V^yiNOSTRAND I y ^NTiFic Books | l0l>a;t g^nnj ®Itttj;iSit0tt ^ mn ta lana AjH^ot H'os^ Long-span railway bridges : 3 1924 031 287 232 Cornell University Library The original of tliis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924031287232 LONG-SPAN RAILWAY BRIDGES. LONG-SPAN RAILWAY BRIDGES; COMPEISINO IHTESTIGSATIONS OP THE COMPARATIVE THEORETICAL AND PRACTICAL ADVANTAGES OF THE VARIOUS ADOPTED OR PROPOSED TYPE SYSTEMS OF CONSTRUCTION. WITH NUMEROUS FORMULiC AND TABLES, GIVIlfS THE WEIGHT OF lEON OR STEEL REQUIRED IN BRIDGES FROM 300 FEET TO THE LIMITING SPANS. b: bakee. {Reprinted from BNOiifBEEiiiK}. The whole carefully revised and extended.) PHILADELPHIA: HENRY CAREY BAIRD, INDUSTRIAL PUBLISHER, 406 WALNUT STREET. 18 68. D PREFACE. The contents of the following pages have already ap- peared in the columns of Engineering. The purpose of this ^^ replica" is to present the revised results, and tables, in a more accessible form than they could attain scattered in a 'desultory manner through successive numbers of a periodical. The subject, in its present form, was suggested by the discussion, at the Institution of Civil Engineers, follow- ing Mr. Barlow's paper on the Clifton Suspension Bridge ; when the absence of any simple generalisation of the question was evidenced. Prior to that time, however, the consideration of " Long-span Railway Bridges " de- volved upon the author in the com'se of his professional duties, and some valuable data had accumulated. On proceeding with the investigation, it was at once seen that a strictly mathematical treatment of the subject would entail lengthy and involved formulae, and absorb VI PEEPACE. far greater space than was available for the purpose ; indeed, the works of Gaudard and Schwedler, treating on the same subject, but within very narrow limits, plainly illustrated this fact. Accordingly, the various hypo- theses, which it is absolutely necessary to make in an in- quiry of this nature, are framed as comprehensively as possible ; and in many instances the result of a careful balancing of probabiHties is given without exhibiting the process by which it has been evolved. In short, elimina- tion, and not elaboration, has been the aim throughout. B.B. CONTENTS. Definition of long-span bridge — Circumstances justifying adoption — General problem of indefinite solution — Importance of super- structure — Want of information on the subject — Possible to approximate — Object of paper, and method proposed to be adopted 1 — 5 Relative strains on webs and flange — Lattice and plate webs — Minimum thickness of plate governs depth — ^Limit of depth for lattice — Method for arriving at weight of ironwork necessary — Limiting strain — Types of construction to be investigated in iron and steel 5 — 8 Type 1. Box girders — Economic depth small — Buckling of plates and waste of metal at centre — Weight of web governs depth- General principles determining proper depth — Formulae for depth, and minimum thickness of plate allowable — General formulae for strains and multiples — Tables of same . . . 8 — 13 Theoretical deductions overruled by practical — Position of plate and lattice reversed — Advantage of lattice on account of in- creased economic depth — Stiffness — American and English lattice — Investigation of strains, and proper depths of Type 2 — Lat- tice girders — Tables of strains and multiples .... 13 — 16 Type 3. Bowstring girders — Uniform and unequal loads — Bracing requires little metal, otherwise proves disadvantageous — Stiff- ness — Investigations of mass required — Influence of load — Strain on diagonals — Tables of strains and multiples .... 16 — 23 Type 4. Straight-link girders — No example in this country — Chepstow bridge— Bollman truss — Discussion at Institution — Similarity to bowstring — Influence of load — Reversed conditions — Inclination of bows — Deflections peculiar — Practical difiicul ties — Strains, masses, and multiples— Tables— Conclusion of first 23—31 Type 6. Cantilever — Appearance same as Type 2 — Web same also — Mass and moment of flange theoretically less — Extra Vlll CONTENTS. PAGE metal in adjacent spans diminish economy — Mass of metal — Tables of constants, strains, and multiples .... 31 — 3S Type 6. Cantilever varying depth — Modification of form de- sirable — Curved-top flanges diminish strain on web — Depth and stiffness greater — Mr. Fowler's Severn bridge — Tables of mul- tiples, &c 36—38 Type 7. Continuous — Maxiravim span — Sedley's bridge no prac- tical difficulty — Economical results surpass other systems — Tables 38—43 Type 8. Arched rib — Early form of long-span bridge — Indefinite- ness of opinions concerning it — Hypotheses vary — Rib jointed at three points — ^Nicety in proportioning metal to strain — Ex- pansion and contraction entail no additional strain — Investiga- tion of strains — Tables, &c. . 43 — 49 Type 9. Suspension with stiffening girder — Lightness and strength of rope between supports — Earliest form of long span — Insta- bility at first inadequately appreciated — Check ties — No im- portant difficulty in obtaining any required amount of stability — Transverse strength necessary — Vibration always exists, but not detrimental — Great variety of designs for rigid bridges — Inves- tigation of strains on chains and stiffening girders — Tables, &c. 49 — 55 Type 10. Suspended girder — Eeasons for rigidity of girder as compared with suspension — Inverted bowstring — 'Seduction of mass by initial tension on boom — Mr. Fowler's Thames bridge — Freedom from vibratory impulses — Expansion provisions — Investigation of strains, masses, &c. Tables .... 65 — 60 Type 11. Same as straight-link girdle, less the boom — KoUing — Dead and mixed loads — Tables of strains and multiples . . 60 — 62 Conclusion of tables of multiples — Investigation of specific loads — Weights of platform — Cross girders — Useful load — Formulae and classification — Gross loads 62 — 66 Tables of loads and weight of iron in cwts. per foot run . . 66 — 69 Adaptation of formulae to steel structures — Available strength for useful load higher ratio than limiting strains — Tables of mul- tiples, strains, and weight of metal 69 — 78 Summary of results, illustrated by diagrams — Comparative eco- nomy refers to superstructure only— Expense of piers Influences economy — Fairest comparison obtained by taking average weight per foot of viaduct — Tables of same — Difference less marked — Influence of cost of scaffolding on designs for long-span bridges . 78 — 84 LONG-SPAN KAILWAY BRIDGES. AccoEDiNG- to Dr. Johnson, a bridge is " a structure to carry a road across a watercourse ;" and although this interpretation of the word is not sufficiently comprehen- sive to include all cases in the present progressed stage of the art of building, yet, if we limit its application to long spans alone, we may even render it still more ex- plicit, and with very little liability to error define a long- span bridge to be a structure for carrying a railway across a watercourse. The reasons why this is the case are sufficiently obvious : in the first place, the condition necessitating the adoption of a long span is generally either that a certain width of opening must be provided clear of all obstructions, or that the expense of carrying up a number of lofty piers is, owing to some difficulty in obtaining secure foundations, so great as to render it more economical to reduce the number of individual supports, and so concentrate the resulting greater load 2 LONG-SPAN EAILWAT BEIDGES. on fewer points. Neither of these conditions is likely to occur, except when a watercourse is the obstacle to be surmounted, when, probably, a navigable channel of certain width has to be maintained, with su£Bcient head- way to admit of the free passage of vessels. If in any case it should be desirable for the span to be greater than the minimum amount dictated by the compliance with these conditions, it could only be when the depth and rapidity of the current, or the treatherous nature of the bottom, rendered it desirable to reduce the risk of construction to a minimum. As steep gradients are now worked with ease and economy, it is not at all probable that any other case — such as that of carrying a line across a ravine — will ever occur in which it would be economical to introduce longer spans than 300 ft. ; and it is only spans above that amount we designate long spans in the present paper. Again, it