Abstract Summary
The behaviour of thin-walled members subjected to non-uniform bending cannot be properly predicted by the Euler-Bernoulli and Timoshenko models. The inadequacy of the classical beam theory depends on several phenomena occurring in real box girders, namely: (i) warping, (ii) shear flange deformation (shear-lag), (iii) shear web deformation, as well as (iv) distortion of the cross-section in its own plane. In this paper a free vibration analysis of a rectangular box girder is carried out; the problem is addressed in two steps: (i) first, the simplest case of a box girder with undeformable but warpable cross-section is approached; (ii) then, the most comprehensive case of a box girder with a deformable cross-section is dealt with. For the box girder with undeformable cross-section various approaches are followed. A simple but efficient method is proposed to study the combined effect of shear-lag (flange deformation) and web shear deformation. A new analytical expression for the effective flange width is derived by the equilibrium condition of the flange, under the hypothesis of transverse inextensibility. Moreover, the web deformation is taken into account considering an effective shear area, instead of the traditional shear area: indeed, the shear lag reduces the width of the flange and this, in turn, reduces the effective geometric characteristics. The effective flange width and the effective shear area are used to account, in approximate way, for shear flange and web deformation in the (no warping) Euler-Bernoulli and Timoshenko models. An alternative two d.o.f. model for the shear-flexural behaviour of box-girders with undeformable cross section, based on the Generalized Beam Theory, is formulated. Such a model takes in account warping, so that it does not require the use of the effective flange width and effective shear area concepts. Concerning box girder with deformable cross section, a four d.o.f. model is proposed. It is obtained by adding two degrees of freedom to the former GBT model, describing cross-section distortions, of symmetric or antisymmetric type with respect the flexural axis. The influence of the distortional modes on the overall mechanical behavior is investigated, as a function of the geometrical characteristics of the box-girder. All the analytical methods discussed here are validated by comparisons with finite element analyses.
