Empirical technique predicts failure loads for centrally loaded columns with thin-walled, open cross sections. Interaction of two failure modes is predicted by modification of the Johnson-Euler equation

Walls, J. C.

English

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December 1970	 Brief 70-10598 
S	 NASA TECH BRIEF 
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application. Tech Briefs are available on a subscription basis from the National Technical Information Service, Springfield, 
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nology Utilization Division, NASA, Code UT, Washington, D.C. 20546. 
Interaction of Crippling and Torsional-Flexural Instabilities

for Centrally Loaded Columns 
An empirical technique is proposed for prediction 
of failure loads for centrally loaded columns, with 
thin-walled, open cross sections, which may fail by 
a combination of torsional-flexural buckling and 
crippling. Knowing the torsional-flexural buckling 
load and the crippling load for a column, their inter-
action can be predicted by a modification of the 
Johnson-Euler equation which is often used to relate 
crippling and Euler-type buckling: 
-	 Pc.=PCs _ ( PCs 2/4P*) 
where PC is thecritical load:(pounds) in combined crip-
pling and torsional-flexural buckling, P C, is the crip-
pling load (pounds), and * is the critical load 
(pounds) in torsional-flexural buckling. 
For such loaded columns that fail at stresses within 
the elastic range, the critical mode of failure is often 
torsional buckling or a combination of torsional and 
flexural buckling; it depends primarily on the ge-
ometry of the cross section and the length of the 
column. 
There are methods for evaluation of this torsional 
or torsional-flexural buckling load for many variations 
in cross-sectional geometry and restraint conditions. 
All such methods, however, are based on the assump-
tion that the cross-sectional shape does not change 
during buckling; that is, the theories consider primary 
failure of columns, rather than secondary failure, 
characterized by distortion of the cross section. For-
mulation of a theory incorporating coupling distortion 
and flexure with local buckling would be extremely 
complex. 
For very short columns of thin-walled, open cross 
sections the failure stress is determined by the crip-
pling-stress method, which does provide for local 
distortion of elements of the cross section. 
Thus the coupling of these two failure modes by 
empirical means would provide a simple means for 
prediction of failure loads of columns that may fail 
by a combination of the torsional-flexural mode and 
the crippling mode. This approach has been followed 
already in the coupling of crippling and Euler buckling 
for closed sections (Johnson-Euler equation); the 
approach is the same in this coupling of crippling and 
torsional-flexural buckling. Although no attempt has 
been made to generate or correlate test data to con-
firm the accuracy of this technique, it is believed to 
be accurate. 
Notes: 
I. The following documentation may be obtained 
from: 
Clearinghouse for Federal Scientific 
and Technical Information 
Springfield, Virginia 22151 
Single document price $3.00 
(or microfiche $0.65) 
Reference: 
NASA-CR-61287 (N69-32465), Interaction 
of Crippling and Torsional-Flexural Instability 
for Centrally Loaded Columns 
2. Technical questions may be directed to: 
Technology Utilization Officer 
Code A&TS-TU 
Marshall Space Flight Center 
Huntsville, Alabama 35812 
Reference: B70-10598
(continued overleaf) 
Now
This document was prepared under the sponsorship of the National 
Aeronautics and Space Administration. Neither the United States 
Government nor any person acting on behalf of the United States
Government assumes any liability resulting from the use of the 
information contained in this document, or warrants that such use 
will be free from privately owned-rights.
https://ntrs.nasa.gov/search.jsp?R=19700000579 2020-03-17T01:00:20+00:00Z
Patent status: 
No patent action is contemplated by NASA. 
Source: J. C. Walls of 
Brown Engineering Co.. Inc. 
under contract to 
Marshall Space Flight Center 
(M FS-20556) 
Brief 70-10598	 Category 06


Interaction of crippling and torsional-flexural instabilities for centrally loaded columns

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