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National Advisory Committee for Aeronautics, Technical Notes - Lateral Instability of Deep Rectangular Beams

Experimental and analytical studies were made of
solid ani hollow deep rectangular beams to study their
lateral instability under various conditions of loading
and restraint., The tests were made on bare and tubes
of 178T aluminum alloy. Failure by lateral buckling oc—
curred only in tests on the solid beams. It was found
that, within the elastic range, the test results were in
agreement With the classical theory for the lateral
buckling of deep beams as given by Prandtl, Michell, and
Timoshenko. The tests were extenied to the inelastic
range where it was found that the substitution for __
Young's modulus of an average modulus of elasticity is-
-rived from the stress-strain curve made it possible to
predict instability at high stresses.

Rectangular bars are occasionally used in the form
of beams With the lone dimension of the rectangle in the
plane of the loads. When the depth of such a beam is
sreat compared with the width, the beam may become un—
stable in a lateral direction with a consequent sidewise
buckling, perhaps at a stress below the yield strength
of the material.. This action is similar to the buckling
of a column under an axial load. In the lateral buck—
ling of beams, however, the stability depenisyon_the tor-
sional as well as the flexural stiffnese.y A considera—
tion of stability is frequently of greater importance in
designing with aluminum alloys than it is with other
structural materials having higher moduli of elasticity.
It seems desirable to include in the Handbook. "Struc—
tural_Aluminum," a section on lateral stability of beams.
In order to arrive at a suitable formula for allowable
working stresses, it is necessary to have an understand-
ing of the factors contributing to the lateral stability
of such a beam, and the effect of different conditions of
loading and restraint.

The problem of the lateral instability of deep rec—
tangular beams appears to have been treated first by
Prandtl (reference 1) in 1899. In the same year the prob—
lem was discussed by A. G. M. Michell (reference 2). Both
investigators arrived at substantially the same solution.
The subject was further discussed by S. Timoshenko (refer-
ence 3), who treated various conditions of loading and
lateral restraint. More recently, treatments of the prob—
lem have appeared in various textbooks.