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### A thick cylinder with both external and internal pressure

Date : 2016-06-23 12:24:21

Introdcution:

It is important to remember that if σθ works out to be positive, it is tensile and if it is negative, it is compressive whereas σr is always compressive irrespective of its sign.

Description:

A standard solution for equation is σr = c rn

where c and n are constants. Substituting this in equation and also combining with equation

we have

where c1 and c2 are constants.

Boundary conditions for a thick cylinder with internal and external pressures pi and po respectively are:

The negative signs appear due to the compressive nature of the pressures. This gives

The radial stress σr and circumferential stress σθ are now given by

It is important to remember that if σθ works out to be positive, it is tensile and if it is negative, it is compressive whereas σr is always compressive irrespective of its sign.
Stress distributions for different conditions may be obtained by simply substituting the relevant values in equation above. For example, if po = 0 i.e. there is no external pressure the radial and circumferential stress reduce to