Hydrostatic and Axial Collapse Tests of Stiffened Cylinders
Authors: Kinra R.K. 
Published: October 2008

ABSTRACT
This paper describes the results of collapse tests on two models of longitudinally and circumferentially stiffened leg sections of an offshore platform. The observed failure modes of instability include shell buckling between rings and general instability under hydrostatic external pressure and panel buckling under axial compression. Methods of predicting the corresponding buckling loads are described, and the predicted buckling loads are compared with the model test results.

INTRODUCTION
Structural elements are subject to collapse either due to material failure or geometric buckling. Cylindrical shells of low diameter to thickness (Oft) ratios, such as tubular members of conventional offshore platforms, are generally not subject to buckling and can be designed on the basis of material failure. Cylindrical shells of relatively high D/t ratios, on the other hand, may be subject to local shell buckling.
Unstiffened thin-walled cylinders are prone to sudden and disastrous failures at loads well below the theoretical buckling loads predicted by classical small-deflection theory. The behavior of unstiffened cylinders is especially unpredictable when subjected to axial compression and bending loads. In fact, the scatter of test data may range up to 500 percent or more. Donnell and Wan[l] showed theoretically, by means of an imperfection analysis, that a possible reason for the discrepancy was initial imperfections caused by fabrication tolerances or otherwise. This hypothesis is now generally accepted to be true. The effect of imperfections is most severe for axially compressed unstiffened cylinders. Similar discrepancies, though generally not as severe, have been observed for other loading conditions[2] and shell shapes.
In addition to geometric imperfections, experimental and theoretical evidence has also shown that the buckling load may be affected by the boundary conditions[3], and by residual stresses introduced during the fabrication process. The presence of residual stresses changes the effective stress-strain curve of the material, and causes inelastic action to commence before the yield point is reached. As a result, the buckling process is hastened.
The elastic post-buckling behavior of perfect and imperfect axially compressed unstiffened cylinders is demonstrated qualitatively in Figure 1. There is a sudden drop in load carrying capacity upon buckling. Since there is no post-buckling reserve strength, the buckling of an axially compressed unstiffened cylinder is coincident with failure. The failure, moreover, is sudden and drastic. For this reason, the relative confidence level in the buckling load should be higher for unstiffened cylinders than for most other structural elements. This is made very difficult by the severe lack of agreement between theoretical and experimental results for unstiffened cylinders, and dictates conservatism in their design.
In order to improve their resistance to buckling, large diameter cylinders are frequently stiffened using longitudinal stiffeners (called stringers) and circumferential stiffeners (called rings). Stiffened cylinders are somewhat better behaved than their unstiffened counterparts. This is demonstrated qualitatively in Figure 2. Two aspects of the behavior of stiffened cylinders are of particular significance. First, the detrimental effect of geometric imperfections is less pronounced than for unstiffened cylinders. Second, the drop in load capacity upon buckling is much smaller than for unstiffened cylinders.