CHAPTER II

FORM

Form as important as substance . . . Why a joist is stiffer than a plank . . . The girder is developed from a joist . . . Railroad rails are girders of great efficiency as designed and tested by Mr. P. H. Dudley.

One January morning in Canada I saw a striking experiment. The sun was shining from an unclouded sky, while in the shade a Fahrenheit thermometer stood at about twenty degrees below zero. A skilful friend of mine had moulded a cake of ice into a lens as large as a reading glass; tightly fastened in a wooden hoop it focussed in the open air a sunbeam so as to set fire to a sheet of paper, and char on a cedar shingle a series of zigzag lines. There, indeed, was proof of the importance of form. To have kept our hands in contact with the ice would have frozen them in a few minutes, but by virtue of its curved surfaces the ice so concentrated the solar beam as readily to kindle flame. Clearly enough, however important properties may be, not less so are the forms into which matter may be fashioned and disposed. Let us consider a few leading principles by which designers have created forms that have economized their material, time and labor, and made their work both secure and lasting. We will begin with a glance at the rearing of shelter, an art which commenced with the putting together of boughs and loose stones, and to-day requires the utmost skill both of architects and engineers.

Strength and Rigidity.

Building in its modern development owes as much to improvement in form as to the use of stronger materials, brick instead of clay, iron and steel instead of wood. A stick as cut from a tree makes a capital tent-pole, and will serve just as well to sustain the roof of a cabin. For structures so low and light it is not worth while to change the shape of a stick. By way of contrast let us glance at an office building of twenty-five stories, or the main piers of the new Quebec Bridge rising 330 feet above their copings. To compass such heights stout steel is necessary, and it must be disposed in shapes more efficient than that of a cylinder, as we shall presently see.

In most cases strength depends upon form, in some cases strength has nothing whatever to do with form; if we cut an iron bar in two its cross-section of say one square inch may be round, oblong, or of other contour, while the effort required to work the dividing shears will in any case be the same. But shearing stresses, such as those here in play, are not so common or important as the tension which tugs the wires of Brooklyn Bridge, or the compression which comes upon a pillar beneath the dome of the national capitol. When we place a lintel over a door or a window, we are concerned that it shall not sag and let down the wall above it in ruin: we ensure safety from disaster by giving the lintel a suitable shape. When we build a bridge we wish its roadway to remain as level as possible while a load passes, so that no hills and hollows may waste tractive power: levelness is secured by a design which is rigid as well as strong. If a railroad has weak, yielding rails, a great deal of energy is uselessly exerted in bending the metal as the wheels pass by. A stiff rail, giving way but little, avoids this waste. To create forms which in use will firmly keep their shape is accordingly one of the chief tasks of the engineer and the architect.

Plank and Joist.

Forms of this kind, well exemplified in the steel columns and girders of to-day, have been arrived at by pursuing a path opened long ago by some shrewd observer. This man noticed that a plank laid flatwise bent much beneath a load, but that when the plank rested on its narrow edge, joist fashion, it curved much less, or hardly at all. Thus simply by changing the position of his plank he in effect altered its form with reference to the strain to be borne, securing a decided gain in rigidity. Let us repeat his experiment, using material much more yielding than wood. We take a piece of rubber eight inches long, one inch wide and one quarter of an inch thick. Placing it flatwise on supports close to its ends we find that its own weight causes a decided sag. We next place it edgewise, taking care to keep it perpendicular throughout its length, when it sags very little. Why? Because now the rubber has to bend through an arc four times greater in radius than in the first experiment. Suppose we had a large board yielding enough to be bent double, we can see that there would be much more work in doubling it edgewise than flatwise. The rule for joists is that breadth for breadth their stiffness varies as the square of their depth, because the circle through which the bending takes place varies in area as the square of its radius. In our experiment with the rubber strip by increasing depth four-fold, we accordingly increased stiffness sixteen-fold; but the breadth of our rubber when laid as a joist is only one-fourth of its breadth taken flatwise, so we must divide four into sixteen and find that our net gain in stiffness is in this case four-fold.

Girders.

