Abstract
At previous conferences the authors have examined the buckling and postbuckling behaviour of reinforced plastic plates subject to in plane loading, both theoretically1 and experimentally.2 That work has been extended to cover the buckling and post buckling behaviour of orthotropic box sections.3 The present contribution extends this work further to examine the instability of orthotropic channel sections. The sections are considered as a series of linked plates with rotationally restrained unloaded edges or rotationally restrained and free unloaded edges. These conditions have been considered for the plates alone. The linking procedure enables the instability of the section to be evaluated.
After buckling the linked plates are given a common end displacement. The moments and slopes at each edge are related to this and combined in such a way as to ensure that equilibrium and compatibility are satisfied at the plate edges, using an iterative procedure. Thereafter the relevant postbuckling stiffnesses and coefficients are obtained.
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Abbreviations
- a, b:
-
Plate dimensions in x and y directions respectively
- D11, D22:
-
Flexural rigidity of plate per unit width for bending about the y and x axes respectively, given by
$${D_{11}} = {E_{11}}{t^3}/12(1 - {v_{12}}{v_{21}}) {D_{22}} = {D_{11}}{E_{22}}/{E_{11}}$$ - E11, E22:
-
Modulus of elasticity in the x and y directions respectively
- e :
-
Ratio of buckle half wavelength to plate width
- G 12 :
-
Elastic shear modulus in x−y plane
- K :
-
Elastic buckling coefficient for orthotropic plates
- t :
-
Plate thickness
- Y(y):
-
Deflections across buckled plate
- v12, v21:
-
Poisson’s ratio in the x and y directions respectively
- σ cr :
-
Critical buckling stress
- w :
-
Out-of-plane deflections of the plate
References
Banks, William M., Harvey, James M. and Rhodes, James, The nonlinear behaviour of composite panels with alternative membrane boundary conditions on the unloaded edges, Proc. 2nd Int. Conf. Composite Materials, Toronto, April 1978.
Banks, William M., Experimental study of the nonlinear behaviour of composite panels, Proc. 3rd Int. Conf. Composite Materials, Paris, 1980.
Banks, William M. and Rhodes, James, The postbuckling behaviour of composite box sections, in: Composite Structures, Proc. 1st Int. Conf. Composite Structures (ed. I. Marshall ), Applied Science Publishers, 1981, pp. 402–414.
Banks, William M., A contribution to the geometric nonlinear behaviour of orthotropic plates, Ph.D. Thesis, University of Strathclyde, 1977.
Banks, William M. and Rhodes, James, The buckling behaviour of reinforced plastic box sections, Proc. R.P. Congress, 1980, Brighton, November.
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© 1983 Applied Science Publishers Ltd
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Banks, W.M., Rhodes, J. (1983). The Instability of Composite Channel Sections. In: Marshall, I.H. (eds) Composite Structures 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6640-6_31
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DOI: https://doi.org/10.1007/978-94-009-6640-6_31
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-6642-0
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