Introduction

When a drinking-straw is bent between the fingers into a uniformly curved arc of steadily increasing curvature, there comes a point when the tube suddenly collapses locally and forms a kink. If the experiment is repeated with a fresh straw, and the specimen is observed more carefully, it is found that the cross-section of the entire tube becomes progressively more oval as the curvature increases: and the kink or crease which suddenly forms involves a complete local flattening of the cross-section, which then offers virtually no resistance to bending.

These observations suggest that the buckling of a thin-walled cylindrical shell which is subjected to pure bending involves behaviour which is of a different kind from that which we have encountered in chapters 14 and 15; for we have previously not come across major changes in geometry, spread over the entire shell, before buckling occurs.

The first investigation of this effect was made by Brazier (1927). He showed that when an initially straight tube is bent uniformly, the longitudinal tension and compression which resist the applied bending moment also tend to flatten or ovalise the cross-section. This in turn reduces the flexural stiffness EI of the member as the curvature increases; and Brazier showed that under steadily increasing curvature the bending moment – being the product of curvature and EI – reaches a maximum value. Clearly the structure becomes unstable after the point of maximum bending moment has been passed; and it is therefore not surprising to find that in experiments the tubes ‘jump’ to a different kind of configuration, which includes a ‘kink’.