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National Advisory Committee for Aeronautics, Technical Notes - Critical Combinations of Bending, Shear, and Transverse Compressive Stresses for Buckling of Infinitely Long Flat Plate

Three-dimensional interaction surfaces are presented for the com—
putation of elastic buckling stresses for an infinitely long flat plate
subjected to combinations of bending, shear, and transverse compression
in its plane — a loading approximating that occurring in a shear web.
Surfaces are presented for two sets of edge conditions: both edges
simply supported and lower edge simply supported, upper edge clamped.
Eresént results are in good agreement with data for one-load and two-
load limiting cases previously published.

A loading that occurs in the shear webs of thin wings of aircraft
is a combination of bending, shear, and transverse compression, the
transverse compression being induced by spanwise bending of the covers.
The buckling strength of an unstiffened infinitely long flat plate under
such a loading is computed approximately in the present paper by the
minimum-potential—energy method.

The assumptions made for the analysis are that the plate is elastic
and infinitely long, and that the bending moment, shear, and transverse
compression are constant along the length of the plate. The lower edge
is assumed to be simply supported and the upper edge, either simply
supported, elastically restrained against rotation, or clamped. The
neutral axis for bending stress is assumed to be halfway between the
upper and lower edges.

The results of the analysis are given in the form of interaction
curves and the details of the solutions are given in the appendixes.
A comparison of the present results with existing analytical data for
one-load and two-load conditions is made. No previous data are known,
however, for a supported or restrained flat plate subjected to combina-
tions of bending, shear, and transverse compression.

Results in chart form are presented for the case of both edges
simply supported and for the case of lower edge simply supported, upper
edge clamped. The solution, however, for the case of lower edge simply
supported, upper edge elastically restrained against rotation is given
in the form of a determinantal buckling equation.