Avery Architectural and Fine Arts Library 
 Gift of Seymour B. Durst Old York Library 
 
f 
 
53d Congress, ) 
 3d Session. ) 
 
 SENATE. 
 
 ( Ex. Doo. 
 I No. 12. 
 
 IN THE SENATE OF THE UNITED STATES. 
 
 LETTER 
 
 FROM 
 
 THE SECRETARY OF WAR, 
 
 IN RESPONSE TO 
 
 Senate resolution of December 10, 1894, transmitting the *eport of the 
 Board of Engineers and bridge-building experts, with other information, 
 relative to the subject of a bridge across the Hudson River at New YorJc 
 City. 
 
 December 17, 1894. — Referred to the Committee on Commerce and ordered to be 
 
 printed. 
 
 War Department, 
 Washington, D. C, December 14, 1894. 
 Sir: I have tlie honor to acknowledge the receipt of the following 
 resolution of the United States Senate, dated December 10, 1894: 
 
 Resolved, That the Secretary of War be, and he is hereby, requested to transmit 
 to the Senate the report of the Board of Engineers and bridge-building experts 
 appointed under the act of Congress entitled * 4 An Act to authorize the New York 
 and New Jersey Bridge Companies to construct and maintain a bridge across the 
 Hudson River," between New York City and New Jersey," approved June 7, 1894; 
 and also the report of any board of engineers which may have been appointed by 
 the Secretary of War within the past five years to investigate the subject of a 
 bridge across the Hudson River at New York City; and also to inform the Senate 
 what, if any, action has been taken on either of said reports. 
 
 In reply there is transmitted herewith a printed copy of the report 
 of the Board of Engineers appointed by the President, dated August 
 23, 1894, on page 53 of which will be found attached a copy of the 
 indorsement of the Secretary of War, dated December 12, 1894, 
 approving the report. 
 
 With reference to so much of the resolution as calls for " the report 
 of any board of engineers which may have been appointed by the Sec- 
 retary of War within the past five years to investigate the subject of a 
 bridge across the Hudson River at New York City," there is transmitted 
 d d advance copy of a report of a Board of Engineer Officers convened by 
 an order of the Secretary of War, dated January 27, 1894, to ; ' investi- 
 gate and report their conclusions as to the maximum length of span 
 practicable for suspension bridges, and consistent with an amount of 
 traffic probably sufficient to warrant the expense of construction." This 
 report is now in the hands of the Public Printer, and the appendices 
 are not yet printed. 
 
2 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 In connection with the subject there is forwarded a copy of a joint 
 letter from the president of the New York and New Jersey Bridge Com- 
 pany of New York and the president of the New York and New Jersey 
 Bridge Company of New Jersey, dated November 21, 1894. A copy of 
 the reply of the Secretary of War to this communication, dated Decem- 
 ber 12, 1894, is also herewith. 
 
 Very respectfully, Daniel S. Lamont, 
 
 Secretary of War. 
 
 The President op the United States Senate. 
 
 [The New York and New Jersey Bridge Company, office of the president, 214 Broadway. New York 
 and New Jersey Bridge Company, 80 Broadway, City.] 
 
 New York, November 21, 1894. 
 
 Dear Sir : The New York and New Jersey Bridge Companies, after 
 a careful consideration of the conditions involved in the construction 
 of a bridge crossing the North Biver between Fifty-ninth and Sixty- 
 ninth streets, have become convinced that, in order to perfect a sound 
 financial basis for the enterprise, it is essential that a guaranteed esti- 
 mate of cost should be obtained from parties whose reputation and 
 experience in the construction of large works would insure the accuracy 
 of their estimates and the practicability of the plans selected by them. 
 
 In accordance with this view, the New York and New Jersey Bridge 
 Companies have entered into a contract with the Union Bridge Com- 
 pany, whereby the Union Bridge Company are to furnish plans and 
 construct a cantilever railroad bridge across the Hudson Biver, having 
 a main span not exceeding 2,000 feet, at a total cost guaranteed by the 
 Union Bridge Company not to exceed $22,000,000, including interest 
 charges growing due during construction, and to render such assist- 
 ance as may be in their power in securing the necessary capital for the 
 completion of the bridge. 
 
 This contract is of course expressed to be conditional upon the 
 approval by the honorable Secretary of War of the plan for a canti- 
 lever bridge having a main span not exceeding 2,000 feet. 
 
 Under this contract the Union Bridge Company has presented gen- 
 eral plans and estimates for a u cantilever" bridge, having a span of 
 2,000 feet in the clear, and is prepared to execute the work at a price 
 which it is believed will prove remunerative to the capital invested. 
 
 These plans and estimates, together with the reports accompanying 
 the same, have been accepted and adopted by the New York and New 
 Jersey Bridge Companies, and with your kind permission will be pre- 
 sented for your consideration. 
 
 The New York and New Jersey Bridge Companies are satisfied that 
 a "suspension" bridge spanning the North River without a pier would 
 involve such elements of uncertainty as regards first cost, novelty in 
 its magnitude as a hitherto untried engineering feat and time of con- 
 struction, to say nothing of the well-founded prejudice against the 
 "suspension" principle for railroad purposes, as would render the 
 enterprise impracticable from a financial standpoint. 
 
 On the other hand, we firmly believe that the "cantilever" plan pre- 
 sented by the Union Bridge Company can be executed within practi- 
 cable limits of time and cost, and that when finished the bridge will be 
 capable of fully meeting the demands of the heaviest railroad traffic. 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 3 
 
 In addition to the records contained in the printed report of the 
 Board constituted under the act, a further report of Mr. Macdonald, 
 approved by us, is herewith presented, giving in detail some of our 
 reasons for considering the "suspension" bridge impracticable. 
 
 In view of the foregoing facts, we respectfully request that the canti- 
 lever bridge, with a main span not exceeding two thousand feet, upon 
 the plans prepared by the Union Bridge Company, may receive your 
 favorable consideration and decision. 
 
 Respectfully submitted. 
 
 John B. Kerr, 
 Presdt. of New York and New Jersey Bridge Go. of Neic York. 
 
 H. M. Haar, 
 
 Presdt. of New York and New Jersey Bridge Co. of New Jersey. 
 
 The Secretary of War, 
 
 Washington, D. G. 
 
 War Department, 
 Washington, December 12, 1894. 
 
 Gentle:\ien : I beg to acknowledge receipt of your letter of the 21st 
 ultimo, by which it appears that your company has entered into a pro- 
 visional contract with the Union Bridge Company for the construction 
 of a cantilever bridge between Xew York and Xew Jersey on plans 
 involving the erection of a pier within the lines of the navigable waters 
 of the harbor of Xew York. 
 
 The present Congress, at its first session, passed an act which would 
 have permitted the construction of a bridge such as you now propose. 
 After much consideration and a public hearing, where representations 
 of the commercial organizations speaking for the vast interests of the 
 commerce of that port affecting all sections of the country were sub- 
 mitted and the public demands for quick and convenient transit over 
 the river at this point were expressed, that bill failed to receive 
 Executive sanction, and was returned to the House of Representatives 
 where it originated. 
 
 The reasons for disapproval were stated in part in the veto message, 
 as follows: 
 
 This bill authorizes the construction of a bridge over the North River between the 
 States of New York and New Jersey, the terminus of which in the city of New York 
 shall not be below Sixty-sixth street. It contemplates the construction of a bridge 
 upon piers placed in the river ; no mention is made of a single span crossing the entire 
 river, nor is there anything in the bill indicating that it was within the intention of 
 the Congress that there should be a bridge built without piers. I am by no means 
 certain that the Secretary of War, who is invested by the terms of the bill with con- 
 siderable discretion so far as the plans for the structure are concerned, would have 
 the right to exact of the promoters of this enterprise the erection of a bridge span- 
 ning the entire river. 
 
 Much objection has been made to the location of any piers in the river for the reason 
 that they would seriously interfere with the commerce which seeks the port of New 
 York through that channel. It is certainly very questionable whether piers should 
 be permitted at all in the North River at the point designated for the location of 
 this bridge. It seems absolutely certain that within a few years a great volume 
 of shipping will exteud to that location which will be seriously embarrassed by such 
 obstructions. 
 
 I appreciate fully the importance of securing some means by which railroad traffic 
 can cross the river, and no one can fail to realize the serious inconvenience to travel 
 caused by lack of facilities of that character. At the same time it is a plain dictate 
 of wisdom and expediency that the commerce of this river be not unnecessarily inter- 
 fered with by bridges, or in any other manner. 
 
4 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 Engineers whose judgment upon the matter can not be questioned, including the 
 engineer of the company proposing to build this bridge, have expressed the opinion 
 that the entire river can be spanned safely and effectively by a suspension bridge, 
 or a construction not needing the use of piers. 
 
 The company to which the permission to bridge the river is granted in the bill 
 under consideration was created by virtue of an act of the legislature of the State 
 of New York, which became a law, by reason of the failure of the governor to either 
 approve or veto the same, on the 30th day of April, 1890. It may be safely assumed 
 that the members of the legislature which passed this law knew what was necessary 
 for the protection of the commerce of the city of New York, and had informed, 
 themselves concerning the plan of a bridge that should be built in view of all the 
 interests concerned. By paragraph 24 of the law creating this company it is pro- 
 vided that "the said bridge shall be constructed with a single span over the entire 
 river between towers or piers located between the span and the existing pier-head 
 lines in either State," and " that no pier or tower or other obstruction of a permanent 
 character shall be placed or built in the river between said towers or piers under 
 this act." 
 
 In view of such professional judgment, and considering the interests which would 
 be interfered with by the location of piers in the river, and having due regard to 
 the judgment of the legislature of the State of New York, it seems to me that a 
 plan necessitating the use of piers in the bed of the river should be avoided. The 
 question of increased expense of construction or the compromise of conflicting 
 interests should not outweigh the other important considerations involved. 
 
 This message was referred to the Committee on Interstate and For 
 eign Commerce, and subsequently a bill was introduced "intended to 
 conform to and meet the objections urged by the President." In pre- 
 senting this substitute bill to the favorable consideration of Congress 
 that committee submitted a report which I am justified in assuming 
 clearly shows the purpose of Congress in its subsequent legislation 
 upon this subject, and from which I make the following extracts: 
 
 The main objection urged by the President to the bill heretofore passed was that 
 it allowed a bridge to be built with a pier in the river. * * * 
 
 The bill as now presented directs the President to create a board of five competent, 
 practical, disinterested, expert bridge engineers, of whom one shall be a member of 
 the Corps of Engineers, United States Army, and the others from civil life, who 
 shall, in the time stated, meet, investigate and examine into, determine and decide, at 
 what length of span not less than two thousand feet a safe, practicable railroad bridge 
 can be constructed, and make their determination as to the length of the span 
 final. As this is the chief difference between the executive and legislative depart- 
 ments in the passage of a bill to bridge the Hudson River, which is not only a 
 question of State but of national importance, there can be no better plan devised 
 or determined, at what span the river can be safely bridged, than by a board of the 
 character described in the act and appointed under the authority of the President. 
 
 Bridge-building is a science which has advanced probably as much as any other 
 within the last twenty years. What was impracticable twenty years ago is practi- 
 cable now; what could not be safely done twenty years ago may be safely done now, 
 and there is no more accurate way of ascertaining what can be scientifically done, 
 from a practical standpoint, than the one proposed in the bill for ascertaining what 
 length of span can be made, taking into consideration all the possibilities of the 
 weight and strain on the steel of which it is to be constructed. It is far safer, in 
 the opinion of the committee, to leave this important question to disinterested expert 
 bridge- builders to be selected by the President than even to the opinion of the engi- 
 neers of the War Department, however able they may be in other branches or other 
 lines of engineering. These questions will be familiar to the commission. They have 
 dealt with many such problems, having in mind not only the possibility of length of 
 span, but also the obstruction which may occur to the navigation of the river. And 
 their opinion is certainly, when disinterestedly expressed, the most valuable verdict 
 which can be finally rendered in settlement of a dispute in a matter of this character. 
 
 It will be seen that * * * all plans for the construction of the bridge as to 
 length of span must conform to the decision of this board. 
 
 The committee are satisfied that if, in the opinion of the board of competent engi- 
 neers established under the act, a safe and practicable bridge can be built of a greater 
 length than 2,000 feet, as shown in the plans of the bridge companies exhibited to 
 the committee, they will, as they must, adopt it. 
 
 They do not believe that any better or more reliable way can be found than to 
 leave it to a settlement by a board of competent engineers, selected by the President 
 himself, and sitting under the direction of the Secretary of War. 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 5 
 
 The act, as thus presented, was passed by both Houses, and was 
 approved by the President June 7, 1894. Under its provisions the 
 President appointed Maj. Charles W. Raymond, of the Corps of Engi- 
 neers, United States Army; Prof. William H. Burr, of Columbia Col- 
 lege ; G. Bouscaren, of Cincinnati ; George S. Morison, of Chicago ; and 
 Theodore Cooper, of Xew York, "as a board of competent, disinterested 
 engineers to examine and recommend what length of span not less than 
 two thousand feet would be safe and practicable for a railroad bridge 
 to be constructed over said river." After a thorough investigation 
 covering every phase of the problem this Commission submitted an 
 exhaustive report, signed by all of its members, which closed with the 
 following recommendation : 
 
 The only subject referred to your Board is "to recommend what length of span 
 not less than 2,000 feet would be safe and practicable for a railroad bridge to be con- 
 structed over the Hudson River between Fifty-ninth and Sixty-ninth streets." A 
 single span from pier-head to pier-head, built on either the cantilever or suspension 
 principle, would be safe. The estimated cost of the 3,100-foot clear-span cantilever 
 being about twice that of the shorter span, your Board consider themselves justified 
 in pronouncing it impracticable on financial grounds. As the cost of the single- 
 span suspension bridge is at most (not more than) one-third greater than that of 
 the 2,000 cantilever, your Board are unable to say that such greater cost is enough 
 to render the suspension bridge impracticable. 
 
 The Board have reached this conclusion after careful study, and they have thought 
 it best to give the full course of reasoning which they have followed. They feel 
 that the contingency attending the construction of the deep-river foundation of the 
 cantilever bridge, even waiving the absolute necessity of carrying this foundation 
 to rock, is enough to balance a part of the greater cost of the suspension bridge. 
 
 The conclusion of this Board is that of a Board of Bridge Engineers acting in a 
 professional capacity. While from such professional view they must pronounce 
 the suspension bridge practicable, they do not in this conclusion give an opinion on 
 the financial practicability and merit of either plan. 
 
 This finding is confirmed and strengthened by the unanimous report 
 of a Board of Officers of the Corps of Engineers of the United States 
 Army, appointed prior to the legislative provision for a Board, with 
 instructions to ''investigate and report their conclusions as to the 
 maximum length of span practicable for suspension bridges and con- 
 sistent with an amount of traffic probably sufficient to warrant the 
 expense of construction." 
 
 The conclusion of this Board, which is indorsed by the Chief of 
 Engineers of the United States Army, has been reported to me as 
 follows : 
 
 The final plans for a work of such magnitude would only be adopted after the 
 most extended tbeoretical and experimental investigations, and the estimated cost 
 would undoubtedly be much reduced by such studies. Assuming the most favorable 
 location and the most competent engineering management, the Board believe that 
 $23,000,000 is a reasonable estimate for a six-track railroad suspension bridge 3,200 
 feet long, and they consider the amount of traffic which such a bridge would accom- 
 modate sufficient to warrant the expense of construction. They believe, however, 
 that the bridge should be so constructed that its capacity can be readily increased, 
 and with the suspension system this can be provided for by giving suitable dimen- 
 sions to the towers and anchorages. 
 
 If sufficient inducements were offered to competent engineers to prepare competi- 
 tive designs and estimates for a single-span bridge at this locality, the Hoard do not 
 doubt that perfectly satisfactory plans would be obtained within the limit of co^t of 
 the estimate given above. 
 
 Briefly stated, the finding of the engineers is that both the 2,000-foot 
 cantilever bridge wnich requires a pier in the river, and the 3,100-foot 
 in the clear suspension bridge without a center pier are safe and not 
 impracticable as to cost, the estimates being as follows: 
 
G 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 PIER BRIDGE (CANTILEVER) SIX TRACKS. 
 [Clear span, 2,000 feet.] 
 
 Total length, 4,320 feet; moving load, 3,000 pounds per foot of track. $25, 443, 000 
 Total length, including necessary viaduct, making it equal in length 
 
 to a suspension bridge having a clear span of 3,200 feet, 5,600 feet; 
 
 moving load, 3,000 pounds per foot of track 26, 723, 000 
 
 SUSPENSION BRIDGE, SIX TRACKS. 
 
 [Clear span, 3,200 feet; total length, 5,600 feet.] 
 
 Moving load, 3,000 pounds per foot of track $35, 367, 671 
 
 Moving load, 1,500 pounds per foot of track; strain on cables, 60,000 
 
 pounds per square inch 30, 743, 000 
 
 Moving load, 1,500 pounds per foot of track; strain on cables, 50,000 
 
 pounds per square inch 31, 671, 000 
 
 Location near Sixty-ninth street, moving load, 3,000 pounds per foot of 
 
 track 31, 917, 671 
 
 Location near Sixty-ninth street, moving load, 1,500 pounds per foot of 
 
 track 27,771,000 
 
 Location near Sixty-ninth street (Army Engineer Board), moving load, 
 
 1,500 pounds per foot of track 23, 000, 000 
 
 And I am further assured by members of the Commission that the 
 time required for construction would be approximately the same. 
 
 In view, therefore, of these facts and findings, and of the very serious 
 objections to a pier in the harbor, with its attendant delay and constant 
 menace to navigation, I am constrained to require that the bridge to be 
 built by the New York and New Jersey Bridge Companies across the 
 Hudson Eiver shall have a single span between the pier lines of the 
 harbor of New York. 
 
 While I do not undertake w say that the objection of an obstruction 
 in the harbor is sufficiently grave to prohibit the construction of a pier 
 bridge, were a suspension bridge impracticable, it is a matter for public 
 congratulation that a scientific investigation of the subject by skilled 
 and experienced engineers determines that both the traffic on the river 
 as well as that over it can be accommodated without interference and 
 the rights of all protected with only such an increase of expense, if 
 any, as is clearly demanded by the conceded advantages to follow. 
 Very respectfully, 
 
 Daniel S. Lamont, 
 
 Secretary of War. 
 
 Mr. John B. Kerr, 
 
 Presdt. of New York and New Jersey Bridge Co. of Neiv York. 
 and 
 
 Mr. H. M. Haar, 
 
 Presdt. of New York and New Jersey Bridge Co. of New Jersey, 
 
Office of the Chief of Engineers, 
 
 United States Army, 
 Washington, D. C, October 35, 1894. 
 Sir: I have the honor to submit herewith a printed copy of the 
 report of the Board of Engineer Officers convened in accordance with 
 your order, dated January :27, 1894, to investigate and report their con- 
 clusions as to the maximum length of span practicable for suspension 
 bridges. The report is a very valuable one, shows careful research, 
 and I approve and concur in its conclusions. 
 
 Very respectfully, your obedient servant, 
 
 Thos. Lincoln Casey, 
 Brig. Gen., Chief of Engineers. 
 
 Hon. Daniel S. Lamont, 
 
 Secretary of War. 
 * 7 
 
REPORT 
 
 OF 
 
 BOARD OF ENGINEER OFFICERS TO MAKE INVESTI- 
 GATIONS OF CERTAIN BRIDGES. 
 
 United States Engineer Office, 
 Philadelphia, Pa., September 29, 1894. 
 
 General : The Board of Officers of the Corps of Engineers appointed 
 by Special Orders No. 5, current series, Headquarters Corps of Engi- 
 neers, U. S. Army, January 29, 1894, to make investigations as to cer- 
 tain bridges, in accordance with instructions of the Secretary of War, 
 have the honor to submit the following report: 
 
 The instructions of the Board are contained in a letter from the Sec- 
 retary of War to the Chief of Engineers, dated January 27, 1894, and 
 in the indorsement of the Chief of Engineers thereon, dated January 
 30, 1894. Copies of this letter and the orders convening the Board are 
 appended hereto. 
 
 The Secretary of War, in his letter of January 27, 1894, remarks that, 
 " in view of the importance of questions arising in this Department in 
 connection wi&li the building of bridges over navigable streams, it is 
 essential that it should be possessed of accurate and full information 
 necessary to their intelligent and proper determination and directs 
 the formation of u a Board of Officers of the Engineer Corps, who shall 
 investigate and report their conclusions as to the maximum length of 
 span practicable for suspension bridges and consistent with an amount 
 of traffic probably sufficient to warrant the expense of construction." 
 
 The indorsement of the Chief of Engineers of January 30, 1894, directs 
 the Board to include in its investigations u strength of materials, loads, 
 foundations, wind pressure, oscillations, and bracing." 
 
 The Board convened at Kew York City on February 13, 1894, and 
 remained in session until February 15, 1894, when it adjourned to 
 collect information. The Board held a session at Philadelphia, Pa., 
 from March 6 to 10, 1894. An extended preliminary investigation of 
 the subject under consideration had already been made when a Board 
 of expert bridge engineers was appointed by the President, on June 
 15. 1894, under the provisions of the act approved June 7. 1894. to 
 recommend what length of span, not less than 2,000 feet, would be 
 safe and practicable for a railroad bridge to be constructed across 
 the Hudson Biver between Xew York City and the State of Xew 
 Jersey. The Xew tork Board was composed of five engineers, four 
 of whom were civil engineers of long and varied experience in the 
 designing and construction of bridges and of the highest profes- 
 
 9 
 
10 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 sional standing. It was therefore considered desirable to delay the 
 completion of this report nntil the determinations of the New York 
 Board could be ascertained and studied. The present Board has 
 derived much assistance from the published report of the New York 
 Board, as will be indicated below. At the last session, which was 
 held at Philadelphia from September 20 to September 29, 1894, this 
 report was unanimously adopted. 
 
 The question of the maximum practicable span may be investigated 
 as a purely engineering problem, when certain preliminary conditions 
 are established. The bridge will doubtless be a railroad bridge, since 
 with the largest span the traffic capacity would not otherwise justify 
 the cost. This assumed, the width, must be at least sufficient to accom- 
 modate a double track. The number of double tracks required must 
 be established so as to give a traffic capacity "probably sufficient to 
 warrant the expense of construction." 
 
