Accuracy and range of applicability of the single degree-of-freedom method

This paper describes an investigation to determine the accuracy and range of applicability of the Single Degree-of-Freedom method for protective structures. The investigation method was as follows. The most simple structure that still has practical relevance, i.e. a simply-supported beam, has been chosen for the analysis. The properties of the beam were scaled with respect to the applied loading. Two methods were used to predict the response of the beam to a shock wave: the SDOF method and the finite element method, the last method being the most accurate method available. The results of both calculations were compared and interpreted. A SDOF rnodel is basically designed to predict deflections. This is done by assuming that the main response is in the first normal mode. The predictions of the deflection were very accurate, even under extreme load conditions. The shear forces are derived from the assumed shape of the deformations in the SDOF method. It turned out that this leads to inaccuracies. The SDOF method predicted on average a 30 % lower reaction force, and the differences could rise to 250 % for certain ranges. The causes for the inaccuracies were investigated and it was found that they were due to: - the excitation of higher modes when the resistance of the structure suddenly changes at the moment the structure becomes plastic; - the broadening of the plastic hinge into a plastic region; - the excitation of higher vibration modes due to the sudden load application. It can be concluded that application of the SDOF method to calculate the deflection is possible almost without limitations. To calculate the shear forces, however, it is less accurate, and can only be applied for a limited range of loads. It was possible to define the accuracy and range of applrcability of the SDOF method.