is highly impro- bable that any long-span bridge should be other than a railway bridge, because the great expense involved in the construction must be justified by necessity ; in other words, by the probability of such large traffic as a railway alone coidd accommodate. Even when we have thus limited the question to railway bridges crossing a water- course, where a given span and height has to be main- tained, we have by no means obtained all the conditions enabling us to pronounce upon the proper type of con- struction to be adopted. Thus, if the banks of a river are lofty, and aflEord a firm foundation for the super- structure with little or no piers, an arch or suspension- bri%e may possibly be the most economical construction, althotigh the resulting span may be greater than abso- Imtely required ; aad if the banks are nearly levd with LONG-SPAN EAILWAY BEID^ES. 3 the stream, it may or it may not be advisable to make the adjacent spans of greater length and weight than would ordinarily be required, in order to enable them to contribute more effectively to the support of the larger centre span. In short, it is plain that the determination of the most economical construction for a bridge of given span is a problem admitting of no definite solution. We may, however, facilitate the process much, and obtain valuable positive results, if we confine our attention at first to the comparative weights of iron required in the different methods of constructing the superstructure, which, after all, is by far the most iniiportant element in determining the cost of a long-span bridge. The size of a bridge is veiy commonly the popular standard by which the eminence of its engineer is mea- sured ; we may, therefore, naturally e^ect to find engi- neers ambitious of excelliag one another in;this particular branch of their profession, but, for the same reason, as so muich consideration must necessarily at one time and another have been devoted to the elucidation of the sub- ject, a student of engineerkig may justly be surprised to find so little definite information existing as to the capabiHties of all possible combinations of design to do the required work effectively and economically. Yet the number of patents taken out by professional and other quacks indicates clearly the want of appreciation of the fact that the problem is one admitting of a rigid theoretical solution, and that the limit beyond which the quantity of metal required in the actual construction exceeds the amount theoretically required will be a factor , of the latter quantity, the value of which maybe approxi- mated to very nearly, if we avail 'ourselves of the stock b2 4 LONG-SPAN EAILWAT BEIDGBS. of information afforded by existing though smaller structures. Although, as we urge, it is possible to approximate very nearly to a true result in every case, a considerable amount of intricate calculation and considerable space would be required to treat the subjfect exhaustively. Yet a great deal may be done with little labour if we base our investigations on the simplest and broadest principles, avoiding all complications and neglecting altogether minute details. If we proceed thus, we may, by making, so to speak, a cartoon of the different systems, exhibit in bold outline the respective advantages and disadvantages appertaining to each. This will be our aim in the present paper. We shall investigate on the above broad principles the weights of different types of girders, in- cluding all probable combinations, from the minimum span of 300 ft. to the hmiting span, beyond which it would be impossible to construct a bridge of the class capable of carrying more than its own weight without exceeding the given limiting strain per square inch. We shall carry out similar investigations both for iron and steel, and so conduct them, that by arranging the results graphically in the form of a diagram we may obtain a comprehensive view of the properties of the different designs and the nature of the laws governing the increase of weight, and consequent relative cost of the different constructions in the two materials. The general principles on which we shall proceed are identical with those already advanced by the author in a paper on "The Proper Depth of Girders" (Engimenty\ vol. ii. p. 224). We shall, where we consider it advisable, sacrifice mathematical exactness of formulae to simplicity, LONG-SPAN EAILWAY BRIDGES. 5 and generally allow a very; free interpretation of theo- retical deductions; the. numerical results will be worked out with the slide rule, and, in short, the process through- out will be consistent with our professed object of exhi- biting a cartoon-like view of the subject under consider- ation. In the paper alluded^to, we observed that the maximum strain on each flange of a girder of uniform depth is, by the simple principles of leverage, equal to the distributed load multiplied by the span, and divided by eight times the depth, the strain being greatest at the centre, and less elsewhere in proportion to the ordinates of a parabola ; and as this strain on the flange could only have been transmitted througt the web, a little consideration will make it evident that for a distributed load, whatever the resultant strain may be, the total amount on the half web, resolved horizontally, must be equal to the maximum strain on the flange, or, in other words, thQ horizontal sectional area of a plate web should be equal to double the sectional area of the flange at the centre. For a lattice web the gross sectional area of all the bars should be greater than this in the same ratio as the length of a. bar exceeds the horizontal distance included between its two ends, which for the most economical angle of 45° for the bars amounts to 'v/2 times the section required in a. plate web, and the mass vrill consequently be i/'i x v/2 = double that of the plate web. Expressed algebraically, S being the span, and d the depth in feet, a the sectional area of each flange, x and y coefficients depending upon the practical construction of the flange and web respect- ively; the mass of the plate girder will be=2a (Sa;+2/t?), and that of the lattice girder will be=2a (S^+2y which would obviously be the same amount per unit .of area, whatever th© gross section of the flange might he^ We have given, the limiting strain per square inch due to the entire load= T, the strain per_ square inch due to tha weight of the f^er itself =«, and, consequently, we have also T—^ tbe stcaifi available for the useful lead carried. Again, it follows that— Element of weight of girder : moment of useful load : : t : T — t; and that, if the weight of the girder be uniformly distributed in the same manner aathe remaining load, we have; — weight, ef girder : wseful load : : t : T — t. Or, in oth^a? words, the weight of iron required ia the coastractaoo csf a girder to eacjEy a given load will be the multiple = — of that load. By adojiting the above method, we have much facili- tated the solutioiL of the problems befcwe us, as we can now proceed with our investigations without complicating the question by the introduction of the varying loads, to which we are in each individual case liable. The types of construction to one cor the other of which we consider all forms of bridges, not absolute eccentrici- ties, may be referred, and to which, consequently, we h^ve confined our investigations, are the following : 1. Box-plate girders, including tubular bridges. 2. Lattice do. do. Warren truss, «SiC. 3. Bowstring do. do. Saltash type. 4. Straight links and boom. BoUman truss. 5. Cantilever lattice parallel depth. 6. Do. do. varpng economic depth. 7. Continuous do. do. do. 8 lONG-SPAN EAILWAY BEIDGES. 8. Arched ribs with braced spandrils. 9. Suspension with lattice stiffening girders. 10. Suspended girders. 