This document discusses stresses in thin cylindrical shells. It defines a thin cylindrical shell as having a thickness to diameter ratio of 1/20 or less. When a thin cylindrical shell is subjected to internal fluid pressure, it develops hoop/circumferential stresses around the circumference and longitudinal stresses along the shell's length. Radial stresses are small and can be neglected. It provides examples of structures that can be considered thin cylindrical shells like boilers, tanks, pipes. It also gives some numerical problems to calculate stresses and required thickness for cylindrical shells under different pressures.

1. WITH NUMERICALS

2. THIN CYLINDRICAL SHELLS
A Cylindrical vessel or shell may be thin or thick depending upon the
thichness of plate in the relation to the internal diameter of the cylinder.
20
1

d
t where, t= thichness of plate
d= internal dia of cylinder
In thin cylinders, the stress may be assumed uniformaly distributed over the wall thickness.
Boilers , Tanks , Steam pipes , water Pipes etc. are usually considered as tin cylinders.
Thin cylinders are frequently required to operate under pressure upto 30MPa. For high pressure such as
25MPa or more , thick cylinders are used.

3. GENERATION OF STRESSES
When these cylinders are subjected to internal fluid pressures the
following two types of stresses are developed.
Hoop/Circumferential
Stresses
Longitudinal stresses Radial stresses
These act in a tangential
direction to the circumference
of the shell.
These act parallel to the
longotudinal axis of the shell.
These act radially and are too
small and can be neglected.

4. Stresses in Thin Cylinder

5. Stresses in Thin Cylinder

6. Strains in Thin Cylinder

7. For Objective Questions

8. SOME IMPORTANT NUMERICAL PROBLEMS
1. Calculate the bursting pressure for a cold drawn seamless steel tubing of 60mm
inside diameter with 2mm wall thickness. The ultimate strength of steel is 380MPa.
2. Calculate the thickness of metal required for a cast iron main 800mm dia for water at
a pressure head of 100 meter. if the maximum permissible tensile stress is 20MPa and
weight of water is 10 KN/m3.
3. A cylinderical vessel whose ends are closed by means of rigid flange plate is made of
steel plate 3mm thick. The internal length and diameter of vessel are 50 cm and 25 cm
respectively. Determine the Longitudinal and Ciumferential stresses in the cylindrical
shell due to an internal fluid pressure of 3MPa. Also calculate increase in length,
diameter and volume of the vessel. Take E= 200GPa and μ= 0.3
4. A 3 m long shell which is closed at the ends has an internal diameter of 1meter
andwall thickness of 15mm. Claculate the circumferential and longitudinal stresses
induced and also change in dimensions of the shell if it is subjected to an internal
pressure of 1.5MPa. Take E= 200 GPa and μ= 0.3