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National Advisory Committee for Aeronautics, Technical Notes - Critical Combinations of Shear and Direct Stress for Simply Supported Rectangular Flat Plates

The buckling of a simply supported rectangular flat plate
under combinations of shear and direct stress was investigated by
means of an energy method. The critical combinations of stress for
several length-width ratios were determined to an accuracy of about
1 percent by the use of tenth-order determinants in conjunction wifil
a modified matrix iteration method. Curves were drawn which can be
used to obtain the critical stress combinations for the case of
interaction of shear and longitudinal direct stress and for the case
of interaction of shear and transverse direct stress.

The problem of buckling of plates under the action of more than
one stress has been given considerable attention. For plates
subJected to two stresses the critical combinations are usually given
by means of interaction curves, that is, curves that can be used to
obtain the value of one stress required to produce buckling when a
given value of another stress is also present. The stresses are
ordinarily given nondimensionally in terms of either stress ratios
or stress coefficients.

In reference 1 the interaction curve for infinitely long flat
plates under combined shear and longitudinal direct stress was
shown to be very nearly a parabola as indicated in figure 1 of the
present paper. In this figure R8 is the ratio of shear stress
present to the critical stress in pure shear and Ex is the ratio
of the longitudinal direct stress present to the critical stress
in pure longitudinal compression. (All symbols are defined in
appendix At) This curve is shown in figure 1 of reference 1 to
aptly to plates having edges either simply supported, clamped, or
elastically restrained against rotation. Reference 2 demonstrates
that the parabola also applies, to a high degree of accuracy, to
nearly square plates with simply supported edges.