Girder

“ A person who can accomplish the task without the trouble I felt must be a practised athlete or a monkey with a ringed tail.
I came mighty near slipping from the girder the moment I put my knee to it. The wind seemed to come with a sort of broadside force. What saved me I don’t know. At the end of the girder I found a plank, and the solution of my troubles, in part.260 This plank was not so heavy as the others and had not been so thoroughly frozen to the iron that a strong gust of wind could not sweep it toward the right side of the bridge, one end more than the other. ”

“ The horizontal stresses in the flanges are greatest at the centre of a span. The stresses in the web are greatest at the ends of the span. In the most numerous cases the flanges or chords are parallel. But girders may have curved chords and then the stresses in the web are diminished.
Fig. 15.—Flanged Girder.
At first girders had solid or plate webs, but for spans over 100 ft. the web always now consists of bracing bars. In some girder bridges the members are connected entirely by riveting, in others the principal members are connected by pin joints. ”

“ Determining Size of Girder for Supporting Floor.
Girders 10 ft. apart from centre to centre carry a floor weighing 11/4 cwt. per ft. super. Required, the breadth and depth for strength; span 20 ft. (1) The total load carried by the girder is 20 x 10 x 1.25 = 250 cwt.—that is, the length multiplied by half the bay on either side multiplied by the load per ft. super. (2) Let B.W. = 7 times the safe load = 250 x 7 = 1,750 cwt. (3) Let breadth be .6 d. (4) Let c the constant be 4 cwt.
Then
Therefore, the breadth and depth of a suitable girder for the required purpose must be 11.5 in. ”

“ Let w = total live load per ft. run of girder; w2 the weight of platform per ft. run; w3 the weight of main girders per ft. run, all in tons; l = span in ft.; s = average stress in tons per sq. in. on gross section of metal; d = depth of girder at centre in ft.; r = ratio of span to depth of girder so that r = l/d. Then
w3 = (w1+w2) l2/ (Cds-l2) = (w1+w2) lr/ (Cs-lr) ,
where C is a constant for any type of girder. ”

“ That there is no single instance of compression in a vertical member of the bowstring girder, b. That every one of the diagonals is subjected to compression at some point or other in the passage of the live load over the bridge, c. That the maximum horizontal component of the stresses in each of the diagonals is a constant quantity, not only for tension and compression, but for all the diagonals. ”

“ But it is possible that the modern engineer might be disposed to criticise the skeleton girder at two or three points; and in particular he might think the girder, as we see it for instance in Diplodocus or Stegosaurus, not deep enough for carrying the animal’s enormous weight of some twenty tons. If we adopt a much greater depth (or ratio of depth to length) as in the modern cantilever, we shall greatly increase the strength of the structure ”

“ Most people are willing to concede the antiquity of the arch and of the suspension system, but are doubtful whether the "continuous girder," if it be rechristened "cantilever and central girder," be not a modern and patentable invention. ”

“ This circular girder, supported on thirty-eight pillars, was constructed in four parts, and bolted together in the usual way.
“You know all this. What you do not know is now to come. At two opposite joints of the circular girder certain holes were drilled in accordance with my drawings. These holes were explained to the workmen as mistakes—unimportant, since they could not weaken the girders. But they were not mistakes; they were the heart of my design. My design was to destroy the Arena and all the people in it by one simple act. ”

“ I decided not to mention to him that a foot-thick metal girder is a hell of an easier target than a one-inch diameter of flexible tubing. What the hell. I had Snow; Clatclit had a whole skin; and—Well, growing boys need their ego. ”

“ Camber.—In order that a girder may become straight under its working load it should be constructed with a camber or upward convexity equal to the calculated deflection. Owing to the yielding of joints when a beam is first loaded a smaller modulus of elasticity should be taken than for a solid bar. ”

