CHAPTER III

FORM--_Continued_. BRIDGES

Roofs and small bridges may be built much alike . . . The queen-post truss, adapted for bridges in the sixteenth century, was neglected for two hundred years and more . . . A truss bridge replaces the Victoria Tubular Bridge . . . Cantilever spans at Niagara and Quebec . . . Suspension bridges at New York . . . The bowstring design is an arch disguised . . . Why bridges are built with a slight upward curve . . . How bridges are fastened together in America and England.

Roofs and Bridges Much Alike.

Rails are girders used by themselves: girders are often combined in trusses; of these much the largest and most important are employed for bridges. There is now under construction near Quebec a cantilever bridge whose channel span of 1,800 feet will be the longest in the world. See page 29. It will take us a little while to understand how so bold a flight as this was ever dared. We will begin with a glance at a truss of the simplest sort, such as we may find beneath the roof of an old-fashioned barn. A pair of rafters, AB and AC, are inclined to each other at an obtuse angle, and are fastened to the horizontal beam, BC, at B and C. Their apex, A, is joined to BC by the king-post, AK, which binds the three strongly and firmly. This whole structure makes up a triangle, and so does each of its halves, ABK and AKC. No other shape built of straight pieces will keep its form under strain. Take in proof say four pieces of lath and unite them with a freely turning pin at each corner to make the frame, ABCD; it is easily distorted by a slight pull or push; but insert cross-pieces, AC and BD so as to divide the square into triangles, and at once the frame resists any strain not severe enough to break the wood or crush its fastenings. As the roof presses down the frame ABC, its sides, AB and AC, tend to slide away at their lower ends, B and C, but this is prevented by the horizontal beam, BC, which while it holds them in place is itself so stretched as to be held level and straight. This calling into play of tension constitutes the chief merit of the truss, and enables it in roofs and bridges to span breadths impossible to simple beams bending downward under compressive strains. Not only in houses, but in ships, the truss has great value; it was introduced in this field by Robert Seppings of Chatham, in England, about 1810. To resist the pressure of grinding ice, the “Roosevelt” is built with trusses of great strength. She sailed in 1905, under Commander Peary, for a voyage of Arctic discovery.

Were our barn roof flat instead of sloping to form a truss, its supporting timbers, under compression, would have a decided sag from which BC is free. When we fashion a small model of a king-post truss, its sides, AB and AC, must be of metal or wood because they will be in compression; the king-post, AK, and the base, BC, which will be under tension, may be of rubber or cord. Always as in this case the parts of a truss exposed to compression must be of rigid material. When a part may be of cord, rope or wire, we know that it is resisting tension.[2]

[2] A model easily put together illustrates the truss in its simplest form. Take a pair of wooden compasses, each half of which is 15 inches long, such as are sold for blackboard use by the Milton Bradley Co., Springfield, Mass., at 50 cents. At each tip fasten, by the ring provided with the compasses, a chair castor such as may be had at any hardware store. Join the tips of the castors by a rubber strip. Holding the compasses upright, and applying pressure from the hand, they will extend until the rubber will be so stretched as to become almost perfectly horizontal. Various weights may in succession be suspended from the compass-joint, replacing manual pressure, and serving to measure the exerted tensions.

Wrought iron exerts about as much resistance to compression as to tension; so does steel. For this reason, and on account of their great strength, they have immense value in building. Cast iron can bear only about one sixth as much tension as compression, so that it is useful as foundations, for the bed-plates of engines and machinery and the like, but is unsuitable for girders. Wood is much stronger under tension than compression; in white pine this proportion is as eight to one. In designing timber bridges the strains are, therefore, as far as possible, arranged for tension.

Let us now enter another barn, about one half wider than the first, and look upward at its rafters. We see its roof sustained by timbers disposed as DCMH, to avoid the undue weight necessary for a design resembling that of our first roof, ABC. Instead of one upright post, AK, as in that case, we have now two, DE and HO, called queen-posts, sustaining the horizontal beam, CM. In large modern roofs the simple queen-post is modified and multiplied, as in the main power house of the Interborough Rapid Transit Company, West 59th St., New York. Returning to our simple queen-post design, let us imagine a creek flowing between walls spanned by DCMH; that truss and a mate to it, parallel at a distance of say ten feet, would easily carry a roadway and give us a bridge. A truss for a bridge must be much stronger than for a roof of equal span, because a bridge has to bear moving loads which may come upon it suddenly, giving rise not only to serious strains but to severe vibrations, all varying from moment to moment.

Palladio’s Long Neglected Truss.