 The New York and Brooklyn bridge, the longest suspension bridge 
 yet constructed, consists in reality of two similar bridges suspended 
 side by side and braced together, the promenade being supported 
 between the bridges as an extra weight on the interior cables. Follow- 
 ing this idea, the Board in its preliminary investigation assumed a 
 double- track railroad bridge as the unit bridge, bracing together side 
 by side as many such bridges as were considered necessary to accom- 
 modate the traffic contemplated. The engineering problem was thus 
 limited to the question of determining the maximum span for a double- 
 track railroad bridge. It was found, however, that there are many 
 serious practical objections to such an arrangement in a long-span 
 bridge carrying very heavy loads. In this investigation, therefore, the 
 loads will be assumed to be supported by only two sets of cables, one 
 on each side of the bridge; an arrangement whioh was adopted as a 
 basis of estimate by the New York Board. 
 
 In the various projects for long-span bridges across the Hudson Biver 
 at New York the least traffic capacity assumed was six tracks, and the 
 New York Board adopted this number of tracks in its investigations. 
 In this report, therefore, it is proposed to first consider the question of 
 the maximum span for a six-track railway bridge as an engineering 
 problem, after which the relations between span, traffic, and cost of 
 construction will receive such investigation as the nature of the sub- 
 ject will permit. 
 
 Since much of the information with reference to strength of materials, 
 loads, etc., collected by the Board as directed by the Chief of Engi- 
 neers, is necessary for the proper investigation of the question of the 
 practical maximum span, this part of the subject will first receive 
 attention. 
 
 STRENGTH OF MATERIALS. 
 
 The supporting cables of a suspension bridge of long span are made 
 of steel. They are either chains composed of connected links or cables 
 formed of parallel wires or twisted wire ropes. To obtain the longest 
 span possible the weight of the cable must be a minimum as compared 
 with its carrying capacity. The connections of a series of links add 
 from 20 to 25 per cent to the dead weight of the chain, while in the 
 wire cable the connections add, at most, only 2 or 3 per cent. More- 
 over, steel in the form of wire has a minimum strength more than double 
 its maximum strength in the form of bars suitable for the construction 
 of a suspension chain. A link chain, therefore, will weigh about two 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 11 
 
 and one-half times as much as a wire cable of equal carrying capacity; 
 or in other words, a wire cable can be stretched about two and one-half 
 times as far as a steel chain before being broken, other conditions 
 being the same in both cases. Moreover, it is stated by Melan* that 
 considerable bending moments are sometimes produced by the friction 
 between the links of chains, but the effects due to the stiffness of cables 
 are so small that they may be neglected. It is therefore assumed that 
 the cables are made of steel wires laid parallel to each other. 
 
 The strength of the suspension cable will depend upon the tensile 
 strength of the steel employed in its construction and upon the num- 
 ber of wires it contains. The wire employed in the cables of the New 
 York and Brooklyn bridge had a tensile strength of 170,000 pounds 
 per square inch, and the cables were originally designed to contain 
 each 6,188 wires of No. 7, B. W. G., but as some heavier wires were 
 introduced during construction, the actual number of wires was only 
 5,100. These are the largest cables made up to the present time, hav- 
 ing a diameter of 15| inches. The cables of the Cincinnati suspen- 
 sion bridge have a diameter of 12 inches and each contains 5,200 No. 
 9 wires. 
 
 There is a practical limit to the number of wires which can be 
 united in a cable, since as the number increases it becomes more and 
 more difficult to adjust the Avires so that each will bear its due propor- 
 tion of stress under the varying conditions of temperature and load- 
 ing. No unusual difficulties, hoAvever, were encountered in the manu- 
 facture of the cables above referred to, but it is believed that with the 
 method employed for making the cables of the East Eiver bridge the 
 practical limit of the number of wires was very nearly, if not quite, 
 attained. With improved methods the construction of much larger 
 cables might be found practicable. An increase in the size of the 
 wire does not materially increase the difficulty of construction. No. 3 
 wire having a tensile strength of 180,000 pounds per square inch, can 
 now be readily obtained at a reasonable price. Indeed steel wire much 
 stronger than tnis can be obtained (up to more than 300,000 pounds 
 per square inch) but its present cost would prohibit its employment. 
 
 The Board therefore assumes for the purposes of this investigation 
 a suspension cable formed of 6,000 parallel steel wires, No. 3, B. W. 
 G. The area of its cross-section will be 1316 square inches without 
 wrapping, and its breaking tensile strength will be 56,880,000 pounds, 
 or 1:8,410 tons. With a safety factor of 3, Avhich was adopted by the 
 New York Board, and will be adopted in this investigation for reasons 
 to be given hereafter, the working strength of this cable will be 
 18,900,000 pounds or 9,180 tons. Its diameter with wrapping will be 
 21i inches. The New York Board have adopted a cable of about this 
 size and strength in their estimates. 
 
 The total cable strength available for the support of the bridge 
 depends upon the number of cables which can be practically combined 
 as a single cable system on one side of the bridge. If many cables are 
 employed it becomes difficult to distribute the strains among them so 
 that each shall carry its proportionate load under the varying condi- 
 tions of temperature and traffic. It is not easy to decide what is the 
 practical limit of the number of cables to be assembled together. 
 Where parallel wire cables are used they must be sufficiently separated 
 horizontally and vertically to give room for the operation of the wire- 
 
 *HaiKlbucb der Ingenieurwissenschaften. Band n. Der Briickenbau — J. Melan, 
 Leipzig, 1888. 
 
12 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 wrapping machine and this requires intervals of at least 3 feet during 
 construction. 
 
 The cables may cross the saddles on top of the towers side by side or 
 they may be arranged in one or more vertical or nearly vertical planes. 
 In the first case the cradling of the cables in converging planes (which 
 is desirable for lateral stability), requires considerable intervals 
 between the saddles. In the investigations of the New York Board an 
 interval of 20 feet was found to be necessary for such an arrangement. 
 But the cables on one side of the bridge may also be arranged side by 
 side in parallel inclined planes and held the same distance apart 
 throughout their length by irou separators between the suspender 
 clamps, in which case the saddles on the towers would be closer together. 
 Still the number of cables suspended on each side can not be made very 
 large without increasing the dimensions of the towers and the piers 
 supporting them far beyond the requirements of the roadway and sus- 
 pended loads. 
 
 The vertical arrangement of the cables (or a combination of vertical 
 and horizontal arrangements) certainly presents some very decided 
 advantages. It requires less width at the top of the towers, and a large 
 part of the stiffening of the bridge may be obtained by trussing the 
 cables in a manner which will be again referred to. Moreover, with 
 this arrangement the towers can be so constructed that new cables can 
 be readily added to meet future demands for increased traffic capacity. 
 This method, however, is not so simple as the other, and with large 
 loads and cables involves mechanical difficulties which can be properly 
 dealt with only after an extended investigation of the problem as a 
 special case. In this general investigation the Board consider it best 
 to adopt the simpler arrangement, as has been done by the New York 
 Board. Whatever arrangement is adopted, the Board are of the opinion 
 that it would not be found convenient to work more than eight cables 
 together as one cable system. For the purposes of this investigation, it 
 is therefore assumed that the suspension bridge of maximum span is 
 supported by sixteen 21}-inch cables. The following list giving the 
 arrangements employed in a number of important bridges, may be of 
 interest in this connection : 
 
 New York and Brooklyn Bridge, 1,595.5 feet span, has one 15|-mch 
 cable on each side. 
 
 Niagara Bridge, 821.3 feet span, two 10-inch cables, one vertically 
 over the other. 
 
 Wheeling Bridge, 1,010 feet span, two 8-inch cables, side by side. 
 Fairmount Bridge, 550 feet span, seven cables, 6 side by side and 1 
 above. 
 
 Freiberg Bridge, Switzerland, 870 feet span, three cables, 2 side by 
 side and 1 above. 
 
 Dordogne Bridge, France, 350 feet span, three cables, side by side. 
 
 Niagara Bridge, at Lewistown, 1,400 feet span, had four cables side 
 by side. 
 
 Menai Bridge, 600 feet span, four chains in the same vertical plane. 
 Tweed Bridge, Berwick, 450 feet span, three chains in the same ver- 
 tical plane. 
 
 Tersing Bridge, over the Maas, two chains, one over the other, 
 Bridge Yoconilans, St. Honorine, two chains, one over the other. 
 La Roche Bernard Bridge, over the Yilaine, 050 feet span, two cables, 
 side by side. 
 
 Lambeth Bridge, England, two cables, side by side. 
 
 Donau Bridge, Pesth, 600 feet span, two chains, one over the other. 
 
 Moldau Bridge, Prague, four chains in pairs, over each other. 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 13 
 
 LOADS. 
 
 The total load supported by the bridge will consist of two parts, viz, 
 the live load or weight of the passing traffic and the dead load or 
 weight of the structure. It will be convenient to consider the load 
 under these two heads. 
 
 1. Live load. — In another part of this report the difference in the 
 character of the action of the live load upon a structure in stable 
 equilibrium having a certain degree of flexibility from that of its action 
 upon a more rigid structure in unstable equilibrium will receive due 
 consideration. For the present we will only determine the magnitude 
 of the live load. The live load per linear foot of span will be repre- 
 sented by q. 
 
 The greatest static effect upon the cable will be produced by the 
 maximum load; that is, when the whole platform from tower to tower 
 is covered with the heaviest possible railroad trains. 
 
 A suspension railroad bridge of very long span will as a rule be 
 built only over a wide river or estuary navigable by ocean craft and 
 therefore requiring a great height of the bridge above the water. To 
 limit the expense of the shore extensions the approaches must be 
 given as steep a grade as is admissible for a railroad bridge. It is 
 therefore assumed that the approaches will have a grade of 1 per cent. 
 
 The weight of a railroad train passing over the bridge need not be 
 considered as any greater than that which the heaviest freight loco- 
 motive is capable of hauling up a 1 per cent grade. From a list pub- 
 lished by the Baldwin Locomotive Works it appears that exceptionally 
 heavy locomotives are built with 170,000 pounds on the drivers and a 
 totafweight of 192,500 pounds. The Baldwin Works allow 9 tons for 
 each 1,000 pounds on the drivers as the maximum efficiency on a grade of 
 1 per cent. This extra heavy locomotive can therefore pull up on the 
 bridge 1,530 tons including its own weight. Subtracting 96 tons for 
 the weight of Jhe locomotive, we have for the weight of the train, 1,434 
 tons. This is equal to 41 hopper-bottom gondola cars each 27 feet 2 
 inches long and weighing 35 tons. The length of the engine and ten- 
 der being 54 feet, the total length of the train will be 1,168 feet, and 
 the weight per linear foot of track will be 2,620 pounds, equal to 1.31 
 tons. If we suppose all 6 tracks to be loaded from end to end with such 
 trains, the live load per linear foot will be 15,720 pounds, equal to 7.86 
 tons. 
 
 Any such loading as this, however, is so extremely improbable as to 
 be a practical impossibility; indeed, at the height above water level at 
 which such abridge must be carried, the transportation of passengers, 
 and not of freight, must be the main consideration. A purely freight 
 traffic would in no conceivable location require six tracks over a bridge 
 of very long span. Such a number of tracks would only be justified by 
 the location of the bridge near a very large city and by a large pas- 
 senger traffic. The trains passing over such a bridge would undoubt- 
 edly be controlled on the block system and not more than one train 
 on each track would be allowed upon the bridge at the same rime. If 
 the stiffening girders could do their full duty the weights upon the 
 bridge would be uniformlv distributed and the live load per linear foot 
 
 ■ 3,060,000 n 18,360,000 = m a . ± . 
 
 would be ^ — X 6 = — — ^ pounds. Tbe distribution, how- 
 ever, is not perfectly uniform, and there are occasionally other causes 
 which produce an increase in local stresses. The Board consider it best 
 to add 50 per cent to this estimate to cover these uncertainties. In 
 
14 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 computing the cable strength, therefore, the adopted value of the live 
 load will be — 
 
 27,540,000 
 g= L 
 
 The live load assumed for the Niagara Suspension Bridge, which has 
 a span of 800 feet, is 350 tons in a length of 450 feet of single track, 
 which is equivalent to 1,600 pounds per linear foot of train, or less 
 than 1,000 pounds per linear foot of the entire span, with a factor of 
 safety of 4.41 in the cables and 4.0 in the stiffening girders.* The 
 bridge, however, safely carries heavier trains in daily operation. 
 
 The largest existing railroad bridge is the Forth bridge, in Scotland. 
 It has 2 tracks and 2 spans of 1,700 feet each. It was tested with 2 
 heavy trains side by side, each 1,000 feet long and weighing 900 tons. 
 Each train was drawn by 2 locomotives each weighing 72 tons. This 
 load was equivalent to 1,800 pounds per linear foot of track, or 3,000 
 pounds per linear foot of span. These were considered extra heavy 
 train loads, very seldom occurring in actual operation on English roads.t 
 
 Making allowance for the heavier train loads of American railroads, 
 it will be seen that 3,000 pounds per linear foot of track for a length of 
 1,500 feet, considered as distributed over the bridge from tower to 
 tower (which is the value given by our formula), is an exceedingly safe 
 assumption of the live load for a very long bridge in which the span 
 exceeds the length of the maximum train. This value agrees very 
 nearly with that assumed by the New York Board in its estimate for a 
 u lighter structure." 
 
 It is very evident that the assumed live load per unit of track ought 
 * to diminish with the number of tracks and with the length of span. A 
 single-track bridge of short span is strained nearly to its maximum 
 every time a train goes over it. A 6-track bridge is strained to its 
 maximum only when 6 maximum trains are abreast of each other; and 
 when the span exceeds the maximum train length the maximum stress 
 ought never to occur. 
 
 2. Bead load. — This produces at all times constant strains in the 
 members of the bridge. It is composed of the weights of the following 
 parts: The suspension cables with their wrapping, the platform, the 
 stiffening girders, the wind and sway bracing, and the suspenders. 
 The weights of these parts per linear foot of span will be represented 
 as follows : Cables = w ; cable wrapping = w ; platform =p Y .; girders = 
 p 2 ; bracing = p 3 ; suspenders =p 4 . 
 
 (1) WeU/ht of the suspension cables. — The weight of a cable formed of 
 6,000 parallel steel wires, No. 3, B. W. Gr., having a diameter of 21^ 
 inches, without wrapping, will be 1,075 pounds, or 0.538 tons per run- 
 ning foot. If we assume 16 cables for the support of the entire bridge, 
 the total cable weight per linear foot will be w' = 17,200 pounds = 
 8.6 tons; and w = 17,917 = 8.959 tons. 
 
 (2) Cable tvrapping. — The cable will be wrapped with iron wire of 
 No. 9, B. W. Gr. The weight of this wrapping will be 26 pounds per 
 linear foot, and for 16 cables, 416 pounds. The weight of wrapping per 
 linear foot of span will therefore be tc = 433 pounds. 
 
 It will be found convenient for the purposes of this investigation to 
 know the relation between the weight of the cable per linear foot of 
 horizontal span (w) and its weight per foot measured in the direction 
 
 * Proceedings Am. Soc. C. E., Vol. x, p. 195. 
 t Record of the Forth Bridge, p. 64. 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 15 
 
 of its axis (w f ). The cable curve will be approximately a parabola, 
 and its approximate length will be fl + -jgp J L,in which L is the hori- 
 zontal span in feet and R is the ratio of theversine of the cable to the 
 span. Hence w = ^1 w f . For reasons which will be given 
 
 in the sequel the value of R will be assumed as 8 in this investi- 
 gation. For this value we have w = 1.0417 w' and ic' = 0.900 w. 
 
 (3) Weight of the platform. — In the arrangement adopted in tins 
 investigation for the purposes of estimate the cross-girders sustain the 
 weight not only of the live load but also of the stiffening girders and 
 lateral bracing. The distance between the cross-girders is 30 feet. 
 
 The platform further consists of longitudinal girders (stringers), the 
 permanent way consisting of ties and rails and the covering. Its con- 
 struction is the same as in any other railroad bridge. 
 
 The weights of the stiffening girders and lateral bracing (which 
 increase with the span), are imposed upon the cross-girders so very 
 near the points of suspension that the weight of the platform may be 
 considered practically independent of the span. The weight per linear 
 foot of span for a 6-track platform, carrying stiffening girders and brac- 
 ing, for a span of 3,200 feet, was determined by the New York Board 
 to be 7,200 pounds. We may therefore adopt in this investigation the 
 constant value ^ = 7,200 pounds=3.6 tons. 
 
 (4) Weight of the stiffening girders. — It will be shown under the head 
 of Vertical Bracing that the weight of the two stiffening girders per 
 linear foot of 6-track bridge may be found in pounds from the for- 
 mula p,= 3,281+ 2.754 L + 0.0005312 L 2 . This includes an allowance of 
 material in the lower chords to provide for the stresses due to wind. 
 
 (5) Weight of the lateral bracing. — As will be shown under the head 
 of Lateral Bracing, the weight of the wind and sway bracing per 
 linear foot of 6-track bridge (so far as not provided for in the preceding 
 paragraph) will be given in pounds by the formula p 3 = 2,420 -f 
 0.3889 L. ? 
 
 (6) Weight of the suspenders. — The suspended load is connected with 
 the cables by 8 wire suspenders on each side of the bridge at each 
 cross-girder. The suspenders at each girder are equal in length and 
 are supposed to be adjusted so as to carry practically equal portions of 
 the load. At the middle of the span the cables are 60 feet above the 
 
 level of the suspension pins. The versine of the cable being ^ the 
 
 average length of a suspender is ^ + 60. Assuming a unit working 
 
 stress of 30,000 pounds and adding 20 per cent for constructive details, 
 the weight of the suspenders per linear foot of span will be 
 
 *< = tbSrf (h + 60 ) ^-».) 
 
 in which p' = q + Pl + p 2 + p 3 + p 4 + w . 
 
 For the purposes of this computation we may assume p 4 = 1,300 in 
 the value of p' — ic a . 
 
 From values previously given we find p' — w o =14200-f-27540000 L 1 
 + 3.1429 L+0.0005312 L 2 ; and i> 4 =272+224726 L ^O.IOOIO L + 
 0.00002215 L 2 + 0.000000003 L 3 . 
 S. Ex. 1 7 
 
16 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 (7) Total suspended iceight. — The total suspended weight per linear 
 foot of span exclusive of the cables will be p' =q+pi+p2+p-i-\-Pt+ w = 
 13605 + 27764726 ^+3.24906 L + 0.00055335 L 2 + 0.000000003 L 3 . 
 
 WIND PRESSURES. 
 
 The wind pressure upon a large bridge is of such magnitude as to 
 require especial consideration. In the principal members of the Forth 
 bridge (a cantilever construction), the maximum stresses due to wind 
 have been stated by its engineer to be more than one-quarter greater 
 than those due to the dead weight of the bridge and nearly three 
 times as great as those due to the live load of passing trains. In sus- 
 pension bridges these wind stresses, though they may be less than in 
 other bridges, are still of very great importance, and must be carefully 
 provided against by the introduction of metal which, while adding 
 nothing to the carrying capacity of the bridge, does add considerably 
 to its dead load, and therefore necessitates an increase in the strength 
 of suspenders, main cables, towers, anchorages and foundations, and 
 thus may add enormously to the total cost of the bridge. Under such 
 circumstances, while it is, on the one hand, important to secure a suffi- 
 ciency of wind bracing, it is, on the other hand, equally important not 
 to use any more than is actually necessary. 
 
 Since the existing fund of information as to wind pressures, as to 
 their effect on bridges, and as to the present most used methods of 
 dimensioning wind bracing, is either quite limited or else is not easily 
 accessible, it has been thought well to attach hereto a full history of 
 past work in this direction with suggestions of rules for use in the 
 dimensioning of large structures in places exposed to heavy winds. 
 (See Appendix 0.) 
 
 Past history shows the possibility, at almost any place, of an occa- 
 sional tornado of power sufficient to destroy almost any existing engineer- 
 ing structure. Such tornadoes, like violent earthquakes, are so rare that 
 no large constructions of to-day are made thoroughly proof against them. 
 In such a tornado, however, a suspension bridge would fare much bet- 
 ter than any other form of bridge, as it offers the least surface to the 
 wind, as its overturning is almost a physical impossibility, and espe- 
 cially as the loss of large parts of its roadway and stiffening trusses 
 would not necessarily destroy its main cables and towers (these being 
 its essential and costly features). The Board have therefore (for rea- 
 sons stated in the Appendix) considered a maximum steady wind 
 pressure of 30 pounds per square foot over the entire structure and 
 over a continuous train, reaching entirely across the bridge, and also a 
 similar 30-pound pressure over the unloaded bridge, accompanied by 
 an added pressure of 20 pounds per square foot (making 50 pounds in 
 all) over 1,000 feet of the unloaded bridge; this latter allowance being 
 made to provide for occasional severe gusts. 
 
 The exposed surface of the bridge and load per running root (by the 
 method of calculation given in full in the Appendix) is taken at 30 
 square feet for the cables and suspenders, 49 square feet for the stiffen 
 ing girder (including the upper chord, lower chord, web members, 
 horizontal diagonals, and sway bracing), 18 square feet for the plat- 
 form (including track, guard rails, ties, cross-girders, and stringers), 
 and 8 square feet for the train (excluding the portion sheltered by the 
 high bottom chords and other adjacent parts of the stiffening girders). 
 In view of th£ heavy weights and consequent great inertia of the cables 
 and stiffening girders, the resulting wind pressure is treated as uni- 
 formly distributed over the entire bridge from end to end; chough a 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 17 
 
 more careful distribution, perhaps saving considerable metal, would be 
 adopted in actual practice. 
 
 The cradling of the main cables and suspenders is considered suffi- 
 cient to amply resist the 1.050 pounds per square foot of wind pressure 
 due to the 30 square feet per linear foot of their own surfaces. 
 
