DESIGN OF LARGE BRIDGES WITH SPECIAL REFERENCE TO THE QUEBEC BRIDGE \ BY RALPH MODJESKI, D.Eng., Consulting Engineer, Member of the Institute. PRESS OF J. B. LIPPINCOTT COMPANY I 9 I 3 (Reprinted from the Journal of The Franklin Institute, September, 1913.) DESIGN OF LARGE BRIDGES WITH SPECIAL REFERENCE TO THE QUEBEC BRIDGE.* BY RALPH MODJESKI, D.Eng., Consulting Engineer, Member of the Institute. It is rather a difficult matter to draw a line between a large bridge and one of ordinary size. My definition of a large bridge would be a bridge which involves a considerable expenditure of money, or presents unusual difficulties of construction, or both. Bridges which by force of circumstances and local conditions span long distances may, therefore, be classed as large bridges. It has been my good fortune to be connected with the design and construction of several large bridges, and I shall deal, in the course of this paper, with the salient features of those struc¬ tures, while at the same time trying to deduce a few general principles which should govern the design of large bridges. I shall also refer to structures designed by other engineers. It would, of course, be impossible in a single paper to cover the field in detail and in an exhaustive manner; I can only bring out some of the more important questions which should be considered by the designer of such structures. In what follows, * Presented at the meeting of the Mechanical and Engineering Section held Thursday, May 1, 1913. 240 [J. F. I. Ralph Modjeski. the Quebec Bridge, with its single span of 1800 feet, 100 feet longer than the Firth of Forth Bridge, 1 will be referred to frequently. As that bridge is now under construction, and as the first attempt to build it resulted in a great disaster, the structure will be of particular interest. Location .—The first question which the engineer has to deal with, when considering a bridge project, is the location. In the majority of cases this location has previously been fixed, either exactly or within a small range. Whenever this location is not fixed exactly, the engineer makes surveys of the various possible locations, from which surveys preliminary sketches are drawn and estimates prepared. One of the most important conditions to consider in this comparative study is the character of the foundations. Complete borings to determine the kind and quality of the material through which the foundations are to be built, and on which the finished work is to rest, are indispen¬ sable. In the case of a railroad bridge it is not always the location giving the cheapest bridge which gives the most economical re¬ sults. As an instance, let us consider the Celilo Bridge across the Columbia River. A bridge at the Dalles, 12 miles below Celilo, would have been cheaper, but the bulk of the traffic over this bridge being east-bound, the location at Celilo was, on the whole, more economical, as saving about 24 miles in the dis¬ tance to be traversed by such east-bound traffic. Another im¬ portant feature in deciding on a location is the permanency of the river bed. A bridge should not be located where there is a reasonable possibility that the stream may change its course. If such a location is unavoidable, the shores should be protected and the river regulated for some distance above the bridge. When the location has finally been fixed, more borings should be taken, several at each pier, to establish beyond any reasonable doubt the character of the materials. I am laying great stress on this point, because it is so frequently neglected. Such neglect often results in serious disappointment as to the ultimate cost of the bridge, in differences as to settlement with the contrac¬ tors, and in delays. Length of Spans .—While sometimes the length of spans is 1 The span of the Forth Bridge is sometimes erroneously given as 1710 feet. This is the distance between centres of main end uprights, but the distance between centres of bearings at the bottom chord is 1700 feet. Sept., 1913-] Design of Large Bridges. 241 governed by the cost of the foundations and piers, more often such length of spans is fixed by requirements of navigation or other circumstances. The Government, in giving permission to build a bridge over navigable waters, generally imposes the clear opening of one or more spans, and passes on the design as a whole. It also imposes the minimum clear height above water. Sometimes the ruling of the Government results in an injustice to the railway corporations, as for instance in the case of the Memphis Bridge. The minimum clear height imposed for this bridge by the War Department was 75 feet above highest water known. A clear headroom of 65 feet would have been sufficient, and, if permitted, would only have involved the removal of use¬ less ornaments on pilot-houses of three or four boats, and a provision for lowering the smokestacks on a few boats, similar to the provision existing in the Ohio River, where the required clear headroom above high water is only 53 feet. The addi¬ tional ten feet not only increased the cost of the bridge consid¬ erably, but resulted in heavy grades in the approach in Memphis and a disturbance in street grades. 