In this paper, an exact dynamic stiffness element under the frame work
of finite element approximation is presented to study the dynamic res
ponse of multi-span structures under a convoy of moving loads. A dynam
ic model coupled with a FFT algorithm is developed. The model is highl
y efficient for calculating the response of bridges under multiaxle mo
ving forces. All the vibration frequencies and mode shapes of the beam
-structure may be calculated exactly using the Wittrick and Williams a
lgorithm. Examples show that with only one element per span, exact fre
quencies and modes could be obtained. Some results on the dynamic ampl
ification factor are presented also as a function of the speed of the
moving loads. (C) 1997 Academic Press Limited.