Here let us for a moment dwell upon the two opposite ways in which strength may be brought into play, as either compression or tension is resisted. An example presenting both is a telegraph pole, with well-balanced burdens of wires. Its own weight and its load of wires, compress it, as we can prove by measuring the pole as stretched upon the ground before being set in place, and then after it is erected and duly laden. Should this downward thrust be excessive, the pole would be crushed and broken down. The strung wires are not in compression, but in the contrary case of tension, and are therefore somewhat lengthened as they pass from one pole to the next. Now observe a mass first subjected to compression, and next to tension. In bearing a pound weight a rubber cylinder is compressed and protrudes; when the weight is suspended from this cylinder, the rubber is lengthened by tension. In each case the effect is vastly greater than with wood or steel, because rubber has so much less stiffness than they have.

Both tension and compression are exhibited in our little rubber joist, which illustrates the familiar wooden support beneath the floors of our houses. This form in giving rise to the girder has been changed for the better. Let us see how. As the rubber joist sags between its ends, we observe that its upper half is compressed, and its lower half extended, the two effects though small being quite measurable. As we approach the central line, A B, this compression and tension gradually fall to zero; it is clear that only the uppermost and undermost layers fully call forth the strength of the material, the inner layers doing so little that they may be removed with hardly any loss. Hence if we take a common joist and cut away all but an upper and lower flange, leaving just web enough between to hold them firmly together, we will have the I-beam which among rectangular supports is strongest and stiffest, weight for weight. In producing it the engineer has bared within the joist the skeleton which confers rigidity, stripping off all useless and burdensome clothing. An I-beam made of rubber when laid flatwise over supports at its ends will sag much; when laid edgewise it will sag but little, clearly showing how due form and disposal confer stiffness on a structure.

Girders of steel are rolled and riveted together at the mills in a variety of contours, each best for a specific duty, as the skeleton of a floor, a column, or a part of a bridge. Their lengths, if desired, may far exceed those possible to wood. Their principal simple forms are the I-beam; T, the tee; L, the angle; C, the channel; and the Z-bar. Of these the I-beam is oftenest used; its two parallel flanges are at the distance apart which practice approves, they are united by a web just stout enough not to be twisted or bent in sustaining its burdens. Crank shafts of engines, to withstand severe strains, are built in girder fashion; so are the side-bars of locomotives and the braces of steel cars. Plates riveted together may serve as compound girders or columns of great strength and rigidity. In the New York subway the riveted steel columns which support the roof have a contour which enlarges at the extremities.

The Rail.

By all odds the most important girder is the rail in railroad service. Let us glance at phases of its development in America, as illustrating the importance of a right form to efficient service. At the outset of its operations, in 1830, the Mohawk & Hudson Railroad, now part of the New York Central & Hudson River Railroad, employed a rail which was a mere strap of iron two and one half inches wide, nine sixteenths of an inch thick, with upper corners rounded to a breadth of one and seven eighths inches; it was laid upon a pine stringer, or light joist, six inches square, and weighed about 14 pounds per yard. Thin as this rail was, its proportions were adequate to bearing a wheel-flange which protruded but half an inch or even less. Where the builders of that day sought rigidity and permanence was in the foundations laid beneath their stringers. Except upon embankments there were for each track two pits each two feet square, three feet from centre to centre, filled with broken stone upon which were placed stone blocks each of two cubic feet. On the heavy embankments cross-ties were laid; these were found to combine flexibility of superstructure with elasticity of roadbed, so that they were adopted throughout the remainder of the track construction and continue to this hour to be a standard feature of railroad building.

It was soon observed that the surface of a track as it left the track-maker’s hands, underwent a depression more or less marked when a train passed over it. With a strap-iron rail this depression was so great that engines were limited to a weight of from three to six tons. Before long the strap form was succeeded by a rail somewhat resembling in section the rail of to-day. Year by year the details of rolling rails were improved, so that sections weighing thirty-five to forty pounds to the yard came into service. These at length united a hard bearing surface for the wheel-treads, a guide for the wheel-flanges, and a girder to carry the wheel-loads and distribute them to the cross-ties. Thereupon the weights of engines and cars were increased, leading, in turn, to a constant demand for heavier rails. In 1865 a bearing surface was reached adequate for wheel-loads of 10,000 to 12,000 pounds, the rail weighing fifty-six to sixty pounds to the yard. But the metal was still only iron, and wore rapidly under its augmented burdens. Then was introduced the epoch-making Bessemer process and steel was rolled into rails four and one-half inches high, of fifty-six to sixty-five pounds to the yard, of ten to fifteen-fold the durability of iron. In design the early steel rails were limber so that they rapidly cut the cross-ties under their seats, pushing away the ballast beneath them. Because they lacked height they had but little stiffness, one result being that the spikes under the rails were constantly loosened, exaggerating the deflection due to passing trains. Throughout the lines every joint became low, and the rails took on permanent irregularities under the pounding of traffic, dealing harmful shocks to the rolling stock.