2 Often draw spans or movable bridges are required over streams where there is no navigation, on the theory that some boat might wish to come through some day. But it must be said that in the majority of cases the rulings of the Government engineers are just and necessary for the proper protection of navigation. Where no limitation is placed by the Government as to length of all spans, as in the Columbia River Bridge at Van¬ couver, for instance, in which only the lengths of the draw span and of the adjacent or raft span were stipulated, the spans should be made of economical length, provided the piers do not reduce the cross-section of the river sufficiently to cause an undesirable increase in the current velocity. This economical length may be determined by trials, and will be attained approximately when the cost of the superstructure and of the substructure are nearly equal. This well-known principle has been applied in determin¬ ing the length of the six 265-foot spans of the Columbia River Bridge (Plate I). The charter for the Thebes Bridge provides that it “ shall have at least one channel span, with a clear channel way at low "See Geo. S. Morison: A Report to Geo. H. Nettleton on the Memphis Bridge, 1894. 242 Ralph Modjeski. U- F. !• \ water of not less than 650 feet, and all other spans over the waterway, at a bank-full stage, shall each have a clear channel way at low water of not less than 500 feet, and all such spans shall have a clear headroom of not less than 65 feet, etc.” So here the length of spans as well as the clear headroom is definitely fixed by the Government requirements. In the case of the Quebec Bridge, while the navigation in¬ terests fixed the clear height of the structure above high water at 150 feet, the length of span is entirely due to the physical Fig. 1. Original project for the Quebec Bridge in 1884-1885 by Messrs James Brownlee, A. Luders. Light, and T. Claxton Fidler. conditions of the crossing. The stream at this point is narrow and deep, the depth in the centre of the stream being about 190 feet. The current velocity at ebb-tide is very high—about nine miles per hour. Very heavy ice runs at times and tends to gorge. The bed rock, as shown by the borings, while accessible near the shore lines, dips rapidly towards the centre of the stream. All these conditions made it imperative to build a span of great length. The information as to bed rock which we now have would indicate that the original project could have been designed with a somewhat shorter span. Yet we should remem¬ ber that this original project was undertaken by a private cor- Sept., 1913.] Design of Large Bridges. 243 poration, and we should perhaps recognize the value to it of such advertisement as the building of the longest span in the world would obviously afford. The next longest span is that of the Firth of Forth Bridge, and is 1700 feet long. It is doubtful if a shorter span than 1700 feet would have been practicable at the location adopted for the Quebec Bridge. I consider it per¬ fectly legitimate to build a more expensive structure than economy of the work itself would call for, if the more expensive structure will afford sufficient advertisement and publicity to compensate for the additional expenditure. Cases also often arise where a purely economical and utilitarian structure would be entirely out of harmony with the surroundings. We have a good illustration of this policy in the magnificent stations which the railway companies are constantly building. A project to build a large bridge at Quebec, presumably in the same location as the present one, was seriously considered in 1884 and 1885. Messrs. James Brownlee, A. Luders Light, and T. Claxton Fidler designed a structure with a clear span of 1442 feet 3 (Fig. 1). The description of that project men¬ tions rock foundations. The more complete information we now have, and which was obtained by a costly series of borings, shows that at the present location rock could not have been at¬ tained in both piers with any known method of foundation if the piers had been spaced only 1442 feet apart, even if the great depth of water could have been overcome. It may be remembered that after the disaster of August 29, 1907, the Dominion Government took up the reconstruction of this bridge. A board of three engineers, including myself, was appointed to design and construct the bridge. After some study of the situation, the board decided that the new bridge should be made wider between trusses and designed to carry heavier loads than those originally contemplated; that, further, none of the old steel work could be used to advantage. It also decided to keep the same location. To discuss the reasons for these con¬ clusions would take up too much space in this paper. The final outcome is a double-track span of 1800 feet, with a width of 88 feet between centres of trusses, designed to carry on each track a live load consisting of two E 60 engines 4 placed in any posh 3 London Engineering, vol. xxxix, 1885, P- 336. 4 Theodore Cooper’s specifications. 