11. Straight link suspension. The comparative weights of the above constructions, both in iron and steel, will be investigated ; but we shalj first complete the necessary calculations for obtaining the weight of each of them in iron before we introduce^ the more novel material steel. Commencing with the most unfavourable type for long -span railway bridges which it will be neces- sary for us to investigate — the box girder with plate webs — ^we might, without any preliminary calcu- lation, and with a very little amount of consideration, foretel the uneconomical results which must necessarily follow the distribution of metal in such an unsuitable form. Thus, the economical depth will be much less, and consequently the sectional area of flange required for a given load will be much greater, than in any other type of girder. Again, the amount of metal required to prevent the buckling of the deep thin plates would be nearly sufficient to form the struts of a lattice girder; therefore, the effective duty of such a web will be little more than the resistance it offers to tensional strains. But these strains may be more economically disposed of by means of lattice bars than by a solid plate ; for, in the first case, the section may always be made proportional to the strain on the individual bar, whereas in the latter instance a certain minimum thickness of plate must be carried throughout, thus involving a waste LONG-SPAN RAILWAY BEIDGES. 9 of metal throughout nearly the entire length of the girder. Now the mass of a plate girder for each square inch sectional area of flange at centre we have found to be equal to 2 (Sx+yd). Taking the weight of a bar of iron 1 ft. long and 1 in. square at .03 cwt., the above mass multiplied by .03 will give the weight of the girder in cwts. for each square inch section of flange. But the weight multiplied by i span will give the moment fi : 4 , Again, the strain, t, in cwts, per square inch resulting from the weight of the girder itself will be — ; hence, since Sx=Si/d when d is the most economical depth, we have : .015 S"* t=- d Now, the influence of the weight of the web is the most important element in determining the proper depth for a girder, because whilst all the disturbing influences affecting the flanges also affect the web, there is, in ad- dition, another element introduced, namely, the limiting thickness below which the plates may not be reduced ; this is never taken at less than ^in., and in situations not easily accessible for the purpose of painting this thickness should be increased to | in. ; again, when the load per foot is large, a thicker plate is usually employed. Now, the effective horizontal section of a web of uniform thickness, taking, as in the case of the flanges, a reduced strain to compensate for the loss of section through the 10 IQNG-SPAN EAUiWAT BEIEGBS. rivet-holes, will, since the strain increases nniformly from, the centre to the ends, and the span, S, being in feet, be equal to 12 Sxixithickness=3Sx thickness; consequently, as the least thickness of plate is ^ in., the least effective horizontal section, of any web will be fS; and there^can he but a small reduction in the weight of a web of unifonn. thickness,, whatever tibe lightness of the bad. As far as the web is concerned, there would obviously be a practical advantage in making the depth of a girder small in proportion to the span and load. Thusi, in shallow girders heavily loaded the gross average thick- ness varies from twice the net for short to two and a half times for long spans ; but as the small depth is a disad- vantage to the flanges, the determination of the depth at which the joint weights of the flanges and web would be a minimum is the problem to be solved. Now, W being -the distributed load, the other notation remaining as before, the sectional area (a) at the centre of the flange, WS in square inches, will be «=-o3rpj which amount will. also represent the actual horizontal section required in the haK web ; but we have seen that in practice this latter area is never less than f S ; consequently, the value of a for the web must never be taken at fess than that amount. As we laiow the mass, and consequently the .weight, of a girder to be proportioned to a {Sai+ftd), it is only necessary now to ascertain to what extent the limiting value of a for the web will affect the question. Now, taking a web of uniform thickness, and adopting liONG-SPAlir EAIL"WAT EEIDGES. 11 the highest value of 3/1 and the lowest of x, it is obvious that, if the mass of the flanges exceed that of the web, the depth must necessarily be too small, since an in- creased depth would similarly affect the weight of the web directly, and the flange inversely; thus, assuming the mass of the flange to be that of the web as 6 : 4, _the sum. being 10, then, if the depth were increased ^,. the 4x5 mass of the web would be —j- =5 ; andthat of the flange — p- = 4.8, the sum being 9.8. Again, taking the highest value of x and the lowest of yi, we can arrive in the same manner at the maximum depth. If the web be not of uniform thickness,, it is even more apparent that an excess in the mass of the flanges over that of the web indicates deficient depth, since increased depth would involve a proportionally less increase in the weight of the web. "We have, therefore, aa;S=aiyi „ practical „ b=15. It follows, therefore — T being the limiting strain in cwts, per square inch — the value of b, corresponding to the required strain, t, will be : j_15H-n^T-«) T Substituting this value in the former equation, and taking T = 80 cwts., 2/=2.5 + .001S, and a; =.6, we obtain : i=\/l28+.005 8^+12100-110; which equation gives the following results : LOirG-SPAir EAILWAY BEIDGES. 35 Depth. Strain in cwt. Span ia feet. per sq, in. 300 17.2 400 23.2 500 29.2 600 33.1 700 41.7 800 48.0 900 54.4 1000 60.5 1100 67.0 1200 73.8 1300 80.0 1 12 We have already observed tliat for a distributed load, such as the weight on the platform of a railway bridge, 6=8; and we have also found its value for the girder weight required to carry this load at the various spans. We can, therefore, at once obtain the weight of iron reqtiired in the construction of the main girders, as it will be the multiple of the load expressed by the equa- tion : ^I^lAXUXk/. "- 8(T- -0 Span in feet. Multiple. 300 .39 400 .61 500 .88 600 1.23 700 1.64 800 2.5 900 3.6 1000 5.43 1100 9.25 1200 21.6 1300 00 d2 36 LONG-SPAN RAILWAY BEIDGES. Type 6. — Cantilever Lattice Girder, varying economic depth. The most superficial examination of the method and results of our investigations concerning the cantilever lattice girder of uniform depth could hardly fail to suggest a desirable modification in its outline. Thus, if we lay off 300 ft. span and plot the economic depth at each end, and then, adding 50 ft. to each end, plot the economic depth for 400 ft. span, we shall, if we carry on the process up to the limiting span, and con- nect the, various plotted heights by lines, obtain a curve the ordinates of which will represent the economic depth for the different sections of the girder, and, conse- quently, if there be no new condition introduced, of the entire girder. But the alteration of the top flange from a straight line parallel to the bottom flange, to a curved line in- clined to the latter, does introduce a new element into the case, as a portion of the shearing strain will now pass through the top flange, and to that extent, of course, the web will be relieved of its strain. Now an examination of our last investigation will show that the depth of the girder, and, necessarily, to a great extent the weight also, is governed by the mass of the web portion. It follows, therefore, that the more we can reduce the strain on and, consequently, the mass of, those portions, the greater will be the economic depth, and, within certain limits, the smaller the total mass of metal required in the construction of the girder. It is not difficult, then, to see that we should employ every LONG-SPAN EATLWAT BEIDGES. 