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National Advisory Committee for Aeronautics, Technical Notes - Critical Combinations of Shear and Longitudinal Direct Stress for Long Plates with Transverse Curvature

A theoretical solution is presented for the buckling stresses
of long plates with transverse curvature loaded in shear and longi-
tudinal direct stress. II‘he theoretical critical-stress combinations .
for plates having either simply supported or clamped edges are given
in figures and tables and a comparison is made with a previous theo-
retical solution for simply supported. plates.

In the compression range theoretical curves are unsuitable for
use in design because long plates with substantial curvature loaded
in axial compression buckle at stresses that are much less than the
theoretical values of critical stress. An investigation was there-
fore made to determine the modifications required to make the theo-
retical curves compatible with the available experimental data for
plates in axial compression. Interaction curves based upon this
investigation are provisionally recanmended for. use in design. Both
theoretical and. suggested design curves are. essentially parabolas,
a circumstance which permits simple approximate interaction formulas
to be given.

Theoretical solutions to a number of problems concerned with
the determination of the critical stresses which cause long curved
plates to buckle have been presented in various investigations. In
references 1 to 3 shear alone acting onboth simply supported and
clamped plates is investigated; in references ’4- and 5 direct axial
compression. alone acting on both simply supported and clamped plates
is investigated, and in reference 6 the critical combinations of
shear and direct axial stress for simply supported plates only are
given.

The present paper deals with the determination of the combina-
tions of shear and direct axial stress which cause plates with either
simply supported or clamped edges to buckle (appendix A). The
present solution as well as the solutions of references 1 to 6 is
based upon the small-deflection theory. As curved plates loaded in
axial compression may buckle at a stress much less than the theo-
retical value, the theoretical interaction curves of reference 6 and
the present paper must be modified in the compression range for use
in design.