“ In girder-work generally, and more particularly in plate-girders, considerable latitude obtains in the amount of bearing allowed. Clearly, the surface over which the pressure [3] is distributed should be sufficiently ample to avoid overloading and possible crushing or fracture of bedstones where these exist; but if no knuckles are introduced, this is an extremely difficult matter to insure. A long bearing may deliver the load at the extreme end of the surface on which it rests, or, more probably, near the face. ”

“ The girders, of which some are of cast and some of wrought iron, are all of the same depth, namely, three feet, with the exception of four, to be specially named hereafter, and by this arrangement the same horizontal lines are preserved throughout the whole of the building. They are also all similar in appearance, forming a kind of lattice-work, by which construction they do not look too heavy for the slight supports; and large solid masses are avoided, practically showing how great strength may be combined with elegance and lightness. ”

“ Each girder is 1511 ft. long and weighs 4680 tons. In cross section (fig. 17) , it is 15 ft. wide and varies in depth from 23 ft. at the ends to 30 ft. at the centre. Partly to counteract any tendency to buckling under compression and partly for convenience in assembling a great mass of plates, the top and bottom were made cellular, the cells being just large enough to permit passage for painting. The total area of the cellular top flange of the large-span girders is 648 sq. in., and of the bottom 585 sq. ”

“ Next let the girder carry a uniform load w per ft. run (fig. 40) . The total load is wl; the reactions at abutments, R1 = R2 = 1/2wl. The distribution of shear on vertical sections is given by the ordinates of a sloping line. The greatest bending moment is at the centre and = Mc = 1/8wl2. At any point x from the abutment, the bending moment is M = 1/2wx (l−x) , an equation to a parabola.
23. Shear due to Travelling Loads.—Let a uniform train weighing w per ft. run advance over a girder of span 2c, from the left abutment. ”

“ We may now pass without difficulty from the two-armed cantilever supported on a single pier, as it is in each separate section of the Forth Bridge, or as we have imagined it to be in the forequarters of a horse, to the condition which actually exists in that quadruped, where a two-armed cantilever has its load distributed over two separate piers. This is not precisely what an engineer calls a “continuous” girder, for that term is applied to a girder which, as a continuous structure, crosses two or more spans, while here there is only one. But nevertheless, this girder
Fig. ”

“ A main girder consists of an upper and lower flange, boom or chord and a vertical web. The loading forces to be considered are vertical, the horizontal forces due to wind pressure are treated separately and provided for by a horizontal system of bracing. For practical purposes it is accurate enough to consider the booms or chords as carrying exclusively the horizontal tension and compression and the web as resisting the whole of the vertical and, in a plate web, the equal horizontal shearing forces. Let fig. 37 represent a beam with any system of loads W1, W2, . ”

“ It is usual in both girders and beams to provide not only for the safe support of the greatest possible distributed load, but for the greatest weight, such as that of a safe or other heavy piece of furniture which may be moved over the floor at its weakest points, the centres of the girders and beams. It must always be borne in mind that the formulae for the ultimate strength of the "I" beams only hold good when the upper chord or flange is supported laterally. ”

“ Sometimes a girder is rolled out about one-third of its length, and then supported on a floating pontoon.
(4) Some types of bridge can be built out from the abutments, the completed part forming an erecting stage on which lifting appliances are fixed. Generally, in addition, wire cables are stretched across the span, from which lifting tackle is suspended. In bridges so erected the straining action during erection must be studied, and material must be added to resist erecting stresses. ”

“ Movement at each end of the end cross-girders of 3⁄10 inch, equivalent to a force of 71⁄2 tons, tending to bend them horizontally, and a mean stress on the outer edges of the girders, 12 inches wide, of 8 tons per square inch due to flexure, which, compounded with the ordinary flange stresses, will seem to give rather alarming results. ”

“ Figs. 160 to 194 give diagram sketches of a few out of the many forms of open, or truss, girders which have been adopted for large spans. There are many types from which to make a selection, each one possessing its own special features and [Pg 151] advocates. In working out the details of any, or all of them, there are some points which should always be kept in mind when deciding the distribution of material in the main booms. ”