37 available economical means of reducing the strain on the web portions. We can, fortunately, effect this by the very simple process of giving the upper flange a downward curvature. The tendency of the tension member to pull straight will react on the long struts, and by the production of an initial tension reduce the mass of metal required for those members of the web ; whilst, if we make the cxu^v^ed outline include the various economic depths, we shall arrive at a stiffer form of girder than before. It would be foreign to our present purpose, and incon- sistent with our avowed intention of viewing our subject in the broadest possible light, were we to endeavour to deduce the precise amount of curvature which would give the most favourable general results. It will be a suiHciently near approximation to the correct average proportions, if we assume the depth at the centre of the girder to be one-fourth that at the ends, and the curvature of the top flange to be the segment of a circle passing through those three points. The form of bridge to which we have been thus, as it were, irresistibly driven is, we believe, almost identical in general and outline proportions with the structure designed by Mr. Fowler to span the 600 ft. centre opening, and the two 300 ft. side openings, of his viaduct for carrying the proposed "South Wales and Great. Western direct" railway across the Severn estuary. It will be unnecessary to give a detailed investigation; of this modified form of the cantilever lattice girder. The horizontal components of the diagonals will be, pro- portionally, the same as before ; the vertical components, 38 LONG-SPAN BAU-WAT BRIDGES. however, will be less, as a propcirtion of the shear:mg strain is tranBmitted through the curved top flange. The struts, again, wiU be lighter, on aieeount of their dimi- nifihed length, and, for the same reason, the flanges will be heavier. The ■cenitre of gravity of the mass of the entire girder being aibont the same as in the previous inslanee, we have iHfirely to substitute new values of x and y in the equation already deduced fox the parallel cantilever girder. Taking a;=.7, ajMiy=2 + .001S,tbe strain in cwts. per square inch due to the weight of the girder itself will be : <=y9.6S + .004S2+ 12100 -no, wMcfa equation gives the following resulfe : Strain in cwts. Span in feet. per sq, in. Depth. 300 14 J- 400 19 500 24 600 29 700 34.5 800 40 900 45.5 1000 51 1100 56.5 1200 62 1300 68 1400 74 1500 80 1 The multiple, as in last case, will be given by the equation : Multiple=-4^,. ^ 8(T— LONG-SPAN EAILWAT BEIDGES. 39 Span m feet. Multiple, 300 .3 400 .46 500 .65 eoo .88 700 .1,2 800 1.61 900 2.17 1000 2.96 1100 4.15 1200 6.1 1300 11.2 1400 22.6 1500 0© Type 7. — Contirmous Girder, varying economic depth (incluMng Sedle^s pcUent). Our last icivestigation show? us tjiat with aa unUmited supply of metal we may construct a cantilever bridge ijp to 1500 ft. span ; it follows, as a coroUaryj that it is also possible to construct a cantilever, or bracket, 750 ft. projection, capable of carrying any required load at its ejstremity. For, suppose we support tliis load by a simple triangular frame, consisting of an inclined tie and a h^ffizQntal strut, then the weight of this frame will not produce a strain on either of those members, since the whole affair will be borne by the original cantilever as a portion of its imiform load ; and, consequently, it will be possible to construct this triangular bracket, or what amouints to the same thing, the original cantilever, of sufficient strength to carry any required load at its ex- tremity. This being so, it necessarily foUows that it will be practicable to support the two ends of either of our independent girders on the extremities of a pair of 40 LONG-SPAN EAILWAT BEIDGES. these cantilevers, as securely as if they rested on their original piers. It is evident at once that if we do thus insert an in- dependent girder between the two halves of a cantilever bridge, the limiting span of the entire structure will be equal to the sum of the limiting spans of the two systems of which the bridge is composed ; that is, if we take our last type and the bowstring bridge, the limiting span will be 1500 + 1000=2500 ft. Now, what conclusion must we draw from this fact ? It appears we may on this system, with a definite amount of metal, bridge an opening which could not be spanned by either of the other systems we have yet investigated with an infinite quantity; and the irresistible conclusion is that at the high spans a much smaller amount of iron will be re- quired in the construction of a " continuous " bridge of this class than would be necessary in one constructed on either of the other systems. This theoretical deduc- tion is fully corroborated by the indisputable economy obtained in the bridges on this principle erected under Sedley's patent. The only thing we have to determine, then, is the span at which this superiority will begin to manifest itself, and that, of course, will vary with the degree of economy obtained in practice in the other systems with which it is to be compared. In our present investigation — as we have in all instances supplied a very liberal amount of metal for the construction of the several types — it will be when the sum of the multiples for the cantilever bracket and bowstring, reduced to the equivalent value when measured over the whole span, is smaller in amount than the multiple of the cantilever LONG-SPAN EAILWAY BEIDGES, 41 bridge for the same span. The tables we have already calculated for the two systems of which this type con- sists will enable us to ascertain when this condition is obtained almost by inspection. There is no practical diiHculty in the construction of this compound structure calling for special notice. The bridge may be made in one connected length, and merely jointed at the points of contrary flexure occurring at the junctions of the bowstring with the cantilever, expansion being provided for at the piers in the usual way, or the bowstring may be slung from the ends of the cantilevers, and the expansion allowed to take effect at those points of the span. In the latter case, precautions must be taken to ensure the maintenance of the strength of the horizontal bracing past those points, so as to check all tendency to lateral movement. The deflection will, of course, be the sum of the de- flections of the two smaller spans into which the bridge may be broken up. This will give a rather smaller proportional deflection than that appertaining to either system individually. Now let a=the sum of the lengths of the two cantilevers, and let 6= the span of the centre portion, or the bowstring girder; then a+&=span of the "continuous" girder. Also let n be the multiple corresponding to span a, and m the multiple for span h, given in the tables of multiples for Types 6 and 3 respect- ively. Then the load per foot on the cantilever in terms of the useful load as before, reduced to the equivalent load per foot distributed over the entire span, will be —^ — r^. In the same manner the load from the bow- a+o 42 LONG-SPAN' BAILTVAT BBIDGES. string will he -^ — 7^ ; and assuming the weight po the end of the bracket as equivalent to double the amouHit distributed, the load from the « triangle" will be 2b (m+ 1) _, . - .,, , , — — , , ■ . ihe sum of these amounts wiU be the mean a+o equivalent load; and that amount, less the unit usefid load, wili be the mean equivalent multiple ; therefore, M.itijl^?(!!±2±gfc±il Substituting the valves of m and n obtained from Tables 3 and 6, we find, by the preceding equation, that in higher spans than 550 ft, the " continuous " girder is lighter than the cantilever. At 550 ft. span, then, the economic span of the centre portion on the bowstring ^der^ ; and we know that at 2500 ft. the econoioic span is also the limiting span =1000 ft. Now — Vono ' '^^•^^'' ^*^<^ i* "^^ ^^ sufficiently accurate for our purpose if w:e assume the economic span of the cejitce portion .generally to be : Span^550 Econonuc span=^^ — 5 Substituting this value of h in our former equation, we obtain the following results : Span. Mnltiple. 300 .3 400 .46 500 . .65 600 .85 700 1.1 800 1.33 LOITG-SPATr EAXrrWAT BEIDGES. 43 Span. Mojltiple. 