Page:Encyclopædia Britannica, Ninth Edition, v. 4.djvu/363

Rh FEAMES.] BRIDGES the saving to be obtained by increasing the depth beyond about -jVth of the span. The diagonal bracing in the Warren and bowstring girders is sometimes arranged as in fig. 73 ; the girder is then called a lattice-girder. It is to be treated as a series of superposed Warren girders, each bearing its share of the load. This form has a slight advantage inasmuch as the diagonal struts are stiffened by being pinned to the ties where they cross. Fig. 74 shows a very common and useful form of girder J.J D where the uprights between the top and bottom members are able to sustain both tension and compression, while the diagonals are only &quot;semi- members,&quot; being flexible rods or bars. The reciprocal for this design is shown in fig. 74a with two joints more heavily loaded than the others. The members in fig. 74 which have no arrows on them are idle or unused, with this particular distribution of load. When the permanent load is considerable as com pared with the passing load, the end or two end diagonals A K II Fig. 74rt. shown dotted will not come into action with any distribu tion of load, and may therefore be omitted. This form is much used when wood is employed for the compression members. It has in every case the advantage that the struts in the bracing are shorter than in the Warren girder. The lettering is arranged so that only those spaces have letters which are divided by members actually in use under this -particular load. Figs. 75 and 75a show a modification of this truss for small spans, and its reciprocal when loaded on one joint ; Fig. 75. the lettering here also only suits the one distribution of 1 &amp;gt;ad, and the idle members have no arrows on them. 50. Framed Suspension Bridges and Arches. These frames, like the girders, consist of top and bottom mem bers, braced together by tics and struts. The bridge is a suspension bridge, if the frame is supported by inclined forces pulling outwards from the bridge as ia fig. 76, and an arch is supported by forces pushing inwards as 77. The reciprocals of these two forms with the at the platform uniformly loaded are annexed. These reciprocals are drawn on the hypothesis that the direction of the thrust or pull is known ; and this has been chosen in this case so as to reduce the stress on NG to zero, as would necessarily be the case if NG were omitted or cut. When this is not the case the direction of the thrust or pull at the abutments must be found in the manner explained below. 319 in fig. joints X It is easy to design the bridge so that both the top and bottom members of the suspension bridge remain in tension, and both those of the arch in compression under all distributions of load. This would allow wire rope to be used for both members of the suspension bridge, and cast-iron or steel for both members of the arch. The stresses on the bracing are very uniform and small as compared with those on the diagonals of a girder. Fig. 78 shows a slight modification of the design for a suspension bridge, very suitable for spans so large that the end struts in the pre ceding form would be in conveniently long. The re ciprocal annexed is drawn for the case in which a double load is half the bridge. placed on The same design is suitable for an arch. The resultant thrust ex tension at the supports of framed suspension bridges or arches can only be found by a method analogous to that already explained for the solid metal rib. This method was first given by Prof. Clerk Maxwell. Consider any member A, fig. 79, of length L and cross-section a, made of a material having the modulus of elasticity E ; under the action of a stress F, the length L will be altered by an amount _L E.a