General Instability of Stiffened Cylinders Page: 2 of 27
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TECH LIBRARY KAFB, NM
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
TECHNICAL NOTE 4237
GENERAL INSTABILITY OF STIFFENED CYLINDERS
By Herbert Becker
Theoretical buckling stresses are determined in explicit form for
circular cylinders with circumferential and axial stiffening. The
loadings are axial compression, radial pressure, hydrostatic pressure,
and torsion. Analyses were confined to moderate-length and long cylin-
ders. The investigation was based upon the use of a form of Donnell's
equation derived by Taylor which is applicable to orthotropic cylinders.
The derivation of this equation is presented in this report.
General instability in stiffened circular cylinders has been inves-
tigated for several cases of loading and types of stiffening. Analyses
were performed utilizing energy methods, the three differential equations
for orthotropic cylinders of FltUgge (ref. 1), and various forms of
Donnell's equation (ref. 2) applicable to orthotropic cylinders.
Except for the analyses by Dschou (ref. 3) and Taylor (ref. 4),
these investigations have not yielded explicit solutions for buckling
stress. Furthermore, the analyses for external-pressure loadings have
been confined to ring-stiffened cylinders. In the present report,
explicit expressions are presented for axial-ccmpression, external-
pressure, and torsional loadings on moderate-length and long cylinders
with both axial and circumferential stiffening.
The axial-load solution is that developed by Taylor, who utilized
the simplifications employed by Donnell, together with the effects of
orthotropicity, and derived an eighth-order partial differential equa-
tion for axial-compression buckling. In this report, the equation of
Taylor has been extended to include torsional and pressure loadings.
In addition, Taylor's assumption of a zero value for Poisson's ratio
has been retained.
The analyses are confined to moderate-length cylinders, for which
the boundary conditions influence the buckling stress, and to long
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Becker, Herbert. General Instability of Stiffened Cylinders, report, July 1958; (digital.library.unt.edu/ark:/67531/metadc57302/m1/2/: accessed December 12, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.