900 1.61 1000 1.84 1100 2.1 1200 2.49 1300 2.87 1400 3.37 1500 3.91 1600 4.58 1700 5.35 1800 6,47 1900 7.98 2000 10.42 2100 14.32 2200 21.14 2300 29.12 2400 50 2500 00 Type 8. — Arclied Mibs with Braced Spandrils. With very few exceptian^ all the earlier examples of wJjat would, .at the time of their erection, he considered long-span bridges ars constxucted on the principle of the arch ; indeed, in comparison with that construction, all the types axe in their inf aacy ; and yet, perhaps, with reference to no other system does there exist so much in- deflniteness and difference of opinion as to the real direction and amount of the strain at any given pojat.in the structure. The explanatjoB of this is simple enough, since, before we can attempt to determine the strains on an ordinary arch, we must .make certain assumptions, the probable truth of which may be sufSdently proved in our opinion, but n.ot so in tbe judgment of others. As we cannot absolutely demonstrate the truth of our hypo- thesis, any one elge is, of course, at perfect liberty to 44 LOXG-SPAN RAILWAY BRIDGES. make a different one, which may, very probably, give an entirely different result. If, however, we have given the relative position of three points through which the centre of pressure on the arch passes, its position is defined at every other point, for just the same reasons that the radius of a curve is defined when it has to pass through three points. It follows that if we arrange the details of an arched rib so as to ensure the centre of pressure passing through three loiown points, we shall be enabled to determine all the conditions with the same precision, and therefore to pro- portion the strength of the several members to the maximum strains occurring on each with the same ease as we do in the most elementary form of truss. We have already adopted a similar method in the instance of the continuous girder, by first determining the most economical position for the points of contrary flexure, and then, by constructional arrangements, secur- ing the constant position of those points under all con- ditions of loading. By this means we not only obtained a great theoretical advantage, but, by reducing the com- plicated and, in fact, almost indeterminate problem of the determination of the actual strains occurring on a continuous girder to the simple case of the independent girder, we were enabled in practice to effect an additional saving by proportioning the several members with much greater nicety to the maximum strains on each. The desideratum in the design of an arched rib is, therefore, that the centre of pressure should, under all conditions of loading, pass through the same three given points. The most obvious way of effecting this is by making the arched rib movable on pivots at the centre LONG-SPAN EAILWAT BRIDGES. 45 and at each springing, thus hinging, as it were, the rib at those three points. If the frictional resistance to turning on these pivots he small — that is, if their dia- meters he small — the centre of pressure would always pass through their centres, which, for a symmetrical cross section of rib and uniform unit strain, should correspond with the axis of the rib at those points. Again, in this design, expansion and contraction will merely produce a rise or fall of the arch at the crown, without any incidental strain; whereas if the rib were continuous there would have been additional strain with the consequent loss of metal on that score. We shall therefore confine our investigations to the arched rib jointed at the centre and at each springing. This, of course, assumes intermediate piers of sufficient stability to take up the unbalanced thrust due to the rolling load, if the arch be one of a series in a viaduct. If the piers be too lofty to admit of this necessary pro- vision, we should adopt an arched rib of an entirely different pattern, which will be referred to in considering Type 10. The problem reduced to its present dimensions is a very simple one, admitting of a definite solution; and on that account, partly, there is no reason why the aesthetically perfect form of the arch should not be eco- nomically employed in wrought-iron bridges. The deflection of an arched rib will be very nearly the same as that of a lattice girder of similar depth and strain per square inch. In considering the strains to which an arched rib is liable, it will be necessary to resolve the gross load into its two elements — dead and rolling ; for in this instance, =a(S + 46 LONG-SPAN EAILWAT BBIDGES. as in several previous ones, the strain will be to a great extent governed by the nature of the load as well as by its amount. Dead Load. With a dead load uniformly distributed, it is not ne- cessary for the spandril fillings of the arch to possess any bracing power, for the same reasons that the diagonals of the bowstring girder were dispensed with tinder similar conditions. The mass of the arched rib will be the same as in the instance of the same girder : tJ' that of the verticals wUl be less, on account of their ad^ decreased length, the mass being about -^ . Taking the coefficients, a; and y, for the horizontal and vertical components of the strain, as before, the total mass of the arch for each square inch sectional area at crown will be : But the mass, multiplied by .03 cwts. and by ^th span, equals the moment : S^ic ~ S fx^ Since economic ^-=-5— , we have depth =j5-^7r\J— ; ot/ '■ 2.00 y and since the strain in cwts. per square inch (i) equals le dead load : «=.03(.71 SaNjZ). — , we have for the dead load : LONG-SPAN EAILWAT BBIDGES. 47 Soiling Load. With a I'ollhig load it will be necessary to introduce bracing between the arched rib and the "horizontal girder," of such strength that the moment of resistance to a transverse strain at any point of the spandrils may be equal to the bending moment at the same point, due to the imequal distribution of the load. We shall assume the depth of bracing at the centre of the span to be |th the rise of the arch, which wiU give us an effective depth of ird the rise at the point of maximum bending stress. This proportion will limit in all our examples the maxi- mum strain on the arched rib to the same amount as it would be were the load entirely dead. The mass, there- fore, wiU be the same as before : Now the maximum bending moment will occur when the rolling load is half-way over the bridge, at which time it will, in terms of the bending moment on the entire span, be equal to (^)'. Since, however, the effective depth is only equal -^rd the rise of the arch, the mass of metal required in the horizontal girder, or top member of the braced spandrils, wiU be equal to (i)^-^i— f aS. The mass required for the sum of the horizontal components of the strain on all the diagonals will, if we provide a double set of 10 bays of bars, be equal to Again, the mean square of the verticals being . about, it follows that the mass required in the vertical components of the same double set of diagonals wiU be — n — . The total mass of metal required in the arch 48 LONG-SPAIT EAILWAY BEIDGES. for each square incli of sectional area at the crown will, therefore, taking coefficients x and y, as before, be equal to : 1.88..+?^. Since the mass multiplied by .03 cwts. and by \ span equals the moment, we have : ,i = .03(.225S=a;+3^V)- But ^=strain in cwts. per square inch (t) ; and eco- nomic flf2=-V3 — ; hence (?=73-\| -, and by substitution 24y 18 y J=.03(l.62Sa;/sJ^). Mixed Loads. . Assuming, as before, the useful load on a railway bridge to be composed of f rolling and ^ dead load, the mean coefficient will be 1.62 xfx .71x;^=1.4 ; or, taking the coefficient for the dead load=,71 as the unit of measurement for the mixed load, it will be about double that amount. Hence the strain in cwts. per square inch (<) due to the weight of a girder for carrying a railway bridge will be : Putting a=.021 S«N!^, when « = 1.25, and y=3.5+ .002S, we have : a = .0268 V2.8 + .0016S. LONG-SPAN RAILWAY BRIDGES. 49 And, taking the limiting strain at 80 cwts. per square inch as before, we have : ^_ 160a 80 + a' which equation gives the following results : Strain in cwts. Span in feet. per sq. in. Depth. 300 23.8 I 400 31 500 37.7 600 43.8 700 48.6 800 55 900 60 1000 64.9 1100 69.3 1200 73.5 1300 77.4 1400 81 i The value of the multiple rp_. , that is, the weight of iron in terms of the useful load, will be as follows : Span in feet. Multiple- 300 ■5^:5 = .42 5 6-2 400 U = -63 500 l±z = .9 600 till = 1.22 700 11^ = 1.55 800 11* = 2.2 900 1* = 3 1000 fl^ = 4.3 1100 il^ = 6.5 10-7 I 1200 ^ = , 11.3 1300 iiil = 30 1400 00 50 LONG-SPAN RAILWAY BRIDGES. Type 9. — Suspension with Stiffening Girder. The combined lightness and strength of an ordinary- rope stretched between two supports, and the almost unlimited distance apart at which those points of support might be placed, as compared with that which would have been the limit' Ijad the' intervening! ?pace been spanned by a solid bar even of iron of the same size as the rope, if merely resting on the supports,' could hardly have failed to attract, at 'a very early date, the attention of thoughtful practical men. "When, therefore, the occasion arose of throwing a light structure across a wide obstruction, the similarity of the conditions to the case of the rope with its two distant points of support must almost necessarily have suggested a similar mode of procedure; and knowing- the great superiority of the tensional strength of iron over rope, it was only natural that the "suspension bridge," in its -simplest form, should be evolved, and that it should be the earliest form; of the "long-span bridge," as undferS^toSd in our definition. . Thei- great instabiHty, however, of this m6de. of con- struction was at first inadequately appreciated. It was not until' numerous failures had occurred that it began to be clearly understood that a moderate force, applied at regular intervals, would produce an isochronous move- ment of sufficient extent to effect at last the destruction of the structure. The first modification suggested by these accidents was the insertion of check ties, or even inverted suspension chains, to hold down the platform and so prevent its oscillation. This, however, was a mere empirical remedy, and a more complete and scien- LONG-SPAN BAIL WAY BEIDGES. 