Page 59 - Mechanical Engineer's Data Handbook

48 MECHANICAL ENGINEER’S DATA HANDBOOK

Le = actual length of pinned end strut
=0.7 x actual length of fixed ends strut Maximum compressive stress U, =My+! A
I
= 2.0 x actual length of strut with one end fixed,
M
wLz
one end free Maximum deflection y, = - 3 + -
=OX5 x actual length with one end pinned and P 8P
one end fixed
71ZE where: a=&
U, = Euler buckling stress = -
(LJkIZ
U, =Yield stress in compression w per unit IecgM
i c c c c c le
I .7.6 Pinned strut with uniformly L
distributed lateral load

Maximum bending moment M, =

1.8 Cylinders and hollow spheres

In engineering there are many examples of hollow failure may be due to buckling. In the following, p is the
cylindrical and spherical vessels subject to internal or difference between the internal and external pres-
external pressure. The formulae given are based on sures.
Lam& equations. In the case of external pressure,

I .8. I
Buckling of thin cylinder due to external
Thin cylinder, internal pressure pressure

Hoop stress o,=pD/2t (1) Long tube, free ends:
Longitudinal stress uL =pD/4t
D
Radial displacement x, = - (u,, - vuL)
2E
where: v= Poisson’s ratio.
For external pressure, use -p.