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Referring to Fig. 25, the dimensions are closely those of a typical through span. When one track only is loaded, in round figures, 20/29 of the panel load W is applied to the near side main girder A and 9/29 of W to the far side girder B. Girder A will deflect by an amount C, and girder B by a smaller amount D. These deflections will be proportionate to the loads producing them, and the difference in deflection which is proportional to the shear strain on the sway bracing is due to the unbalanced vertical shear of 11/29 W or the difference of the loads applied to the two main girders. Referring to the lower diagram of Fig. 25, A and B represent in an exaggerated form the relative deflections of the girders in the upper sketch. Under uniform load the deflection will be sensibly parabolic, and the maximum deflection sensibly 1 1/2 times the mean deflection. The strains on the sm7ay frames will be proportional to the differences d1, d2, etc., of deflection of the main girders, and as, these differences are also sensibly parabolic, the strain on the central sway frame will be closely 1 1/2 times that which would obtain if all the frames resisted equally. The unbalanced shear of 11/29 W represents the mean unbalanced shear per panel and by multiplying this by l 1/2 we obtain C.57 W. The above argument assumes the main girders to remain in truly vertical planes, and that no lateral deflection takes place. Actually the unequal horizontal deflections of the upper and lower lateral systems permits the main girders to twist and to take up positions slightly inclined to the vertical. This departure from the vertical plane relieves the sway frames of a considerable amount of the shear stress which they would otherwise suffer. The amount of this twisting action is greatest near the centre of span, diminishing towards the ends and so tends more to the relief of those sway frames which would otherwise be the more heavily stressed. Moreover, this relief is greater in through spans than in deck spans, since in the former the sway bracing may only be brought down to the clearance line leaving it considerable length of relatively flexible post below. The lateral bending of the posts
still further contributes to the relief of the vertical shear stress in the sway frames. In deck bridges with full depth cross bracing the transverse rigidity is proportionately greater, and the relief of the vertical shear stress somewhat less. A detailed investigation shows that not more than 20 per cent. of the load on one track is likely to be transferred as vertical shear through the transverse bracing from the near to the far side main girder, in the case of deck bridges, and less than 10 per cent. in the case of through bridges.
Professor J. Husband
When a rectangular beam is supported at both ends and loaded transversely the upper fibres are compressed and the lower extended, the stresses being greatest in the outer fibres, and proportionally less towards the middle of the depth, until a layer is reached where they both vanish. This may be shown experimentally by marking parallel vertical lines upon a beam of indiarubber as Fig. 1, and supporting it at the ends with a load on top, when the lines will be found closer together in the upper part of the beam and further apart in the lower, as Fig. 2, while at some intermediate depth their distances will be unaltered, as in line a b marking the neutral layer, or neutral
axis of the cross section, and showing that neither tension nor compression exists there. If A, B, C, D, Fig. 3, represent a cross section through the centre of a beam under transverse load, e f the maximum intensity of compression drawn to scale, and g h the maximum intensity of tension, then when these stresses are produced, the neutral axis will pass through the intersection k of lines eh, fg, and when ef and gh are equal this will also be the centre of gravity of the beam. When the stress and strain are proportional to each other, and equal in tension and compression, the horizontal lines will show by their length the intensity of the tensile and compressive stress respectively in the various layers.
Professor Henry Adams
In view of the increasing demand for Aluminous Cements, perhaps some particulars of the methods of the production of its principal raw material-Bauxite-may be of interest. The photographs are of various sections of the plant, which will illustrate some of the conveying methods.