STRENGTH OF MATERIALS

Longitudinal stress. The force tending to separate the right- and left

hand halves is the pressure multiplied by the area of one end, Fig. 1.8,

i.e. Pi = px-d

2

4

This is resisted by the stress acting on the circumferential section, YY,

. . . (1.9)

i.e,

σι

=

4*

FIG. 1.8

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

circumferential joints is r\

z

then the average stress in the joint is given by

(1.10)

It is evident from equations (1.8) and (1.10) that the efficiency of the

circumferential joints need only be half that of the longitudinal joints.

1.7 Stress in thin spherical shells. Let the internal diameter be d,

the thickness of metal be t and the internal pressure be p, Fig. 1.9. Then the

force tending to separate the two halves on a section XX is the pressure

multiplied by the projected area in the direction perpendicular to XX,

i.e. Ρ = ρχΐ ί

4

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

i.e.

π

<

ndt

pd

Tt

. (i-ii)

If the shell is made up from riveted plates and the efficiency of the joints

is η, then

pd

a —

. (1.12)