A 1 m diameter pipe contains a fluid at a pressure of 30 N/mm2. If the permissible stress in tension is 90 N/mm2. Find the minimum thickness of the pipe.

4. A hollow cylinder drum with closed ends, 2 m long, 1 m in diameter, thickness of metal 10 mm is subjected to an internal fluid pressure of 1.4 MN/m2. Calculate the maximum shear stress induced and also the changes in dimensions of the shell. Take E = 2 × 105 N/mm2 and Poisson's ratio = 0.3. 

5. A steel cylindrical tube of 80 mm internal diameter, 1 m long and 1.55 thick has closed ends and is filled with a fluid under pressure. Neglecting any distortion of the ends plates, determine the alteration of pressure when an additional volume of 5 c.c., of fluid is pumped into the tube. Given E = 200 GPa, 1/m = 0.3 and bulk modulus of water K = 2 GPa.

6. A steel cylinder is 2.5 m long, 1.2 m diameter, thickness of the metal 12 mm. After being filled with a liquid at atmosphere level, more liquid is pumped until the pressure is 2.5 MPa, on relieving the pressure, the liquid escaped until the pressure falls to atmospheric pressure. Estimate the amount of liquid that has escaped, if E for steel is 2 × 105 N/mm2, Poisson's ratio = 0.3 and bulk modulus of liquid 2.67 GPa.

7. A thin cylinder of 75 mm internal diameter and wall. thickness 2 mm is subjected to an internal pressure of 1.5 N/mm2. The cylinder is also subjected to a torque of 50 N-m, the axis of the torque coinciding with that of the cylinder. Find the principle stress and the maximum shear stress at a point on the surface of the cylinder.

8. A closed thin copper cylinder of 200 mm internal diameter having a wall thickness of 5 mm is closely wound with a layer 2.5 mm diameter steel wire under a tensile stress is 55 N/mm2. Find the stresses induced in the cylinder and wire when the cylinder is subjected to an internal pressure of 3.5 MPa. For take E copper take Ec = 1 × 105 N/mm2, Poisson's ratio = 0.3. For steel take Es = 2 × 105 N/mm2.

9. A thin spherical shell 2 m diameter is subjected to an internal pressure of 1.8 N/mm2. If the permissible stress in the plate material is 120 N/mm2. Find the minimum thickness.

10. A seamless spherical shell, 750 mm diameter is 12 mm thick. It is being filled with a fluid under pressure until its volume increases by 250 c.c. Calculate the pressure exerted by the fluid on the shell. Given E = 2 × 105 N/mm2, Poisson's ratio = 0.29.

11. A thin spherical vessel 150 mm diameter and 14 mm thick is filled with water. More water is pumped in until the pressure reaches 3.8 MPa. How much extra water was required to reach this pressure?

12. A thin spherical copper shell of internal diameter 500 mm and thickness 3 mm is subjected to an internal pressure of 1.65 N/mm2. Calculate the increase in diameter and increase in volume of the shell. Take E 1 × 105 N/mm2, 1/m = 0.28.