Information Sheet

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15 Νοε 2013 (πριν από 3 χρόνια και 11 μήνες)

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1

Downhill Ski Project


Information Sheet


Sandwich Beams

The behaviour of sandwich b
eams is not very different to that of beams of
monolithic construction. The subject is dealt with in detail in: H.G. Allen,
Analysis
and design of Structural Sandwich Panels
, Pergamon Press, Oxford, 1969.

Consider a sandwich beam, illustrated in Figure 1,
under a load
F

in three
-
point
bending. It has stiff outer faces of thickness
t

and a softer core of thickness
c
. The
geometrical and material parameters used in this analysis are given in Table 1.


Figure 1:

Dimensions of sandwich beam. Section A
-
A on rig
ht. (After H.G.
Allen, 1969)


Table 1:

Geometrical and material parameters of sandwich beam.

Geometrical parameters

b

Width of a rectangular sandwich beam [m]

c

Core thickness [m]

d

Distance between centre lines of faces [m]

h

The overall thickness of
the beam [m]

L

Length of sandwich beam [m]

t

Face thickness [m]

Material properties

E
f

Modulus of elasticity (Young’s modulus) of the face [Pa]

E
c

Modulus of elasticity (Young’s modulus) of the core [Pa]

G
c

Shear modulus of the core [Pa]



2

The equiv
alent flexural rigidity of a rectangular cross
-
section
EI
eq

is the sum of the
flexural rigidities of the two separate parts, faces and core, measured about the
centroidal axis
C
-
C
:


(1)

The equivalent shear rigidity is given by:


(2)

Displacement

When a beam is loaded, the relationship between bending moment (M) and
curvature (1/R) at any point is:


(3)

The displacement can thus be obtained by integrating along the length of th
e
beam. For the simple case of cantilever bend or symmetrical three
-
point bending
the displacement is given by:


(4)

where
x

is distance along the beam and the integral is taken over the distance from
the support to the loading p
oint. With numerical data, the integral could be
calculated graphically by plotting
Mx/(EI)
eq

versus
x

and measuring area under the
curve.