51 tific investigation of the conditions of a suspension bridge was required before a successful result could be obtained. As the problem presented no important diffi- culties, the solution of it was delayed an unreasonable length of time. A little consideration will show that, to secure the stability of a suspension bridge, it is only necessary to prevent any considesrable change of form, in the chains, and the conseqfuent tremor and oscillation. This means that the forces acting on the chains should maintain always the same direction and the saime relative' propor- tions to one another, although it is not essential to the conditions of equilibrium that the amount of these strains should remain constant. This being so,, it follows that if the distribution of the^ load, or , other conditions, be such that tlxe: relative proportions, of the forces iwould- not be maintained, sufficient transverse strength must be pro- vided in the i structure to effect the required distribution of the forces acting on the chain.. It niatters little where ' this strength be supplied ; in some few instances it has been obtained* by. bracing togeither two sets of chains, one lying under the other, thus assimilating the chains to an inverted arched rib ;i in fact, a girder sec- tion ' for the suspension >has . been patented ; ordinarily, however, the required transverse strength is obtained in the construction of the- platform, where it is equally efficient, and rather adds to, than detracts from, the ele- gance of the structure. Although by this arrangement we effectually coun- teract the dangerous isochronous movement, still, as the economic depth of the stiffening girder is compara- tively very small, and as a double wave of deflection e2 52 LONG-SPAN EAILWAY BRIDGES. precedes and follows the load as it rolls over the bridge, a considerable amount of vibration must necessarily still exist, although not dangerous in its effects. This objec- tionable peculiarity of the suspension principle is pro- bably the reason why that class of bridge is almost uni- versally condemned as unfit for railway purposes. We believe, however, that the bad proportions of the earlier bridges, and the consequent failures, has created an unwarranted prejudice against the system. There is no theoretical or practical reason why a suspension bridge should not be made of any required degree of rigidity; but whether this could be done economically remains to be seen. Whatever can be effected on the principle of the arch may also be obtained in a suspen- sion bridge. Thus, if Ave were to invert our last type, the arched rib with braced spandrils, jointed at three points, we should obtain a rigid suspension bridge, free to expand and contract under changes of temperature. Again, provided we supply adequate transverse strength to the two halves of the bridge, it is immaterial what form our bracing may assume. As, however, we must have a horizontal girder at the level of the platform, it is more convenient to truss between that member and the arched ribs or chains, as the case may be, than to insert a special member. It is obvious, then, that it is possible to design an im- mense variety of forms of rigid suspension bridges ; the most elementary type being probably a couple of inclined straight beams, the outer ends of which are attached to the top of the piers, and the near ends jointed together. All that class may be referred to our last type, and the other systems will be included in our remaining types. LONG-SPAN EAILWAT BEIDGES. 53 At present we shall confine our attention to the ordinary suspension bridge with stiffening platform girder. CJiains and Suspending Bars. In order to obtain great stiffness in the suspending bars and other portions of the structure, and so fit it for its duty of carrying a heavy rolling load with little vibration, we shall provide a mass of metal for the con- struction of the suspension portion of the bridge, exclu- sive of the stiffening girder, equal to the amount we have found necessary in an arched bridge carrying an entirely dead load. The strain per square inch will therefore be the same in both instances: f=.021sW-. a; where x=1.2o, and2/=3.2 + .002S. Lattice Stiffening Girder. Eliminating the complicating elements the unequal defiections of the chain and girder introduce into the question by assuming a certain amount of preliminary adjustment to be effected diiring the erection of the bridge, we find the maximum bending moment on the stiffening girder takes place when* the bridge is two- thirds loaded, at which time it will, in terms of that on the entire bridge, be equal to \ (|)^=^. Therefore, w being the load in cwts. per foot run, and T the strain in cwts. per square inch, the required sectional area of flange will be : &w 54 LONG-SPAN EAILWAY BEIDGES. But, since all parts of the girder are successively exposed to nearly the same amount o£ strain, the theoretical mass of the web of the stiffening girder will be about H times that of a similar ordinary girder; therefore economic Sx " depth = — H^ce, since weight run of the girder in cwts. (W)' equals .03 cwts.x4aa', we have: Putting the rolling load w=25cwts. per foot, the gross usefid load= 32 ' cwts. pei* foot, and T= 80 cwts. per square inch,' the weight of the stiffening girder, in terms ' ! ' ■ t^ "■ of the useful load* will be= ., .^a^ ; and the total load on loOOO the chains=lH — 15000 We have the strain in cwts. per square inch on the chains due to the suspension portion of the bridge equal ■t=.026Sy/2.5'6+.0016S^ Strain in cwts- m in feet. per square in. 300 13.5 400 18.6 500 24 600 29.4 700 .35 800 40.8 900 46.8 1000 53 1100 59.4 i200 66 1300 73 1400 80 iQepthiOf Deflection Stiffening Girder, of Chains. LONG^SRAN .RAILWAY BEIDGES, 55 The -total weigHt of iron; in the suspension jfoAion of the bridge 'and=in the 'stiffening girder will be ©spressed in terms of the useful load by Jthe equation : ' Taking y= 5+ .0035, the results are as follows : % Span in feet. 15000' Multiple* 300 .12 .36 400 .17 .53 500 .22 .76 600 .27 1.02 700 .33 1.4 800 .39 1.9 , 900 .46 2.6 1000 .53 3.5 1100 .61 5.4 1200 -.68 8.7 , , 1300 .77 19.4 1400 00 Type 10. — Suspended Girder. A perfect suspension bridge would be a structure com- bining the rigidity of a girder with the lightness charac- teristic o'f the former system. In atteriipting to an-ive at this desideratum, the question naturally suggests itself, what is the fuiidainental difference between the two systems, giving them these attributes of rigidity and lightness respectively ? Now, the girder is rigid because the depth of bracing, arid consequently the resistance offered to change of form, is comparatively large ; and the suspension bridge is light, because the compression member of the girder is dispensed with ; for although an 56 LONG-SPAN RAILWAY BEIDGES. equivalent resistance must be supplied elsewhere in the land chains and anchorage, yet the mass of metal so em- ployed does not add to the load on the bridge, as it would have done had it been in the form of a compres- sion member* Let us imagine an inverted^bowstring girder, the top compression member being straight, and braced to the curved tension member in the usual manner, then it must be granted that this girder will present equal rigidity with the bowstring type, and that it will also require about the same mass of metal in its construction. But the problem to be solved is how to reduce the mass without impairing the rigidity ; and, from what we have already observed, it will be seen that this can only be effected by transferring a portion, or the whole, of the metal required in the top member to some other point where it will be equally efficacious, and will not add to the load on the girder. Now, the strain on the top member of the girder is compression (+ ), and it is obvious that if we can put an initial tension (— ) on that member, the resulting strain to be provided for will be the difference between those strains, and the mass of metal required will be propor- tional to that difference. We shall now show how, by a very simple contrivance, we shall be enabled to put any required degree of initial tension on the top member of our girder. Let one end of the girder be made fast to its pier, and let the other end, instead of resting immediately on the pier, be suspended by an inchned link from it; then, by the resolution of forces, it follows that the initial tension on the top member will bear the same ratio to the entire LONG-SPAN EAILWAY BRIDGES. 