Metal Foams: A Design Guide

;;
;;;
;;
M
;;
;;;
;;
;;;
;;
;;
;;
;;;
;;
;;
;;;
;;
p′
Buckling of columns, panels and shells
p
;;
;;;
;;
r′
p
M
F
F
F
F
F
F
F
n
1 2
1
1
3 2
2
Design formulae for simple structures 71
F CRIT =
OR
FCRIT =
A
F = Force (N)
M = Moment (Nm)
E = Youngs modulus (N/m 2 )
= Length (m)
A = Section area (m 2 )
n2π2EI 2
n 2 π 2E
( /r) 2
k = Foundation stiffness (N/m2 I = See Figure 6.1 (m
)
4 )
r = Gyration rad. ( ) (m)
n = Half-wavelengths in
buckled shape
p′ = Pressure (N/m2 1
I 2
A
)
F CRIT = π2EI
2
F CRIT = n2 π 2EI
2
−
3EI
p′ CRIT = (r′) 3
Figure 6.4 Buckling of columns, panels and shells
M 2
4EI
+ k
n2 2
The addition of the bending moment, M, reduces the buckling load by the
amount shown in the second box in Figure 6.4. A negative value of Fcrit
means that a tensile force is necessary to prevent buckling.
An elastic foundation is one that exerts a lateral restoring pressure, p,
proportional to the deflection (p D ky where k is the foundation stiffness per
unit depth and y the local lateral deflection). Its effect is to increase Fcrit by
the amount shown in the third box.