Page:Encyclopædia Britannica, Ninth Edition, v. 4.djvu/329

] public road, 12 feet, 15 feet, and 10 feet in the same places ; private road, 14 feet for 9 feet in the middle ; for excep tions the Acts must be consulted. In designing a bridge to cross a stream care must be taken to insure that the openings are suitable for the maximum floods. The load which the superstructure of a bridge has to carry in addition to its own mass may be estimated as follows:— 1. For a public road; one hundredweight per square foot will represent the weight of a very dense crowd. This is greater than any load which ordinary carts or vans will bring on the bridge, but of late years traction engines and road rollers have been introduced, and a weight of perhaps 10 tons on each wheel on one line across the bridge ought in future designs to be provided for. The bridge must be strong enough to bear this maximum weight applied at any point, and also to bear all possible distributions of the crowd. A bridge might be fit to carry the crowd uniformly distributed over its surface, and yet fail when the crowd covered one-half of its length or width. 2. For a railway ; the maximum passing load on each line of rails may be taken as the weight of a train composed exclusively of locomotives. The bridge must be fit to bear this load distributed in all possible ways along the line. For spans above 60 feet on the usual 4 feet 8^- inches gauge this load may generally be taken as equivalent to 1 ton for each foot in length of each line of way, or in engineering language, &quot; one ton per foot run.&quot; Where a very heavy class of locomotives is in use 1 tons per foot run must be provided for. For small spans the distribution of the load as a locomotive passes is such that the above allowance is barely sufficient. For very small spans of 8 or 10 feet the maximum passing load is a little more than the weight on the driving axle of the locomotive, or say 14 tons.

§2. Classification.—Bridges are classed, according to the design of their superstructure, Q& girders, arches, and suspen sion bridges. A beam of wood crossing a stream, a brick arch, and a platform hung to a flexible wire rope are common examples of the three types. The essential distinction be tween the three types may be said to be, that in all forms of the suspension bridge the supporting structure (i.e., the wire rope in the above example) is extended by the stress due to the load ; in all forms of the arch the supporting structure (i.e., the ring of bricks in the above example) is compressed by the stress due to the load ; and in all forms of the beam or girder the material is partly extended and partly compressed by the flexure which it undergoes as it bends under the load, thus when a beam of wood carrying a load bends, the upper side of the beam is thereby shortened and the fibres compressed, while the lower side of the beam is lengthened and the fibres extended. Beams or Girders may be of various materials, wrought iron, cast-iron, and wood being chiefly employed. Arches may be of masonry, or they may be of wrought or cast iron or steel, in which case the compressed sector of a ring is usually a continuous and stiff structure. Suspension bridges are made of wire ropes or of separate links of wrought iron or steel pinned together so as to form a chain. The metal beam, arch, or suspension bridge may be a continuous structure or an open frame; we shall also find that in some designs the several simple types are combined so as almost to defy classification. Whatever design be adopted, the strength or efficiency to carry a given load depends on similar considerations. The designer selects that form of superstructure which the principles of statics show to be most desirable; he calculates the maximum stress which the load can produce on each part, and then so distributes his material that the maximum intensity of stress on every part shall be a definite fraction of the ultimate strength of the material. In metal structures, where the above principle can be very perfectly carried out, this fraction varies from one-sixth to one third, according to the certainty with which the stresses and strength of the materials are known. In stone struc tures the engineer has greater difficulty in calculating the stresses on each part, and relies more on empirical rules based on long experience.

I.

§3. Classes of Stress.—There are three kinds of stress, due to tension, compression, and shearing. Tension tends to cause failure by the extension or lengthening of the part strained ; compression tends to cause failure by the crush ing of the part strained ; and shearing stress tends to cause failure by the sliding of one part of the piece across the other from which it is shorn off.

§4. Tenacity, or Strength to resist Tension.—When tension is applied to a rod or link of any material so as to be resisted equally by each element of any imaginary section in a plane normal to the direction of the pull, this section, which is called a cross section, is said to be subject to a stress of uniform intensity. This intensity p is equal to the quotient of the whole pull P divided by the area S of the cross section, or

1. The ultimate strength of a rod subject to uniform stress is proportional to the section S, and the ultimate strength of the material is measured by the maximum intensity of stress which it can bear, or in other words, by the stress which the unit area of cross section can bear ; for example, if the unit of force employed be the weight of a ton, and the unit of area the square inch, the strength of materials will be measured in tons per square inch, or by the number of tons which will just tear asunder a rod one inch square, great care being taken that the load is so hung on the rod as to bear equally on all parts of the cross section. The following table gives in tons or Ibs. per square inch the ultimate strength f t of some of the materials used in bridges:— I.—Tensile Strength of Materials ? f t. Name of Material. Tons per iq. inch. &quot;Wrought Iron Plates 20 to 25 ,, Bars and Bolts 25 to 30 ,, ,, Wire 30 to 45 Steel Plates 30 to 40 Steel Rivets 41 to 48 Steel Wire 50 to 100 Cast-iron 6 to 8 Red Pine 5-1 to 6 3 Larch 4 to 5 5 Oak 4 5to8 5 Teak 6 to 9 Lbs. per eq. Inch. Brick (specimens of) 250 to 300 liasalt 1000 Sandstone ,, 285 Common Mortar 10 to 50 Hydraulic Mortar 85 to 140 Roman Cement, 12 months old 46 Portland Cement, 7 days old 270 ,, 12 months old 350to470 The ultimate strength P x of a bar with the cross section S to resist a stress uniformly distributed over that section is given in terms of/, by the expression—

2 P! = S/ ( . Table I. gives some idea of the tensile strength of the materials, but for a full comprehension of the subject special treatises, or the article on the, 