Metal Foams: A Design Guide

H
H
Core shear
Core shear
Collapse mode A
F
;;
a;;
;;
;;
Collapse mode B
F
a;;
;;
;;
;;
M p
M p
H
H
Sandwich structures 119
Figure 10.4 Competing collapse modes A and B for core shear of a
sandwich beam in three-point bending
We note from equation (10.17) that FA increases linearly with the length of
overhang, H, beyond the outer supports.
Second, consider collapse mode B. As sketched in Figure 10.4, this collapse
mechanism involves the formation of plastic hinges in the face sheets at both
mid-span and at the outer supports. The core undergoes simple shear over the
length, L, between the outer supports, with no deformation beyond the outer
supports. A work calculation gives for the plastic collapse load FB,
FB D 4bt2
ℓ
f
y C 2bc c y
⊲10.18⊳
Since the two calculations given above are upper bounds for the actual
collapse load, the lower is taken as the best estimate for the actual collapse
load. It is instructive to compare the collapse loads as a function of overhang
length H, as sketched in Figure 10.5. Collapse mode A is activated for small
lengths of overhang, whereas collapse mode B has the lower collapse load
and is activated for large overhangs. The transition length of overhang, Ht, is
determined by equating (10.17) and (10.18), giving
Ht D 1 t
2
2
c
f
y
c
y
⊲10.19⊳