244 Ralph Modjeski. [J. F. I. tion in a train weighing 5000 pounds per foot so as to produce greatest strains. The old piers were not large enough for the new design and could not, therefore, be used. The centre line of the bridge running north and south the two main piers on each side of the stream will be designated as north pier and south pier respectively. At first the board contemplated building an entirely new pier 57 feet south of the present north pier, and enlarging the foundation of the south pier by sinking additional caissons adjacent to the old caisson. The neces¬ sary span length would then have been 1758 feet, and it was on that length of span that tenders were asked. It developed later, from the experience of sinking the north caisson, Fig. 2. Aqueduct of Gard at Nimes, France. that the method proposed for enlarging the south foundation would not be safe, even if it were practicable, and so an entirely new foundation and pier were decided on for the south shore. The new north pier could not be placed farther out in the river because of the sloping bed rock and great depth of water. The south pier could not be placed on the north, or river, side of the old south pier, because of the old wreckage, so it was placed 64 feet 8 inches south of the old pier, or as close as possible to it. Both new piers being placed 64 feet 8 inches south of the old piers, measured between centres, the new span remains 1800 feet long. The piers are all of granite backed with concrete. There is an increasing tendency now to build everything of concrete. Certainly, concrete is a most convenient material and quite eco- Sept., 1913.J Design of Large Bridges. 245 nomical. When it comes, however, to providing supports for a very important and expensive structure, cut stone masonry should be used in preference to concrete, except for backing. There are many varieties of excellent building stone on this con¬ tinent. I have used granite, some varieties of oolitic limestone, also sandstone, which all show excellent lasting qualities in works constructed many years ago, while concrete presents some un¬ certainties and requires expert care to give good results. Concrete may in ages prove to be as lasting as stone masonry, but as yet we do not know. We know that well-constructed stone masonry will last for centuries. A notable example of this is the great Aqueduct of Gard, built by the Romans in the first century b.c. (Fig. 2). Types of Superstructure .—Having fixed the span lengths of a bridge, the next thing to determine is the type of superstruc¬ ture to be used. The various types usually applied to long spans may be classified as follows: I. Arches (steel). a. Three-hinged. b. Two-hinged. II. Simple spans. III. Cantilever structures. a. With suspended span. b. Without suspended span. IV. Suspension bridges. I have purposely omitted masonry and concrete arches as structures not coming clearly within the scope of this paper. Steel arches have a rational application only where Nature has provided natural abutments, as at Niagara Falls, for instance, or where natural surroundings lend themselves to ornamental construction. Crooked River Arch .—I have recently completed an arch bridge for the Oregon Trunk Railway in the Crooked River Canyon (Fig. 3). It is a two-hinged spandrel braced arch. Three- hinged arches are now seldom used for railway bridges, because they are less rigid than two-hinged arches. They still have a good application in roof trusses which are not subject to heavy and rapidly-moving loads. In several large arch spans the central connection offered considerable difficulties. The reason 246 Ralph Modjeski. [J. F. I. is that the top chords at the centre of a purely two-hinged arch are calculated to have stresses in them, due to dead load and temperature, when the span is riveted up and ready to receive the rolling load. These stresses had to be introduced by powerful jacks, or other means, before the final joint could be riveted up. To avoid this difficulty, I have proceeded as follows in the Crooked River arch. It was assumed that the dead load and temperature stresses at 60 0 F. in the top chord at centre are zero. This being the case, the arch acts as a three-hinged structure under Fig. 3. Crooked River arch. View showing completed bridge. those conditions,—namely, with all dead load in place and at 60 0 F. The span was therefore erected as a three-hinged arch (Figs. 4 and 5), all dead load, or the equivalent, including the decking, was placed thereon, and at a time when the temperature was very nearly 60 0 the centre panel of the top chord was in¬ serted and riveted up. The calculations were simple. The dead-load stresses were calculated as in a three-hinged arch, the temperature and live-load stresses as in a two-hinged arch, and the various results combined. This made the erection very simple and the ultimate distribution of stresses more accurate. A two-hinged spandrel braced arch is probably the best type Sept., 1913.] Design of Large Bridges. 