Errors in Step Wise SOlutoins to Bridge Vibrations

Step—integration techniques have often been used to obtain dynamic responses in highway bridges without regard to efficiency or to the errors they incur. Quantitative estimates for the discretization errors are given for Newmark's method, the fourth order Milne and Hamming methods, and the Adams methods of orders two through six. These errors are given with respect to the single and multi—axle sprung wheel loads which traverse an elastic beam at constant velocity. Because all error relations are given as functions of the product of the step size and the fundamental bridge frequency, it is possible to select a step size for a specific bridge—vehicle system which will yield a predetermined accuracy in the maximum midspan response or for the maximum expected error throughout the entire solution. The mechanism of how the actual error propagates is also defined and compared with a classical error bounding technique.