 The wind bracing of the stiffening truss will then have to resist only 
 the wind pressure on the stiffening truss, platform, and train; which 
 amounts to 2,345 pounds per linear foot for the unloaded bridge, and 
 2,250 pounds per foot for the loaded bridge. 
 
 As the stiffening truss is hinged at its middle, the wind bracing (at 
 least near the ends of the half trusses) must be arranged to»carry all 
 the wind stresses to the bottom chord; so that this bracing is taken as 
 composed of a very light upper horizontal truss (not theoretically 
 necessary), of a strong vertical sway bracing, and of a heavier lower 
 horizontal truss. Since the wind trussing may be combined with the 
 adjacent parts of the stiffening girder and platform, this lower wind 
 truss will be built up by increasing, where necessary, the dimensions 
 of the cross girders of the platform, and the lower chords of the stiffen- 
 ing truss, and by inserting cross diagonals between them. 
 
 Because of the great size of these cross girders and lower chords, 
 and therefore the great excess of strength in this lower truss when the 
 bridge is unloaded, the Board regard the 2,250 pounds per linear foot 
 of wind pressure on the loaded bridge as the one which throws the 
 greatest strain upon its members, and therefore take this value as the 
 one to be used in combination with the other loads upon a bridge of 
 maximum length. 
 
 In case further lateral stiffness against wind should, at any time, be 
 thought desirable, it may be obtained by the use of horizontal wind 
 cables under the platform; and small main cables may at any time be 
 added, if found necessary, to support the added weight of such wind 
 cables; but the Board consider the use of such wind cables unnec- 
 essary. # 
 
 OSCILLATIONS. 
 
 In considering the character and importance of small motions in 
 bridges it is necessary to distinguish carefully between stability and 
 rigidity. A suspension bridge is the most stable of all bridge struc- 
 tures. The locus of the centers of gravity of its vertical cross-sections 
 lies far below the points of support. The live load, which is the main 
 cause of its vertical oscillations, always moves below the gravity-line, 
 thereby increasing the lateral stability of the structure. As the span 
 is increased the gravity-line rises, but the resulting slight decrease in 
 stability is more than compensated for by the diminution in the ratio of 
 the live to the permanent load. The small motions of erect-arch and 
 deck bridges must be carefully conlined within small limits to insure the 
 safety of the structures, but there is no such necessity in the case of 
 suspension bridges, where the system is in stable equilibrium and sure 
 to return to its position of rest whatever may be the magnitude of the 
 displacement. 
 
 The lateral oscillations are due mainly to the action of the wind. 
 These are met not only by the great weight of the structure, but also by 
 the cradling of the cables, which much increases the lateral stability. 
 
 It is possible to construct a suspension bridge so that it will have 
 any degree of rigidity desired, but it will appear from the above that 
 rigidity is in this case of much less importance than it is in most other 
 kinds of bridges; indeed, it may be shown that a certain small flexi- 
 bility is a positive advantage in suspension bridges. 
 
 S. Ex. 12 2 
 
18 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 The Board do not consider it necessary to give in this report an 
 elaborate development of the theory of bridge oscillations, because it 
 is perfectly easy to stiffen a suspension bridge so as to reduce both its 
 vertical and lateral deflections, and consequently the duration of its 
 oscillations, within any desired limits; and in bridges of very long- 
 span, where the ratio of live to dead load is comparatively small, no 
 difficulty from this cause need be anticipated. The following brief 
 remarks on this subject relate to suspension bridges of comparatively 
 small weight and span. 
 
 As before remarked, oscillations in suspension bridges are mainly 
 produced by the impulses of the moving load and by the pressure of 
 the wind. The magnitude of the oscillations is sometimes increased by 
 the lengthening of the central part of the cable, due to the straighten- 
 ing of the chains of the side span under the action of a load on the cen- 
 tral span. Theoretically an infinitely small impulsive force may produce 
 an infinitely small amplitude of oscillation of finite duration. If such 
 impulses are repeated a summation of their effects may result. This 
 will occur when the interval between two impulses is equal to the time 
 of oscillation, and may occur when it is greater. Under these circum- 
 stances small impulsive forces, by many repetitions, may produce a 
 great oscillation in an elastic or suspended body. In this way the wind 
 has been known to raise waves in the platform of a light suspension 
 bridge. 
 
 In the case of a bridge truss it is important that the time of oscilla- 
 tion produced by a load acting impulsively should not exceed a certain 
 amount, in order that the oscillations may not be cumulative. 
 
 In highway bridges it is especially the measured step of pedestrians 
 which gradually augments the amplitude of the oscillation when the time 
 of oscillation is equal to or greater than the time of a step, which may 
 be assumed as from 0.6* to 0.7 second. If the time of oscillation of the 
 structure is greater, it can adjust itself to the time of a step by the for- 
 mation of centers of oscillation. The result is that by the gradual 
 accumulation of energy changes of form are produced which are con- 
 siderably greater than those produced by an equivalent static load. 
 
 These oscillations occur not only in elastic or stiffened systems, bu* 
 also in slack systems. A freely suspended heavy chain moved from 
 the position of equilibrium in its vertical plane will assume oscillating 
 motions which will gradually increase if new impulses occur in the 
 time intervals corresponding to the time of oscillation or a fraction 
 thereof. It is shown by Melan that the time of oscillation of a slack 
 chain is materially greater than that of even a very elastic construc- 
 tion, which explains the well-known fact that unstiffened suspension 
 bridges can very easily be brought into great oscillations by a few 
 pedestrians. 
 
 Prof. Melan in his treatise on Bridge Construction deduces the equa- 
 tions t = 1.806 \// and t= 2.0063 \/ u + 0.8 for the times of oscilla- 
 tion in a slack and a stiffened system, respectively; in which t is the 
 time of oscillation in seconds, /is the versine of the cable in meters, 
 u is the deflection in the middle due to the uniformly distributed dead 
 load, and u is the increase of deflection due to a concentrated load in 
 the position of. rest in meters. 
 
 From these formulas it follows that the time of oscillation of a bridge 
 structure depends only upon the magnitude of its deflection in the 
 position of rest, no matter what may be the character or size of the 
 structure. Hence the deflection must be kept within certain limits, in 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 19 
 
 order that the bridge may not be set in vibration by the steps of 
 pedestrians or other regularly repeated impulses. 
 
 The time of oscillation and consequently the deflection must be the 
 smaller the more rapidly the repetition of impulses occurs. Hence 
 greater stiffness is required in a railroad suspension bridge than in a 
 similar highway bridge. 
 
 As the deflection u due to the uniformly distributed load is in general 
 proportional to the fourth power of the span, it follows that the time 
 of oscillation varies approximately as the square of the span. There- 
 fore, this time may be diminished by fastening the structure at interme- 
 diate points to the shore or ground so as to form a number of centers 
 of oscillation. 
 
 The occurrence of cumulative oscillations may also be prevented by 
 employing together several systems for stiffening the cables, these sys- 
 tems having different periods of oscillation; and where a number of 
 cables are assembled on each side of the bridge, the same result may 
 be accomplished by employing different versines for the cable curves. 
 Thus, in the bridge designed by Mr. Gustav Lindenthal for the North 
 River Bridge Company, the stiffening is obtained by trussing between 
 the cables and by continuous longitudinal platform girders. As these 
 two systems have different periods the chance of cumulative oscilla- 
 tions is greatly reduced. In the Niagara Suspension Bridge the two 
 systems of cables have versines of 54 and 64 feet, respectively, and 
 consequently different periods of oscillation. 
 
 The arrangements to prevent deflections due to the moving load 
 and the wind will receive consideration in other parts of this report. 
 
 BRACING. 
 
 The bracing required to stiffen the bridge may be conveniently con- 
 sidered under two heads, vertical bracing and lateral bracing. 
 
 1. Vertical bracing. — It is the object of this bracing to confine within 
 definite and small limits the oscillations and deflections caused mainly 
 by the rolling load. Various methods have been employed for this 
 purpose, the principal of which are as follows: 
 
 (1) Stays extending from the tops of the towers to the platform. 
 
 (2) Stays extending from the bottoms of the towers to the cables. 
 
 (3) Longitudinal stiffening girders connected with the platform and 
 extending over the whole length of the bridge. 
 
 (4) Bracing between two cables hanging in the same vertical plane. 
 
 (5) Trussing the cable on its concave side. 
 
 (6) Trussing between the cable and the platform. 
 
 Two or more of these methods of stiffening are frequently ejnployed 
 together in the same bridge. For example: Methods (1) and (3) are 
 employed at the East River Bridge; method (3) at the Niagara Bridge; 
 method (4) at the Allegheny River Bridge at Seventh street, Pitts- 
 burg; method (5) at the Point Bridge over the Monongahela at 
 Pittsburg; method (6) at the Lambeth Bridge, England. Experience 
 has proved all these methods to be effective, and for some of them 
 special advantages of economy are claimed. Thus the over-floor stays 
 of method (1) not only prevent the development of large vertical 
 oscillations in the platform, but also relieve the suspension cables of a 
 considerable part of the load. In method (2) the stays add to the 
 weight on the cables instead of relieving them, and in this respect it is 
 not as good as method (1). It has been objected, however, to the use 
 
20 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 of stays in bridges of large span that they complicate the conditions 
 of equilibrium, as it is difficult to adjust them so as to bear a definite 
 portion of the stresses under the varying conditions of load and 
 temperature. By bracing two cables — method (4) — we utilize the cables 
 as the chords of the stiffening girder and save the material otherwise 
 required for the chords. Still greater economy is claimed for combina- 
 tions of the stiffening systems. 
 
 The simplest and most employed stiffening system is the longitudi- 
 nal stiffening girder. Such girders are convenient for supports to the 
 lateral bracing and for side guards, and at none of the existing bridges 
 where other methods were employed was the girder entirely dispensed 
 with as a part of the stiffening system. The girder rests upon the 
 floor beams and is thus suspended from the cable. It does not support 
 any load, but merely distributes it, hence it is absolutely a dead weight, 
 adding nothing to the strength of the bridge. 
 
 The Board consider it very probable that for a given special case a 
 lighter and better stiffening system than that supplied by the simple 
 longitudinal platform girder could be worked out by combining the 
 trussed cables and longitudinal girder systems, as has been done by 
 Mr. Gustav Lindenthal in his elegant design for the North Biver 
 Bridge. In applying this method, however, to wire cables carrying 
 very heavy weights over a very long span some new questions of con- 
 structive detail will require solution, and for the purposes of a general 
 investigation it seems best to follow the usual method of stiffening. It 
 will, therefore, be assumed that vertical stiffness is obtained entirely 
 by longitudinal platform girders with parallel chords. 
 
 These girders are usually of the open frame or lattice type. While 
 their rigidity does not affect the actual safety of the cables which 
 carry the entire dead and live load, it does determine the suitability of 
 the bridge for railroad purposes. There is no doubt that a suspension 
 bridge can be made as rigid for railroad trains as a bridge of any other 
 system. 
 
 If a flexible cable be loaded ununiformly it will be depressed on the 
 side of the heaviest load and will rise on the opposite side. It is the 
 object of the stiffening girder to reduce the distortion of the cable to a 
 practical minimum. There are two practical ways in which the girder 
 may be constructed: 
 
 (1) As a continuous girder, loosely supported at the ends with reac- 
 tions in both vertical directions, but permitting horizontal motion. 
 
 (2) As a girder loosely supported at the ends, as in the first case, 
 and hinged in the middle. 
 
 For the first case the problem of equilibrium is statically inde- 
 terminate; that is, the conditions of equilibrium can not be formulated 
 without including the elastic forces developed in the girder. In the 
 second case we have only to deal with static forces, and the stresses in 
 the girder can be calculated with a close degree of approximation by 
 the simple law of the lever. 
 
 In the designing of stiffening girders the formulas given by Prof. 
 Kankine have generally been employed. The formulas for the continu- 
 ous girder are deduced in his Applied Mechanics (p. 370). The 
 formulas for the hinged girdei are given, but not deduced, in his Civil 
 Engineering (x>. 579). Bankine's methods, which are approximate in 
 character, have been extended to a high degree of accuracy by subse- 
 quent investigators. Probably the most complete investigation of the 
 straight stiffening girder is that of Prof. J. Melan, of the Technical 
 High School at Briinn. 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 21 
 
 Rankine's values of tlie maximum bending- moments for the hinged 
 and continuous girders are as follows: Hinged girder, M=0.0156r/L 2 ; 
 continuous girder, M=0.017SbV/L 2 ; while Melan, by more accurate 
 methods, obtains for the hinged girder M=0.018S3f/L 2 , and for the 
 continuous girder M=0,01652gIA It will be noticed that with Ran- 
 kine's values the maximum bending moment is smaller for the hinged 
 girder than for the continuous girder, while with Melan's values the 
 reverse is the case. 
 
 Although the hinged girder presents very decided theoretical advan- 
 tages, especially in the determination of the stresses, it has some dis- 
 advantages which have prevented its employment in any important 
 practical case. The introduction of the middle joint lias for its princi- 
 pal object the attainment of a static determination, but, as Melan has 
 pointed out, the theoretical conditions can not be fully satisfied unless 
 the girder and cable have a common joint at the middle. If the girder 
 alone is jointed, increased bending strains must be produced in the cable 
 directly over the joint. The arrangement of the wind-bracing becomes 
 more troublesome, for, since the upper chords of the girders are cut, 
 all the wind stresses must be transferred to the lower chords. The 
 wind-bracing would doubtless be heavier than for a continuous girder. 
 
 Mr. Lindenthal has shown that while there are no temperature 
 stresses in a three-hinged arch at the middle hinge they do exist for 
 any change from the normal temperature in the connected half-arches. 
 His investigation of this important question (which originally appeared 
 in the Engineering News of March 10, 1888, and which has been revised 
 by him for the Board) will be found in Appendix D. For the purposes 
 of this investigation, however, there is no question that the hinged 
 girder ought to be adopted, in order to avoid the complicated formulas 
 which would be required in the other case. It will give results as 
 accurate as the nature of the inquiry permits and on the safe side as 
 regards weight of metal, which could be considerably reduced for 
 any given casein practice by the use of continuous girders, or by other 
 methods requiring more extended computations. The New York Hoard 
 employed the same method. 
 
 It will appear hereafter that when considerable rigidity is required, 
 as in railroad bridges, the stiffening truss becomes the greatest single 
 element of weight and therefore its economical designing is a matter of 
 the highest importance. The Board therefore appends to this report a 
 translation of Prof. Melan s complete investigation of the straight stif- 
 fening girder, which it is believed is unknown to most American bridge 
 engineers. A simpler investigation, but sufficiently rigorous for all 
 practical purposes, covering both the hinged and continuous girders, 
 has been attached by the New York Board as an appendix to its report. 
 
 In the case of the hinged girder the greatest distortion of the cable 
 occurs when the moving load covers the platform from one tower to a 
 point at a distance 0.105 L from the middle of the bridge. It is here 
 assumed that there will be practically no temperature strains and the 
 simple statical conditions will enable us to express with sufficient 
 accuracy the weight of the girder in terms of the span. 
 
 The values of tlie bending moments and shears which will be used 
 in determining the weight of the girder are based upon the following 
 assumptions: 
 
 1. The stiffening girders are supposed to have a height sufficient to 
 prevent great vertical flexure. So far as the vertical strains due to 
 loading are concerned it is most economical to make the height as great 
 as is practically possible, and with the hinged girder this may be done, 
 
22 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 since changes of temperature are without material influence. The 
 height of the girder will therefore be assumed at 120 feet, as adopted 
 by the New York Board. 
 
 2. The tensions on the suspenders are supposed to be always equal; 
 that is, the vertical reaction between the cable and the girder is uni- 
 formly distributed over the whole length of the span ; and the tensions 
 on the cable are assumed to be invariable. It has been shown by M. 
 Boulongne* that in the case of the suspenders the values obtained on 
 this hypothesis can not be in error more than 5 per cent, and for the 
 cables the error is on the safe side, since it increases the amount of 
 work required of the girder. 
 
 3. The effects of the elastic elongation of the suspenders, due to live 
 load and temperature changes, are neglected. As remarked by the 
 New York Board, these disturbances can be avoided by omitting the 
 suspenders for a short distance next the towers. 
 
 The discussion of the values of the maximum bending moments and 
 shears is omitted from this report, as it is given fully in Melan's investi- 
 gation (Appendix E), and also in Appendix E to the report of the New 
 York Board. 
 
 The curve of maximum bending moments covering the half girder, 
 whose length is ^ L, is very nearly a parabola, and its area is very nearly 
 
 § X i> X 0.01883 q It 2 . The average maximum bending moment will there- 
 fore be 
 
 M m =0.01255 q, L 2 . 
 
 The average maximum chord-stress is found by dividing this moment 
 by the height of the girder; the area of the cross-section of the chord 
 in square indies is obtained by dividing this chord stress by the 
 assumed working unit stress; and the theoretical weight of the chord 
 per linear foot by multiplying this area by 3.4 pounds. To obtain the 
 practical weight the theoretical weight must be increased by about 25 
 per cent for constructive details. Although the chords are subject to 
 reversal of strains, the Board have assumed a unit working stress of 
 15,000 pounds, for reasons which will be fully explained elsewhere. 
 
 The weight of the upper chord in pounds per linear foot will there- 
 fore be — 
 
 0M25 %^^ ^000000008968 «, LV 
 
 The dimensions of the lower chord will have to be considerably 
 increased, as it serves also as a chord in the wind girder. Assuming 
 for computation a wind pressure of 2,250 pounds per linear foot, for 
 reasons before given, the average maximum bending moment due to 
 the wind will be — 
 
 M mw =187.5 L 2 
 
 The unio working stress will be assumed at 30,000 pounds per square 
 inch for reasons which will be given elsewhere. Kemembering that 
 the width of the track-platform between the axes of the girders is 100 
 feet, we obtain for the weight per linear foot of materia) to be added 
 to the lower chord to take care of the wind-stresses 
 
 187.5 Lx3.4xl.25 =0 0002656 u 
 30,000x100 
 
 * Note sur les Pouts Suspendus, Amiales des Ponts et Chaussees, 7 Serie. Tome 1, 
 1892, p. 742. 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 23 
 
 The average total weight per linear foot of the lower chord is there- 
 fore 
 
 (0.0002656+0.00000002963 q x ) L 2 
 
 The shearing stresses due to a continuous moving load are greatest 
 at the origin of the span and diminish to 0, changing from upward to 
 
 downward stresses at a distance ^ from the origin. The average max- 
 imum shear without regard to sign for all positions from the origin to 
 the middle pin is S= 0.1038 qjj. 
 
 The theoretical weight of the web must be increased by about 50 per 
 cent for constructive details and to provide for the transfer of weight 
 from the upper to the lower chord. The lattice bars being placed at 
 an angle of 45°, the weight of the web per linear foot of span will be 
 
 0J0381 jL L^4 L xl.5><2 =0 00007058 qJj 
 15,000 
 
 For the total weight per linear foot of each stiffening girder we 
 finally obtain by addition 
 
 P ^=qi (0.00007058 L+ 0.00000005926 L 2 ) + 0.0002650 L 2 . 
 
 The value of q i9 which is to be employed in this formula, must now 
 be determined. It will be remembered that the stiffening girders 
 carry no weight, not even their own. They simply distribute the 
 inequalities of the live load and limit the deflections in the cables and 
 floor system. The girders must be dimensioned with special reference 
 to those positions of the live load which correspond to the greatest 
 deflection. The maximum bending moment in either half- girder 
 corresponds to a continuous live load extending from the origin 
 towards the middle of the span and covering a distance 0.395 L. For 
 all spans up to#2,957 feet (equal to the maximum train length divided 
 by 0.395), the single freight train on each track (all six trains being 
 supposed to advance together with their engines abreast) will produce 
 the maximum bending effects, the length of such a train being 1,168 
 feet. For greater spans it is evident that the maximum effect will not 
 be thus produced. Accordingly, for spans greater than 2,957 feet we 
 should divide the maximum train load by 0.395 L to obtain the live 
 load per linear foot of span to be used in determining the weight of the 
 stiffening girders. 
 
 The weight of the train is 3,060,000 pounds ; hence for each girder 
 we obtain 
 
 _ 3060000 x 3 _ 23210506 
 qi - 0.395 L - L 
 and by substitution in the preceding equation 
 
 | 2 = 1640.3 + 1.377 L + 0.0002656 L 2 
 
 The total girder-load per linear foot for the whole bridge will there- 
 fore be p 2 = 3281 + 2.754 L + 0.0005312 L 2 . 
 
 This formula leaves entirely out of consideration the fact that part of 
 the live load is taken up directly by the cables, yet it is certain that a 
 considerable part of the action of "the live load may be thus absorbed. 
 In his reconstruction of the Niagara Suspension Bridge, Mr. L. L. Duck, 
 the engineer in charge, provided for a maximum deflection of 15 inches 
 in 500 feet, and thus reduced the value of 2q { in his formulas from 0.8 
 ton to 0.6 ton. Mr. W. Hildenbraud, in his reports relative to a pro- 
 
24 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 posed suspension bridge across the Hudson Kiver, which are appended 
 to the report of the isew York Board, provides for a maximum deflec- 
 tion giving a grade not exceeding 1 per cent. He thereby reduces 2q { 
 from 9,000 pounds to 7,800 pounds. The Board do not doubt that within 
 narrow limits a certain degree of flexibility is an advantage to the 
 bridge. Deflections in a system of stable equilibrium do not impair the 
 safety of the structure as they do in an unstable system like the upright 
 arch, and they may exert a very beneficial influence in modifying the 
 dynamic effects of a rapidly varying live load. On the other hand, it 
 is to be remarked that any increase in the grade of the track -platform 
 is accompanied for fast trains by a certain increase in the dynamic 
 action of the live load. 
 
 The proportion of live load absorbed by the cables increases as the 
 catenary becomes flatter, but the cables must be made heavier. It is 
 not easy to determine satisfactorily the resultant effect of these deflec- 
 tions, and in order to be on the safe side the Board make no allowance 
 for them in this investigation. 
 