247 to use for railway traffic, where the natural abutments permit of sufficient rise, which will often be the case where the arch type of bridge is a logical solution. This particular type of arch is Fig. 4. Crooked River arch under construction. more rigid and less subject to vibration than the other types of arch, and presents the advantage of easier erection, which can then be simply performed by treating each half as a cantilever 248 Ralph Modjeski. [J. F. 1. arm held back by suitable temporary anchorages until the centre connection is made (Fig. 5). An arch bridge is a somewhat special structure and rarely used for very long spans, except, as I remarked; before, where Nature has provided abutments (Figs. 4 and 6). Fig. 5. Crooked River arch. Temporary anchors and adjustments. Simple Spans. —Twenty-five or thirty years ago the system of truss most favored for long simple spans was a double inter¬ section Pratt truss with parallel chords. Nowadays the type most used is a single intersection Pratt truss with subdivided Fig. 6. Berne, Switzerland. A very graceful highway arch bridge. panels and curved top chord. Fig. 7 shows the former type being replaced by the latter in the Bismarck Bridge (see also Fig. 12). The curved top chord is an element of economy. The single system has also a slight advantage of more definite stresses. It has its disadvantages, such as, for instance, the lack of uni for- Sept., 1913J Design of Large Bridges. 249 mity in deflection, about which I will speak more in detail in con¬ nection with cantilever system. There is no doubt that a bridge composed of simple truss spans is a better bridge than a cantilever system or a suspension design, chiefly because of its rigidity. This rigidity results from the fact that a load placed on one span has no lifting action on the adjacent spans, as in a cantilever system, or on other portions of the same span, as in a suspension bridge. But long simple spans must be erected on falsework or floated into Fig. 7. Bismarck Bridge. Replacing old spans by spans of present type. position. The first method is often inadmissible on account of the necessity of keeping the channel open for navigation, as in the Memphis and Thebes Bridges, or excessive depth of water com¬ bined with navigation requirements, as in the Quebec Bridge, or other local conditions. The floating of a span into position is not only costly but hazardous. It has been successfully performed, but is not always feasible or safe (Figs. 8 and 9). Then, too, generally speaking, a cantilever bridge is more economical for long spans. These considerations often lead to the adoption of a cantilever design in preference to simple spans. A cantilever span 250 Ralph Modjeski [J. F. I Fig. 8. Floating span into position at Louisville, Ky. Fig. 9. Floating span into position at Louisville, Ky Sept., 1913.] Design of Large Bridges. 251 can always be erected without falsework, although the adjacent or anchor spans must generally be erected on falsework. Sometimes simple spans are erected without falsework. Fig. 10 shows the 340-foot simple span over the main channel and Fig. 11 the 230- foot span of the Columbia River at Celilo, Ore., being erected as a cantilever. The length of simple spans has been growing from year to year. It may be remembered that the Cincinnati Southern Bridge at Cincinnati, built in 1877, contains a simple span of 515 Fig. 10. Columbia River Bridge at Celilo, Ore. Main span 340 feet long, being erected by cantilever method. feet. In 1891 George S. Morison built the Cairo Bridge, con¬ taining a span 518 feet in length, single track. The Municipal Bridge in St. Louis has three simple spans of 668 feet in length, no feet high at centre, double track and roadways. The Metropolis Bridge over the Ohio River, if the present design is carried out, will have a simple span 720 feet long, double track. This increase is due largely to the use of higher grade materials, such as nickel or chrome-nickel steel, and to the improvement in shop and field methods. And here we may say a few words about wind forces. In 252 Ralph Modjeski. [J. F. I. small spans the action wind rarely affects the main members of the span, and the wind-bracing used is calculated more to . make the structure rigid against lateral motion under rapidly- Fig. ii. ) * Columbia River Bridge at Celilo, Ore. One of the 230-foot spans being erected by cantilever method. v. moving loads than to take care of actual wind stresses. As the length of span increases, this element of wind becomes more and more important, until in very long spans it may become as Sept., 1913.] Design of Large Bridges. 253 important as the moving load. In a simple span the heaviest members, as well as the greatest height of truss, occur near the centre of the span. In other words, the resistance to wind per lineal foot of truss in a simple span is greatest at the centre of the span, and, owing to the overturning moment due to wind, grows in importance with the height. In a cantilever span the greatest height of truss and the heaviest members are near the piers, hence the greatest resistance to wind per lineal foot of truss is near the piers. This remark is sufficient to explain Fjg. 12. McKinley Bridge across the Mississippi River at St. Louis. One of three 518-dioot spans. why wind stresses are easier to provide for in a cantilever struc¬ ture than they are in a simple span of the same length. I shall return later to wind forces and their importance while discussing provisions made for wind in the Forth and Quebec Bridges. Longest Simple Span .