Contribution of ring resistance in the behaviour of steel tubes subjected to a lateral impact

The work described in this paper forms part of a closed analytical solution for the response of tubes subjected to lateral quasi-static or dynamic impact loads. The results can be used in the analytical study of the response where the tubes are usually modeled as a series of beams resting on a deformable foundation (of rings). An attempt has been made to evaluate the characteristics of this deformable foundation or in the other words the contribution of the rings to the tube resistance. Both analytical and numerical approaches have been used. It has been found that by assuming a rigid-perfectly plastic behaviour for the ring resistance, accurate results for long tubes (L/D>15) are obtained. For tubes of moderate length, using rigid-perfectly plastic behaviour underestimates the ring resistance. A rigid-plastic expression with quadratic strengthening has been proposed for tubes of moderate length. This expression has been found to provide results which are much closer to the ring resistance for tubes with 5⩽L/D⩽15. In very short cylinders (L/D<5), it has been found that the ring resistance is dominated by the stiffness of the beams. The validity of these conclusions has been investigated by undertaking a parametric study. In this parametric study different material and geometrical properties have been examined.