Keywords: bridges, dynamic loads, flexure, Fourier integral transformation, multifunctioning, shear lag, technical theory of thin-walled structures, torsion.

The neglect of the shear lag leads to an underestimation of the stress developed in the flange plates of thin-walled box girders at positions adjacent to the webs and resulting in an unsafe design. Its importance has long been appreciated by the designers of aircraft structures in their use of thin plates in the construction of wings and fuselages; it is the advent and use of plates of similar proportions in the design of large box girder bridges that has caused increased attention to the shear lag problem in structural engineering.

The stress distribution in thin-walled members of modern box bridges is given by combination of sectorial influences stated in the torsion-bending theory and additional sectorial influences arising from distortion and shear. The sectorial relations adopted in the Bernoulli-Navier approach assume the plane configuration of cross-sectional members in the deformed state of the thin-walled box bridges. As consequence sectorial relations and stresses in thin-walled box cross-section can be established. The decrease of rigidity in thin-walled box members is specified by the shear lag appearing in additional degrees of freedom in the mechanics of cross-sectional distortion. In order to take into account the decrease of normal rigidity, additional sectorial functions are introduced due to the distortional kinematics of the thin-walled box cross-sections studied.

For dynamic assessment of the problem the implementation of the Fourier integral transformation into the transfer matrix method is adopted.

The application of the approach developed is made to the actual thin-walled box bridges with evaluation of the results obtained. The results were adopted in the monitoring of the slender Old Bridge crossing the Danube in Bratislava which is made of thin-walled box members. The bridge was subjected to dynamic testing and monitoring, with respect to the influence of the shear lag. As part of the dynamic testing and monitoring the frequency spectra were obtained for the specification of dominant natural frequencies in flexure and in torsion. Corresponding time response and power spectra of the bridge with consideration of shear lag are presented.

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