ME Dept., NIT Jalandhar, Regular Course: Jan 2020, MEX206,
Course Coordinator: Dr. Manoj Kumar; Email ID: kumarm@nitj.ac.in
Submission Date: 13thMay 2020
Homework 10
THICK CYLINDER
1. What is a thin cylinder? What are the stresses a thin cylinder is subject to? State their formula's?
2. What is a thin cylinder ?What are the stresses a thin cylinder is subject to? State their formula's?
3. Derive the Lame's equation for thick cylinder, name various terms used in equation, When it is used
to find wall thickness?
4. What is autofrettage, What are the methods of Prestressing the cylinder?
5. Define Circumferential and Hoop stress in thick and thin cylinder.
6. A steel cylinder is 160 mm ID and 320 mm OD. If it is subject to an internal pressure of 150 MPa,
determine the radial and tangential stress distributions and show the results on a plot (using a
spreadsheet). Determine the maximum shear stress in the cylinder. Assume it has closed ends.
7. The internal and external diameter of a thick hollow cylinder are 80 mm and 120 mm respectively. It
is subjected to an external pressure of 40 N/mm2 and an internal pressure of 120 N/mm2. Calculate
the circumferential and radial stresses at the mean radius.
8. A cylinder is 150 mm ID and 450 mm OD. The internal pressure is 160 MPa and the external
pressure is 80 MPa. Find the maximum radial and tangential stresses and the maximum shear stress.
The ends are closed.
9. A cylinder has an internal radius of 200 mm and external radius of 300 mm. Permissible stress for the
material is 15.5 N/mm2. If the cylinder is subjected to an external pressure of 4 N/mm2, find the
internal pressure that can be applied.
10. A cylinder has an ID of 100 mm and an internal pressure of 50 MPa. Find the needed wall thickness if
the factor of safety n is 2.0 and the yield stress is 250 MPa. Use the maximum shear stress theory, i.e.
maximum shear stress = yield strength/2.
11. A 400 mm OD steel cylinder with a nominal ID of 240 mm is shrunk onto another steel cylinder of
240 mm OD and 140 mm ID. The radial interference δ is 0.3 mm. Use Young's Modulus E = 200 GPa
and Poisson's Ratio n = 0.3. Find the interface pressure pi and plot the radial and tangential stresses in
both cylinders. Then find the maximum internal pressure which may be applied to the assembly if the
maximum tangential stress in the inside cylinder is to be no more than 140 MPa.
12. A pipe with internal diameter 400 mm is to carry a fluid pressure of 12 MPa. If the maximum stress in
the material of the pipe is restricted to 110 MPa, calculate the minimum thickness of the pipe
required.
13. A cylinder with closed ends has outer diameter D and a wall thickness t = 0.1D. Determine the %age
error involved in using thin wall cylinder theory to calculate the maximum value of tangential stress
and the maximum shear stress in the cylinder.
14. A compound tube is composed of a tube 25 cm internal diameter and 2.5 cm thick shrunk on a tube of
25 cm external diameter and 2.5 cm thick. The radial pressure at the junction is 80 MPa . The
compound tube is subjected to an internal fluid pressure of 845 MPa. Find the variation of the hoop
stress over the wall of the compound tube.
15. A thick cylinder of external diameter 40 cm and internal diameter 30 cm is shrunk on to another
cylinder of external diameter 30 cm and 5 cm thick. If the radial pressure at the junction to shrink fit
is 15 MPa, calculate the initial difference in radii at the junction.
16. A thick cylinder of 100 mm internal radius and 150 mm external radius is subjected to an internal
pressure of 60 MPa and an external pressure of 30 MPa. Determine the hoop and radial stresses at the
inside and outside of the cylinder together with the longitudinal stress if the cylinder is assumed to
have closed ends.
ME Dept., NIT Jalandhar, Regular Course: Jan 2020, MEX206,
Course Coordinator: Dr. Manoj Kumar; Email ID: kumarm@nitj.ac.in
Submission Date: 13thMay 2020
Homework 10
THICK CYLINDER
17. An external pressure of 10 MPa is applied to a thick cylinder of internal diameter 160 mm and
external diameter 320 mm. If the maximum hoop stress permitted on the inside wall of the cylinder is
limited to 30 MPa, what maximum internal pressure can be applied assuming the cylinder has closed
ends? What will be the change in outside diameter when this pressure is applied? E = 207 GPa, ν =
0.29.
18. A thin uniform steel disc of diameter 500 mm is rotating about its axis at 3000 rpm. Calculate the
maximum principal stress and maximum in plane shear stress in the disc. Draw the circumferential
stress and radial stress distribution along the radius of the thin disc.Given Poisson’s ratio, ν = 0.3, ρ =
7700 kg/m3 g = 9.81 m/s2
19. A thin uniform disc of inner radius 50 mm and outer radius 200 mm is rotating at 6000 rpm about its
axis. What are the maximum hoop and radial stresses? Draw the distribution of hoop and radial
stresses along the radius of the disc.Given ρ = 7800kg/m3, ν = 0.3, N = 6000rpm.
20. A solid long cylinder of diameter 600 mm is rotating at 3000 rpm. Calculate (i) maximum and
minimum hoop stresses and (ii) maximum radial stress.Given ρ = 0.07644 N/cm3, g = 9.8 m/s2, ν =
0.3.
21. A long cylinder of steel of outer diameter 750 mm and inner diameter 250 mm is rotating about its
axis at 4000 rpm. Determine the radial stress and circumferential stress along the radius of
cylinder.Given ρ = 0.078 N/cm3, ν= 0.3, g = 9.80 m/s2