JEC COMPOSITES MAGAZINE - Issue #88 - April 2014 - Special JEC Americas Spring Edition - 43

results obtained using Nastran for box
beams and EALPATAR for buckling.
In addition, a percent relative error was
introduced to demonstrate the accuracy
of the method.

Thin-walled beam
A cantilever box beam of length L (L=2
m) subjected to a concentrated load of
1780 η at its tip was considered. The
cross section is shown in Fig. 1 (w=300
mm, η=100 mm). The composite box
beam lay-up is [0/±45/90]8S and the
box beam axis coincides with 0°.

move through a laminate made with
the same material but with different ply
orientations. For the T300/N5208 box
beam with homogenized lay-up, the scaled deflection can be computed once the
normalized in-plane trace A11* is known
using the following equation:
ηscaled=ηref (A(11 )*)/A(11 )*)
(2)
ref

case

Tab. 2: Comparison of tip deflection [mm] for
different materials

180.27

-

257.60

258.36

-0.30

301.42

300.79

0.21

202.72

202.72

0.00

In case (a), the tip deflection taken as
reference is the one in Table 2 for T300/
N5208, while in case (b), the reference
tip deflection is 203.53 mm. In both
cases, the percent relative error underlines that, for shallow angles, the tip
deflection is well scaled. A maximum
error of 1.79% can occur with θ=30° for
laminate families [0/±θ/90]8S. In the
case of [0/±θ/90]16T, the maximum error
for shallow angles is 1.62%. However,
when the ply orientation angle becomes
deeper, the error becomes higher but still
remains less than 6%.
Tab. 3: Comparison of tip deflection [mm] for
different stacking sequence, respectively (a)
[0/±θ/90]8S and (b) [0/±θ/90]16T

ηscaled

Err.%

120.77

120.58

0.16

30

147.98

150.68

1.79

60

249.34

259.48

3.91

270.35

286.56

5.66

15

T300(b)

η

75

T300(a)

θ
15

Material

121.059

121.061

0.00

30

148.84

151.284

1.62

60

250.63

260.519

3.80

75

271.87

287.706

5.50

Analytical and experimental results for
the structural efficiency of aerospace
structures under compression and shear
loads have demonstrated the mass saving
potential of advanced composite panels
to meet buckling requirements. Several
analytical works are available on buckling
of composite panels under combined
loads. In most cases, the experimental
results relate to uniaxial compression or
shear only; very few papers report results
where a combination of the two loads
was applied.
In real conditions, however, biaxial compression and shear load may be applied
simultaneously to a panel. Theoretical
analysis can predict the buckling load
when combined loads are applied.
Several results are available in literature
or can be obtained using the EALPATAR
software program. Linear equations for
laminated cylindrical shells, Donnelltype equations, were used in conjunction
with the Galerkin method to determine
the critical buckling loads in the form
of an eigenvalue problem. Theoretical
analysis and computer software were
developed for both simply-supported
and clamped boundary conditions and
for any un-symmetric and unbalanced
laminates. The results obtained with
the anisotropic solution indicated that
significant non-conservative errors (up
to 50%) can occur in buckling predictions in comparison with the orthotropic
solution. In particular, the direction of
the shear load must be considered with
great care.
Since no experimental results were
available, a new test facility was built
at the Technical University of Turin in
order to apply biaxial compression and
shear loads simultaneously (Fig. 2). A
maximum longitudinal compression or
tension load of 500 kN, a transverse compression or tension load of 200 kN and a
positive or negative shear load of 200 kN
can be applied to panels with dimensions
lower than 1000 by 700 mm. The load
and supporting frames are made of steel
alloy and 2024 aluminium alloy. A longi-

No88 April 2014 /

Special JEC Americas 2014

The in-plane trace can also be used to

180.27

T300/N5208

The tip deflection for different materials
is reported in Table 2. The first column
lists the FEM results and the second one
the results obtained with the present
theory, while the last column shows
the percent relative error. In this case,
the scaling was performed considering
the in-plane trace since the membrane
approach gives good results for slender beams. The percent relative error
is very low (max |Err%|=0.3%). As a
consequence, the scaling method can
be used to scale the tip deflection of
different box beams, once the trace is
known, without making other computation and with good accuracy.

Err.%

C-Ply

ηscaled=
(1)
ηref (In plane Traceref )/(In plane Tracecase )

ηscaled

AS4/3501

The IM6/epoxy composite was chosen
as a reference material for this case study;
thus the reference trace will be 232 GPa.
The tip deflection of the box beam was
computed using Nastran. Using the scaling method, the tip deflection of other
box beams can be evaluated as follows:

η

IM6/epoxy

Fig. 1: Box beam cross section

Material

Buckling of laminate panels

jec composites magazine 43
JEC COMPOSITES MAGAZINE - Issue #88 - April 2014 - Special JEC Americas Spring Edition

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