—No hard-and-fast rule can be laid down as to the length at which a simple span becomes uneco¬ nomical as compared with a cantilever span. Generally speaking, considering the present knowledge of materials, a simple span of 700 feet may be taken as the practical economical limit, be¬ yond which it is not advisable to go without a thorough inves¬ tigation and comparison with a cantilever system. Where con- 254 Ralph Modjeski. [J. F. i. clitions require unusual methods of erection this limit may be much lower. For instance, in the Thebes Bridge (Plate II) it was necessary to erect the 671-foot channel span without false¬ work (Figs. 13 and 14). A simple span would have required the addition of a considerable amount of metal, both in the span itself and in the adjacent spans,'to permit of its being erected as. a cantilever; this excess of metal would have been useless after the completion of the bridge, and its cost would have made the Fig. 13. Thebes Bridge. Erecting main span by cantilever method without falsework. bridge more expensive than the adopted cantilever design. This was shown to be true by careful estimates made at the time. General Dimensions of Simple Spans .—In designing long simple spans the following general principles should be observed. The width, centre to centre, of trusses should not be less than one-twentieth of the span, preferably one-eighteenth. In double¬ track spans the width required for clearance generally governs, except in very long spans. The height at centre of span, for a Pratt system of truss with subdivided panels, should be from one-seventh to one-fifth of the length. The table below shows the proportions of the width and height to the length of span in some of the curved top chord bridges built recently: Pier X er Plate I. Pier X PierIX n : ~r . PierYK PierYK PierYT Pier Y" M L 13 Zl PierEZ" vIPlQlAt' PierUT VANCOUVER Pier IE Pier f N.Abulment Columbia River Bridge at.Voncouver, Washington, channel crossing. 3 v 4 vfc^ tso\ c/oc trac/cs Section at center- S pan III~TV r/fi c j/i fycrter ' | fZotr 7}~ - 1 r _ |/Tm7 1 ^ 5/0-6’ 52/-Z’ L - -.-.-.— f J _ 67/' Z7SO-4-’ *5/3-6' the Thebes Bridge f Thebes, I//.) ^JGGQQOGGCKX y4M4\X4\14M/K^ M/iph fYo/er Y/ae 7 'O «3 . 333-9’ T — _——J - e ?r 62 /' - 9597-0 ' 7SO/S' 995-/O’ the Memphis Bridge fMemphis, 7es?n) THE MONONGAHELA BRIDGE (P/i/sburyh, Pa.) the Quebec Bridge New Pcj/?n Quebec, Qoc.J Great Cantilever Bridges Scale in Feet 0 ** Too Soo mo SOpf Sept., 1913-] Design of Large Bridges. 257 simple span is about 700 feet. With the use of certain known alloys of steel of greater strength than medium carbon steel this limit may become as much as 750 feet. Beyond this limit the weight of simple spans becomes so great, in comparison with can¬ tilever spans, that the latter must be considered. A mistaken idea sometimes prevails that the weight of steel in a span increases in proportion to the square of the length. This is, in a measure, true for short spans, say 100 to 300 feet. This ratio of increase, however, is not a constant, but increases with the span. A simple span above 1200 feet in length increases in weight ap¬ proximately as the cube of the length, and this exponent increases more and more rapidly until at about 2000 feet the weight of carbon steel required to carry the weight of such a span and of a moderate live load becomes infinite. For a span built of nickel-steel the weight becomes infinite when the length reaches 2700 feet. Simple spans much below those limits, even if pos¬ sible, would still be very uneconomical until we get down to spans 700 feet or under. Cantilever Spans .—This leads us to cantilever spans (Plates III and IV). I mentioned two types of such spans : one without a suspended span, and the other with a suspended span. A remark¬ able example of a cantilever bridge without a suspended span, which may be called a semi-continuous structure, is the Blackwell’s Island, also called the Queensboro Bridge, in New York. There seems to be no advantage in omitting the suspended span; on the contrary, the structure differs from a true continuous bridge over several supports only by the introduction of a hinge at the centre of the main span which transmits shears but not moments. The vibrations and deflections of each segment are, therefore, trans¬ mitted through those hinges to all the other segments. Further¬ more, since the stresses in such a structure depend on deflections, there is more or less uncertainty in the calculations. I do not wish to be understood as objecting to any type of structure seriously, because of the uncertainty of calculations. In any logical construction the calculations can always be made with sufficient accuracy for the safety of the work. It is only when everything else is equal that determinate stresses should be pre¬ ferred. Let us consider the usual type of cantilever bridges, the one in which two cantilever arms support a suspended span. We 258 Ralph Modjeski. [J. F. I. may assume that in bridges requiring the construction of a canti¬ lever span the length of the main span is usually determined by local conditions. The general dimensions to be fixed by the de¬ signer are, therefore, the length of the suspended span, the length of the anchorage spans, when these are not determined by local conditions, the height of the trusses at various points, the relative distances and positions of trusses to each other. Let us discuss these various dimensions in connection with the new Quebec design (Fig. 15). The Quebec Bridge, with its longest span in the world, has justly attracted much attention among engineers and has naturally elicited comment and criticism. It is acknowledged that a discussion of a scientific subject by pro¬ fessional men is often of greater value than an elaborate paper on this same subject by one individual. If I refer to some of the criticisms, let it be considered as a friendly discussion which may be of value to the profession. General Description of the New Quebec Bridge .