SUSPENSION BRIDGES.] BRIDGES 305 shall combine the lightness of the true suspension briigc with the stiffness of the girder. Mr Dredge s design with sloping rods (fig. 38) gives a somewhat stiffer structure Fig. 38. than the bridge with vertical suspension rods ; the inclined rods throw a strain on the platform, which must be resisted cither by ties along the central portion, or by struts abut ting against the piers. The stresses on each part will be shown under the heading " Compound Structures " ( 62). The design fig. 39 has been proposed by many, but is Fig. 30. worthless. The object of the proposers is to support each part of the platform by rods which are quite independent of other parts of the structure, and which, being originally straight, do not alter their form under stress. The un equal stretching of the long and short rods under a stress, or with a rise of ( temperature, is a radical defect. Mr Ordish has proposed a plan in which the road is supported by sloping tie rods, arranged like the struts in fig. 87, inverted. Flexible chains, like that of an ordinary suspension bridge, carry the weight of these tie rods by vertical rods, which keep the sloping rods straight. The chain in this form is not subjected to unequal loading. Various forms of bridge have been proposed, in which, as in figs. 76 and 78, two chains are braced together. These may be made thoroughly stiff bridges, with a moderate increase in the amount of metal required for the flexible bridge. They will be described under the head of "Frames." Stiffness has also been obtained in some structures by using an auxiliary girder to stiffen the platform. This is best effected by the use for each chain of two girders, each half the length of the platform. These girders are placed as in fig. 40, being hinged together by a strong pin at B, and Fig. 40. held down by pins at A and A 1? which should, however, be left free to move horizontally. These girders are not sensibly strained by the rise and fall of the chains due to a fall or rise of temperature ; they can also deflect freely as a whole when the chain is deflected under strain ; nevertheless, they serve to distribute the weight of a passing load over the chain, so that it cannot be sensibly distorted. Rankine has given the following rule for designing these stiffening girders. Let u be the greatest rolling load per foot run ; let x be the half span of the chain ; let M be the greatest bending moment which the auxiliary girders will have to resist (i.e., at the centre of each) ; let F be the greatest shearing force (at the end and central pins), then 1. and Each auxiliary half girder is in fact to be designed as a beam of half the span of the bridge, and capable of carry ing half the passing load per foot run (but not its own weight). This plan of stiffening is quite effective, but adds considerably to the weight and cost of the whole structure ; for not only have we to provide these extra girders, but extra material in the chains to carry this extra dead load. 35. Maximum Span. If we assume that wire can be obtained which will safely bear 15 tons per square inch, a rope (or single wire) with a dip of -j^th of the span would safely bear its own weight over a span of about one mile, and would not break till the span exceeded 4 miles. With a dip of |th of the span a steel wire rope of the best quality would not break until the span exceeded 7 miles. These lengths are not given as indicating practical spans for bridges, but to show the limits which with our present materials cannot be exceeded, however light the passing load may be. IV. THE AKCH. 36. General Description. An arch may be of stone, brick, wood, or metal. The oldest arches are of stone or brick. They differ from metal or wooden arches, inasmuch as the compressed arc of materials called the ring (fig. 41, London Bridge), is built of a number of separate pieces FIG. 41. Half Elevation and Half Section of Arch of London Bridge. having little or no cohesion. Each separate stone used in building the ring has received the name of voiissoir, or archstone. The lower surface of the ring is called the soffit of the arch. The joints, or bed-joints, are the sur faces separating the voussoirs, and are normal to the soffit. A brick arch is usually built in numerous rings, so that it cannot be conceived as built of voussoirs with plane joints passing straight through the ring. The bed-joints of a brick arch may be considered as stepped and inter locked. This interlocking will affect the stability of the arch only in those cases where one voussoir tends to slip along its neighbour. The ring springs from a course of stones in the abutments, called quoins. The plane of demarcation between the ring and the abutment is called the springing of the arch. The crown of the arch is the summit of the ring. The voussoirs at the crown are called keystones. The haunches of the arch are the parts midway between the springing and the crown. The upper surface of the ring is sometimes improperly called the extrados, and the lower surface is more properly called the in trades. These terms, when properly employed, have reference to a mathematical theory of the arch little used by engineers. The walls which rest upon the ring along the arch, and rise either to the parapet or roadway, are called spandrils. There are necessarily two outer spandrils forming the faces of the bridge ; there may be one or more inner spandrils. The backing of an arch is the
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