In the fatigue design of bridges, the influence line is inevitable to properly determine the stress at the point of interest generated by the moving loads. To obtain the influence line for a 3-D finite element model by conventional analysis with unit load requires the same number of analyses as the number of nodes on the surface to which the load is possibly applied. On the other hand, some methods based on the M¨uller-Breslau principle, which enable us to obtain the influence line by performing the finite element analysis only once, have been proposed. However, the methods require modification of the finite element model at each point of interest because it is necessary to provide a discontinuous displacement to determine the influence line of an internal force. Therefore, this paper proposes an analysis method for influence lines that is based on the reciprocal theorem and does not require model modification. The validity of the proposed method is confirmed by comparing the influence lines obtained by the proposed method with the results of the conventional analysis with unit load for a finite element model discretized with shell elements. Furthermore, it is shown that the proposed method enables more efficient fatigue life evaluation than the conventional method for the example of fatigue problems in an orthotropic steel deck.

Key Words : reciprocal theory, influence line, finite element model, fatigue, orthotropic steel deck

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