57 weight of the bridge as the horizontal component of the inclination of the link bears to double the vertical compo- nent. It follows from this that if the inclination of the link be tangential to the curve of eqnilibrimn, due to the load, the initial tension will just neutralise the final com- pression. As, however, the direction of the tangent to the curve of equilibrium varies with the position of the rolling load, whilst the inclination of the link necessarily remains constant, we shall have to reserve a certain pro- portion of the compression member to meet the conse- quent strains. We have, nevertheless, by this arrange- ment, disposed of the great mass of the compression member without impairing the rigidity or the freedom of movement under changes of temperature, pertaining to the ordinary bowstring girder. The " suspended girder," as, for want of a better name, we have christened the foregoing type, was, to the best of our belief, first introduced by Mr. Fowler, who pro- posed constructing his 750 ft. span high-level bridge over the Thames on that principle. There can be no doubt that, had that structure been carried out, the great depth of bracing maintained at the centre of the span — the point of maximum deflection — would have secured for it almost perfect immunity from those vibrating impulses which, although not appearing in theoretical calculations, manifest themselves in a very palpable manner in ordi- nary "rigid" suspension bridges. Dead Load. With a dead load uniformly distributed, the mass of metal required wiU be similar to that employed in the suspension portion of our last type. The strain in cwts. 58 LONG-SPAlir.EAIEWAY BEIDGES. per square inch due to the weight of the structure itself will therefore be : - *=.03(.7lsWj). . Soiling Load. The mass required in the suspension portiQin will be the same as that for a dead load = a (S+ -^ J- That of the bracing will be identical with the^to^efeponding members of the bowstring girder=/zr-|-^^+-; j. ^The mass of the compression member necessary to be fetaified, in order to proyide for the strains resulting from the un- equal distribution of the rolling load, will be ."^ilfcS. Taking x and y coefficients as before, the total mass for each square inch sectional area of chains will be : 1.47Sa;4 — 5-^. b But mass x ^th span X .03 cwts. equals the moment in cwts. ^=.03(.18Sa;+2.62 Type 4.- —Straight Link Girder (Steel). f — * 7aT T-.3a 02 S, we have a=.059 S^/ 2/=4.2 + .0( 3.36 + .00166 M= -^.- - = 40+^^8. W = ML+L-40. 300 25.4 .24 21 400 35.8 .38 29 500 46.2 .55 40 600 58.8 .83 55 700 71.5 1.22 78 800 86.5 1.99 123 900 101.6 3.58 214 1000 124.6 23.1 1304 1100 140.7 00 00 Type 5. — Cantilever Lattice, uniform Depth (Steel). < = v/26S+.008 8^ + 32000-179. When ?/= 3.3 + . 001 S M=: ^^ • L=40 + -I-J^ 8(T-0 18 M "W=ML + L-40. 7- 74 LONS-SPAN aAlL"WAT BEEDGlS. Span in feel t. *. M. W. 300 22 .29 22 400 30 .45 31 500 38 .62 42 600 46 .86 54 700 54 1.13 70 800 63 1.5 91 900 70 1.93 116 1000 78 2.53 152 1100 86 3.34 198 1200 95 4.74 280 1300 103 6.76 397 1400 111 • 11.1 650 1500 120 22 1288 1600 128 120 7000 1700 137 00 00 ! 6. — Cantilever varying Economic Depth t= V21S+.00682 + 3200-: 179 M: - .? L= =40+1 J 8 18^ 8(T-i) "W"=ML + L-40. 300 18 .23 19 400 24 .32 24 500 31 .47 33 600 37 .61 41 700 44 .79 48 800 50 1.0 64 900 58 1.27 76 1000 64 1.57 98 1100 71 1.98 124 1200 79 2.6 158 1300 85 3.23 195 1400 91 4 242 1500 98 5.35 315 1600 106 7.84' 481 1700 113 12.0 720 1800 120 22 1326 1900 128 120 7150 2000 134 00 00 LOH'G-SPAirEa:iLWATBRIBG:ES. 75 Type 7. — Continuous Girder, varying Economic Depth (.Steel). a+b 18"" W-MT, + L— 40. Span in feet. M. w. 300 .23 19 400 .32 24 500 .47 33 600 .61 41 700 .79 48 800 .97 63 900 1.15 75 1000 1.3 84 1100 1.5 96 1200 1.7 109 1300 1.91 123 1400 2.12 137 1500 2.37 152 1600 2.63 168 1700 2.94 189 ISOO 3.26 210 1900 3.67 237 2000 4.08 264 2100 4.6 297 2200 5.13 332 2300 5.93 885 2400 6.7 434 2500 7.8 506 2600 9 585 2700 11 716 2800 13.2 861 2900 17.5 1141 3000 24.9 1625 3100 52 2821 3200 11.8 7000 4000 00 00 76 LONG-SPAN EAILWAY BEIDGES. Type 8. — Arched Ribs with Braced Spandrils (Steel). . 2aT D02S, we -T+a ! have a=.0268v iy=4.5 + ( '3.6 + 0016S M= t T-t L = 40+1nJs ■W=ML+I .-40. )an in feet. i. M. W. 300 27.6 .27 21 400 36.8 .39 28 500 44.8 .52 36 600 63.2 .69 46 700 58.5 .87 57 800 68 1.1 71 900 74.8 1.35 84 1000 81.5 1.68 102 1100 87 2.02 125 1200 94.5 2.66 163 1300 100 3.33 203 1400 105 4.2 255 1500 110 5.5 333 1600 116 8.3 500 1700 120 12.2' 735 1800 124 20.7 1240 1900 128 64 3836 2000 133 00 00 M= Type 9. — Suspension with Stiffening Girder (Steel). <=.026SV3.36 + .0016S. When y=4.2 +.0028. L=40+iv'Sr 000"^ lT=tl,^^ 20000/ (, TV lie "2/i=y-r- w= ML + L- -40. 300 15.3 .23 17 400 20.8 .34 24 500 26.5 .45 31 600 32.4 .6 39 700 38.5 .77 49 LONG-SPAN BAIL WAY BRIDGES. 77 Span in feet. t. M. W. 800 44.8 .97 60 900 51.3 1.22 74 1000 58 1.52 91 1100 64.9 1.9 113 1200 72 2.38 148 1300 79 2.98 175 1400 87 3.92 228 1500 93 5 289 1600 101 6.98 402 1700 109 10.51 600 1800 117 18.34 1055 1900 125 , 51.5 2910 2000 134 00 00 Type 10. — Suspended Girder {Steel). 1.73aT «=n "T+.73a When y=4.2 + .002S, we have a=.026Sv/3.36 + .00168. A. '^ T-t- ^^ • sy " W = ML+L 1-60. 300 24.4 .23 17 400 31.6 .32 22 500 39.7 .43 28 600 47.5 .57 36 700 53.7 .72 44 800 64.5 .9 54 900 69 1.13 66 1000 75.5 1.4 81 1100 82.5 1.74 102 1200 88 2.14 124 1300 95 2.7 152 1400 101 3.3 186 1500 105 4.2 234 1600 110 5.5 307 1700 117 9 500 1800 123 17.5 961 1900 127 42.3 2320 2000 132 00 00 78 • LONG-BPAN EAILWAT BEIDGES. Type 11. — Straight Link Suspension {Ste&T). J78aT T-.22a' When ^=4.2 + .002 S, we have a=.G37 Sv'S.SG + .OOieS T-t ^ W= ML+40-L. Span in feet. t. M. W. 300 17.8 .16 14 400 24.2 .23 18 500 31.5 .3 23 600 39.4 .43 30 700 48 .58 38 800 56.5 .77 49 900 64.6 .96 60 1000 73 1.28 78 1100 84.5 1.86 110 1200 95.5 2.77 160 1300 109 5.2 368 1400 118.8 10.6 597 1500 129.5 359 2000 1600 00 The results of our various investigations are shown collectively in a graphical form in diagrams Nos. 1 and 2, the curved lines of which are obtained by plotting the gross weight of metal in cwts. per foot span, given in the final tables for each type, to the vertical scale of 100 cwts. to the inch. A carefiil inspection of these diagrams will enable us easily to trace the comparative merits of the respective systems as far as the super- structure of the main span itself is involved, and to note the varying influence of the span in each instance. A glance will be sufficirait to assure us that the several LONG-SPAJr. SPON, 48, CHARING CROSS 2500 Fi Span KellBro? lidiF? CastlsS'Bolborji. suosAMa Of TYPi FsaMS Of isfls e?A^ lAiofAY iimsis. Illllllllll Tx-pe 1. StKc (rirtiers. Sf* :. ZaHur einitrr- IifrX CrJtrx. 1^^^^^^^ TfT Si- S mt Hm Almi fJmmt Mntlfri p^ 4; Siraufht Luih^ SrSoonu '^na^ S- /ixfMitJevfrr LaHie^i Tvf^ «L f^ i i ii ^iBf r Idi A ^^c S. Arched Bibs with Juvceti Spniuiriis. ;^ Tiiwp 7 Suspermm mnA ^/Srmuf l^tntrr. TtfT Ki AofnUai Ctnhr- ^if» a. .(Ina^fft* UJt Jbw|WiwM>. E, i F. K Sr?K, 45 rHAEISO &£!n» lap ."