 Lateral bracing. — The principal duty of the lateral or sway bracing 
 is to resist the action of the wind. The top lateral system is a light 
 riveted lattice connecting the top chords of the stiffening girders. 
 Since these chords are cut at the middle, the entire work of resisting 
 wind pressure is done by the bottom lateral system. The top system, 
 in conjunction with the cross-frames and hangers in a vertical plane 
 above each cross-girder, serve simply to transfer the wind stresses and 
 a portion of the load to the bottom system. We may assume for the 
 weight of the top system 500 pounds per linear foot, and for the cross- 
 frames and hangers, 1,920 pounds per linear foot, as computed by the 
 New York Board. These weights may be considered constant for all 
 values of the span within the limits of this investigation. 
 
 In the bottom system the chords are the bottom chords of the stiffen- 
 ing girders, in the dimensioning of which the wind stresses have 
 already been provided for. The cross girders of the floor system form 
 the lateral struts, and the diagonals are strained in tension. It only 
 remains to determine the weighi per linear foot of the diagonals. The 
 depth of the wind-girders (d) is 100 feet, and the theoretical panel 
 length (b) is 120 feet. The number of panels (n) on each side of the 
 
 middle point is therefore ^ The theoretical panel load is 2,250 b; the 
 
 assumed unit stress is 25,000 pounds ; and 25 per cent is added for con- 
 structive details. The weight of the diagonals per linear foot of span 
 will then be 
 
 2x1.25x3.4x2250 b {b 2 +d>) T 
 
 mwi^iv = °* 3889 L - 
 
 For the weights in pounds per linear foot of the lateral or sway 
 bracing, including the cross-frames and hangers, we therefore have 
 jp 3 =2420+0.3889 L. 
 
 WORKING STRESSES. 
 
 In determining the weights of the two most important members of 
 the bridge — the cables and the stiffening girders — the Board have 
 assumed working stresses which are greater than those generally 
 adopted in truss or arch bridges of moderate span, and which, there- 
 fore, require explanation. 
 
 The most approved formulas for the determination of working 
 stresses are based upon the experiments of Herr Wohler, made for 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 25 
 
 the Prussian Ministry of Commerce, and published at Berlin in 1870.* 
 These experiments not only confirmed the earlier result obtained by 
 Sir W. Fairbairn and others, that with repeated applications of a load 
 a bar breaks under less than its static breaking load, but they also 
 showed that the breaking load varies inversely with the difference 
 between the maximum and minimum stresses. Furthermore, it was 
 found that a bar may be broken by a still smaller fraction of the static 
 breaking load if it is alternately strained in opposite directions, the 
 stress alternating between a positive and a negative quantity. 
 
 The principal formulas representing these results are based upon two 
 radically different interpretations of the observed facts. In one case 
 it is assumed that the repeated alternations of stress produce an actual 
 weakening of the material which has been called " fatigue." This view 
 is represented by the Launhardt-Weyrauch formulas, which are as fol- 
 lows: 
 
 For stress in one direction — 
 
 For alternating positive and negative stresses — 
 
 u — s , x 
 a = u(l - -— 
 
 in which $ = j^!^'^ = rlie ratio of the least to the greatest stress ; 
 
 a = breaking strength under the assumed conditions, which is to be 
 divided by the factor of safety (generally 3) ; t = breaking strength 
 under a static load; u = the limiting strength (LJrsprungsfestigkeit), 
 measured by the greatest load the bar will bear with an indefinite num- 
 ber of alternations between and u without reversal ; and s = vibration- 
 resistance, which is the limiting strength for alternations of equal mag- 
 nitude with reversal. 
 
 In the othej' ease it is assumed that the alternations produce no 
 change whatever in the molecular condition of the material, but that 
 the increased effects are produced entirely by an increase in the stresses 
 due to dynamic action, the stress being equal to the load only when all 
 the forces acting are in static equilibrium. This view is represented 
 by the so-called dynamic formula, which is 
 
 «=max. S+7; (max. S— min. S) 
 
 In this formula ?] is a coefficient depending upon the violence and 
 time-rate of the load-changes. 
 
 The Launhardt-Weyrauch formulas are based entirely upon Wohler's 
 experiments, and do not take into consideration variations in the rate or 
 violence of the dynamic action. Prof. Fidler says that in these experi- 
 ments the load was applied about four times per minute. 
 
 Prof. Fidler has shown that when the alternations are rapid (for 
 which case //= 1) the dynamic formula represents Wohler's experi- 
 ments as accurately as the Launhardt-Weyrauch formulas. No satis 
 factory determination, however, has been made of the value of // for 
 the various cases occurring in practice. In the case of cross-girders 
 and vertical suspenders, which receive the full action of the elastic 
 vibrations due to a sudden imposition of the load, Prof. Fidler assumes 
 i = 1, and he adopts the same value for the diagonals of the web brac- 
 ing. For the flanges of a girder or in the principal members of an 
 arch or suspension bridge, in which the stress-changes take place more 
 gradually, he recommends a reduced value bearing some unknown 
 
 * Uber die Festigkeitsversuche mit Eiseii imd Stahl. 
 
26 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 relation to the length of span. He considers the value r?= J to be large 
 enough for all spans down to about 100 feet. 
 
 It is not possible in this report to make an extended comparison of the 
 merits of these formulas. It maybe remarked, however, that the effects 
 of variations in dynamic action certainly play an important part in the 
 determination of ultimate strength, although there are as yet no experi- 
 ments showing how far this strength is affected by the frequency as 
 distinguished from the mere number of the stress-changes, nor whether 
 a period of rest after "fatigue" restores strength. These effects of 
 dynamic variations, which are entirely unrepresented in the Launhardt- 
 Weyrauch formulas, really exist, and are of special importance in the 
 theory of suspension bridges. A clear and able discussion of the whole 
 subject will be found in Chapter xiii, of Prof. Fidler's Practical Treatise 
 on Bridge Construction. 
 
 The Board have adopted for the cables a working stress of 60,000 
 pounds, which is one-third of the static breaking load. Prof. Melan 
 says that, owing to the lack of experiments with steel wires, we can 
 consider the laws of Wohler only so far as to allow for large spans a 
 somewhat greater value of the working stress. For ordinary spans he 
 adopts a working strength of about one-fourth the ultimate strength of 
 the wire. The Board believe that a safety factor of 3 is amply sufficient 
 to cover both the effects of variations in stress and the imperfections 
 of manufacture and adjustment in the cables. As regards variations 
 in stress, it is to be remarked that there are no reversals, the wire 
 being always intension; that considerable deflections correspond to 
 relatively slight changes in stress -; and that the stresses are slowly and 
 gradually applied, and well witbin the high elastic limit. 
 
 This latter point is of special importance, for it is probable that 
 Wohler's law of reversals does not hold good for stresses well within 
 the elastic limit. For example, in the balance spring of a watch, ten- 
 sion and compression succeed each other some 150,000,000 times in a 
 year, and the spring works lor years without apparent injury.* In 
 this connection it may be remarked that, although cables which have 
 been long in use have been frequently examined, no deterioration of 
 strength which could be attributed to variations of stress has ever 
 been discovered. If we use the Launhardt formula, we are justified 
 in making u very nearly equal to /. 
 
 If we employ the dynamic formula, the factor max. S — Min. S will be 
 very small, for the reasons just given. As for the coefficient t?, we only 
 know that it diminishes as the span increases, and, according to Prof. 
 Fidler, it need not be greater than £ for a span as small as 100 feet; it 
 must therefore be a very small fraction for spans as large as those now 
 under consideration. The variation- term of this formula will probably 
 be so small that it may be safely neglected. 
 
 As regards imperfections of manufacture and adjustment, which are 
 covered in general practice by the safety factor 3, the following points 
 are to be noted. The uniformity of strength is greater for wire than 
 for any other form of steel. The process of manufacturing a wire cable 
 is in itself a test of the material and insures a more nearly uniform 
 distribution of stress over the cross-section than can be obtained in any 
 other structure formed of a very great number of parts. If a factor 
 of 3 is sufficient to cover the defects of material and construction of a 
 riveted bridge-member, a somewhat less factor ought to be sufficient for 
 a wire cable. 
 
 " Prof. Ewing, Strength of Materials, Eiic. Brit. 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 27 
 
 For the reasons above given, the Board are of the opinion that a 
 safety factor of 3 is sufficient, and have therefore adopted 60,000 pounds 
 per square inch as the working- stress for the cables. 
 
 The New York Board adopted the same working stress, giving as 
 their reason that this is "the same proportion of the ultimate strength 
 that the 20,000 pounds adopted in the cantilever structure bears to the 
 probable strength of eye-bar steel.*' 
 
 The Board have adopted 15,000 pounds per square inch for the work- 
 ing strength- of the stiffening girders. The Few York Board limited 
 the stresses due to a moving load to 12,500 pounds, because there is a 
 reversal of strains, but allowed the stresses from the combined effects 
 of moving load and wind to run up to 22,500 pounds. The reasons of 
 this Board for adopting a higher working stress in the stiffening gird- 
 ers are as follows : 
 
 Although there is a theoretical reversal of strains, it will rarely and 
 perhaps never occur with the maximum stress, since this would require 
 six of the heaviest freight trains, abreast of each other, to cross and 
 recross the bridge, first in one direction and then in the other. This 
 would probably never happen on a bridge devoted principal!} 7 to pas- 
 senger traffic, and it could be prevented by the simplest police* regula- 
 tions. Again, the lower chords of the girders have been made of suf- 
 ficient strength to resist the combined maximum stresses of the live 
 load and the wind; but the maximum chord-stresses could never occur 
 at the same time, since with the maximum wind pressure no trains 
 could cross the bridge. 'Some allowance has been made for this by the 
 adoption of a working' strength of 30,000 pounds for that part- of* the 
 material added to resist wind. The only duty of these girders is to 
 distribute the live load and thus prevent inconvenient deflections. It 
 is not necessary to give them the margin of strength which they would 
 require- if they were essential to the stability of the bridge. 
 
 The Board are of the opinion that the great distinction between the 
 stable equilibrium of a suspension bridge, which can not break down 
 from the failure of any stiffening member, and the unstable equilib- 
 rium of a truss, arch, or cantilever bridge, in winch, they >fa dure of a 
 member may involve the collapse of the entire bridge, ought to receive 
 full recognition in the adoption of unit stresses and safety factors. 
 The weight of the stiffening girders constitutes the most important 
 single element in the suspended weight? of the bridge, being for the 
 maximum span about one-half the entire permanent load. It should 
 be made no greater than is absolutely necessary, for the structure 
 ought not to be kept under a continuous stress to provide a larger 
 margin for stresses which may never occur. The Board believes that 
 the working stresses adopted are amply sufficient for the members of 
 the bridge. 
 
 TOWERS. 
 
 The weight of the towers forms no .part of the suspended load, and 
 therefore is only indirectly connected with the question of* the maxi- 
 mum span. There is, of course, a practical limit to the height to which 
 the towers can be carried, and the relation between their cost per ver- 
 tical linear foot and the cost of the suspension system per linear»foot 
 of span will be an important element in determining the most econom- 
 ical versine for the cables. 
 
 The towers will be supposed to be formed of steel columns braced 
 together, and will start from the upper surface of the masonry, 105 feet 
 below the lowest point of the cables. An empirical formula, giving 
 
28 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 The approximate weight of metal (W t ) in the tpwers, has been deduced 
 by Mr. Linden thai from various estimates of designs for suspension 
 bridges, as follows: 
 
 Since the section of the cable is throughout the same, the tangent to 
 the cable at the tower in the end span should intersect a horizontal 
 line tangent to the cable curve at a distance from the axis of the tower 
 not greater than that of the intersection of the similar tangent in the 
 middle span; hence the end spans should each beat least one-fourth of 
 the main span, and the entire length of the bridge from face to face of 
 anchorage should be at least 1.5 L. Subject to this condition, the end 
 spans should be made as short as convenien t to save cable weight. This 
 is also important, when the backstays carry any directly suspended 
 load, because the bending moments from the live load in their stitfening 
 girders may otherwise become greater than in the main span. In the 
 present investigation, however, the loads in the side spans are supposed 
 to be supported from beneath, and the backstays have simply to trans- 
 mit the suspended load of the main span to the anchorages, the pres- 
 sure on the top of each tower being equal to the total dead and live 
 load of the main span. 
 
 Let L a = length of th^ bridge exposed to wind pressure reacting lat- 
 erally on the towers, in this case equal to L. 
 
 h t = height of the metallic portion of the towers from bedplate to 
 cable bearing. 
 
 W a = suspended dead load plus maximum live load per unit of span. 
 E t = reaction at top of towers, = 2 L W B (for both towers). 
 W\ = weight of steel per linear foot of square inch cross section = 3.4 
 pounds. 
 
 8= factor of safety. This will be assumed as 3. 
 
 u = ultimate strength of steel per square inch, corresponding vO S = 1. 
 
 a — coefficient of practice, including stairways, housings, cable bear- 
 ings, etc., deduced from actual designs = 1.65 (Lindenthal). 
 
 Steel having an ultimate strength of from 90,000 to 100,000 pounds 
 per square inch, and an elastic limit from 56,000 to 60,000 pounds, is 
 considered by Mr. Lindenthal more suitable and economical for heavy 
 towers than a forgeable or punchable steel, with an ultimate strength 
 of 60,000 pounds. All rivet holes in such high steel must be drilled and 
 not punched and reamed. 
 
 The metal m the towers is proportional to the reaction E t and the 
 height h t . The weight of metal in the towers, exclusive of bracing, will 
 
 therefore be — * —-7 - - -• 
 
 The towers require bracing against wind pressure and bending from 
 temperature changes in the cables. The metal in the braces will be 
 proportional to the square of the height of the towers and to the length 
 L exposed to wind pressure and temperature changes; hence the weight 
 of the bracing in tons will be L h t 2 S b 1 in which b is the coefficient of 
 proportional weight deduced from actual designs = 0.001 (Lindenthal). 
 
 The weight of the towers will therefore be 
 
 W t =R t h t s a Wi+L h t 2 s b—li t S (R t a w x + L h t b) 
 n u 
 
 Making *=3, m 1= 3.4, a= 1.65, &=0.001, R t =2 W 8 L, and ^=60000, we 
 obtain for the weight of the towers in pounds 
 
 W t =L7f t (0.187 W„+7*t) 
 333 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 29 
 
 This is on the assumption that the towers are constructed on the plan 
 followed by the Xew York Board, so that the cables may be arranged 
 side by side, and that steel of an ultimate strength of 60,000 pounds 
 per square inch is employed in their construction. 
 
 BACKSTAYS. 
 
 The length and consequently the weight of the backstays will 
 depend entirely upon the arrangement of the end spans, and this will 
 in every case be determined by the local conditions. If I represents 
 the length of a single backstay, the total weight ( W b ) of the backstays 
 for the whole bridge will be W b =2 / w! in which w'=tihe weight of all 
 the cables per linear foot. 
 
 If the backstays intersect the horizontal plane, tangent to the cable- 
 curve at a distance i Lfrom the axis of the towers (which is the most 
 economical arrangement so far as the total amount of cable metal is 
 concerned), the length of each stay from the floor level to the top of 
 the tower (the floor being considered horizontal and 60 feet below the 
 
 lowest points of the cables) will be 5 (^4- 60), to which should be added 
 
 o 
 
 a constant length of about 100 feet to carry the end of the stay to its 
 point of connection with the anchor chain, which should be well below 
 the floor level. For this case the formula becomes 
 
 W b = (468.3 + 0.559 L) w'= (449.6 + 0.537 L) w. 
 
 ANCHOR CHAINS AND PLATES. 
 
 The anchor chains are formed of steel eye bars and connect with 
 the cables outside of the masonry of the anchorages, and with bearing 
 plates of rolled steel at their lower ends. They are proportioned for a 
 stress of 20,000 # pounds per square inch with an allowance of 40 per 
 cent for the weight of pins and constructive details. The tension on 
 each backstay is 18,960.000 pounds. The weight of the anchor-chains 
 per linear foot tor each backstay will therefore be 
 
 18,960,000x3.4x1.4 , - 10 , 
 oTTTuwa =4,ol2 pounds. 
 
 20,000 
 
 The length of each chain may be assumed as 200 feet. The weight 
 of chains for each backstay will therefore be 902,400 pounds. The 
 weight of steel in each anchorage plate may be assumed as 100,000 
 pounds, making the total weight of anchorage metal for each back- 
 stay 1,002,400 pounds. If n represents the number of standard cables 
 in the bridge, the total weight of the anchorage metal (W a ) will be 
 \Y a = 2,004,800 n. 
 
 In this formula no deduction of weight is made for the diminution of 
 the tension due to the friction of the chains on their supports. 
 
 For the bridge of maximum span with 16 standard cables we have 
 W a =32,076,800 pounds= 16,038.4 tons. 
 
 HASONRY AND FOUNDATIONS. 
 
 Anchorages. — As the anchorage masonry acts merely as a weight, an 
 inexpensive class of masonry can be used everywhere except, perhaps, 
 in the immediate vicinity of the bearings of anchorage cables and 
 plates. The foundations need go no deeper than necessary to obtain a 
 
30 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 soil giving sufficient resistance to horizontal sliding, and therefore will 
 be of comparatively simple and easy construction. 
 
 Tower foundations. — The lower portion of the towers above ground 
 and all that below ground will naturally be built of masonry, and 
 may be all treated as constituting the tower foundations. Being pro- 
 portioned directly to the weight which they have to carry, such foun- 
 dations for suspension bridges differ from those of other bridges only 
 so far as affected by the great height of the towers proper and their 
 consequent great weight and leverage; and therefore are like other 
 foundations except that they must be given more cross-section, more 
 care, and a better footing upon their beds. 
 
 In proportioning such piers, the New York Board adopted the fol- 
 lowing limits of stress: 
 
 The pressure between the metallic bed- plates and the top of the 
 masonry should not exceed 20 tons to the square foot. The pressure 
 within the masonry and on the foundation should not exceed 10 tons 
 to the square foot; but in determining these pressures, the weight of 
 materials displaced by the pier is to be deducted. 
 
 The New York Board remark that u while these pressures have been 
 exceeded in some structures, they are higher than in usual practice, 
 and call for masonry of good quality and of more than ordinary cost." 
 
 The method of foundation construction will depend greatly upon 
 local considerations. For a bridge of maximum span these founda- 
 tions should rest upon solid rock, if possible, and at least upon hard, 
 incompressible impermeable soil. Modern methods have already estab- 
 lished foundations at a level of 162 feet below the water surface, and 
 provide means for going still deeper, if necessary, and for obtaining a 
 properly leveled surface in the rock when found; so that the question 
 of foundations affects to-day only the economy and not the engineer- 
 ing practicability of bridge construction. 
 
 It is now proposed to investigate the maximum length of span prac- 
 ticable for a suspension bridge entirely from an engineering point of 
 view, leaving the question of the relation between traffic capacity and 
 cost of construction for subsequent consideration. 
 
 If we suppose the cable-curve to be referred to rectangular axes 
 through the lowest point as an origin, we have from the construction 
 of the funicular polygon — 
 
 in which Q represents the constant horizontal tension at any point of 
 the polygon, and P the total suspended load per linear foot of span. 
 The units are the pound and the foot. 
 
 The load P is composed of the weights per unit of span of the live 
 load, track-platform, bracing, cables and suspenders, some of which 
 vary slightly with x\ but the Board has found by a careful analysis that 
 even with the unusual weights and spans considered in this investiga- 
 tion, the error involved in the assumption that P is constant is too 
 small to be of any practical consequence. It is therefore assumed that 
 the load is uniformly distributed, in which case we obtain by integra- 
 tion for the equation of the cable-curve y which represents a par- 
 
 THE ENGINEERING PROBLEM OF MAXIMUM SPAN. 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 31 
 
 abola. If L represents the span and R the ratio of the span to the 
 
 P L K 
 
 versine of the cable we obtain Q = — 6 — • 
 
 o 
 
 The greatest stress on the cables is at their highest points, and for 
 this maximum tension the strength of the cables must be proportioned. 
 Its horizontal component is the constant horizontal tension Q and its 
 
 vertical component is the weight on the half span, -jr- m If T repre- 
 sents this maximum stress we obtain 
 
 v -I 8 8 
 
 If we represent by Li the limiting span, that is, the span at which 
 the cable will carry its own weight with a given stress per unit of cross- 
 section without carrying any other load whatever, we obtain from the 
 above equation, by making p'=0 and L=Lj 
 
 t _wJa 
 8 
 
 hence 
 
 p'+w_ln 
 w ~~ L 
 
 From the above equations we obtain 
 
 1 WR 2 + 16. 
 
 For metallic towers and large spans the value R=8 will be generally 
 about the most economical value for the ratio of the span to the cable 
 versine, when the cost of the foundations is taken into consideration. 
 If we make E = 8 and substitute for T the working strength per square 
 inch of the material of the cable, which we have assumed as 60,000 
 pounds, and for w the weight of a linear foot of the cable measured 
 horizontally and having a cross-section of one square inch, which is 
 3.54 pounds, we obtain L : =15100 feet; 
 and 
 
 p' + w_ 15160 
 w L 
 
 The values of p' and w in pounds, as determined previously, are as 
 follows : 
 
 p' =13605 + 27761726 Lr 1 -}- 3.21906 L + 0.00055335 L 2 + 0.000000003 L 3 
 10=17917. 
 
 Substituting these values and reducing we obtain 
 31522 L + 3.21906 L 2 + 0.00055335 L 3 -j- 0.000000003 L 4 = 213S56991, 
 the solution of which gives for the practical maximum span 
 
 L=1335 feet. 
 
 This span is measured between the highest points of the cables at 
 opposite ends of the bridge. 
 
 The Board consider this a conservative value of the maximum span, 
 as it is based upon assumptions well within the limits of theory and 
 experience. * 
 S. Ex. 1 S 
 
32 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 The elements of the bridge, deduced by the preceding formulas, are 
 as follows: 
 
 Span between tops of cables feet.. 4,335 
 
 Height of towers above masonry : do. 707 
 
 Number of cables 16 
 
 Diameter of each cable with wrapping inches.. 21A 
 
 Suspended iceiglit per linear foot of span. 
 
 Pounds. 
 
