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National Advisory Committee for Aeronautics, Technical Notes - Local Instability of Columns with I-, Z-, Channel, and Rectangular Tube Sections

In the.design of compression members for aircraft,
whether they be stiffeners in stressed~skin structures or
struts in trussed structures, the allowable stress for the
member is equal to the lowest strength corresponding to _
any of the possible types of failure,_ In references 1 and
2, all types of column_failure are classed under two head;
ings: _ ' ' ‘*

(a) Primary, or general, failure.
(b) secondary, or local, failure.

Primary, or general, failure of.a column_is defined
as any type of failure in which the cross sections are
translated, rotated, or both translated and rotated but
not distorted in their own planes.(fig. 1). Secondary: or
local, failure of a column is defined as any type of fail—’
2 N.A.C.A. Technical Note No. 743

ure in which the cross sections are distorted in their own
planes but not translated or rotated (fig. 2). Consider-
ation is given in this paper_only to local failure.

One of the factors to be considered in a study of lo~
cal failure is the critical compressive stress at which
the cross section begins to distort. This critical stress
can usually be given in coefficient form. In two previous
papers, coefficients are given for the rectangular tube
(reference 3) and for columns of channel section and Z—
section (reference 4). The purpose of the present paper
is to summarize the results embodied in references 3 and 4
and also to present coefficients that will permit the crit-T
ical compressive stress to be computed for an I—section
column. '

The calculations required to evaluate the coefficients
plotted in the charts were made by the energy method of
Timoshenko (reference 5). Because the calculations are
long and were made as a part of a more extended study of
local failure in thinnmetal columns, they have been omit—
.ted from this paper.

Bernard Rubenstein, formerly of the H.A.C.A. staff,
performed a large part of the mathematical derivations
required for the preparation of this paper.