Critical Compressive Stress for Outstanding Flanges Page: 1 of 11
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REPORT No. 734
CRITICAL COMPRESSIVE STRESS FOR OUTSTANDING FLANGES
By EUIIaN E. LURDQIBT and ELBBIDGE Z. STOWELL
A chart is presented for the-values of the coeflcie in
te formula for the critical compressive stress at which
buckling may be e peed to occr in outstanding fanges.
These flanges are fiat rectangular plates supported along
the loaded edges, supported and elastically restrained along
one unloaded edge, and free along the other unloaded edge.
The mathematical derivations of the formulas required
for the construction of the chart are given.
In the design of stressed-skin structures for aircraft
as well as in the design of compression members, it is
desirable to know the compressive stress at which
buckling occurs. In practice the structure is usually
so imperfect or so eccentrically loaded that lateral
deflection starts with the beginning'of loading. When
lateral deflection starts with the beginning of loading,
however, there is usually a verypronounced increase in
deflection at the critical compressive stress for which
buckling would have occurred had the structure been
perfectly straight and centrally loaded. The evalua-
tion of this critical compressive stress for a flat plate,
with certain conditions of edge support, is discussed
in this paper.
When a flat plate is loaded in compression, the two
loaded edges are either simply supported or restrained in
some manner. If the two unloaded edges are not sup-
ported, the plate is considered to be a column. When
one, or both, unloaded edges are also supported or
restrained in some manner, the critical compressive
stress is greatly increased over that for the plate as a
column. That the compressive stress ip increased when
one, or both, edges are supported or restrained in some
manner has been recognized for years. Because of the
importance of the edge conditions, formulas based on
the assumption that each edge of the plate is free,
simply supported, or fixed have been employed in
design. (See the summary of these formulas given in
A study of the theory and the more reliable test
data on the buckling of plate elements in stressed-skin
structures and compression members revealed the neces-
sity for a more careful consideration of the edge condi-
tions of plates than has been previously attempted.
Accordingly studies were made of the critical compres-
sive stress for I-, Z-, channel, and rectangular-tube
sections in which proper consideration was given to the
interaction between the individual parts of the cross
section. (See references 2, 3, and 4.) In order to
make the results of the work more generally applicable,
studies were also made of the basic plate elements that
comprise these sections. All the design charts resulting
from this investigation were made available in 1938.
The combination of the present paper with references
2, 3, 4, and 5 is a more complete presentation of all this
The basic element treated in this paper is a plate
simply supported along the loaded edges, supported and
elastically restrained against rotation alongoneunloaded
edge and free along the remaining unloaded edge. This
basic element is representative of the outstanding flange
on the I-, Z-, and channel-section columns. In reference
5 is treated the basic element representative of the webs
of these sections with elastic restraint along both
The mathematical derivations required for the investi-
gation of the present paper are given in appendixes A
and B. The results of practical use are given in the
body of the paper.
EVALUATION OF CRITICAL STRESS
Within the elastic range.--Within the elastic range
in which the effective modulus of elasticity is Young's
modulus, the critical compressive stress f, for a thin
flat rectangular plate is expressed as (reference 6, p. 331,
kf EF2( b
" I12(1- AP 1
k nondimensional coefficient that depends upon condi-
tions of edge restraint and shape of plate
E Ypung's modulus
t thickness of plate
p Poisson's ratio
b width of plate
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Lundquist, Eugene E. & Stowell, Elbridge Z. Critical Compressive Stress for Outstanding Flanges, report, March 14, 1941; (digital.library.unt.edu/ark:/67531/metadc59989/m1/1/: accessed January 20, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.