BUCKLING OF COMPOSITE PLATES SUBJECTED TO SHEAR AND LINERLY VARRYING LOADS

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BUCKLING OF COMPOSITE PLATES SUBJECTED TO SHEAR AND
LINERLY VARRYING LOADS
Gabriella Tarján and László P. Kollár
Dept. of Mechanics, Materials and Structures, Budapest University of Technology and Economics,
H-1521 Budapest, Mőegyetem rpt. 3. Hungary
KEYWORDS: buckling, plate, elastic support, shear load, linearly varying load
INTRODUCTION
When thin-walled composite beams or columns are subjected to axial load, bending or
transverse loads, their walls may buckle locally. Local buckling analysis of members can be
performed by modeling the wall segments as long orthotropic plates and by assuming that the
edges common to two or more plates remain straight [1, 2, 5]. The rotation of the long edges
is restrained by the adjacent wall segments. A conservative estimate of the local buckling load
can be obtained if the restraining effect is neglected and the long edges (common to two or
more plates) are assumed to be simply supported. Buckling loads of simply supported long
plates subjected to axial load, linearly varying load (bending) and shear load (Fig. 1) are
available in the literature [3]. More accurate solutions can be obtained if the restraining effects
are taken into account.
N
x
,cr
N
xy
,cr
N
xb
,cr
( )a ( )b ( )c
Fig. 1. Uniform compression (a), linearly varying compression (b) and shear (c) of a plate
Buckling loads of long plates with restrained edges subjected to axial load, are also available
in the literature [3], however no solutions are available for long plates subjected to bending or
shear. These cases are important for calculating the web buckling of beams subjected to
bending or transverse loads, and hence it will be treated in this paper.
LONG PLATES WITH RESTRAINED EDGES
Depending on the configuration of the restraining wall, two kinds of restraining effects must
be considered [4]: either both edges are attached to adjacent walls or one of the long edges is
free (Fig 2). In the first case the restraining effect is equivalent to that of a rotational spring:
( )
y
w
kM
y
∂
∂
±=
, (1)
while in the second case it is equivalent to the effect of a torsional stiffener:
( )
2
3
yx
w
GIM
ty
∂∂
∂
±=
, (2)
where
k
= rotational spring stiffness,
GI
t
= rotational stiffness of the stiffener (the calculations
are given in [4]),
M
y
= is the restraining moment,
w
= deflection,
x
= longitudinal coordinate,
and
y
= coordinate perpendicular to the long edges.

GI
t
GI
t
k
k
(a)
(b)
Fig. 2. Web with restrained edges. The restraining wall segment may have (a) two edges attached to adjacent
walls or (b) one edge is free
L
x
k GI
or
1
1
y
x
k GI
or
2
2
Fig. 3. Plate with restrained edges
RESULTS
Explicit expressions are developed for the buckling analyses of rectangular (long) plates
(Fig.3):
•
for
uniform compression
(Fig. 1a) new results are presented when the longitudinal
edges are rotationally constrained;
•
for
linearly varying axial load
(Fig. 1b) the known results for hinged supports are
corrected and new results are presented for constrained and built-in edges;
•
for
shear load
(Fig. 1c) new results are presented for constrained edges.
The results are based on the Rayleigh-Ritz method.
REFERENCES
1.
Bank, L. C. “
Composites for construction”
, J. Wiley & Sons. Hobken, 2006.
2.
Bleich, F. “
Buckling of metal structures”
, McGraw-Hill, New York, 1952.
3.
Kollár, L. P., and Springer, G. “
Mechanics of composite structures”,
Cambridge
University Press, Cambridge, 2003.
4.
Kollár, L. P. “Local buckling of fiber reinforced plastic composite members with open
and closed cross sections.”
J. Struct. Eng.,
129(11), pp. 1503-1513. 2003.
5.
Mottram, J. T. „Determination of critical load for flange buckling in concentrically
loaded pultruded columns,”
Composites Part B: Engineering,
35(1), pp. 35-47. 2004.