Fig. 141.
Fig. 142.
The general principle of the construction of girder bridges is easily explained by considering a simple case, which is almost within everybody’s experience. Let us suppose we have a plank supported as in Fig. [139]. The plank will by its own weight sink down in the centre, becoming curved in the manner shown; or if the curvature be not sufficiently obvious, it may always be increased by placing weights on the centre, as at g. If the length of the plank had been accurately measured when it was extended flat upon the ground, it would have been found that the upper or concave surface, a b, had become shorter, and the lower or convex surface, c d, longer when the plank is supported only at the ends—a result sufficiently obvious from the figure it assumes. It is plain, then, that the parts of the wood near the upper surface are squeezed together, while near the lower surface the wood is stretched out. Thus, the portions in the vicinity of the upper and lower surfaces are in opposite conditions of strain; for in the one the tenacity of the material comes into play, and in the other its power of resisting compression. There is an intermediate layer of wood, however, which, being neither extended or compressed, receives no strain. The position of this is indicated by the line e f, called the neutral line. If the plank, instead of being laid flat, is put upon its edge, as in Fig. [140], the deflection caused by its weight will hardly be perceptible, and it will in this position support a weight which in its former one would have broken it down. There is in this case a neutral line, e f, as before; but as the part which is most compressed or extended is now situated at a greater distance from the neutral line, the resistance of the material acts, as it were, at a greater leverage. Again the portions near the neutral line are under no strain; they do not, therefore, add to the strength, although they increase the weight to be supported, and they may, for that reason, be removed with advantage, leaving only sufficient wood to connect the upper and lower portions rigidly together. The form of cast iron beams, Fig. [141], which were used for many purposes, depends upon these principles. The sectional area of the lower flange, which is subjected to tension, is six times that of the upper one, which has to resist compression, because the strength of cast iron to resist pressure is about six times greater than its power of resisting a pull. If the upper flange were made thicker, the girder would be weaker, because the increased weight would simply add to the tension of the lower one, where, therefore, the girder would be more ready to give way than before. If we suppose the vertical web divided into separate vertical portions, and disposed as at Fig. [142], the strength of the girder, and the principle on which that strength depends, will be in no way changed, and we at once obtain the box girder, which on a large scale, and arranged so that the roadway passes through it, forms the tubular bridge. It is only necessary that the upper part should have strength enough to resist the compressing force, and the lower the extending force, to which the girder may be subject; and wrought iron, properly arranged, is found to have the requisite strength in both ways, without undue weight. The various forms of trussed girders, the trellis and the lattice girders, now so much used for railway bridges, all depend upon the same general principles, as does also the Warren girder, in which the iron bars are joined so as to form a series of triangles, as in Fig. [143].
Fig. 143.
Girders have been made of wrought iron up to 500 ft. in length, but the cost of such very long girders is so great, that for spans of this width other modes of construction are usually adopted.
GIRDER BRIDGES.
Fig. 144.—Section of a Tube of the Britannia Bridge.