—The new Quebec Bridge has been finally designed with two anchor arms 515 feet long, a suspended span 640 feet long, and two cantilever arms 580 feet long. The moving loads finally adopted for the Quebec Bridge are: on each track two Cooper’s Class E-60 en¬ gines, followed or preceded, or followed and preceded, by a train load of 5000 pounds per foot per track. In addition to the actual dead load of the structure, a load of 500 pounds per lineal foot on suspended span and 800 pounds on balance of bridge was allowed for snow. Wind Loads .—The wind loads were taken as follows: A wind load normal to the bridge of 30 pounds per square foot of the exposed surface of two trusses and one and a half times the elevation of the floor (fixed load), and also 30 pounds per square foot on travellers and falsework, etc., during erection. A wind load on the exposed surface of the train of 300 pounds per lineal foot applied nine feet above base of rail (moving load). ’ A wind load parallel with the bridge of 30 pounds per square foot acting on one-half the area assumed for normal wind pressure. In the Forth Bridge the enormous wind load of 56 pounds per square foot was assumed. This load was imposed on the designers by the Board of Trade soon after the Tay Bridge Sept., 1913.] Design of Large Bridges 259 Ralph Modjeski. [J. F. I. 260 disaster. The Tay Bridge was not designed to withstand even d 30-pound pressure. This assumption of a 56-pound wind in the Forth Bridge results in a very large addition of metal in the bottom chords through which the wind stresses are transmitted to the piers. The material in those members is distributed as follows: Dead load. 2282 gross tons Live load . 1022 gross tons Wind load . 2920 gross tons Total . 6224 gross tons The metal here provided for the wind is nearly three times that provided for the live load, and is about 47 per cent, of the total required. In the New Quebec Bridge design the wind pressure is equivalent to about 35 per cent, of the uniform live load near the piers and to about 20 per cent, of the live load near the ends of the cantilever arms. A pressure of 30 pounds, according to German experiments with electric cars, would correspond to a wind of a velocity of over 100 miles per hour. Other experiments made at various times on small surfaces show that a velocity of 85 miles would correspond to a pressure of about 30 pounds. 5 The following formula for wind pressures is generally used: P =kv 2 in which P = pressure per square foot, v- velocity in miles per hour, and k = a coefficient. Eiffel’s two hundred or more experiments show this coeffi¬ cient to vary from 0.0026 to 0.0032, and the average is 0,0030, which he recommends. Trautwine makes k = 0.0050, which seems too high. But, even using the latter, a pressure of 32 pounds would correspond to a “ hurricane ” of a velocity of 80 miles. The German experiments agree with Eiffel’s. Making k = 0.0030, a pressure of 30 pounds would correspond to a velocity of 100 miles per hour, which, according to Trautwine, is a violent hurricane uprooting “ large trees.” 6 See Captain Bixby’s able research on wind pressure experiments in Report of Engineer Officers as to Maximum Span Practicable for Suspen¬ sion Bridges. Forth Bridge Blackwell’s Island Bridge 9 34-£S/g/v C-r or rrtf 3z Apivpr/vcr 3r/nor Co. &GCf/OS7 £ 7 / P/e/T3 OVC/-/A/1 f 3//7GP/7/V3 Or/7CC£/>r££ 3£3/s 30", 8L S 6\4", 7- aphis Bridge "Wore/- Cen/ro/ Spar? i/e Lacing SH@ //S l 5 46 -A /pe ' , P/S 3Zr Vs ' \8’.7S' J ! Z Wefts 46 \ ?p/s ' Z J/c/e P/s 3Z", Vs '} Oi/As Wefts 4P8’. d’.ys' / Weft 46',/fP i Center Weft 4P 8',8~.?i>' ( ZP/s /3", Ps i ^ 4’r4% fr'S Ce ” r&r O/opftrog/7, ■* , 37 i‘, ' 7 e') J 6 Wefts 54', '?* ZS/de P/s 37i 4l J S', 6", 'p/e ] 4Wefts S4'.r 'f>s 4 • 46", '7s | los ■ 4 P/s <9',3p, 'fie‘/ftve/p P/apftragm 6P3'/ Z . 3/z'ps I 7? p/s Oo/s Wefts Wefts Sections or Large Compression Members Scale in Feet 12 3 0 / S 6 J 0 S/r Plate VI. S s 0“ b.fob of& /-d‘ /-S' /-S' /-2 /-//#• / l 2 //* //* Blackwells Island Bridge ZOW&r Ct/Orct Z 5> I/O dnct/Or dr/77 3/og/e tac/ng 3% fie 4 Wets 36 %/z' 4 Side P/s Z3i',fr 8L 3 6"*6*- fs' D/pp/?rapms ,/ZL s 313", % /z ’p/a/e-s . Poob/e lac/ng SVz j 8 WePs 30 % I 836%4%3e- -Plate £3*/z‘t-9 ab! every 7 fee! Thebes Bridge lower Cdorct LC3 -Z C4 Cc/ntde/er dr/n Memphis Bridge Lower Cdord- Centra/ Cpart Beaver Bridge Lower C/7ord L6 / Oo/s Wets 8 Webs 34 % 'fie Z S/de P/s37i‘. ■ 43 6% O’- 'tip 4 Wets 34 % 'fie 4 - 46 'fie \lrs Wets 4 P/s 9’r3b% 'fie ‘f bentj P/ophnogrrr 833te .3/z‘' 3 /e fb P/s Quebec Bridge (LVew Des/gn J Lower Cdord dL /3 dl /4 Quebec Bridge fo/d Oes/gr? J L o/ver Cdord do dr/cdor drrr? Sections of Large Compression Members Scale in Feet s-fb Sept., 1913.] Design of Large Bridges. 277 Quebec Bridge was the elimination of untried features and ex¬ periments. In a span of this length some new features must necessarily be introduced, but they are limited to those only which grow out of the unprecedented length of span. Suspension Bridges .