Page 60 - Mechanical Engineer's Data Handbook

STRENGTHS OF MATERIALS 49

pb=- 1.61Et2 /F Change in inner radius x, =
(2) Short tube, ends held circular:
-.-
4
LD -v’)~ D2
Change in outer radius x,, =
Thin spherical vessel, internal pressure

Dah
= aL =pD/4t; X, =- (1 - V)
2E
For external pressure use -p.

Thick cylinder, internal pressure, all directions

ah and a, as above.
Thin cylinder with hemispherical ends
Longitudinal stress a,=p
For equal maximum stress t,=O.St, (r,,!ra)
For no distortion t,s0.4tc

Thick cylinder, internal pressure, no longitudinal
pressure

Thick sphere, internal pressure

Symbols used:
(at inner radius); oL=0 a = direct stress
‘t = shear stress
p = pressure
Maximum radial stress 6, = p v = Poisson’s ratio
Maximum shear stress T,,, =pr;/(r; - r.f ) t = thickness
D = diameter
(at inner radius) r = radius