Shear-flexural beam models for free vibration analysis of warpable cross-undeformable box girders

A linear free vibration analysis of a rectangular box girder is carried out by different approaches. A simple yet efficient method is proposed to study the combined effect of shear-lag of the flanges and shear deformation of the web. A new analytical expression for the effective flange width is derived, by using equilibrium conditions under the hypothesis of transverse inextensibility of the flange. The web deformation is also taken into account via an ‘effective shear area’, replacing the traditional shear area, accounting for the reduced geometric characteristics of the cross-section, caused by the shear-lag of the flanges. The effective flange width and the effective shear area are used in classic unwarpable models, namely Euler–Bernoulli and Timoshenko beams. An alternative 2 d.o.f. model for the shear-flexural behavior of box-girders, based on a semi-variational approach, is formulated. Such a model takes warping into account, so it does not require the use of the effective geometric characteristics. Finally, the analytical models proposed are validated by comparison with numerical results supplied by Finite Element analyses.