 Live load 6,353 
 
 Platform 7,200 
 
 Stiffening girders 25.202 
 
 Wind bracing 4. 106 
 
 Cables 17,917 
 
 Cable wrapping 433 
 
 Suspenders 1, 445 
 
 Total suspended weight per linear foot , 62, 656 
 
 = 31. 328 tons. 
 
 Tons. 
 
 Suspended weight for whole middle span = 135, 807 
 
 Weight of backstays 24, 882 
 
 Weight of aut hor chains and |)lates 16, 038 
 
 Weight of towers . 57, 172 
 
 Total weight of metal in the bridge 233,899 
 
 THE RELATIONS BETWEEN SPAN, TRAFFIC AND COST. 
 
 In the preceding pages the Board have determined to the best of 
 their ability the maximum span practicable for a suspension bridge 
 from a purely engineering point of view. Their instructions further 
 require them to investigate the maximum span " consistent with an 
 amount of traffic probably sufficient to warrant the expense of con- 
 struction." This involves the consideration of two subjects; the cost 
 of construction and the traffic capacity of the bridge. 
 
 The cost of a suspension bridge can not be determined simply as a 
 function of the span and traffic. In the construction of every such 
 bridge there are elements of cost which depend almost entirely upon 
 local conditions, and can not be estimated even with the roughest 
 approximation until these conditions are fully known. For example, 
 the cost of the piers will depend upon the depth of the solid foundation 
 below the bottom of the stream or the surface of the ground; the cost 
 of the towers and anchorages will depend upon the height at whicli it 
 is necessary to elevate the roadway above the- water surface, which 
 again will depend upon the character of the river navigation; the cost 
 of spaces for anchorages, approaches and terminal facilities will depend 
 upon the local land values. 
 
 By examining the detailed costs of several very large bridges, it is 
 found that these indetermiu ate local elements constitute on the average 
 more than GO per cent of the cost of such bridges in cities. It has been 
 stated that in the case of the New York and Brooklyn Bridge, the cost 
 of the bridge structure proper was only one-third of the expenditure 
 for the entire work. In the case of the suspension bridge to cross the 
 Hudson at New YoTk, estimated for by the New York Board, the local 
 elements determine about 54 per cent of the whole estimated cost, 
 although the cost of approaches, terminal facilities and land are not 
 included. 
 
 The determination of any relation between traffic capacity and the 
 cost of construction warranted thereby is equally difficult. It may, of 
 course, be assumed that the bridge of maximum span will be constructed 
 only in a locality where the conditions of commerce justify the belief 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 33 
 
 that the traffic capacity of the bridge will be fully utilized. But in the 
 general case it is impossible to determine what charges the traffic will 
 bear. Moreover, the construction of such a bridge might be desirable 
 even if the traffic were not likely to give a sufficient return for the vast 
 sum invested. By the combined action of railroad companies, such a 
 bridge might be built for the general benefits resulting from increase 
 and facility of traffic, even though it might fail to earn directly a reason- 
 able interest on its cost ; and the enterprise might be assisted by adja- 
 cent cities, as was done in the case of the New York and Brooklyn 
 Bridge. 
 
 But while the Board have been unable to arrive at definite conclusions 
 in the general case, they believe that much may be learned from the 
 study of the problem as limited by the conditions of a special locality, 
 and the material for such an inquiry is furnished by recent investiga- 
 tions in connection with proposed bridges across the Hudson River at 
 New York. 
 
 It is said that the number of ferry passengers crossing from New 
 Jersey to New York City now exceeds 85,000,000 per year, and the 
 passenger and freight traffics are growing rapidly. It can scarcely be 
 doubted that a bridge in this locality wonld be used to its full capacity. 
 Such a bridge wonld, however, be employed principally for passenger 
 traffic, the facilities for moving freight on floats at water level to any 
 point on the water fronts being ample and convenient. 
 
 The Hudson River at New York forms the most important part of 
 the interior harbor. Its mid-channel depth of at least 49 feet, and its 
 clear width of at least 2.800 feet between pier-head lines, make it one 
 of the finest roadsteads in the world. It is navigated by an enormous 
 commerce. Strong protests against its obstruction by a pier in the 
 channel have been made by the commercial interests of the port. The 
 least objectionable location for such an obstruction would be not far 
 from the middle point, between the pier-head lines, where it would 
 divide the upstream and downstream traffic, but this location is pro- 
 hibited by the great depth to a firm foundation. 
 
 The New York Board reported that it is safe and practicable to cross 
 the river with a single span, and estimated the cost of a suspension 
 bridge for that purpose, its New York pier being between Fifty-ninth and 
 Sixtieth streets, at $30,743,000. This is the estimate for their Lighter 
 Structure, but it provides for a bridge amply sufficient for the purposes for 
 which it is intended. Moreover, the estimate was made for the purposes 
 of comparison, and the report of the Board distinctly states that it is not 
 to be taken as an absolute estimate of cost. This Board considers this 
 estimate perfectly satisfactory for the purpose for which it was made, 
 but they think it desirable to determine a minimum as well as a maxi- 
 mum estimate, to show the variations to which such estimates are liable 
 and how much they are affected by legitimate differences in the assump- 
 tions upon which they are based. An estimate has therefore been made 
 on the following assumptions : 
 
 The cost of structural steel is taken at 4 cents per pound, in accord- 
 ance with the views of a majority of the New York Board, as indicated 
 in their report. 
 
 The cost of wire work is taken at 7 cents per pound, which is based 
 npon prices given by leading manufacturers and upon actual experi- 
 ence in the case of the New York and Brooklyn Bridge. 
 
 The weights of metal are determined by the formulas given in this 
 report. 
 
 The bridge is supposed to be located near Sixty-ninth street, New 
 S. Ex. 12 3 
 
34 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 York, and the cost of the substructure is assumed to be the cost at the 
 lower location (between Fifty-ninth and Sixtieth street), as estimated 
 by the Xew York Board, less $2,900,000, which they state would be 
 saved by adopting the upper location. The minimum estimate is as 
 follows : 
 
 Structural steel : 
 
 Suspended weights. pounds. . 90, 870, 000 
 
 Towers do.... 52,313,000 
 
 Chains and anchor plates do 18, 324, 000 
 
 Total do.... 161,507,000 
 
 At 4 cents per pound $6, 460, 280 
 
 Wire work: 
 
 Main cables and wrapping pounds. . 30, 358, 000 
 
 Backstays and wrapping do 22, 738. 000 
 
 Suspenders do 3, 222^ 000 
 
 Total do.... 56,318,000 
 
 At 7 cents per pound $3, 942, 260 
 
 Cost of superstructure 10, 402, 540 
 
 Cost of substructure 11, 784, 000 
 
 Total cost of bridge 22, 186, 540 
 
 The final plans for a work of such magnitude would only be adopted 
 after the most extended theoretical and experimental investigations, 
 and the estimated cost would undoubtedly be much reduced by such 
 studies. Assuming the most favorable location and the most compe- 
 tent engineering management, the Board believe that $23,000,000 is a 
 reasonable estimate for a six-track railroad suspension bridge 3,200 feet 
 long, and they consider the amount of traffic which such a bridge would 
 accommodate sufficient to warrant the expense of construction. They 
 believe, however, that the bridge should be so constructed that its 
 capacity can be readily increased, and with the suspension system this 
 can be provided for by giving suitable dimensions to the towers and 
 anchorages. 
 
 If sufficient inducements were offered to competent engineers to pre 
 pare competitive designs and estimates for a single- span bridge at this 
 locality, the Board do not doubt that perfectly satisfactory plans would 
 be obtained within the limit of cost of the estimate given above. 
 
 The Board desire to express their obligations to Mr. Gustav Linden- 
 thai, C. E., Mr. W. Hildenbrand, O. E. and Mr. L. L. Buck, O. E. for 
 information and valuable suggestions. 
 
 The following appendices accompany this report : 
 
 Appendix A. — Orders and instructions. 
 
 Appendix B. — Correspondence with wire manufacturers. 
 
 Appendix C. — Wind pressure. 
 
 Appendix D. — Temperature Strains in Three Hinged arches, by Gustav Linden- 
 thai, C.E. 
 
 Appendix E. — The Theory of the Stiffening- Girder, by Prof. J. Melan. 
 
 Respectfully submitted. 
 
 C. W. Raymond, 
 Major, Corps of Engineers. 
 
 Wi. H. Bixby, 
 Captain, Corps of Engineers. 
 
 Edw. Burr, 
 CaptaifZ, Corps of Engineers. 
 
 Brig. Gen. Thomas L. Casey, 
 
 Chief of Engineers, U. 8. A. 
 
REPORT 
 
 OF 
 
 BOARD OF EXGIXEEES 
 
 9 
 
 NEW YORK AND NEW JERSEY BRIDGE. 
 
 So 
 
Extract from act of Congress entitled "An Act To authorize the New York and New 
 Jersey Bridge Companies to construct and maintain a bridge across the Hudson River 
 beUveen New York City and the State of New Jersey," approved June 7, 1894. 
 
 Be it enacted by the Senate and House of Representatives of the United States of America 
 in Congress assembled, That * * * the President shall appoint a hoard, consist- 
 ing of five competent, disinterested, expert bridge engineers, of whom one shall be 
 either the Chief of Engineers or any member of the Corps of Engineers of the United 
 States Army, and the others from civil life, who shall, within thirty days after their 
 appointment, meet together and, after examination of the question, shall, within 
 sixty days after their first meeting, recommend what length of span, not less than 
 two thousand feet, would be safe and practicable for a railroad bridge to be con- 
 structed over said river, and file such recommendation with the Secretary of War, 
 but it shall not be final or conclusive until it has received his written approval. In 
 case any vacancy shall occur in said board, the President shall fill the same. The 
 compensation and expenses of said board of engineers shall be fixed by tne Secre- 
 tary of War and paid by the said bridge companies, which said companies shall 
 deposit with the Secretary of War such sum of money as he may designate and 
 require for such purpose : Provided, always, That nothing herein contained shall be 
 construed as preventing the said board of engineers from meeting, investigating, 
 and filing their recommendation after the expiration of said time herein mentioned. 
 
 MEMBERS OF BOARD APPOINTED BY THE PRESIDENT. 
 
 C. W. Raymond, 
 
 Major, Corps of Enqineers, TJ, S. Army. 
 Mr. G. Bouscaren. 
 
 Mr. W. H. Burr. 
 
 Mr. Theodore Cooper. 
 
 Mr. Geo. S. Morison. 
 
 36 
 
REPORT 
 
 OF 
 
 BOARD OF ENGINEERS ON NEW YORK AND NEW 
 JERSEY BRIDGE. 
 
 Office of the Chief of Engineers, 
 
 United States Army, 
 Washington, D. C, September 29, 1894. 
 Sir: Beferring to report, dated August 23, 1894, by the Board 
 appointed under the provisions of the act of Congress of June 7, 1894, 
 to consider length of span of proposed bridge across Hudson Eiver 
 between Fifty-ninth and Sixty -ninth streets, Sew York City, I beg to 
 recommend that 500 copies of the report of the Board be printed at the 
 Government Printing Office. 
 
 Very respectfully, your obedient servant. 
 
 Thos. Lincoln Casey, 
 Brig.-Gen., Chief of Engineers. 
 
 Hon. D. S. La^iont, 
 
 Secretary of War, 
 
 Approved: 
 
 Daniel S. Lamont, 
 
 Secretary of War, 
 
 REPORT OF BOARD OF ENGINEERS. 
 
 New York, August 23, 1894. 
 Sir: The Board of Bridge Engineers appointed by the President 
 under the act of Congress, approved June 7, 1891, authorizing the New 
 York and New Jersey Bridge companies to construct a bridge across 
 the Hudson Eiver, met at the Army Building, New York City, on Mon- 
 day. June 25. 
 
 Your Board organized by electing Maj. C. W. Baymoud, Corps of 
 Engineers, U. S. A., chairman, and Mr. Cooper, secretary. 
 
 Your Board began the examination of the question submitted to them 
 and gave it careful and continuous consideration up to the present 
 time ; they have held 29 regular meetings. 
 
 Your Board personally visited and examined the site of the proposed 
 bridge as defined by the act. 
 
 They applied to the New York and New Jersey Bridge companies 
 for their surveys, borings, plans, estimates, and such other data as 
 referred to the proposed bridge. The surveys and borings furnished 
 
 37 
 
38 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 upon this application having been made for a former location not within 
 the limits stated in the act, other surveys and borings upon lines 
 within these limits were made at the request of the Board. 
 
 The New York and New Jersey Bridge companies, by their engi- 
 neering representative, Mr. Charles Macdonald, presented plans pre- 
 pared by the Union Bridge Company tor the proposed bridge, with a 
 statement as to cost, estimated traffic, and other data, which are given 
 in Appendix B. 
 
 During the sessions public hearings were given to a special com- 
 mittee of the New York Chamber of Commerce, through its chairman, 
 Mr. Gustav H. Schwab, and its engineering counsel, Mr. W. Hilden- 
 brand, and also to Mr. G. Lindenthal, chief engineer of the North 
 Biver Bridge Company. Their statements will be found in Appen- 
 dixes C and D. 
 
 The duties of your Board as prescribed by the act are to " recom- 
 mend what length of span, not less than 2,000 feet, would be safe and 
 practicable for a railroad bridge, to be constructed over said river." 
 The act provides that this bridge "shall not be located below Fifty- 
 ninth street, New York City, nor above Sixty-ninth street, New Y^ork 
 City." Your Board, therefore, understand their duties to be to recom- 
 mend what length of span, not less than 2,000 feet, would be safe and 
 practicable for a railroad bridge to be constructed over the Hudson 
 River between Fifty-ninth and Sixty-ninth streets in the city of New 
 York. 
 
 In making comparative estimates, your Board selected a location 
 midway between Fifty-ninth and Sixtieth streets, but the difference 
 between this location and one further north within the limits of the 
 act has been considered so far as it affects the general conclusions. 
 
 The minimum length of span which may be considered is 2,000 feet, 
 which your Board have interpreted as meaning 2,000 feet in the clear. 
 The maximum length of span would be a clear span between the pier- 
 head lines, this distance varying from 3,130 feet at Fifty-ninth street 
 to 3,080 feet at Sixty-ninth street. 
 
 The objections which have been raised to a pier in the river apply 
 with equal force to any pier located between the end of a 2,000-foot 
 span and the pier-head line, the pier being objected to as interfering 
 with the use of the river for harbor purposes rather than for through 
 navigation. The plans submitted to your Board have located the 2,000- 
 foot span, in accordance with the requirements of the New Y A ork char- 
 ter, next to the New York pier-head line, thus placing the west pier 
 about 1,000 feet from the New Jersey pier-head line; if the span is 
 increased beyond 2,000 feet any injury done to the harbor by obstructing 
 the approach to piers on the New Jersey shore would be greater than 
 any benefit gained by increased width of channel span. Your Board 
 have considered that navigation would not be benefited by making a 
 span of greater length than 2,000 feet, unless such span could reach from 
 pier-head line to pier-head line; they have therefore confined their 
 examination to a span of 2,000 feet in the clear, as compared with such 
 single span. It must be noted, however, that the pier-head lines are 
 artificial and are subject to change under existing laws. The width 
 between pier-head lines at this location is about 400 feet greater than 
 at a point 2 miles below. A small encroachment beyond these pier -head 
 lines could be permitted without essential harm; it would obstruct 
 navigation no more than a vessel lying across the head of a pier; a 
 span of 3,100 feet in the clear would meet all the requirements of a 
 single span. 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 39 
 
 The plans submitted by the bridge companies provide for a cantilever 
 bridge carrying six railroad tracks. This number of tracks is the least 
 that has been proposed by any company which has contemplated bridg- 
 ing the Hudson River opposite the city of iSew York. Your Board 
 have therefore thought it right to make estimates for a bridge furnish- 
 ing this accommodation. 
 
 The fact that the river must be kept unobstructed during erection 
 limits the plans to cantilever and suspension bridges. The plans sub- 
 mitted by the bridge companies provide for a steel cantilever bridge, a 
 description of which is given in Appendix B. 
 
 A cantilever bridge is a rigid structure, subject to those changes of 
 shape only which are due to strains; it is well adapted to railroad uses. 
 
 In the first place, your Board are of the unanimous opinion that a 
 cantilever span of 3,100 feet in the clear could be built and would be a 
 safe structure. 
 
 In the second place, your Board have considered that the practica- 
 bility of such a structure would depend upon its cost, and to determine 
 this practicability, have made comparative estimates of the cost of two 
 cantilever bridges with clear spans of 2,000 and 3,100 feet, respectively. 
 These estimates are comparative rather than absolute; the benefit of 
 the doubt, where any exists, has been given to the longer span. The 
 estimates include both substructure and superstructure, but have been 
 made in round numbers and do not include the cost of tracks and other 
 features which would be common to both plans. 
 
 A series of borings, covering virtually the limits permitted by the act, 
 have been made by the bridge companies under the direction of Mr. C. 
 B. Brush, c. E., at the request of your Board, to determine the character 
 of the bottom of the river. 
 
 These borings have found rock at varying depths, but as the borings 
 were not extended into the rock, the absolute information before your 
 Board is that no rock exists above the reported elevation rather than 
 that solid rock Exists below it; but your Board have considered them- 
 selves justified in assuming that it is a substantial rock, suitable for 
 foundations. The borings outside the limits of the special line consid- 
 ered have confirmed the accuracy of the others. 
 
 The depth to rock is about 125 feet at each pier-head line; it is about 
 260 feet at the site where the pier of the 2,000-foot span bridge would 
 come; the rock rises rapidly from each pier-head line shoreward. The 
 depth of water at the site of the river pier is about 50 feet. Under 
 the water is a layer of mud or silt about 100 feet deep. Below this 
 mud is a fine sand filled with fresh water under a pressure exceeding 
 the head due to its depth. 
 
 The mud or silt is not a suitable material for the foundation of bridge 
 piers. For the comparatively moderate weights carried by bridges of 
 usual dimensions, the sand would be a suitable foundation. For the 
 extraordinary weights and dimensions of the bridge authorized by the 
 act. your Board arc not satisfied that the piers would be safe unless 
 founded on rock, and the comparative estimates have been made for 
 rock foundations. 
 
 The lateral provisions to resist wind and the longitudinal provisions 
 for stability during erection require a considerable base: the plans sub- 
 mitted by the bridge companies propose to use a pier consisting of four 
 cylinders placed 200 feet between centers in each direction. The total 
 reaction, including the effects of wind pressure, carried on each cylin- 
 der is estimated at 25,000 tons. 
 
40 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 In proportioning these piers, your Board have found it necessary to 
 adopt limits of stress. They have based their estimates on the suppo- 
 sition that the pressure between the metallic bedplates and the top of 
 the masonry should not exceed 20 tons to the square foot, and that 
 the pressure within the masonry and on the foundation should 
 nowhere exceed 10 tons to the square foot; they consider, however, that 
 in determining these pressures the weight of the material displaced 
 should be deducted. The weight of masonry per cubic foot was taken 
 at 150 pounds in air, at 87 pounds in water, at 50 pounds in mud, and 
 at 30 pounds in sand. While these pressures have been exceeded in 
 some structures, they are higher than usual practice and call for 
 masonry of good quality and more than ordinary cost. 
 
 Your Board have assumed that the masonry would finish 50 feet 
 above water, and have estimated the cost of these piers, including 
 excavation and sinking, at $1 per cubic foot above a plane 125 feet 
 below water, and have added 8 mills to this price for each additional 
 foot of depth. 
 
 2,000-FOOT CLEAR-SPAN CANTILEVER. 
 
 The east pier of the bridge, with a clear span of 2,000 feet, would 
 be immediately back of the New York pierhead line, where the rock is 
 125 feet below mean high water. The west pier would come in the river, 
 where the rock is 260 feet below mean high water. The east anchorage 
 would be within the shore line, where the rock is not more than 20 feet 
 below mean high water, and the west anchorage would be immediately 
 west of the New Jersey pierhead line, where the rock is 125 feet below 
 mean high water. The site of the west anchorage calls for an anchor- 
 age span 100 feet longer than is shown on the plans submitted by the 
 bridge companies. 
 
 The east pier would consist of four cylinders, each containing 866,000 
 cubic feet, and costing on the basis 0ven above. $866,000, making for 
 the four cylinders, $3,464,000. 
 
 At the site of the west pier the average depth to rock is not less 
 than 260 feet. A foundation carried to rock here would be nearly 100 
 feet deeper than any foundation which has ever been put in. Such a 
 foundation involves very careful consideration, and your Board believe 
 that the additional price allowed for so much of the work as is more 
 than 125 feet below water is none too large. Each of the four 
 cylinders would contain 1,880,000 cubic feet, of which 1,014,000 would 
 be more than 125 feet below water, making the cost of each cylinder 
 $2,427,500, and the cost of the four cylinders $9,710,000. 
 
 The east anchorage pier would be founded on rock about 20 feet 
 below mean high water, and the west pier on rock 125 feet below water. 
 Each of these piers has been estimated on the basis of a pier finishing 
 150 feet above high water, 20 feet thick, and 100 feet long on top, built 
 with a batter of 1 in 20, and founded on a caisson 40 by 120 feet for 
 the east pier and 45 by 125 feet for the west pier. Taking the cost of 
 the work above water at 75 cents per cubic foot, and of the work below 
 water at $1, the cost of the east pier becomes $431,000 and that of the 
 west pier $1,038,000. 
 
 The cost of the substructure for the bridge, with the 2,000-foot clear 
 span, would then be: 
 
 East anchorage $-131. 000 
 
 East pier 3,464,000 
 
 West pier 9,710,000 
 
 West anchorage 1, 038, 000 
 
 Total 14, 643, 000 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 41 
 
 A careful estimate prepared by the bridge companies makes the 
 weight of the superstructure 230,000,000 pounds, including the main 
 span, the towers, and the two anchorage spans, covering a total length 
 of 4,120 feet. This weight has been checked, and may be taken as 
 approximately correct. The plan was prepared for a location at Seventy- 
 second street, where the distance between pierhead lines is 3,070 feet. 
 At Fifty-ninth street the west anchorage span would be lengthened 
 100 feet, and if the bridge is kept symmetrical the whole length will be 
 increased to 4,320 feet, and the total weight to about 240,000,000 pounds. 
 This estimate is based on a moving load of 3,000 pounds per foot of 
 track and on maximum working stresses of from 20,000 to 22,500 pounds 
 per square inch, or about one-third of the ultimate strength of the 
 material; 240,000,000, at 4£ cents per pound, would cost $10,800,000. 
 The cost of this bridge would then be $25,443,000. 
 
