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National Advisory Committee for Aeronautics, Technical Notes - Buckling Stresses of Simply Supported Rectangular Flat Plates in Shear

The present paper evaluates the shear buckling stresses of
rectangular flat plates with simply supported. edges more accurately
than previous work on this problem. Both symmetric (odd number
of buckles) and antisymmetric (even number of buckles) patterns
were considered. A curve is presented. from which the critical
stresses may be obtained when the dimensions of the plate are
known.
In reference 1 Timoshenko presents a solution for the buckling
stresses of simply supported. rectangular flat plates in shear.
Timoshenko considered only the equations which permitted a buckle
pattern symmetric about the midpoint of the plate. This limitation
led to a small error in the critical stress in several cases in
which the governing buckle pattern was antisymmetric instead of
symmetric.
The buckling stresses have been determined more correctly than
in reference 1 by considering both the symmetric and the antisym-
metric buckle patterns- Through the use of the matrix iteration
method described in reference 2 and by a proper choice of the terms
in the series representing the deflection, more accurate results
were obtained. The theoretical analysis given in the appendix is
a brief summary of the derivation given in reference l.
From a consideration of both symetric and antisymmetric
buckle patterns, the shear buckling stresses of rectangular flat
plates with simply supported edges were more correctly evaluated
than in previous work wherein only symmetric buckle patterns were
considered. Through the use of the matrix iteration method and
by a proper choice of the terms in the series representing the
deflection, more accurate results were obtained.
The critical stresses are determined on the basis of the
principle that during buckling the elastic-strain energy stored
in a structure is equal to the work done by the applied load. For
a rectangular flat plate loaded in shear this equality can be
written.