Energy method analysis establishes parameters governing stability of circular rings acted upon by constant, uniformly distributed loads. Energy method is used so that nonlinear behavior of structure before buckling can be accounted for. Method affords conceptually superior basis for analyzing the axisymmetric deviation mode

Williams, H. E.

English

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December 1970
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Stability of Structural Rings Under Uniformly Distributed Radial Loads 
An energy-method analysis establishes the param-
eters governing the stability of circular rings acted 
upon by constant, uniformly distributed radial loads. 
The energy method was used so that the nonlinear 
behavior of the structure prior to buckling could be 
accounted for. In addition, this method affords a con-
ceptually superior basis for analyzing the axisym metric 
deviation mode. The analysis requires that the number 
of displacement variables used in the equation for the 
total strain energy in the ring be the smallest possible 
that will still lead to a realistic description of the ex-
pected behavior. 
One example is a ring stiffener in a thin-walled shell 
of revolution subjected to external pressure. The dis-
placements of the ring depend upon the relative stiff-
ness of the shell in and out of the plane of the ring. 
The problem, then, is that of determining the stability 
of a ring acted upon by a uniform radial load and 
subjected to both in-plane and out-of-plane disturb-
ances that may be constrained. 
It is important that in-plane and out-of-plane dis-
placements be given the same emphasis in a study of 
their interaction during buckling. For this reason, the 
displacements of the ring are described in terms of the 
displacements of its centroidal axis and the rotation 
(twist) of the cross section about that axis.
In general, the analysis shows that critical mode 
shapes are a combination of in-plane and out-of-plane 
displacements and that they occur at loads consider-
ably below the classical (in-plane) critical load. For 
symmetrical cross sections, the critical load for the 
constrained ring is greater than that for the corresp2nd-
ing unconstrained ring. 
Note: 
The following documentation may be obtained 
from:
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Springfield, Virginia 22151 
Single document price $3.00 
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Reference: 
NASA-CR-107848 (N70-17318), The Stability 
of Circular Rings Under a Uniformly Dis-
tributed Radial Load
Source: H. E. Williams of 
Caltech/J PL
under contract to 
NASA Pasadena Office
(N PO- 1 1396) 
Category 06 
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.
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Stability of structural rings under uniformly distributed radial loads

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