STRENGTH OF MATERIALS

1.6 Stresse s in thin cylindrical shells. When a thin cylinder is sub

jected to internal pressure, stresses are induced on the longitudinal section

X X , Fig. 1.5, due to the force tending to separate the top and bottom

halves, and on the circumferential section Y Y due to the force tending to

separate the right- and left-hand ends of the cylinder.

The stress on the longitudinal section is termed the circumferential stress

and that on the circumferential section is termed the longitudinal stress;

the type of stress is determined by the direction of the arrows.

In determining the stresses induced, it is assumed that the thickness is

small in comparison with the diameter so that the stress on a cross-section

may be taken as uniform* and also that the ends give no support to the

sides, an assumption which would be appropriate to a long cylinder such

as a pipe.

Let the internal diameter and length be d and I respectively, the thickness

of metal be t and the internal pressure be p.

Για

. 1.5 FIG. 1.6

Circumferential stress. The force tending to separate the top and

bottom halves is the pressure multiplied by the projected area in a direction

perpendicular to the diametral plane,f Fig. 1.6,

i.e. P

c

= pdl

This is resisted by the stress acting on the longitudinal section, XX ,

i.e.

_ pdl pd

°

=

2 α

=

2 ί

(1.7)

If the cylinder is made up from riveted plates and the efficiency of the

longitudinal joints is η

then the average stress in the joint is given by

pd

* See Chapter 14.

t The radial force on an element subtending an angle

άθ, Fig. 1.7, is ρ χ | άθ χ I The vertical component of

this force ie ^ dö.sin θ so that the total force normal to

(1.8)

de,

FIG. 1.7

X X is

J o

2

sin θ άθ = pdl