The queen-post truss was remarkably developed by Palladio, a famous Italian architect of the sixteenth century. Two of his designs, here given in outline, are from his work on architecture published in 1570; their contours, little changed, are in vogue to-day. Strangely enough the trusses of Palladio, for all their merit, passed out of notice until their principles were revived and improved by Theodore Burr, in 1804, in a wooden bridge over the Hudson at Waterford, New York. This bridge had spans respectively of 154, 160 and 180 feet, stretches impossible to single wooden beams. Professor J. B. Johnson, an eminent engineer, says that this is the most scientific design ever invented for an all-wooden bridge; during fifty years it stood unrivaled as a model for highway purposes in this country. The Burr bridges were usually covered in, so as to resemble the roofs we began by inspecting. In a truss bridge each part bounded by two adjacent uprights, as DOEH in the queen-post figure on page 21, is a _panel_; every part under compression, as DO, HE, is a _strut_, _post_, or _column_; every part subject to tension as DE, HO, is a _tie_.

In 1830 as the first American railroad train sped on its way, a new era dawned for the bridge builder as well as for his neighbors. At once sprang up a demand for bridges longer and stronger than those which in the past had served well enough. A score of wagons laden with wheat or potatoes were a good deal lighter than a locomotive followed by a train of loaded freight cars. A market-wagon, too, could easily be taken aboard a ferry-boat, but for an engine and its cars a bridge was imperative, if the stream were not so wide as to forbid all opportunity to the bridge builder. His response to the demands of the railroad was two-fold. First in the use of metal instead of wood, beginning with iron rods to bind together frames of timber. As iron became cheaper and its value more and more evident, he employed it for additional parts of his structure until at last he built the whole bridge of iron.

To-day good steel is so cheap that railroad bridges are seldom reared of anything else. Besides using stronger materials, the designer has gradually improved the form of his structure, not only in its parts but as a whole, so that to-day, strength for strength, a bridge may be only one tenth as heavy as a bridge of fifty years ago. Advances in form have been due to experience as one type has been compared with another; meanwhile the mathematicians have carried their analysis of strains as far as the extreme complexity of their problems will allow, greatly to the betterment of designs.

In building a bridge, as in rearing many other structures, girders of various contours are used. In bridge building the I-beam is most employed. When the roadway proceeds on the top chord, as DH, in the queen-post figure, page 21, we have a deck bridge; when it is built on the bottom chord, as CM, we have a through bridge.

The Burr Bridge Simplified by Howe and Pratt.

The Burr bridge of 1804, already mentioned, included an arch and was in part sustained by struts projecting from abutments. These features were omitted by William Howe in the bridge which he patented in 1840, and which was, as far as is known, the first successor to a design of Palladio in employing a simple truss for long spans. The Howe truss was built of wood, except its terminal tie-rods, which were of iron; it has been repeated thousands of times throughout the world. In 1844 Thomas W. and Caleb Pratt patented a bridge which in design was the converse of Howe’s. Its diagonals of iron were used in tension, while its vertical struts of timber were in compression; in the Howe pattern the diagonals were in compression, the verticals in tension. This plan, by shortening the struts, diminished the cross-section necessary in a truss. When wrought iron took the place of wood for bridges, the Pratt design became the most popular of all, combining as it did more desirable features than any of its rivals. To-day for long spans the Baltimore truss is much in favor. Its stresses, that is, its resistances to change of form under strain, are readily ascertained; the shortness of its panels means strength; and its diagonals have the inclination which wide and varied experience has shown most desirable. The roadway, it will be observed, is upheld by sub-verticals, that is, by verticals which reach the floor from half the height of a panel.

An important study concerns itself with the intensity and distribution of strains, first in girders, next in trusses, and lastly, in bridges as units, all with intent to ensure the best possible designs throughout. In this field of inquiry the pioneer was Squire Whipple, a maker of mathematical instruments in Utica, N. Y., who published in 1847 his analysis of the strains in a truss bridge due to its own weight and to its moving loads. With the laws of these strains in mind he devised several bridges of great merit, the most noteworthy being reared in 1852 on the Rensselaer & Saratoga Railroad, seven miles north of Troy, which did service until 1883; its sides or web system had ties extended across two panels in double intersection.

In a long truss bridge, which in its entirety may be regarded as a girder of the utmost size, the cross pieces between the main beams of the structure are much less heavy than if continuous plates, of no more strength. The original form of the Victoria Bridge at Montreal was that of a continuous tube of iron, square in section; it has given place to a truss bridge of five times greater capacity which weighs only twice as much. (Illustrations of both on pages 27 and 28.)

Thus to lessen weight in comparison with strength is a matter of great importance in a suspended structure, which must not only bear its own weight, but carry heavy moving loads.

Advantages of the Cantilever, Arch, and Bowstring Designs.