Dudley’s Track Indicator.

This was the state of affairs in 1880, when Mr. Plimmon H. Dudley invented his track-indicator. This apparatus, placed in a moving car, records by ever-flowing pens on paper every irregularity, however slight, in the track over which it passes. When railroad engineers first saw its records, they believed that the thing to do was to restore their roads to straightness by the labor of track-men. It was abundantly proved that the real remedy lay in using a rail of increased stiffness, that is, a rail higher and heavier. Mr. Dudley, in the light of records covering thousands of miles of running, added fifteen pounds to a rail which had weighed sixty-five pounds, and gave it a height of five inches instead of four and one half, while he broadened its upper surface. At a bound these changes increased the stiffness of the section sixty per cent., the gain being chiefly due to added height. Proof of this came when his improved rail was found to be much stiffer than that of the Metropolitan Railway, of London, which weighed eighty-four pounds to the yard and had a base of six and three eighths inches, but a height of only four and one half inches. In July, 1884, the Dudley rail was laid in the Fourth Avenue viaduct, New York; so satisfactory did it prove that in less than two years five-inch rails were in service on three trunk lines. Then followed their introduction throughout America, their smoothness and stability as a track giving them acceptance far and wide.

The performance of the Dudley rail so impressed Mr. William Buchanan, Superintendent of Motive Power for the New York Central Railroad that in 1889 he planned his famous passenger engine, No. 870, which entered upon active duty in April, 1890. It carried 40,000 pounds upon each of its two pairs of driving wheels, instead of 31,250, as did its heaviest predecessor; its truck bore a burden of 40,000 pounds more; its loaded tender weighed 80,000 pounds, making a total of 100 tons, an advance of forty per cent. beyond the weight of the heaviest preceding engine and tender. Mr. Buchanan’s forward stride has been worthily followed up. Since 1890, passenger locomotives have nearly doubled in the weight borne upon their axles, while tractive power has increased in the same degree. Through express and mail trains have more than doubled in weight, and their speeds have increased thirty to forty per cent. The tonnage of an average freight train has been augmented four to six-fold, with reduction of the crews necessary to keep a given amount of tonnage in motion. This economy is reflected in a reduction of rates which are now in America the lowest in the world, and which steadily fall. In capacity for business united with stability of roadbed, mainly due to stronger and stiffer rails and to adapted improvement in rolling stock, railroad progress in the past fifteen years is equal to that of the sixty years preceding. With rails increased to a weight of 100 pounds to the yard there is shown, even in passing over the joints, an astonishing degree of smoothness as contrasted with the jolting action of rails comparatively low and light. Stiffness of rail reduces the destructive action of service, originally enormous, upon both equipment and track, lowering in a marked degree the cost of maintenance. Size of rail as well as form plays a part in this economy. A passenger train weighing 378 tons has required 820 horse power on 65-pound rails, and but 720 horse power on 80-pound rails, the speed in both cases being 55 miles an hour; it is estimated that with 105-pound rails 620 horse power would have sufficed. In freight service Dudley rails have reduced the resistances per ton from between 7 and 8 pounds to one half as much; a further reduction, to 3 pounds, is in prospect. In passenger service, with rails of unimproved type the resistance at 52 miles an hour is 12 pounds per ton; with Dudley rails this resistance for heavy trains is not augmented when the speed rises to 65 or 70 miles an hour. Dudley rails, and rails derived from their designs, are now in use on three fourths of all the trackage of American railroads, effecting a vast economy. Seventy-five years ago the DeWitt Clinton locomotive and tender weighed only five sixths as much as the main pair of driving wheels, boxes, axle, and connecting rods of the present Atlantic type of engine. That such an engine can haul a heavy train at seventy miles an hour largely depends upon the production of that simple and important element in railroading, its rail.[1]

[1] Mr. Dudley’s rails, and those of other designers, are fully illustrated and discussed in “Railway Track and Track Work,” by E. E. Russell Tratman. Second edition. New York, Engineering News Publishing Co.

In Ninth Street, Pittsburg, the rails of the traction line are for some distance carried on steel ties similar in form, as here shown.