Dependency of modeling parameters for the construction of influence surfaces by the finite element method

The concept of influence surface has been largely used for the determination of the internal forces of bridge decks. Differently from the load that acts on usual building structures in bridge decks, those loads are in movement; therefore, a more careful evaluation must be conducted for the determination of the maximum efforts. Equilibrium, Müller-Breslau and Adjoint methods are alternative methodologies for the construction of influence surfaces. This manuscript addresses the implementation of such methods through the finite element method and the application of influence surfaces for the obtaining of internal forces. Parameters, as mesh density and shape functions of finite elements are explored through a numerical example. The results show the three procedures provided similar influence coefficients for shear and bending moments, in nodes distant from the reference point and very sensitive values to the mesh density and shape functions of finite elements in the reference point. The convergence values found for the internal forces calculated with the distributed load of the wheel did not show a strong dependency on the parameters under analysis.