In most cases a bridge crosses a valley or a river in a place which permits the engineer to erect scaffolding to support his trusses until they can be united and become self-sustaining. In some places this course is denied; a river such as the Ohio or the Mississippi may have to be spanned at a point where the waters in a single day may rise forty feet, bearing along trees and timbers with destructive violence. As a rule the difficulty is met by employing cantilever spans which require no scaffolding for their construction. To understand their principle let us suppose that on opposite banks of a creek we roll out to meet each other the joists FG and HI, taking care that the parts over the water shall always be lighter than the parts on land. When the joists at last touch they are secured to each other as a continuous roadway. Or, while they are at a moderate distance apart they may be joined by a third timber laid across the gap from one to the other. In practice the simple principle thus illustrated is developed and varied in many ways, but in every application the one rule is that the trusses as they stretch out from the two sides of a pier shall balance each other, the shore ends being duly weighted down or safely anchored to solid rock. And thus, at length, we come to the wonderful bridge, six miles west of Quebec, whose channel span of 1,800 feet will be the longest ever reared. See illustration, page 29. From the cantilever arms, DA and BE, will be suspended the central truss, AB, of 675 feet. A cantilever span may be much longer than a simple truss because on a pier, as D of this bridge, a part, DA, of the whole span, DE, is balanced either, as in this case, by a shore span, CD, or by a corresponding part of the next span should that span not extend to the shore but pass from one pier to another.

The first cantilever bridge in America was designed by C. Shaler Smith for the Cincinnati Southern Railroad, to cross the Kentucky River; it was built in 1876-7.

Spanning the gorge of Niagara, close to the Falls, is an arch bridge of 840 feet in its central span, which, in its construction during 1898, followed the plan originated by James B. Eads in building the St. Louis bridge nearly thirty years before. As scaffolding was out of the question in both cases, each bridge was built out from its piers on the cantilever principle. An arch is sometimes disguised as a modified bowstring, as in the Burr design of 1804, a horizontal tie connecting the extremities of the arched rib and taking its thrust, dispensing with the abutments demanded by an arch. In the chords of such a pattern the strength comes as near to uniformity throughout as practical considerations permit, avoiding the losses of early days when one part of a bridge might be twice as strong as another. The bowstring was adopted for the great span of 542-1/2 feet over the Ohio at Cincinnati built in 1888, and for the span of 546-1/2 feet erected at Louisville in 1893. A bowstring 533 feet long, forming part of the Delaware river bridge of the Pennsylvania Railroad, built in 1896, in Philadelphia, is outlined on page 32. At Bonn, on the Rhine, there was completed in 1904 a bridge whose central span is a bowstring 616-1/4 feet long.

Suspension Bridges and Continuous Girders.

If we take the design of an arch bridge and turn it upside down we have a contour such as that of the Williamsburg Suspension Bridge, opened in 1903 between Brooklyn and Manhattan, depicted on page 33. For the utmost length this is the only available span; it brings into play the tensile strength of wire, the strongest form that steel can take. A steel cable of suitable diameter, if it had to support only itself, might safely be three miles long. A suspension bridge has another advantage in employing an anchorage to bear strains which would break down a simple truss resting on piers. As first erected suspension bridges were liable to extreme and harmful vibration, in many cases being shaken to pieces by storms of no great violence. It was found that this vibration was checked and that safety was ensured by introducing stiffening trusses which, at the same time, benefited the bridge by distributing the load uniformly throughout the sustaining cables.

At Lachine, about eight miles west of Montreal, on the line of the Canadian Pacific Railroad, a remarkable bridge crosses the St. Lawrence river. Its design is that of a continuous girder of four spans, the two side spans being 269 feet each in length, and the two others each 408 feet. This type is discussed by Mr. Mansfield Merriman and Mr. Henry S. Jacoby in Part IV, page 30, of their work on Roofs and Bridges. One of the advantages presented is that deflection under live load is less, and stiffness greater than for simple, discontinuous girders, the harmful effect of oscillation being thus diminished. Furthermore, less material is required than for simple, discontinuous spans. Both these elements of gain are brought out in placing a strip of rubber, AD, upon four equidistant points of support, when we find that BC, the central third of the strip sags less than either AB or CD, the first or last third. Cutting off one-third of the whole strip we deprive the removed piece, at its surface of separation, of the cohesion which did much to keep the whole strip, before cutting, almost horizontal at that point. We take AB, our short removed piece of rubber, and lay it at its ends on two points of support; it now serves in a rough-and-ready way as a model of a simple truss, all by itself; its decided sag shows it much less rigid than when it formed a part of an unbroken and longer structure. Continuous girders despite their advantages are seldom employed; they are liable to serious difficulties; among these may be mentioned that changes, often unavoidable, of level in piers and abutments cause them to suffer great reversals of stress, always a source of danger; furthermore, variations of length due to changes of temperature are, of course, much greater and more troublesome to provide against than in the case of discontinuous girders.