—With the length of the Quebec span of 1800 feet and with the materials now at the disposal of the engineer, the practical limit of cantilever construction has very nearly been reached. In fact, if economy alone is to be consid¬ ered, a cable suspension bridge would have been cheaper for a span of 1800 feet. The cantilever structure presents a greater rigidity under moving load, and this greater rigidity was the determining factor in the decision of the board to adhere to the cantilever type. Tentative plans of the suspension type with wire cables were, however, partly worked out by the board in the way of study. The comparative rigidity of the cantilever system on one hand and the suspension type on the other may be gauged by the deflections at the centre of the span under full load. New Quebec span, total live load. n ^4 inches A cable suspension bridge, trial design—live load only, over- 2 feet A cable suspension bridge—with 120° variation in temperature and full live load—between highest and lowest position about ... • •. 7 feet There are two reasons for the large deflections in suspension bridges: First, the deflection due to variations of temperature in the cables of a suspension span, which in a cantilever span is inappreciable; and, second, the fact that higher unit stresses arc permissible in the wires of the cable than in the members of the cantilever span. The working unit stress in the wires is gen¬ erally taken at from 55,000 to 60,000 pounds, while less than one-third of this is permissible in rolled carbon steel. When a moving load travels on a suspension bridge it subjects it to partial deflections which may be compared to a wave motion. This motion is greatly obviated by the use of deep stiffening trusses. The deeper those trusses are, the smaller will be the partial deflections. It is, therefore, an advantage to make these stiffening trusses as deep as practical considerations will per¬ mit. But, on the other hand, the deeper the truss the more equalizing will it perform and, therefore, the heavier will it 278 Ralph Modjeski. [J. F. 1. have to be. Each particular case must be studied in this respect, taking into consideration the relative importance of the live load which produces these local deflections, to the dead load. A sus¬ pension bridge generally consists of one main span and two side spans. There are two distinct types of side spans—one where these side spans are suspended from the cables, as in the Man¬ hattan Bridge in New York (Fig. 24), and one where they are supported independently of the cables, as in the Williamsburg Fig. 24. Manhattan Bridge, New York. Showing type of suspension bridge with side spans supported from main cables. Bridge in that city (Fig. 25). There are also two types of stiffening trusses for the main span—a continuous truss, as in the Manhattan Bridge, and a truss hinged at one or more points, as in the Brooklyn Bridge. For a bridge for highway and street car traffic, even though interurban trains are to use it, the most suit¬ able type is the one with comparatively shallow stiffening girders continuous over the main span, with side spans suspended from the cables: this because of the absence of concentrated moving loads which would be heavy enough to cause appreciable local deflections. On the other hand, a bridge for railroad use, single- or double-track, should preferably be built with deep stiffening trusses over the centre span, hinged at centre or continuous, with Sept., 1913.] Design of Large Bridges. 279 side spans supported independently of the cables. It is perfectly practicable to build an efficient and economical suspension bridge for railway use if these principles are adhered to. The main parts of a suspension bridge are the cables. These are sometimes replaced by eyebar chains. The longest eyebar suspension bridge is in Budapest and has a span of 981 feet. The longest cable span is 1600 feet, and the one built by Roebling Brothers is still giving excellent service. There is no doubt, therefore, that the wire cable has been successful for long spans. Fig. 25. Williamsburg Bridge, New York. Showing type of suspension bridge with side span supported independently of main cables. It is doubtful if an eyebar chain suspension bridge of 1800- foot span would prove economical as compared with the canti¬ lever type unless some special steel with which we have had little experience be used. The impact from moving load in the chain would be within 10 per cent, of the impact produced in the top chords of the cantilever arms, so that much higher unit stresses in eyebar chain links than those used in eyebar top chords of the cantilevers would not be justified. The allowable working stress in cables is not less than 55> 000 pounds per square inch, while it is not over 30,000 pounds in nickel-steel eyebars, or a little more than one-half. From what was said throughout this paper it is obvious that 28 o Ralph Modjeski. [J. F. i. the longer the span the greater the need of materials of high resistance. For plate girders and short spans ordinary medium steel does very well and is used exclusively; for longer spans, beginning with 400 feet, alloy steel, such as nickel-steel, nickel chrome, vanadium, etc., may be used to advantage, this advan¬ tage increasing with the length of span. The practical limit of cantilever system for known materials is reached at about 2000 feet for a railroad bridge. For longer spans, suspension bridges should be used, and are