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A General Loading on a Box Girder 1

box girder
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  A general loading on a box girder, such as shown in fig 1 for single cell box, has components which bend, twist, and deform the cross section. Thin walled closed section girders are so stiff and strong in torsion that the designer might assume, after computations based on the elemental torsional theory, that the torsional component of loading in fig 1(c). has negligible influence on box girder response. If the torsional component of the loading is applied as shears on the plate elements that are in proportion to St. Venant torsion shear flows, fig 1 (e), the section is twisted without deformation of the cross section. The resulting longitudinal warping stresses are small, and no transverse flexural distortion stresses are induced. However, if the torsional loading is applied as shown in fig 1 (c), there are also forces acting on the plate elements fig 1 (f), which tend to deform the cross section. As indicated in fig 2 the movements of the plate elements of the cross section cause distortion stresses in the transverse direction and warping stresses in the longitudinal direction.    .   FLEXURE : Fig: 2    A vehicle load, placed on the upper flange of box girder can occupy any position, transverse as well as longitudinal. This load is transferred transversely by flexure of deck to the webs of box girder. For understanding the various stresses generated, initially consider that the webs of box girder are not allowed to deflect. The structure resembles a portal frame. The flexure of deck would induce transverse bending stresses in the webs, and consequently in the bottom flanges of the girder. Any vehicle load can thus be replaced by the forces at the intersections of deck and web as shown in fig 3. Now the supports under the web are allowed to yield. This results in deflection of web and consequently redistribution of forces among web and flanges. Distortion of cross section occurs as a result of the fact that m1 and m2 are not equal resulting in sway of frame, due to eccentrically placed load. The section of box tries to resist this distortion, resulting in the transverse stresses. These stresses are called distortional transverse stresses. The distortion of cross section is not uniform along the span, either due to non uniform loading or due to presence of diaphragms or due to both. However the compatibility of displacements must be satisfied along the longitudinal edges of plate forming the box, which implies that these plates must bend individually in their own plane, thus inducing longitudinal warping displacements. Any restraint to these displacements causes stresses. These stresses are called longitudinal warping stresses and are in addition to longitudinal bending stresses. .   TORSION : The main reason for box section being more efficient is that for eccentrically placed live loads on the deck slabs, the distribution of longitudinal flexural stresses across the section remains more or less identical to that produced by symmetrical transverse loading. In other words, the high torsional strength of the box section makes it very suitable for long span bridges. Investigations have shown that the box girders subjected to torsion undergo deformation or distortion of the section, giving rise to transverse as well as longitudinal stresses. These stresses cannot be predicted by the conventional theories of bending  and torsion. One line of approach to the analysis of box girders subjected to torsion is based on the study of THIN WALLED BEAM THEORY. The major assumptions are: a) Plate action by bending in the longitudinal direction for all plates forming the cross section, namely webs, slabs is negligible. b) Longitudinal stresses vary linearly between the longitudinal joints, or the meeting points of the plates forming the cross section. 
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