Best Proportions for Spans: A Slight Upward Curve is Gainful. Pins or Rivets in Fastening.

Whether spans are long or short, engineers are fairly well agreed as to the best proportions for girders and panels. They consider that a girder should have about one-twelfth to one-tenth as much depth as span; and that the weight of a web should be about equal to that of its flanges. They usually give panels twice as much depth as length, with a tendency to increase the proportion of depth to length, in order to minimize the deflections and oscillations which shorten the life of a structure. For definite lengths of span, particular types of construction are preferred; usually for lengths of from 20 to 125 feet, plate girders are chosen; for spans of 125 to 150 feet riveted lattice trusses are built; for spans of 150 to 600 feet pin-connected trusses are employed. Here we reach the economical limit of a length for simple trusses; beyond 600 feet the engineer is obliged to have recourse either to a cantilever or a suspension bridge.

Whatever the breadth of the stream or the chasm over which he is to build a roadway, each case must be studied in the light of its special circumstances. There must be due regard to business as well as to engineering considerations; the designer will bear in mind that types of parts customarily turned out at great steel works are procurable in less time, and at less cost, than novel types requiring to be manufactured to order. Then, in speed of construction, he will remember that a pin-connected bridge can be built much faster than a riveted structure. Furthermore, every part must be vastly stronger than ordinary duty requires. Tempests and floods may suddenly arise; at any instant a derailment or a collision may create a strain of the utmost severity; and even under ordinary circumstances it must not be forgotten that train loads grow constantly heavier because economy lies that way.

One detail of bridge design is worth a moment’s attention. When a book-shelf is a thin board, quite straight as manufactured, it sags in the middle when fully burdened. This downward dip may be avoided by making the shelf at first with a slight curve which brings the middle a little higher than the ends. In bridge building a like curve, or camber, is given to each span so that when fully loaded it will be level or nearly so. In a span of 500 feet it is found that a rise of half a foot at the centre is sufficient. In suspension bridges, for the sake of strengthening the structure, the camber far exceeds this ratio.

In fastening together the parts of a bridge the usual American practice, already mentioned, is to employ pins which pass through eye bars. In England riveting is preferred, as shown in the figure of the lattice truss, page 36. This difference in methods arose through the use of materials which differed. In the construction of bridges the English engineer started with the flanged girder of cast or rolled iron, or some other form of stiff beam, and as bridges increased in size so as to require the framing of a truss, his whole effort was directed toward making that truss as much like the original flanged or box girder as possible. The American engineer, on the other hand, had at first little or no iron or steel to work with, and of necessity used wood. As the necessary bridges were of considerable span, the only feasible method was to pin together small pieces of wood so as to form a connected series of triangles. To make rigid joints in wood was impracticable, and indeed rigid joints were not desired, because the strength of wood is slight when strains are applied in any direction other than that of the fibres of the piece, and the pin joint insures just this line of action. As a rule a riveted bridge requires more metal than a pin-connected design, takes more time to build, but demands somewhat less skill. To provide for changes in length as a bridge is subjected to variations of temperature, friction rollers are used to support its extremities. In the first suspension bridge at Niagara Falls, built by Roebling, a little cement accidentally covered the friction rollers and prevented them from turning; fortunately the structure escaped the destruction to which it was thus exposed.

We have now taken a rapid survey of some of the methods by which the designer of bridges plans a structure which is at once safe and to the utmost extent economical of material. Step by step he has discovered how little steel he may use for designs all the bolder because his hand is so sparing of weight. His success began in adopting the girder, which we have seen to be in effect the working skeleton long concealed within the common joist; the cantilever span near Quebec, which compasses 1,800 feet in its flight, has been dissected out of preceding burden bearers in the same way. Its metal stands forth as so much sheer muscle kept to the most telling lines, unencumbered by a single pound of idle substance. A designer of such a fabric is an artist skilled in disengaging from masses of material every ounce that can be wisely removed. In some cases, as when Roebling linked together New York and Brooklyn, a bridge is created as much a thing of beauty as of use, as graceful as it is strong.[3]

[3] Mr. David A. Molitor has a chapter, copiously illustrated, on the esthetic design of bridges, beginning page 11 in the “Theory and Practice of Modern Framed Structures,” by Mr. J. B. Johnson and other authors, New York, John Wiley & Sons. Eighth edition, revised and enlarged. $10.00.