made possible by the high resistance of wire cables. The practical span limit of a wire cable suspension bridge has been calculated at 4335 feet, assuming a working stress in the cables of 60,000 pounds per square inch. 7 The breaking load of the cables was assumed at 180,000 pounds per square inch. If an alloy wire be used of a still higher resistance the practicable limit will exceed the one given above. The limit of length of a cable alone without any load except its own, stressed at 60,000 pounds per square inch, is 15,160 feet. 7 This assumes the versed sine of the cable to be %. An eyebar chain of alloy steel, such as now in use, should not be stressed beyond 30,000 pounds per square inch. Assum¬ ing this stress and a versed sine of y$, the limit of length of such a chain will be 7010 feet. Hence, the limit of span length of an eyebar chain suspension bridge to carry live loads would be considerably below that of a cable suspension bridge. The suspension design lends itself better to graceful treatment than a cantilever bridge, and may often be preferred for orna¬ mental highway bridges even where a cantilever were to make a cheaper bridge. Considering the purely utilitarian structures, such as the majority of railroad bridges, the present knowledge of metals and its alloys, and the present loadings, we may sum up the various types of large bridges as follows: For spans up to 750 feet.Simple spans. For spans from 650 feet to 2000 feet...Cantilever spans with suspended span. For spans from 1500 feet to 4000 feet..Cable suspension spans. Arch spans have their place only where natural conditions are favorable, or for ornamental bridges. 7 Report of Board of Engineer Officers (U. S. Army) as to Maximum Span Practicable for Suspension Bridges, 1894. Sept., 1913. J Design of Large Bridges. 281 Chain suspension bridges may be used for ornamental high¬ way or city bridges, but for railroad service and for spans below 1500 feet the cantilever is to be preferred as giving a stiffer and generally a cheaper structure. It will be noticed that the above limits overlap. Local con¬ ditions in each particular case will be considered in deciding whether a span between 650 feet and 750 feet should be simple or cantilever, or whether a span between 1500 and 2000 should be a cantilever or a suspension span. Secondary Stresses .—I shall not dwell long on this latest addition to bridge calculations. That secondary stresses exist is a fact. They may be from three sources: First .—Weight of member. wS' econd .—T emperature. Third .—Bending from loads. In the new Quebec design all secondary stresses were cal¬ culated and taken care of, but as a result of tests made by the Quebec Board, the stresses in tension members due to their own weight will be neglected. It is quite possible that if similar tests could be made for other secondary stresses it would be found that the metal adjusts itself to a large extent in such a manner as to reduce the importance of those secondary stresses and their influence on the elastic limit of the member. Personally, I feel there is a tendency at present to overrate the importance of sec¬ ondary stresses. They should, of course, be considered in de¬ signing a structure; it should be the aim of the designer to reduce these secondary stresses to the minimum, but excessive refine¬ ment should be avoided, and unit stresses for direct loads should be made low enough to include these secondary stresses where they may exist. Materials .—The proper selection of materials for a struc¬ ture is an important part of the design. The ordinary com¬ mercial steel will do for rough plate girder work, but for large bridges a metal of higher quality should be used. The metal or alloy should have a high elastic limit, a high ultimate stress, and possess sufficient ductility, which is characterized by the elonga¬ tion and the reduction of the cross-section of specimens tested, to allow its being worked in the shops without fear of injury. Here, perhaps, climatic conditions should be mentioned. Intense cold makes steel brittle. This is shown by the greatly-increased 282 Ralph Modjeski. [J. F. L number of rail fractures during severe winters. The use of high carbon steel should therefore be avoided in northern climates. The behavior of the various alloys in freezing weather needs yet to be studied. In all that precedes I have endeavored to avoid speaking of matters which are usually given in text-books. I have also avoided mathematical deductions, leaving them to better mathe¬ maticians, and I have attempted to deal with this vast subject from a practical standpoint only. When the final report of the Quebec Board is published it will give in detail what I have merely been able to outline. Numerous most interesting tests and mathematical analyses have been made and will be pub¬ lished in the course of events. It will then, perhaps, be realized, even by the members of the engineering profession who had no opportunity to fully design a very long span, that, while it is very easy to draw a diagram and a few of the principal details, it takes months of study, of retracing one’s steps, of tests and calculations to make a complete design and to learn that the preliminary diagrams and sketch details must often be changed entirely to make a practicable and an efficient structure.