Two mark Questions and Answers

TWO MARK QUESTIONS AND ANSWERS

1. Define thick cylinder.

A cylinder is called as a thick cylinder when the ratio of thickness (†) to internal diameter (d) of cylinder is more than 1/20.

2. In a thick cylinder will the radial stress vary over the thickness of wall? 

Yes, in thick cylinders radial stress is maximum at inner and minimum at the outer radius.

3. How many stresses are developed in thick cylinders? Name them.

Three types of stresses are developed in thick cylinders.

1. Radial stress (σr)

2. Hoop stress (σc)

3. Longitudinal stress (σl)

4. Define compound cylinders.

Compound cylinders are thick cylinders shrinking one tube on the other tube to reduce circumferential stress.

5. Assumptions made in Lame's theory.

• The material is homogeneous and isotropic.

• The material is stressed within elastic limit.

• Plane section perpendicular to the longitudinal axis of the cylinder remain plane after the application of internal pressure.

• All the fibres of the material are to expand or contract independently without being constrained by the adjacent fibres.

6. Write Lame's equation to find out stresses in a thick cylinder.

PROBLEMS FOR PRACTICE

1. A pipe of 800 mm internal diameter and 100 mm thickness contains a fluid at a pressure of 7 N/mm2. Find the maximum and minimum hoop stresses across the section. Also sketch the radial pressure distribution across this section. 

2. Find the thickness of metal necessary for a steel cylindrical shell of internal diameter 350 mm to withstand an internal pressure of 36 N/mm2. The maximum hoop stress in the section is not to exceed 150 N/mm2.

3. A compound tube is composed of a tube 300 mm internal diameter and 20 mm thick shrunk of a tube of 300 mm external diameter and 20 mm thick. The radial pressure at the junction is 8 N/mm2. Find the variation of the hoop stress over the wall of the compound tube.