•»«• S a-Iiss: SEDLEY S PATENT BklDGJii, 38, CONDUIT STREET, BOND STREET, LONDON, For Crossing Rivers and Valleys of any span up to 2,500 feet, without the aid of intermediate piers or supports of any kind. For Railways and ordinary Road Bridges, Soo "Long Span Uritlges, with Diagrams." By U. Baker, Esq. Spon, London. NO SCAFFOLDING OR SUPPORT REQUIRED DURING ERECTION. TMb Bridge is a combination of tho tubular, girder, and suspnnsion principles, and unitos jireat simplicity with easy and economica construction. It maybe built as easily at a height of 500 feet above the level of the Eiver or Valley as at a heightof 25feof, andiswel suited for export, m it can be packed in small space, and creeled very rapidly with bolls instead of rireis, and by uMki/led workmen. TABLE OF CO&IPARISON of Gross Weights of Road or Railway Bridges in Iron, according to best English Practice, from 50 fee span, with those on Sedley's principle, the Roadway beiug in width as stated, and the Bridge equal to a moving load of 112 lb; per foot super. Buckle Plates not included. Span 30 FEET WIDE. 15 FEET WIDE. ORDINARY. Bridge of Single Span, Bridge three or more Bridge of Single Span, Bridge of three or Lattice Girder in Feot. including Anchorage, Spans, each Span, Anchorage included. more Spans, each Span and Road Girders. 30 feet wide, and Road Girders. and Road Girders. and Road Girders. and Eoad Girders. Weight in Tons. Weight in Tons. Weight in Tons. Weight in Tons. Weight in Tons. SO 25 21 135 n 30 60 32 265 17 12? 39 70 30J 32J 21 15 49 80 475 385 265 18J 60 00 66i 45 30} 225 72 100 665 62 365 27 85 120 875 68 60 36J 114 140 113J 87 66 46 160 160 142J 108 86 684 192 180 1765 132 106 73 243 200 214 169 131 90 296 225 2G75 198 164 113} 371 250 331 241 202 141 462 278 412 298 262 173 683 300 484 345 306 210 690 360 682 479 434 297 1160 400 920 640 600 408 1853 450 1206 810 790 635 2940 600 1560 1060 1347 1660 1000 690 650 600 1952 2400 1 700 3.535 2415 Mallett's Buckled Plates for Flooring weigh with connexions 800 900 6000 6705 3400 4590 from 6 Iba. to 17 lbs. per square foot of roadway extra. 1000 8450 6050 For other widths between the limits of 15 feet and 30 feet the weight may be obtained as follows:— Multiply l-15th, the differen "between 15 and 30 feet bridges, by the excess of the required width beyond 15 feet, and to the result add the weight of the 15 fe bridge as given in the above Table. The strains are calculated not to exceed four tons per sectional inch. Prices for construction same as ordinary girders. Bridg up to 100 feet span can be delivered in six weeks from date of order. These Tables may be taken as perfectly correct, having been calculated by a Civil Engineer of eminence, andthefonnulfflcalculab ly Mr. Smith of Glasgow University, and certified by Professor Rankine, of Glasgow, one of the best living authorities on applii nechanics. The Royalty duo to the Patentee is 15d. per square foot of roadway of the Bridge, payable on delivery of the Bridge for Bhipmei Trrms: — Payments must bo made, part in cash, and the balance on delivery in London. Particulars in India of Messrs. W. NICOL & Co., of Bombay and Calcutta, and Messrs. EDMUND JONES & Co., of Kangoon Drawings and Specifications can be obtained on application to the Patentee. A Bridge can bo inspected at Messrs. MACLELLAN'S, Clydesdale Works, Glasgow. These Bridges are aireadv Xn use In England. Calcutta. Samsusar. s urat- B Amtiav- a^^ n^ SEDLEY S PATENT BRIDGE, 38, CONDUIT STREET, BOND STREET, LONDON, For Crossing Rivers and Valleys of any span up to 2,500 feet, without the aid of intermedial piers or supports of any kind. For Railways and ordinary Road Bridges. See " Long Spam Bridges, with Diagrams." By B. Baiter, Esq. Spon, London. NO SCAFFOLDING OR SUPPORT REaUIRED DURING ERECTION. This Bridge is a combination of the tubular, girder, and suspension principles, and unites great simplicity with easy and eeonomioi construction. It may be built as easily at a height of 500 feet above the level of the Biver or Valley as at a height of 25 feet, and is we salted for export, as it can hepacied in small space, and erected very rapidly with tolts instead of rivets, and ty imskOled worimen. TABLE OP OOMPABISON of Gross Weights of Eoad or Bailway Bridges in Iron, according to best English Practice, from 50 fe( span, with those on Sedley's principle, the Boadway being in width as stated, and the Bridge equal to a moving load of 112 lb per foot super. Buckle Plates not included. Span 30 FEET WIDE. 15 FEET WIDE. OEDINABT. Bridge of Single Span, Bridge three or more Bridge of Single Span, Bridge of three or Lattice Girder in Feet. including Anchorage, Spans, each Span, Anchorage included. more Spans, each Span and Boad Girders. 30 feet wide. and Bead Girders. and Boad Girders. . and Boad Girders. and Boad Girders. Weight in Tons. Weight hi Tons. Weight m Tons. Weight m Tons. Weight in Tons. 50 26 21 13J 9i 30 60 32 26^ 17 12| 39 70 39J 32i 21 15 49 80 47J m 25J 18J 60 ■ 90 56 45 30} 22J 72 100 66^ 52 36J 27 85 120 87* 68 60 36} 114 140 113 87 66 46 ISO 160 142 108 86 58i 192 180 176 132 106 73 243 200 214 159 131 90 296 225 267i 198 164 113J 371 250 331 241 202 141 462 275 412 298 252 173 583 300 484 34S 306 210 690 350 632 U79 434 297 1160 400 920 640 600 406 1853 450 1206 810 790 635 2940 £00 1550 1060 1000 1 690 550 1952 1347 600 2400 1660 700 3S3S 2415 Mallett's Buckled Plates for Flooring weigh with connexions 800 900 5000 6705 3400 4690 from 6 lbs. to 17 lbs. per square foot of roadway extra. 1000 8450 6060 For other widths between the limits of 15 feet and 30 feet the weight maybe obtained as follows:— Multiply l-16th, the differei between 15 and 30 feet bridges, by the excess of the required width beyond 15 feet, and to the result add the weight of the 15 ft (bridge as given in the above Table. The strains are calculated not to exceed four tons per sectional inch. Prices for construction same as ordinary girders. Bridj nip to 100 feet span can be delivered in six weeks from date of order. W These Tables may be taken as perfectly correct, having been calculated by a Civil Engineer of eminence, and the f ormulffi calculai [% Mr. Smith of Glasgow University, and certified by Professor Bankine, of Glasgow, one of the best living authorities on appl ' tliechanics. ^ The Boyalty due to the Patentee Is 15d per square foot of roadway of the Bridge, payable on delivery of the Bridge for shipmp Tbrms: — Payments must be made, part in cash, and the balance on delivery in London. Particulars in India of Messrs. W. NICOL & Co., of Bombay and Calcutta, and Messrs. EDMUND JONES k Co., of Bangoon. Drawings and Specifications can be obtained on application to the Patentee. A Bridge can be inspected at Messrs. MAOLELLAN'S, Clydesdale Works, Glasgow. These Bridges are already Ui use in England, Calcutta, San!iygS£,.SH£a£.i,SSI!2KS«>.aild.CaUlllei 150 250 500 25 35 45 'indred always in hand, from which Orders can he 3THERH00D, GHTS, London, B.C. iS Of ELLBRS', ANB L PLANT, &c. KNT • AM PUMP, ng Boilers, &c. &0. of its class." I iirtibcr of Gallots per 0,000. \ ■ ON APPLICATION. STOCKTOir-OISr-TEES. SECTION". r ACTION DONKEY PUMP. ianoe, we have much pleasure in informing our friends that our subjected, and HAS dOME OUT THEfiEFHOH TSWiimmV. J Country, and has been adopted by, and obtained a repetition of he Proprietprs are noW desirous of extending its use, and have !lr ODst We Wg thetef oro to submit the f o(Mo*teg Xtit (tf PrtMs Si-in. 2J-in. Doc 2J-in.! [BLE Ac Sii. TION. i-ii. 45-in. is 75 120 200 250 300 ^00 600 1200 2000 8000 4000 6000 7000 £1414 £1818 £24 £30 £3210 £35 £4l( from which it receives its steam. and will work with only a pressure of 5 lb, ill be found a capital substitute for the " Injector." HARE AND CO. Execute every description of DRAWIKS AND ENGRAVING ON WOC Mecllanioal, Pictorial, ArdKit^ctWat, ttnS Ori(*mentaI. ENQBAVIN6S MADE FROM PHOTOQRAPH Electrotypes taken from Woodcuts. CATALOGUES ILLUBtBATBD AND PEINT! 31, ESSEX STREE T, STRAND, LONDON. fiEBUCfitJ PRICES Of B. DONEIN & Co.' IMPROVED GAS VALV( WITH WHOOSHT IBOH PINIOM ^roffl 2 in. to 18 in., price 9a. 6 12s. per in. dimeter. List cJfpriceB.wlHi full ditaenr of all sizes Up to 3B in,, to ie ha application. These Valves ar proved on i>oth sides to* 30 lb. o square in. fcefdre leaving the W' and are fttways kept in stock. Valves madevrith oajsiaera< order. Ajso Screw Water V with giis metal faces. NEAB GRANQt KOAD, SfeRMONDSET. PICKERING'S xmfroV£:d SFHXNG REGULATO AND FElCTIOlffLESS VALVE , STEAM ENGINES Tliis rcgiilatoT liaviiij; proTSd' So successful in tJnitect States, the Maiiufactuiers kave made am meats and are now prepared to file orders * country. Any party in want of a good Governor ba i'ufnislied with one for trial, in which case e satisfaction will be guaranteed. 'Wteam En Builders will find It to their adYaiit»|» to give Governor a trial. ■ ^ Por further particulars address wii I lAM rjRFnnRv