466. We can explain the reason of this remarkable result by means of [Fig. 64]. Were the thin portion of the girder e f made of two parts placed side by side, the strength would not be altered. If we then imagine the flange a b widened to the width of c d, and the two parts which form e f opened out so as to form a tube, the strength of the girder is still retained in its modified form.

467. A tube of rectangular section has the advantage of greater depth than a solid rod of the same weight; and if the bottom of the tube be strong enough to resist the extension, and the top strong enough to resist the compression, the girder will be stiff and strong.

468. In the Menai Tubular Bridge, where a gigantic tube supported at each end bridges over a span of four hundred and sixty feet, special arrangements have been made for strengthening the top. It is formed of cells, as wrought iron disposed in this way is especially adapted for resisting compression.

469. We have only spoken of rectangular tubes, but it is equally true for tubes of circular or other sections that when suitably constructed they are stronger than the same quantity of material, if made into a solid rod.

470. We find this principle in nature; bones and quills are often found to be hollow in order to combine lightness with strength, and the stalks of wheat and other plants are tubular for the same reason.

THE SUSPENSION BRIDGE.

471. Where a great span is required, the suspension bridge possesses many advantages. It is lighter than a girder bridge of the same span, and consequently cheaper, while its singular elegance contrasts very favourably with the appearance of more solid structures. On the other hand, a suspension bridge is not so well suited for railway traffic as the lattice girder.

472. The mechanical character of the suspension bridge is simple. If a rope or a chain be suspended from two points to which its ends are attached, the chain hangs in a certain curve known to mathematicians as the catenary. The form of the catenary varies with the length of the rope, but it would not be possible to make the chain lie in a straight line between the two points of support, for reasons pointed out in [Art. 20]. No matter how great be the force applied, it will still be concave. When the chain is stretched until the depression in the middle is small compared with the distance between the points of support, the curve though always a catenary, has a very close resemblance to the parabola.

473. In [Fig. 65] a model of a suspension bridge is shown. The two chains are fixed one on each side at the points e and f; they then pass over the piers a, d, and bridge a span of nine feet. The vertical line at the centre b c shows the greatest amount by which the chain has deflected from the horizontal a d. When the deflection of the middle of the chain is about one-tenth part of a d, the curve a c d becomes for all practical purposes a parabola. The roadway is suspended by slender iron rods from the chains, the lengths of the suspension rods being so regulated as to make it nearly horizontal.

474. The roadway in the model is laden with 8 stone weights. We have distributed them in this manner in order to represent the permanent load which a great suspension bridge has to carry. The series of weights thus arranged produces substantially the same effect as if it were actually distributed uniformly along the length. In a real suspension bridge the weight of the chain itself adds greatly to the tension.