“ In continuous girders also, levels having been taken, allowance should be made for effects of settlement, if any; and with arches evidence of movement of the piers or abutments sought for, with the like object. It is seldom that the main flanges of girders show signs of weakness, unless from flexure in the case of long and narrow top members, insufficiently stiffened; but there may be want of truth from other causes already dealt with. ”

“ The girders were carried by, and bolted to, cross-angles attached to the supporting columns. The girders carried safely a distributed load of about 6 cwt. to 7 cwt. per square foot up to 30 ft. clear span between supports. ”

“ For, as the shorter fore part of the lever goes under the weight from the fulcrum that forms the centre, the head of it, which is farther away from that centre, on being depressed, is made to describe a circular movement, and thus by pressure brings to an equilibrium the weight of a very great load by means of a few hands. Again, if the tongue of an iron lever is placed under a weight, and its head is not pushed down, but, on the contrary, is heaved up, the tongue, supported on the surface of the ground, will treat that as the weight, and the edge of the weight itself as the fulcrum. ”

“ In one revolution of the machine the length of rope uncoiled from the wheel is equal to the circumference of the wheel, and through this space the power must therefore move. At the same time the length of rope coiled upon the axle is equal to the circumference of the axle, and through this space the weight must be raised. The spaces, therefore, through which the power and weight move in the same time, are in the proportion of the circumferences of the wheel and axle ”

“ The steeper the incline, the more force necessary to raise a weight; whereas if the incline is small, the necessary lifting force is greatly reduced. On an inclined plane whose length is ten times its height, the lifting force is reduced to one tenth the weight of the load. The advantage of an incline depends upon the relative length and height, or is equal to the ratio of the length to the height. ”

“ It is odd, and to us laughable to see them putting them on. I have seen them fasten the end of their long girdle to a door, post, or table—adjust its folds—regulate [15] its width—put one end to their body, and turn round and round until they have wrapped it all to their liking. Yea, I have seen them do it on the road. On my visit to Nice, not long after I left that plain, I passed a man on the road who from some cause wished to adjust his girdle. ”

“ This done, I will consider the bones and joints of the skeleton which form the levers, and the muscles which move them.
“The Lever.—Levers are commonly divided into three kinds, according to the relative positions of the prop or fulcrum, the power, and the resistance or weight. The straight lever of each order is equally balanced when the power multiplied by its distance from the fulcrum equals the weight, multiplied by its distance, or P the power, and W the weight, are in equilibrium when they are to each other in the inverse ratio of the arms of the lever, to which they are attached. ”

“ An apparatus for weighing.
μ In its simplest form, a balance consists of a beam or lever supported exactly in the middle, having two scales or basins of equal weight suspended from its extremities. Another form is that of the Roman balance, our steelyard, consisting of a lever or beam, suspended near one of its extremities, on the longer arm of which a counterpoise slides. The name is also given to other forms of apparatus for weighing bodies, as to the combinations of levers making up platform scales; and even to devices for weighing by the elasticity of a spring. ”

“ On the principle of the lever are made, scales for weighing different quantities of various kinds of things; the steelyard, which answers the same purpose by a single weight, removed to different distances from the fulcrum on a graduated arm, according as the body to be weighed is more or less in quantity; and the bent lever balance, which, by the revolution of a fixed weight, increasing in power as it ascends in the arc of a circle, indicates the weight of the counterpoise. ”

“ The weight which suspends itself in the angle will give from it some weight at the sides of this angle which will be between them in the same proportion as is that of the obliquity of their sides. Or: one such weight will distribute itself between its supports in the same proportion as is that of the two angles born of the division of the angle where this weight sustains itself, division of angle which is made by the vertical which descends in the center of the suspended heavy body ”

“ If, for example, a weight, hung by a cord at the extremity of a lever arm, oscillates in the manner of a pendulum, it will not weigh at each instant on the lever but by the vertical component of its weight ”