 This is the cost of a cantilever bridge of the minimum span which 
 your Board are authorized to consider, the length of the entire structure, 
 from anchorage to anchorage, being 4,320 feet. As this plan of bridge 
 is the one which the New York and New Jersey Bridge companies 
 have selected as the bridge they wish to build, its cost must be accepted 
 for present purposes as the cost of a practicable structure. 
 
 3,100-FOOT CLEAR-SPAN CANTILEVER. 
 
 The site of the east pier for the span of 3,100 feet in the clear would 
 be the same as that for the 2,000-foot span; the site of the west pier 
 would' be the same as that of the west anchorage for the 2,000-foot 
 span: botli piers would be founded at practically the same depth, or 
 125 feet below mean high water. 
 
 The weight of the trusses of the long span would be about three times 
 the weight of those of the short span, and the weight of the floor and 
 moving load would be about one and a half times that of the short span. 
 The total reacticfn on the piers would be at least two and one-half times 
 that of the short span. On this supposition each of the four cylinders 
 would have to carry 62,500 tons. 
 
 The piers in both bridges are so large that their volume can be pro- 
 portioned directly to the weights they have to carry. This would make 
 the volume of each pier of the 3,100-foot span bridge two and one half 
 times that of the east pier of the 2,000-foot span bridge. The estimated 
 cost of the east pier of the 2,000-foot span bridge was 83,404,000, so 
 that we may estimate the cost of each of the two piers of the 3,100- 
 foot span bridge at $8,660,000. 
 
 The anchorage piers required for the long-span bridge need be little 
 larger above the water level than for the shorter span. The anchorage 
 pier on the east side would be on rock about 20 feet below mean high 
 water: its cost would be about the same as that for the 2,000-foot span. 
 The anchorage pier on the west side would be on rock 40 feet below 
 mean high water, and is estimated to cost 8527.000. 
 
 The total cost of the substructure for the 3,100-foot clear span bridge 
 would then be : 
 
 East anchorage $431, 000 
 
 East pier 8, 660. 000 
 
 West pier 8, 660, 000 
 
 West anchorage 527.000 
 
 Total 18,278,000 
 
42 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 Estimates made by this board show that the weight of the super- 
 structure of this bridge would be approximately 730,000,000 pounds, 
 about three times that of the shorter span bridge ; 730,000,000 pounds 
 at 4J cents per pound is $32,850,000. 
 
 The total cost of the 3,100-foot span bridge, covering a length of 
 6,100 feet from anchorage to anchorage, may, therefore, be estimated at 
 $51,128,000, though this estimate is probably too low. 
 
 The estimated cost of the 2,000-foot span bridge was $25,443,000 for 
 4,320 feet; to bring it into proper comparison with the longer span 
 bridge 1,780 feet of viaduct must be added; estimating this viaduct at 
 $1,000 a foot, the cost becomes $27,223,000. The estimated cost of the 
 long-span cantilever bridge is $23,905,000 more than this amount. 
 
 Your Board are of the opinion that the additional cost of the long- 
 span cantilever bridge is so great that it must be considered imprac- 
 ticable. 
 
 SUSPENSION BRIDGE. 
 
 A suspension bridge is another possible form of construction at this 
 location; like the cantilever, it can be erected without false work; 
 unlike the cantilever, it has not generally been considered well adapted 
 to railroad uses. 
 
 It has less rigidity than the cantilever, and deflects more from the 
 combined effect of temperature and load; the flexibility of the cables 
 tends to cause vertical undulations of the platform under a moving 
 load, which are more objectionable for a railroad bridge than for a 
 highway bridge, where the live load is less concentrated and is applied 
 less rapidly; these objections lessen in importance as the span of the 
 bridge and the proportion of the dead to the live load increase. 
 
 In a bridge with six independent tracks the condition of railroad 
 service approaches that of highway service, and the position of trains 
 which will produce a maximum disturbance would be of very rare occur- 
 rence. The inclination of the platform longitudinally and transversely, 
 arising from the undulations of the cables under the effect of moving 
 trains, can be reduced within unobjectionable limits by a proper system 
 of stiffening; the effect of wind on cables and platform can be taken 
 care of by cradling the cables and by a lateral system of bracing in the 
 platform similar to that used in truss bridges. A single railroad track 
 suspension bridge of 850-foot span has been in continuous use, under 
 restrictions of load and speed, for nearly forty years at Niagara; with 
 this example before us, a six-track railroad suspension bridge of 3,100 
 feet clear span can not be dismissed without careful consideration. 
 
 Your Board have therefore investigated such suspension bridge with 
 great care, and it is their opinion that it could be built and that it would 
 be a safe structure. As this opinion may be thought a departure from 
 general opinion as to the adaptability of the suspension bridge to rail- 
 road service, it is proper that the Board should state their reasons there- 
 for, and explain the features of the plan adopted by them for a com- 
 parative estimate in more detail than was done for the cantilever plans. 
 
 The essential differences between a cantilever and a suspension 
 bridge are, (1) that in place of the compression chords of the cantilever 
 we have land anchorages built of eyebars and masonry; (2) in place 
 of the tension chords of the cantilever we have cables built of wire of 
 a superior grade of metal; (3) in place of the web bracing of the 
 cantilever we have a composite system of suspenders and stiffeners. 
 
 No question can be raised as to the safe and permanent character of 
 the anchorages if built with a sufficient factor of resistance and proper 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 43 
 
 provisions for thorough protection of the anchor chains against rust- 
 ing; they have the advantage over the compression chords of the can- 
 tilever that their weight is supported directly on the ground, instead 
 of forming a part of the dead load to be carried. 
 
 As regards safety and efficiency, the wire cables are fully equal to 
 eyebar chords, if built with the same margin of strength ; experience 
 shows that they can be effectively protected against rusting by wire 
 wrapping and painting; wire at least three times as strong as eyebar 
 steel is a merchantable article, and cables made of this wire have the 
 advantage over eyebar chords of less weight to be carried by the 
 superstructure. 
 
 The objections made to suspension bridges arise only from the third 
 difference. It is often claimed that a sufficient degree of rigidity can 
 not be secured for railroad purposes, and that the stiffening members 
 can not be properly proportioned, owing to the uncertainty which exists 
 in the intensity of stresses due to changes of temperature and elastic 
 deformation in the composite system. The Board has given careful 
 consideration to these objections and believe that for practical purposes 
 they are met in the plan selected. 
 
 Three principal methods have been employed to secure greater 
 rigidity in suspension bridges ; (1) by inclined stays extending from 
 the top of the towers to the platform — this system was advocated and 
 applied extensively by the late John A. Roebling; (2) by trussing the 
 cables either with straight chords, as in the Point bridge at Pittsburg, 
 or by a system of braces between two cables, as proposed by Mr. G. 
 Linden thai for his projected North River bridge; (3) by a stiffening 
 girder fastened to the platform and extending from one tower to the 
 other; this system is a feature common to nearly all suspension bridges, 
 but has seldom been applied in the most approved form to give the 
 best results. The first method is at best incomplete, as a stiffening 
 truss must be used for the middle half of the span. The second 
 method might pr«fve the most economical, but its application to wire 
 cables is still untried. Your Board have, therefore, selected the third 
 method, that of stiffening the truss. 
 
 The suspension bridge which your Board have selected for this loca- 
 tion would consist of a single span of 3,200 feet between saddles, thus 
 giving about 3,100 feet in the clear, the two towers being located at 
 the pierhead lines, and the cables being carried in straight lines from 
 the top of the towers to the anchorages, making equal angles on each 
 side of the towers. This form of bridge has no side spans, but the 
 tracks would be carried on viaducts between the towers and the anchor- 
 ages. While the use of cables outside the towers to sustain side spans 
 is generally considered economical, the arrangement selected gives the 
 least length of cable and reduces deflection from strains and tempera- 
 ture to a minimum. 
 
 The two towers would be located in practically the same position as 
 the towers of the 3,100-foot cantilever. The substructure would be of 
 masonry, finishing at the same height as the masonry of the cantilever 
 bridge piers. 
 
 The towers themselves would be of steel and would be 570 feet high 
 from top of masonry to saddles, or 620 feet from surface of water. 
 For towers of this height there is no question of the economy and 
 expediency of using metallic construction. 
 
 The anchorages would be of masonry, each located about 1,000 feet 
 back of the towers. Both towers and anchorages would have to be 
 founded on rock. 
 
44 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 The cables would be of wire, and the plans have been based on 
 cables containing about 6,000 No. 3 wires (0.259 inch in diameter). 
 Wireinakers are prepared to furnish a wire of this size of a guaran- 
 teed strength of 180,000 pounds per square inch at moderate prices 
 and a much stronger wire at a higher price. Your Board have adopted 
 as the unit stress on cables made of straight wire of this character 
 60,000 pounds per square inch, or one-third of the breaking stress, 
 this being the same proportion of the ultimate strength that the 20,000 
 pounds adopted in the cantilever structure bears to the probable 
 strength of eyebar steel. 
 
 Your Board have estimated on a versed sine of 400 feet, or one-eighth 
 of the span. In the East Eiver bridge the versed sine is less than 
 one-twelfth of the span and about the same as in other long-span sus- 
 pension bridges. In the East Biver bridge the cables are of steel wire 
 and the towers of masonry. With the introduction of steel toAvers, 
 the economical proportions are changed, and it becomes practicable to 
 adopt a greater versed sine than has hitherto been considered wise. 
 
 Stiffening truss. — There are several admissible forms of stiffening 
 truss; to justify the particular form selected by the Board for their 
 estimate it is proper to give a short explanation of its duties and mode 
 of action. 
 
 A stiffening truss is a girder supported by the cables and extending 
 from one tower to the other; it is fastened to the platform at the sev- 
 eral points of suspension to the cables and it may be fastened to the 
 towers in two ways; it maybe held in the vertical direction only, 
 anchored down as well as supported, and acting as a girder resting on 
 two supports, or it may be fastened also in the horizontal direction, 
 acting as a girder fixed at the ends. The Board have confined them- 
 selves to the first case, which has the advantage of greater simplicity 
 in computation of stresses, without material sacrifice of economy. 
 
 The function of a stiffening girder is to distribute a load covering 
 only a part of the span, over the entire span. If this function could 
 be performed without any deformation of the girder, the distribution 
 would be perfect and the symmetrical shape of the cables would be 
 preserved, but as the girder deflects under the load that it carries, it 
 exerts through the suspenders a downward pull on the cables as far as 
 the load extends, and beyond that point the cable exerts a pull upward 
 on the girder. If it is continuous it will take the shape of a reverse 
 curve with its point of contraflexure at the end of the load. The strain 
 in all the suspenders will be uniform for the whole length of span. The 
 weight to be carried by the loaded portion of the stiffening truss will 
 be the moving load upon it, less that carried by the suspenders. 
 
 The suspenders over the unloaded portion, where the cable tends to 
 rise, are strained by the resistance of the stiffening truss against flex- 
 ure upward. The weight per unit of length carried by the suspenders 
 will always be equal to the live weight per unit of length multiplied 
 by the length of load and divided by the length of span. Over the 
 loaded portion this is the actual weight per unit of length, less the por- 
 tion carried by the stiffening truss. Over the unloaded portion this 
 represents the upward pull resisted by the stiffening truss. The 
 upward force per unit of length, which tends to lift the unloaded por- 
 tion, is therefore the assumed weight per unit of length multiplied by 
 the length of load and divided by the length of span. The weight per 
 unit of length carried by the stiffening truss on the loaded portion is 
 the total weight per unit of length less that weight multiplied by 
 length of load and divided by length of span. 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 45 
 
 When one-half of the span is loaded, the weight will be equally 
 divided between suspenders and stiffening truss; the stresses in the 
 chords of the stiffening truss will be oue-eiglith those caused by the 
 same load extending over the whole length of span if the truss were 
 not supported by suspenders. 
 
 The greatest stresses occur in the continuous stiffening truss when 
 either two-thirds or one-third of the span is loaded. In the former case 
 the loaded portion must carry one-third of the load, and the chord 
 stresses at the middle of that two-thirds will be four twenty-sevenths of 
 the maximum stresses at center of span if the truss were fully loaded 
 and not supported by suspenders; in the latter case the chord stresses 
 at the center of the loaded portion will be only two twenty- sevenths, 
 while the chord stresses at the center of the unloaded portion will be 
 the four twenty-sevenths, but reversed. As the two-thirds load may be 
 placed anywhere in the truss, it follows that the chord stresses over 
 the whole central third may be four twenty- sevenths of the maximum 
 stress at center of span if the truss were fully loaded and not supported 
 by suspenders. 
 
 The shearing stresses in the webs of the stiffening truss are deter- 
 mined by the same distribution of loads. 
 
 It must be remembered that the only stresses in the stiffening truss 
 are those due to moving load, all dead weight being carried directly by 
 the suspenders to the cables. 
 
 While this is the simplest explanation of the duties of the stiffening 
 truss, it does not take into consideration all elements. The downward 
 and upward deflection of the stiffening truss must be accompanied by 
 corresponding changes in the shapes of the cables, but as these changes 
 are in the direction in which the cables would move if no stiffening tr uss 
 existed, it follows that the weight is not distributed equally among all 
 the suspenders and the stiffening truss is relieved of resisting so much 
 inequality as is taken by the cables. The elongation of the suspenders 
 is also a slight element of disturbance, but not sufficient to be described 
 here; an analysis of it will be found in Appendix E. 
 
 There are two other strains which the chords of the stiffening truss 
 may be called on to resist. The first of these is due to the deflection 
 of the cables under temperature and under load. As the stiffening 
 truss is not supposed to carry any of its own weight, it must deflect 
 with the deflection of the cables, and this deflection must be accom- 
 panied by the transfer of a portion of its weight to itself with corre- 
 sponding stresses in its chords, these chord strains being determined 
 entirely by the deflection. The other additional stress is due to wind 
 pressure if the chords of the stiffening truss are made the chords of 
 the lateral system, as in ordinary truss bridges. 
 
 The greater the depth of truss the less the chord stresses due to its 
 stiffening duty and the greater the stresses due to deflection of cables. 
 The wind stresses depend on the horizontal distance between the two 
 trusses. 
 
 To avoid the strains due to deflection of cables the stiffening truss 
 may be hinged at the center, which can be done by cutting one chord 
 and putting a pin joint in the other. This arrangement fixes the point 
 of contrary flexure at the center of the span under all conditions of 
 loading, and leaves the stiftening truss free to rise and fall with changes 
 of deflection in the cables without additional strain. As the bending 
 stresses at the center are now eliminated, the only function of the pin 
 joint will be to transfer the shearing stresses. With the introduction 
 of the hinge and the fixing of the point of contrary flexure, the work 
 
46 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 of the stiffening trass is modified, and the investigation becomes more 
 complicated; it is given in Appendix E. The truss still equalizes the 
 weight on all the suspenders, but the total weight carried by the sus- 
 penders is equal to the whole moving load only when that load covers 
 one-halt' the span. The greatest chord stresses in either direction occur 
 at a distance equal to 0.234 of the span from each end, and will be 
 0.1500 of the maximum stresses at center of a continuous span if the 
 truss were fully loaded and not supported by suspenders. The maxi- 
 mum chord stress in the hinged truss is, therefore, 1.017 times that in 
 the continuous truss, but it is a maximum only at two points instead 
 of over one-third the span. 
 
 The continuous truss is better adapted to resist wind than the hinged 
 truss, but its chords have to bear the additional stress due to derlec- 
 tion. As the hinged truss is practicable and more economical than the 
 other, it has been used in the estimates made by your Board. 
 
 The form which your Board have selected for a stiffening truss is a 
 riveted lattice girder 120 feet deep, the two trusses being placed 100 
 feet between centers. The web members are all inclined at an angle 
 of 45 degrees, and are in eight systems, so that the truss is divided 
 into 30-foot panels and the unsupported length of each Aveb member is 
 about 21 feet. The floor beams are hung from the suspenders and 
 carry the stiffening truss, the weight of which is never entirely over- 
 come by the action of the moving load. The top lateral system is a 
 comparatively light riveted lattice. The whole lateral work to resist 
 wind pressure is done by the bottom lateral system, in which the floor 
 beams form lateral struts and .the diagonals are strained in tension. 
 Cross bracing is provided at every panel point, to sustain the floor beams 
 at their centers and to transfer wind pressure to the bottom chord, the 
 pull of this cross bracing being resisted by the top lateral system. 
 
 Proportioning the trusses for a moving load of 3,000 pounds per foot 
 on each of the six tracks, the maximum chord stress at the center of 
 the half span would be 14,461,400 pounds, and the maximum chord 
 stress in the bottom chord at the center, taken on the basis of a wind 
 pressure of 2,000 pounds per linear foot, would be 25,000,000 pounds. 
 As the chords are subject to reversal of strains, your Board have limited 
 the stresses in the chords due to moving load to 12,500 pounds per 
 square inch in each direction, making an extreme variation of 25,000 
 pounds, but have allowed the stresses from the combined effects of 
 moving load and wind to run up to 22,500 pounds, believing that, with 
 the arrangement of cradled cables hereinafter described, the wind 
 strains will never be anything like what has been estimated on. They 
 have also estimated on the chord sections never being less than 400 
 square inches. With these conditions, the average section of the bot- 
 tom chord becomes 996 square inches, and that of the top chord 905 
 square inches, the two averaging 950 square inches. Allowing 25 per 
 cent excess for details, the average weight of each chord will be 
 4,037.5 pounds per linear foot. 
 
 The average shear in the web system will be 3,000,000 pounds, in 
 addition to which the web system has to do a duty in transferring 
 Weight from the upper to the lower chord equivalent to a shear of 
 1,300,000 pounds per linear foot, making the total duty of each web 
 equivalent to an average shear of 4,300,000 pounds. If the web is pro- 
 portioned on the basis of 12,500 pounds per square inch, with an allow- 
 ance of 50 per cent for details and connections, the weight of each web 
 becomes 3,509 pounds per linear foot. 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 47 
 
 The calculated weight of the top laterals is 500 pounds per linear 
 foot. The calculated weight of the bottom laterals, on the basis of 25,000 
 pounds stress per square inch, with an allowance of 25 per cent for 
 details, is 1,150 pounds per linear foot, making a total weight of later- 
 als 1,650 pounds per linear foot. 
 
 The floor beams weigh 90,000 pounds each, or 3,000 pounds per lin- 
 ear foot of bridge. The stringers weigh 1,800 pounds per linear foot of 
 bridge. Floor beams and stringers are proportioned for a consolidated 
 locomotive weighing, with tender, 104 tous. The total weight of the 
 suspended superstructure per linear foot may then be taken as follows: 
 
 Pounds. 
 
 4 chords, at 4,037.5 pounds 16,150 
 
 2 webs, at 3,509 pounds 7,018 
 
 Laterals 1,650 
 
 Cross frames and hangers 1,920 
 
 Floor beams 3,000 
 
 Stringers 1,800 
 
 Total steel per linear foot 31,538 
 
 This amounts to 100,921,600 pounds for the 3,200 feet of span. If to 
 this we add 2,400 pounds for the weight of the ties and rails and 18,000 
 pounds for moving load, we have as the total weight carried by the sus- 
 penders 51,938 pounds or 26 tons per linear foot. 
 
 This stiffening truss is a very different structure from the stiffening 
 truss of any existing bridge. It is what it purports to be, a stiffening 
 truss, with a heavy floor system like that used in the cantilever design, 
 and with stiff connections throughout. This stiffening truss, 3,200 
 feet long with its floor system, weighs two-fifths as much as the entire 
 4,320 feet of steelwork of the 2,000-foot cantilever bridge. 
 
 Suspenders. — The suspenders would be either wire ropes or cables of 
 straight wires, like the main cables. They have been proportioned on the 
 basis of a stress of 30,000 pounds per square inch of section, and on this 
 basis, with an aflowance of 20 per cent for connections, will weigh 1,425 
 pounds per linear foot, making the whole weight transferred to the 
 cables 53,363 pounds. The suspenders weigh 4,560,000 pounds for the 
 3,200 feet. 
 
 Cables. — The average weight of the cables will be 14,792 pounds 
 per linear foot of bridge. The total weight to be carried by the cables 
 may therefore be taken at 68,100 pounds per linear foot, amounting to 
 217,920,000 pounds or 109,000 tons for the span of 3,200 feet. The 
 versed sine assumed is 400 feet, or one-eighth of the span. The great- 
 est strain in the cables will be next to the saddles, and will be equal to 
 the weight carried multiplied by 1.118, amounting to 243,724,000 
 pounds, which, at 60,000 pounds per square inch, will require 4,062 
 square inches. Six thousand No. 3 wires have a total area of 316 
 square inches. The 4,062 square inches may be divided into 12 cables 
 of 338.5 inches each. Your Board believe that these cables can be con- 
 structed now as easily as those of the East River bridge were at the 
 time it was built. 
 
 The arrangement of cables which has seemed most feasible to your 
 Board, and which has been used for the basis of these estimates, places 
 six cables on each side, the cables being 20 feet apart on top of towers, 
 the two cables next to the center on each side being in vertical planes, 
 and the other cables cradled into planes which intersect in the lines of 
 the pins which sustain the floor beams. A separate suspender reaches 
 from each pin to every cable, the suspenders being in the same planes 
 as the cables. Vertically the cradling of the outside cables is 100 feet 
 S. Ex. 1 9 
 
48 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 in a height of 460 feet, or 1 in 4.6. Horizontally it is 100 feet in a 
 total length of 3,200 feet, so that the horizontal cradling of the two 
 outside cables is 200 feet in 3,200 feet, or 1 in 16. A sufficient cradling 
 is obtained not only to resist the entire wind pressure on the cables, 
 but to relieve the lateral system very materially. The distance between 
 the cables will favor simultaneous construction. The suspenders at 
 each point will be of uniform length and will pull together. The length 
 of the suspenders at the center of the span must be enough to allow 
 the cables to clear each other where the attachment is made, and this 
 places the lowest parts of the cables 60 feet above the pins. The total 
 height of the towers above high water is made up as follows: Clear- 
 ance required by law, 150 feet; camber, 10 feet; shortest suspender, 60 
 feet; versed sine, 400 feet; total, 620 feet. 
 
 The total length of each cable, from anchorage to anchorage, is 5,609 
 feet. The weight of each of the 12 cables, per linear foot of cable, 
 including wrapping, is 1,183 pounds. The weight of the 12 cables is 
 14,200 pounds per linear foot, and the total weight of the cables, 
 79,647,800 pounds. 
 
 Towers. — The weight transferred by the cables to each tower is 
 218,000 pounds. The towers are 570 feet high from top of masonry to 
 saddles. As these towers are only in compression and the members so 
 large that they may be treated as short compression members, a stress 
 of 20,000 pounds per square inch at the top is permissible. This 
 requires 10,900 square inches of section. The weight of each tower 
 with an allowance of 80 per cent for details and connections would be 
 38,023,560 pounds or 76,047,000 pounds for both towers. The total 
 weight to be carried on the lower part of the tower would be 128,000 
 tons, making a pressure of less than 24,000 pounds per square inch at 
 the base of the steel columns, which will be very slightly increased by 
 the wind pressure and by the horizontal deflections at the top of the 
 towers if the saddles do not move freely. 
 
 Anchor chains. — The cables are carried in straight lines from the 
 saddles to the anchorages, each anchorage being in two parts, each 
 part anchoring the six cables on its side of the bridge. The upward 
 pull of the cables at each anchorage (one side) is 54,500,000 pounds 
 and the horizontal pull 109,000,000 pounds. The estimates have been 
 made on the basis of connecting the cables with the anchor bars out- 
 side of the masonry of the anchorage, placing these anchor bars in tun- 
 nels, and connecting them with bearing plates at the lower end; every- 
 thing would be accessible for care and repairs. The chains would be 
 of steel eyebars which have been proportioned for a stress of 20,000 
 pounds per square inch with an allowance of 20 per cent for details. 
 The estimated weight of the bars and pins in each of the four half 
 anchorages is 6,825,000 pounds, while the plates at the bottom would 
 add 600,000 pounds to this amount, making the total weight in each 
 half anchorage 7,425,000 pounds, or 29,700,000 pounds in the four. 
 
 Structural steel. — In estimating the cost of the structural steel work, 
 your Board have used the same price per pound as for the work in the 
 cantilever bridge, namely, 4£ cents. On this basis the cost would be as 
 follows : 
 
 Pounds. 
 
 Suspended superstructure 
 
 Towers 
 
 Chains 
 
 Anchor plates 
 
 100, 921, 600 
 76, 047, 000 
 27, 300. 000 
 2, 400, 000 
 
 Structural steel 
 
 206, 668, 600, at 4£ cents, $9,300,087. 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 49 
 
 Tlie majority of the Board believe that this price is too high, owiug 
 to the difference in character of steel work in the two structures, and 
 that the total cost of the structural steel work should not be estimated 
 higher than $8,500,000. 
 
 Wireworlc. — The cables and suspenders have been estimated at 8 
 cents per pound, making their cost — 
 
 Pounds. 
 
 Cables 79, 647, 800 
 
 Suspenders 4,560,000 
 
 Total wire 84. 207, 800, at 8 cents, $6,736,624. 
 
 Superstructure. — The total cost of the superstructure is $10,030,711, 
 on the basis of 4J cents for all structural steel. 
 
 Substructure. — The substructure would consist of two anchorages and 
 the bases for two towers. Each tower base has to carry the following 
 
 weights : 
 
 Tons. 
 
 Suspended weight on top of tower 109, 000 
 
 Tower 19, 000 
 
 Extra effect of wind 4, 000 
 
 Total 132, 000 
 
 Each of the tower bases of the 2,000-foot cantilever bridge carries 
 100,000 tons. In both cases the foundations can be made proportional 
 to the weights carried. 
 
 The east tower is in the same place as the east pier of the canti- 
 lever bridge. The cost of this base for the suspension-bridge tower 
 will be that of the cantilever-bridge pier, or $3,464,000, multiplied by 
 1.32, making $4,572,480. 
 
 The west tower would come immediately west of the New Jersey 
 pier-head line, the average depth of rock being about 10 feet more 
 than on the east* side, requiring 414,000 cubic feet additional in the 
 foundation. Estimating on the same basis as for the west pier of the 
 cantilever bridge, the cost of this 414,000 cubic feet of foundation 
 would be $431,000, which would make the cost of the west tower base 
 $5,003,480. 
 
 The anchorages have been planned on the basis of putting the entire 
 weight which is to resist the pull of the cables above mean high water, 
 and the quantities have been based on a coefficient of friction of 0.6 
 and a factor of safety of 2. The anchorage at each end of the bridge 
 would contain 5,940,000 cubic feet above the foundation. The only 
 duty of the anchorages is to act as weight, and a very cheap class of 
 masonry can be used for this purpose; rubble made of the most avail- 
 able stone, with a faciug of rough ashlar or brick, would do. The cost 
 of this masonry has been estimated at 37 \ cents per cubic foot, although 
 the Board believe it could be built for much less. On this basis the 
 cost of each auchorage above mean high water is $2,227,500. 
 
 The east anchorage would be founded where the rock is 20 feet below 
 mean high water ; the foundation could be put in with an open coffer- 
 dam, and has been estimated as costing 75 cents per cubic foot. There 
 would be 1,150,000 cubic feet in this foundation, making the cost $862,500, 
 and the total cost of the east anchorage $3,090,000. 
 
 The foundation of the west anchorage would have to be sunk 60 feet 
 to reach the rock, and would probably be put in by the pneumatic 
 process. Its volume would be three times that of the east anchorage, 
 and its cost may be estimated at the same price per cubic foot, or 
 $2,587,500, making the total cost of the west anchorage $4,815,000. 
 S. E. 12 4 
 
50 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 The total cost of the substructure would then be: 
 
 East anchorage $3, 090, 000 
 
 Base for east tower 4, 572, 480 
 
 Base for west tower 5, 003, 480 
 
 West anchorage 4, 815, 000 
 
 Substructure 17,480,960 
 
 The anchorages can be adapted to carry the tracks, but the tracks 
 must be carried between them and the towers on viaducts, requiring 
 925 feet of viaduct on each side, or 1,850 feet in all, which has been 
 estimated at the same price as before. The total length of the suspen- 
 sion bridge, including viaducts and anchorages, is 5,600 feet. The total 
 cost will be as follows : 
 
 Superstructure $16, 036, 711 
 
 Substructure 17, 480, 960 
 
 33, 517, 671 
 
 Viaduct 1, 850, 000 
 
 Total 35,367,671 
 
 The estimated cost of the 2,000-foot cantilever bridge was $25,443,000 
 for 4,320 feet; to compare it with the 5,600-foot suspension bridge, 1,280 
 feet of viaduct must be added; this makes the cost $26,723,000; the esti- 
 mated cost of the suspension bridge is $8,644,671 more. The fairest 
 comparison is by percentages; the cost of the suspension bridge is 
 nearly 32J per cent more than that of the 2,000-foot cantilever bridge. 
 If allowance is made for cost oi structural steel in accordance with the 
 views of a majority of the Board, the difference will be reduced to 
 $7,844,584, or nearly 30 per cent. The general conclusion vhich your 
 Board have reached is that the cost of a suspension bridge of a single 
 span, designed for its whole length for the same moving load as the 
 2,000-foot cantilever bridge, would be less than one-third more than that 
 of the cantilever. 
 
 Deflections. — The structure described is one of unusual rigidity. The 
 expansion of the metallic towers counteracts in a degree deflections 
 due to elongation of cables under an increase of temperature, this 
 deflection being further reduced by the large versed sine. Of the 34 
 tons per linear foot, only 9 are moving load, so that the stress per square 
 inch on cables caused by a maximum moving load is less than 16,000 
 pounds ; it would not exceed 5,000 pounds with an ordinary freight 
 train on every track, or 2,500 pounds with a passenger train on every 
 track. The deflections have been calculated for a full moving load 
 with the following results: 
 
 Conditions. 
 
 60 degrees ± F 
 
 Maximum mov. load 
 
 Combined 
 
 Effects of— 
 
 Cable 
 between 
 towers. 
 
 Back 
 stays. 
 
 Towers. 
 
 Sus- 
 penders. 1 
 
 + 2 
 
 -2. 75 
 
 + 0.1 
 -0. 14 
 
 ±0. 22 
 -0.11 
 
 + 0.03 1 
 -0.02 | 
 
 -,75 
 
 -0. 24 
 
 + 0. 11 
 
 -0.05 | 
 
 Total. 
 
 +■1.91 
 -3.02 
 
 In other words, the total deflection at the center of the span below a 
 mean is about 5 feet; the deflection above a mean is less than 2 feet; 
 the total range is less than 7. These deflections are within satisfactory 
 limits for railroad service. 
 
 A deflection of 5 feet in a length of 3,200 feet, calculated for a modu- 
 lus of elasticity of 28,000,000 pounds, corresponds to a chord stress of 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 51 
 
 7,870 pounds per square inch in a stiffening truss 120 feet deep. This 
 is the stress which has been eliminated by the use ef the hinge. 
 
 The calculations of the cost of the suspension bridge which has been 
 described have been made as nearly as possible on the same basis as 
 the estimates for the cantilever bridge, without taking into consider- 
 ation the fact that the cantilever bridge would be strained nearly to 
 its full capacity by a load 1,000 feet long, while the suspension bridge 
 would be fully strained only when covered by a load three times that 
 length. Furthermore, no allowance has been made for the fact that 
 the maximum strains in the stiffening truss would occur only under 
 combinations which might not arise once in a century, and which could 
 be prevented by simple police regulations. 
 
 A moving load of 3,000 pounds per foot, 1,000 feet long, on each of 
 the tracks, crossing the bridge without change of relative position, 
 would produce practically maximum effects in upward moments on a 
 continuous stiffening truss, but it would produce only one-half these 
 moments downward. In other words, the chords of the stiffening 
 truss would be strained 12,500 pounds per square inch by upward 
 bending, but only 6,250 pounds by downward bending, on the assump- 
 tion as before that all the moving load is distributed by the stiffening 
 truss; as only about 88 per cent is distributed by reason of the 
 unsymmetrical deflection of the cable, the maximum chord stresses are 
 reduced and become, respectively, 11,000 and 5,500 pounds. The great- 
 est upward deflection from the action of the cables occurs from the 
 effects of temperature when the bridge is unloaded; under a full load 
 it is eliminated, and under a 1,000-foot load it is reduced to about 1 foot, 
 which corresponds to a chord stress of 1,570 pounds, making a total of 
 12.570. The downward deflection would never exceed 3J feet with 
 the limited leng^i of train, which corresponds to a chord strain of 
 5,509 pounds, or a total of 11,099, so that a continuous truss could be 
 used without exceeding the assumed limits of stress. It should be 
 noted that the only condition which would produce these stresses would 
 be the passage of six maximum trains side by side. A single freight 
 train in the most unfavorable position would produce a stress of not 
 over 3,500 pounds in the chords of the stiffening truss, and a single 
 passenger train a stress of not over 1,800 pounds. In providing for a 
 lighter structure adapted to trains 1,000 feet long, it has been thought 
 best to make no reduction in the weight of the stiffening truss or the 
 floor system, but the continuous form of truss might be selected. 
 
 If the stiffening truss did its complete duty in the distribution of 
 weight, the greatest strain which a train 1,000 feet long, weighing 3,000 
 pounds per foot, could throw upon the cables, would correspond to a 
 uniform load of 937 pounds. If the stiffening truss did no duty what- 
 ever, but the weight was distributed strictly according to the laws of 
 leverage, the greatest strain which such 1,000-foot train could throw 
 upon the cables would correspond to a uniform load of 1.582 pounds 
 per linear foot. Under these circumstances it seems safe, while not 
 reducing the stiffening truss, to provide for a moving load on the cables 
 of only 1,500 pounds per foot of track. For this approximate calcula- 
 tion, the weights per linear foot may then be taken as follows: 
 
 LIGHTER STRUCTURE. 
 
 Suspended superstructure and tracks 
 
 Moving load , 
 
 Cables and suspenders 
 
 Pounds-. 
 34. 000 
 
 !•. « Mil) 
 
 14. 000 
 
 Total 
 
 57, 000 
 
52 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 This is 28 J tons per linear foot, instead of 34 tons, the reduction in 
 the total carrying capacity being about 16 per cent. It should be 
 observed that the live load is only 15.8 per cent of the whole, so that 
 the additional stress put on the cables by the simultaneous passage of 
 six maximum trains would, without allowance for the work of the stif- 
 fening truss, be only 10,000 pounds per square inch. The stress imposed 
 by a 1,000-foot passenger train under the most unfavorable conditions 
 would not be over 1,200 pounds. 
 
 For purposes of the present comparison, the suspended superstructure 
 remains unchanged; all other parts may be taken at 16 per cent less 
 than in the previous estimate. The weights and cost of such a bridge 
 may then be estimated as follows : 
 
 Pounds. 
 
 Suspended superstructure 101,000,000 
 
 Towers 64, 000, 000 
 
 Chains and anchor plates 25, 000, 000 
 
 Structural steel 190,000,000, 4£ cents.. . $8,550,000 
 
 Wire work 5,659,000 
 
 Total superstructure 14, 209, 000 
 
 Substructure 14,684,000 
 
 28, 893, 000 
 
 Add for viaduct 1, 850, 000 
 
 30, 743, 000 
 
 This is $4,625,000 less than the previous estimate, aiid $4,020,000, or 
 about 15 per cent, more than the cost of the cantilever with the 2,000- 
 foot clear span. 
 
 This estimate has been made for the purpose of comparing on the 
 same basis, that of a factor of safety of three on ultimate strength of 
 metal, the 2,000-foot cantilever and the suspension bridge ^hen carry- 
 ing train loads 1,000 feet long. If it be thought that the stress of 
 60,000 pounds per square inch on the wire in the cables is too high, it 
 may be noted that the difference in the cost of wirework in the two 
 suspension bridge estimates is $1,017,624, and if the higher cost is 
 restored it will be equivalent to reducing the stress in wire to about 
 50,000 pounds per square inch. With this change the cost of the 
 lighter structure becomes $31,671,000, this being $5,038,000, or about 
 19 per cent, more than that of the 2,000-foot cantilever. 
 
 If only one train is allowed on one track at a time, maximum stresses 
 will occur in the different members no oftener than the same loads 
 would produce maximum stresses in the 2,000-foot cantilever. More- 
 over, the load of 1,500 pounds per foot adopted for the cables is the 
 full weight of a passenger train and would not be exceeded if the entire 
 span were covered with the heaviest class of passenger equipment. 
 
 UPPER LOCATION. 
 
 If a location near Sixty-ninth street were adopted, the conditions 
 would be a little more unfavorable for the foundations of the towers, 
 but very much more favorable for the anchorages, as rock is found 
 above water on both sides. The cost of the two anchorage foundations 
 is $3,450,000 in the first estimate and $2,900,000 in the second estimate; 
 these foundations would be saved at the upper location. These figures 
 are enough to show that there are points within the limits prescribed 
 by the act where the difference in cost between the 2.000-foot canti- 
 lever and the single-span suspension bridge might be much less than 
 has been estimated. 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 53 
 
 CONCLUSION. 
 
 The only subject referred to your Board is to "recommend what 
 length of span not less than 2,000 feet would be safe and practicable 
 for a railroad bridge to be constructed over" the Hudson River between 
 Fifty-ninth and Sixty-ninth streets. A single span from pier head to 
 pier head, built on either the cantilever or suspension x^rineiple, would 
 be safe. The estimated cost of the 3,100-foot clear-span cantilever 
 being about twice that of the shorter span, your Board consider them- 
 selves justified in pronouncing it impracticable on financial grounds. 
 As the cost of the single-span suspension bridge is at most one third 
 greater than that of the 2,000-foot cantilever, your Board are unable to 
 say that such greater cost is enough to render the suspension bridge 
 impracticable. 
 
 The Board have reached this conclusion after careful study, and they 
 have thought it best to give the full course of reasoning which they 
 have followed. They feel that the contingency attending the construc- 
 tion of the deep river foundation of the cantilever bridge, even waiving 
 the absolute necessity of carrying this foundation to rock, is enough to 
 balance a part of the greater cost of the suspension bridge. 
 
 The conclusion of this Board is that of a Board of Bridge Engineers 
 acting in a professional capacity. While from such professional view 
 they must pronounce the suspension bridge practicable, they do not in 
 this conclusion give an opinion on the financial practicability and merit 
 of either plan. 
 
 Before closing, your Board desire to state particularly that the esti- 
 mates have been made for comparative purposes and are not to be 
 taken as a measure of absolute cost ; they are believed to be thoroughly 
 fair for comparisons ; the prices assumed may be much higher than 
 absolute cost. The plans on which the estimates are made, a sketch of 
 which accompanies this report, would undoubtedly be modified if a 
 bridge were buijt. 
 
 This report is accompanied by the following appendices: 
 
 A. — Act approved June 1, 1894. 
 
 B. — Statement prepared by Mr. Charles Macdonald in behalf of the New York and 
 
 New Jersey Bridge companies. (Six inclosures, including four blue prints.) 
 C— Statements of Mr. Gustav H. Schwab (C) and Win, W. Hildenbrand (C 1 — C 2 ). 
 (Two inclosures, tracings.) 
 
 D. — Statement of Mr. G. Lindenthal. 
 
 E. — Theoretical investigation of stiffening truss. 
 
 Respectfully submitted. 
 
 G. BOTJSCAREN. 
 
 W. H. Burr. 
 Theodore Cooper. 
 Geo. 8. Morison. 
 0. W. Raymond. 
 
 Hon. Daniel S. Lamont, 
 
 Secretary of War. 
 
 INDORSEMENT OF SECRETARY OF WAR ON THE FOREGOING REPORT. 
 
 War Department, 
 
 December 12, 1894. 
 The Board having reported that a single span from pier -head to 
 pier-head would be safe and not impracticable, I approve such report 
 and plans may be submitted for a bridge with a single span from pier- 
 head to pier-head. 
 
 Daniel S. Lamont, 
 
 Secretary of War. 
 
54 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 Appendix A. 
 
 ACT APPROVED JUNE 7, 1894. 
 
 [Public— No. 83.] 
 
 AN ACT To authorize the New York and New Jersey Bridge Companies to construct and maintain a 
 bridge across the Hudson River between New^York City and the State of New Jersey. 
 
 Be it enacted by the Senate and House of Representatives of the United States of America 
 in Congress assembled, That the New York and New Jersey Bridge Companies, here- 
 tofore incorporated by the States of New York and New Jersey, and existing under 
 the laws of said States, are hereby authorized to construct, operate, maintain, and 
 rebuild, in case of destruction, a bridge across the Hudson River between New York 
 City, in the county and State of New York, and the State of New Jersey, subject to 
 the laws of said States, respectively, upon the following terms, limitations, and 
 conditions : 
 
 First. That the location of said bridge shall be subject to approval by the Secre- 
 tary of War, upon such examinations, hearings, and reports as he shall hereafter 
 prescribe: Provided, That it shall not be located below Fifty-ninth street, New York 
 City, nor above Sixty-ninth street, New York City. 
 
 Second. That the said companies may locate, construct, and maintain over such 
 bridge and the approaches thereto railroad tracks for the use of railroads : Provided, 
 That any railroad on either side of said river shall be permitted to connect its tracks 
 with the said bridge approaches, and shall have equal rights of transit for its rolling 
 stock, cars, passengers, and freight upon equal and equitable terms, and if a dispute 
 as to the equality or equity of the terms shall arise it shall be submitted to and 
 decided by the Secretary of War: Provided, That the location of all approaches of 
 said bridge in the city of New York shall be approved by the commissioners of the 
 sinking fund of the city of New York : And provided f urther, That no railroad or rail- 
 roads shall be operated on the approaches of said bridge companies in the city of 
 New York, except on such approaches as shall have been approved by the sinking- 
 fund commissioners of the city of New York : Provided, also, That the term approaches 
 as used in this Act shall be construed to include only such portion of the roadbed 
 and superstructure, on either side of said bridge, as is necessary to reach the grade 
 of the bridge from the grade of the streets at which said approaches begin to rise, 
 in order to bring the two elevations together upon and by a grade of not less than 
 twenty feet to the mile. 
 
 Third. That any bridge built under the authority of this Act shall be constructed 
 with such length of span and at such elevation as the Secretary of War shall approve 
 and require: Provided, however, That it shall afford, under any conditions of load or 
 temperature, a minimum clear headway above high water of spring tides of not 
 less than one hundred and fifty feet at the center of the span; and. all the plans and 
 specifications, with the necessary drawings of said bridge, shall be submitted to the 
 Secretary of War for his approval, and before such approval the construction shall 
 not be begun ; and should any change be made in said, plans during progress of con- 
 struction, such changed plans shall be submitted to said Secretary and approved 
 by him before made; and the President shall appoint a board, consisting of five 
 competent, disinterested, expert bridge engineers, of whom one shall be either the 
 Chief of Engineers or any member of the Corps of Engineers of the United States 
 Army, and the others from civil life, who shall, within thirty days after their 
 appointment, meet together and, after examination of the question, shall, within 
 sixty days after their first meeting, recommend what length of span, not less than 
 two thousand, feet, would be safe and practicable for a railroad bridge to be con- 
 structed over said river, and file such recommendation with the Secretary of War, 
 but it shall not be final or conclusive until it has received his written approval. In 
 case any vacancy shall occur in said board, the President shall fill the same. The 
 compensation and expenses of said board of engineers shall bo fixed by the Secretary 
 of War and paid by the said bridge companies, which said companies shall deposit with 
 the Secretary of War such sum of money as he may designate and require for such 
 purpose: Provided, always, That nothing herein contained shall be construed as pre- 
 venting the said board of engineers from meeting, investigating, and filing their 
 recommendation after the expiration of said time herein mentioned. 
 
 Fourth. The companies oj^erating under this law shall maintain on the bridge, at 
 their own expense, from sunset to sunrise, such lights and signals as the United 
 States Light-House Board may prescribe. 
 
 Fifth.. The said company or companies availing themselves of the privileges of 
 this Act shall not charge a higher rate of toll than authorized by the laws of the 
 State of New York or New Jersey, and the mails and troops of the United States 
 shall be transported free of charge over said bridge. 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 55 
 
 Sixth. That said company or companies shall he subject to the interstate-com- 
 merce law, and to all amendments thereof, and when such bridge is constructed 
 under the provisions of this Act it shall he a lawful military and post road and a 
 lawful structure. 
 
 Seventh. That the said company or companies availing themselves of the privileges 
 of this Act shall file an acceptance of its terms with the Secretary of War, and shall 
 submit to the Secretary of War, within one year after the passage of this Act, for 
 examination and approval, drawings showing plan and location of the bridge and its 
 approaches; and the construction of said bridge shall be commenced within one 
 year after said location and plans have been approved of, as herein provided ; and 
 said company or companies shall expend, within the first year after construction has 
 commenced, as herein required, not less than two hundred and fifty thousand dollars 
 in money, and in each year thereafter not less than one million of dollars in money in 
 the actual construction work of said bridge, which shall be reported to the Secretary 
 of War; and the said bridge shall be completed within ten years from the commence- 
 ment of the construction of the same, as herein required; and, unless the actual con- 
 struction of said bridge shall be commenced, proceeded with, and completed within 
 the time and according to the provisions herein provided, this Act shall be null and 
 void. 
 
 The right to amend, alter, modify, or repeal this Act is hereby reserved. 
 Approved, June 7, 1894. 
 
 Appendix B. 
 
 STATEMENT OF MR. CHARLES MACDONALD, OF UNION BRIDGE COMPANY. 
 
 No. 1 Broadway, New York, July 20, 1894. 
 
 Sir: In accordance with your permission, I have the honor to submit herewith 
 certain general information relating to the proposed bridge across the Hudson 
 River, authorized by recent act of Congress, and under which act your Board has 
 also been constituted. 
 
 The bridge in question must be located between Fifty-ninth and Sixty-ninth streets 
 and your Board is to advise as to what is a safe and practicable span, not less than 
 2,000 feet, for such a location. 
 
 The New York and New Jersey Bridge Company has in view the construction of a 
 bridge for utilitarian purposes only. There is to be nothing of the monumental or 
 sentimental character about it, except in so far as must be inseparably connected 
 with its magnitude. It is intended to build a structure which will safely provide 
 facilities for all the traffic which may be expected to pass over it, as well as under 
 it, and at such practicable cost as will prove attractive to the investors of capital. 
 It is not committed to any particular design of bridge, whether it be cantilever, sus- 
 pension, or a combination of the two. What it intends to build, if permitted to do 
 so, is a structure which will accomplish the desired results with the least expendi- 
 ture of money. 
 
 The first element in this problem is, necessarily, the determination of the proba- 
 ble traffic. From a careful observation of the number of cars arriving at Jersey 
 City, the amount of express freight, and the number of passengers which would be 
 likely to pass over the bridge, it has found that the gross income (from all sources) 
 will not exceed $3,500,000, that the cost of maintenance, taxes, etc., would be 
 $1,250,000, leaving as available for paymeut of interest, after deducting all other 
 charges, $2,250,000. This, at 5 per cent, represents a total investment of $45,000,000. 
 Of this amount about one-half will be required for terminals (including right of 
 way). 
 
 Thus it would appear that if the bridge proper can be built at a cost of $22,500,000 
 the entire investment might possibly be favorably considered. Our efforts have, 
 therefore, been confined within this iiniit of cost, and the results are respectfully 
 presented for your consideration. 
 
 It is proposed to build a "cantilever" bridge, having a span of 2,300 feet between 
 centers ot main towers, or upward of 2,000 feet in the clear, and 2 anchor spans of 
 910 ieet each between center of main tower and anchorage pier. 
 
 The clear height above high water, at center of main span, will be 150 feet. 
 
 There will be 6 railway tracks throughout the entire length of bridge and 
 approaches. 
 
 The main towers will rest upon 4 cylinders, each arranged in the form of a square, 
 of 200 feet between centers. They will finish off with granite masonry at a height 
 of 25 feet above high water. 
 
 The anchorage piers will be founded upon cylinders and finished off with granite 
 masonry to the underside of the bottom chord of the trusses. 
 
56 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 In accordance with the law of the State of New York upon which the charter is 
 based, the main tower on the New York side is placed wholly within the pierhead 
 line. The anchorage pier on the New Jersey side is placed wholly within the pier- 
 head line on that side of the river, and the center of the river pier is about JJOO feet 
 eastward from this same line. 
 
 Accurate borings have been made at different points within the limits of location 
 permitted by the act, from which it appears that the distance from high water to 
 rock or bowlder (at the site of the river pier) is upward ef 250 feet, while sand is 
 found at a depth of 165 feet. 
 
 It is proposed to construct this river pier on a sand foundation, at a depth of 200 
 feet below low water. The diagram submitted herewith indicates the general 
 dimensions and pressures for each of the 4 cylinders composing this foundation. 
 
 The cylinders under the New York pier would be of the same dimensions, but the 
 depth to a suitable sand foundation would be somewhat less. 
 
 Detailed strain sheets are herewith submitted, showing the general distribution 
 of material required to insure safety for the live load on six tracks having an average 
 of 3,000 pounds per running foot on each track. 
 
 Suitable provision has also been made for wind strains and for strains during 
 erection wherever they exceed normal strains. 
 
 It will be observed, by reference to the diagram of the foundation cylinder, that 
 the total pressure (from live and dead loads and wind strains) upon the top of the 
 granite capping is 8.84 tons per square foot, and that the abnormal pressure on the 
 base, where the concrete filling comes into contact with the sand (at a depth of 200 
 feet), is 7.16 tons per square foot. 
 
 The nearest precedent believed to be in existence for a deep foundation of this 
 character is the pier foundation for the Hawkesbury bridge in New South AVales, a 
 diagram of which is herewith submitted. The abnormal pressure per square foot in 
 this latter case is 5.7 tons, with a depth of only 8 feet in the sand, and at a total 
 depth of 162 feet below high water. 
 
 As it is well known that the resisting force increases with the depth, it is believed 
 that the assumption herein taken is justifiable, but in order to make sure it is pro- 
 posed (and provision has been made in the estimate for same) to sink a trial cylin- 
 der, 20 feet diameter, in the center of the square between the four cylinders com- 
 posing the river pier. From the experimental data thus obtained as to the exact 
 amount of skin friction and resistance to settlement, more accurate proportions can 
 be given to the main cylinders, particularly with reference to the relation of weight 
 required to cause settlement during dredging. 
 
 It will be observed that the effect of skin friction has not been considered in cal- 
 culating the supporting value of the foundations. This will be wholly on the side 
 of safety, therefore, and will unquestionably reduce the abnormal pressure on the 
 sand at the foot of the cylinder. 
 
 These cylinders will be filled up with concrete made of the best Portland cement, 
 lowered through the water in the most approved manner, and finished off at about 
 the level of the bottom of the river. The outer skin of the cylinder will be carried 
 up above high water, temporarily, to facilitate the construction of the masonry from 
 the river bottom upward. 
 
 In the completed pier there will be no metal work exposed to corrosion where it 
 might give rise to anxiety. 
 
 It is proper to state that what is called "granite masonry" consists of a 4 feet 
 ring of cut granite and 4 feet of dressed granite coping; the interior to be made up 
 of large irregular masses of stone, set in concrete, exactly as was done in the case of 
 the piers for the "Forth Bridge." 
 
 The estimate of cost of the river pier and the New York pier ie herewith given in 
 detail, together with the cost of superstructure, and other items to make up the total 
 cost of the bridge proper, from which it will appear that, with a span of 2,300 feet 
 between centers of towers (or a clear span of upward of 2,000 feet), the limit of 
 what has been found to be a practicable expenditure is reached. 
 
 In view of the evidence presented, you are respectfully requested to consider favor- 
 ably the following propositions : 
 
 (1) That a 2,000 feet clear span is the longest practicable span wherewith to cross 
 the North River, at the point indicated. 
 
 (2) That any increase of span, short of the entire width of the river, viz, 3,130 feet 
 in the clear, would correspondingly restrict the free use of wharves on the New Jer- 
 sey side. 
 
 (3) That the cost of a river pier, at any point between the present location and say 
 500 feet from the New Jersey side, would be practically the same as already esti- 
 mated ; whereas, the cost of the superstructure would increase materially with the 
 length of the span. 
 
 (4) That the position of the river pier, assumed at 2,000 feet in the clear from the 
 New York side, would be wholly within the space set apart as anchorage grounds on 
 
BRIDGE ACKOSS THE HUDSON RIVEK. 
 
 57 
 
 the New Jersey side; as indicated by diagram attached hereto (taken from the New 
 York Times of Thursday, September 7, 1893) ; from which it will be seen that 1,500 
 feet was assumed to be sufficient for the free and unobstructed navigation of the 
 Hudson at that point. 
 
 And further, that such pier, when provided with suitable warning signals, would 
 be a positive advantage to navigation in time of fog. 
 
 And further, that the piers of the Poughkeepsie bridge, crossing the Hudson River 
 75 miles above, are 500 feet apart in the clear, and have not proved a serious obstruc- 
 tion. 
 
 And further, that the main ship channel to New York Harbor is 1,000 feet wide. 
 
 (5) That the superstructure of a span without a pier in the river, for which it would 
 be necessary to have a clear reach between centers of towers of 3,350 feet, would 
 cost at least three times as much as the estimate herewith submitted; and the total 
 cost of the bridge proper would be more than double the estimate for a 2,000 feet 
 span. 
 
 We have no hesitation in saying that, at such an increase of cost, it would be 
 impossible to raise the necessary capital ; and that, therefore, the bridge would be 
 impracticable. 
 
 In arriving at this conclusion we have been guided by the carefully digested 
 opinions of men of large means, who have expressed a firm belief in the enterprise, 
 if kept within the j)rescribed limit of cost; and from whom we should expect sub- 
 stantial assistance in perfecting a sound financial basis of operations. 
 
 I do not wish to be understood as admitting that a bridge of 3,350 feet can be 
 constructed as a safe structure. 
 
 We have made some preliminary estimates of strains for such a span, and the pro- 
 portions have become so enormous as to raise very grave doubts in our minds of the 
 possibility of designing such a structure, with sufficient rigidity to hold up its own 
 weight — to pass the traffic — and to resist wind pressure. 
 
 All of which, and such other data as may be in my power to procure, is placed at 
 your service. 
 
 In inclosure No. 1 will be found data upon which the estimate of probable traffic 
 is based. 
 
 In inclosure No. 2 references are given to loads upon masonry and foundations as 
 they have been hurriedly collected. 
 
 The following plans accompany this report : 
 
 Five copies, pier foundation. 
 
 Five copies, plan of river, with borings. 
 
 Ten copies, profile at proposed crossings. 
 
 Three copies, strain-sheets of superstructure. 
 
 One copy, articjfe from the New York Times, September 7, 1893. 
 
 Charles Macdonald, 
 
 Of Union Bridge Company, 
 Xo. 1 Broadway, Neio York. 
 
 Maj. C. W. Raymond, 
 
 Chairman Board of Engineers appointed by the President upon the matter of 
 length of span of the New York and Xew Jersey bridge orer the Hudson River. 
 
 NOTES AS TO PRESSURES ON MASONRY AND FOUNDATIONS. 
 
 [Collingwood, "Masonry East River Bridge," Transactions Am. Soc. C. E., Vol. VI, pp. 8 and 9 ] 
 
 Weight per cubic foot: Granite masonry, 153 pounds; concrete, 120 pounds. 
 Pressure on central shaft, 26 tons per square foot. 
 
 [Cresy, "Encyclopedia of Engineering, 1847.' ] 
 
 (Page 705.) Five and one-half tons on 9 square inches, 1,370 pounds per square 
 inch, has stood for several centuries. "Chapter House at Elgin." Two columns in 
 the Church Toussant d'Augers, 12 inches diameter and height 25 feet, carrying pointed 
 arches; load on each, 25 tons, or 400 pounds per square inch. 
 
 (Page 706.) Piers: Dome St. Peters, 1,022^ pounds on 9 square inches, or 113 
 pounds per square inch; St. Paul's, 1,190 pounds on 9 square inches, or 132 pounds 
 per square inch; Invaliues, 9 9 2 pounds on 9 square inches, or 102 pounds per square 
 inch; St. Geuevieve, 1,840 pounds on 9 square inches, or 201 pounds per square inch. 
 Columns: St. Paul's, without the walls, 1,235 pounds on 9 square inches, or 137 
 pounds per square inch; Church Toussant d'Augers, 2,767 pounds on 9 square inches, 
 or 307 pounds per square inch. 
 
 The above is quoted from "Rondelet, Traite d'Arckitecture." 
 
58 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 [John Newman, <( Cylinder Bridge Piers," approximate safe loads per square foot.] 
 
 Firm sand in estuaries and bays, 5 to 5.6 tons. Dutch engineers consider safe 
 loads on firm, clean sand 6 to 6.16 tons. Very firm, compact sand — foundations at 
 considerable depth, not less than 20 feet — and sandy gravel, 6.7 to 7.84 tons. Firm 
 shale and clean gravel, 6.7 to 8.96 tons. Compact gravel, 7.84 to 10.08 tons. 
 
 Clean sand, homogeneous Thames gravel, has been weighted with 280 cwt. per 
 square foot at 3 to 5 feet below the surface, and showed no signs of failure, 15.68 
 tons. 
 
 [Gaudard, "Foundations."] 
 
 Stiff clay, marl, sand, or gravel, 55 to 110 cwt. (3.08 to 6.16 tons). Gorai bridge 
 (close sand), Lock Kew (gravel), Bordeaux (gravel), 165 to 183 cwt. Nantes (sand), 
 152 cwt., some settlement. Szegedin (clay and fine sand), 133 cwt. (7.4 tons), rein- 
 forced by driving piles in interior of cylinder, and sheathing outside. Charing 
 Cross, cwt., 159, including adhesion (8.9 tons). Cannon street, 117 cwt., including 
 adhesion (6.5 tons). Roque Favor aqueduct, 258 cwt., rocky ground (14.4 tons). 
 
 [Leslie, " Transactions Institute of Civil Engineers, January 24, 1888."] 
 
 Hooghly Jubilee bridge, 10 tons net. 
 
 [Engineering News, March 14, 1885.] 
 
 Washington monument : Area of base, 126.5 feet by 126.5 feet, 16,000 square feet. 
 Weight, 81,120 (long tons), 90,850 (short tons). Average pressure on base (exclusive 
 of wind), 11,340 pounds, or 5.67 tons per square foot. Taking out area 45 feet square, 
 2,025 feet, leaves balance under concrete, 14,000 square feet (nearly). Average per 
 square foot under concrete, 90,850 — 14,000, 6.5 tons. 
 
 Square feet. 
 
 Area of bottom of buttress, 101.5 square 10, 302 
 
 Less 45 square 2, 025 
 
 Effective area 8, 277 
 
 Tons. 
 
 14,000 by 13 feet, 182,000 by 150 13, 650 
 
 Original weight 90, 850 
 
 Less 13,650 
 
 77, 200 
 
 On line c — c, pressure 77,200 -r 8,277, 9.32 tons per square foot. 
 Area at c — c, 55 square, 3,025 — 25 square, 2,400 square feet. 
 
 Weight of buttress, 101.5 square 10, 302 
 
 55 square 3,025 
 
 4 by 78 square 24, 336 
 
 37, 663 - 6, 6,277 by 150 by 25 = 23,540,000 
 pounds, 11,770 tons. 
 Weight of shaft, 77,200 — 11,770, 65,430 tons. 
 
 Average per square foot, 65,430 -f- 2,400 square feet, 27.2 tons per square foot. 
 Material is marble. 
 
 At bottom of foundations, 5.67 tons per square foot; at bottom of buttress, 9.32 
 tons per square foot; at bottom of shaft, 27.2 tons per square foot; all exclusive of 
 wind. 
 
 Bunker Hill Monument : On hard sand and gravel, 54 tons, no settlement. 
 
 Tower of brick church (Thirty-seventh street and Fifth avenue) : On hardpan, 
 7 tons per square foot, some settlement. 
 
 Crushing strength of concrete, department of docks : 1:2:5(1 foot cube). Hard- 
 ened in water forty-five days, 425 pounds square inch, 30.5 tons square foot. Hard- 
 ened in water one year, 1,520 pounds square inch. Hardened in air one year, 1,620 
 pounds square inch. 
 
 REVENUE STATISTICS. 
 
 I regret to say that much of the detailed information which I expected to submit 
 in this appendix has been forwarded to London, but the following will be of interest : 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 59 
 
 Xorth River ferries, passengers carried yearly. 
 
 Staten Island 5, 445, 800 
 
 Jersey Central 10, 938, 320 
 
 Pennsylvania 14. 589, 050 
 
 Barclay 12,899,100 
 
 Chambers 10, 868, 240 
 
 Jay 2, 164, 640 
 
 Desbrosses 8,067,960 
 
 Christopher 11, 739, 130 
 
 Fourteenth street 2, 811, 960 
 
 Twenty-third street 3, 594, 520 
 
 Forty-second street 1, 744, 680 
 
 Total 84,663,400 
 
 The number of people crossing the East River ferries is slightly in excess of the 
 above, or more exactly 88,663,500; but this is exclusive of the people who cross the 
 Brooklyn bridge. 
 
 These latter amounted to 42,615,105 in 1893. 
 
 From the opening of the railway to public use, September 24, 1883, to November 
 30, 1893, inclusive, a period of ten years and sixty-seven days, 304,875,286 passengers 
 were carried. During any month the greatest number transported was 4,033,920 
 in October, 1892, which included the week from the 8th to the 15th of the Colum- 
 bian festival. The next greatest number was 3,846,493, in May, 1893, an average of 
 124,080 per day. In one day of twenty-four hours, the maximum number carried was 
 223,625, on October 12, 1892, during the Columbian festival; the next greatest num- 
 ber was 166,403, on Januarv, 14; and the minimum number during the official year 
 1893 was 45,280, on August 20. 
 
 In 1884, the year after the opening, the total number of passengers passed over the 
 bridge was 8,828,200. 
 
 The average number of cars of freight, inbound and outbound daily, on the fol- 
 lowing-named railroads, via New York and Jersey City, during the year 1890, as far 
 as statistics have been obtained, is as follows: 
 
 9 
 
 Pennsyl- 
 vania 
 Eailroacl. 
 
 Erie. 
 
 West 
 Shore. 
 
 Delaware. 
 
 Lacka- 
 wanna and 
 Western. 
 
 Jersey 
 Central. 
 
 Various. 
 
 
 318 
 724 
 300 
 
 322 
 694 
 210 
 
 130 
 260 
 
 144 
 
 402 
 210 
 
 138 
 328 
 200 
 
 48 
 
 244 
 
 
 
 
 1,342 
 
 1, 226 
 
 390 
 
 756 
 
 666 
 
 292 
 
 Grand total, 4,672 cars daily; 1,705,280 cars during year. 
 
 Among the above items of freight which could be handled to advantage in New 
 York may be mentioned — 
 
 Milk daily carloads . . 53 
 
 Flour and meal . . do 397 
 
 Produce do 407 
 
 Grand Central Station.— Total passengers per day, 35,000; or 12,250,000 per year. 
 
 St. Louis bridge. 
 
 
 1890. 
 
 1891. 
 
 1892. 
 
 1893. 
 
 Passenger coaches 
 
 259, 187 
 178, 197 
 111, 350 
 46, 775 
 12. 948 
 $4. 50 
 1,940 
 1, 367, 184 
 25.84 
 4, 149 
 41.77 
 
 224, 784 
 132, 187 
 115, 942 
 50, 009 
 609 
 $4.34 
 1,434 
 1, 375, 057 
 26. 15 
 4,231 
 46. 57 
 
 232, 259 
 141,062 
 125, 676 
 50, 696 
 4,847 
 $4. 46* 
 1.515" 
 1, 522, 037 
 21.7 
 4, 642 
 44.94 
 
 214.816 
 139. 023 
 128, 601 
 51,568 
 7, 605 
 $4.58 
 1,484 
 1, 587, 549 
 24.6 
 4, 848 
 43.31 
 
 Revenue per loaded car. 
 
 Average number of cars per dav 
 
 Keveuue per passenger cents. . 
 
60 BRIDGE ACROSS THE HUDSON RIVER. 
 
 It has been assumed that the suburban traffic which can be brought into the 
 terminal of the North River bridge, at Forty-second street and Seventh avenue, 
 will equal, if it does not exceed, that which is delivered at the Grand Central Station, 
 Forty-second street and Fourth avenue ; and that of the western passenger traffic 
 now reaching New York, of which 70 per cent is carried by the New York Central 
 system, against 30 per cent by all other lines, a very considerable diversion will 
 take place in favor of the new terminal. 
 
 Based upon this, the total number of passengers paying toll over the bridge has 
 been taken at 14,000,000 per year. Of quick freight, including express, it is safe to 
 count upon 1,000 cars per day ; or, say, 350,000 per year. 
 
 In assuming a rate which it would be safe to charge, per passenger and per car, 
 the cost of motive power has been eliminated; that is to say, the cost of moving 
 the passengers and cars would be borne by the railroads transporting them. 
 
 Under this assumption, an average of 15 cents per passenger and $4 per car gives 
 a gross income as follows : 
 
 14,000,000 passengers, at 15 cents $2, 100, 000 
 
 350,000 cars, at $4 1, 400, 000 
 
 Gross income 3, 500, 000 
 
 Less repairs, taxes, and sundries (about 36 per cent) 1, 250, 000 
 
 Net income 2,250,000 
 
 By reference to the St. Louis bridge charges for freight and passengers, which 
 include cost of motive power, these rates are moderate. 
 
 Estimated cost of New York and New Jersey bridge. 
 
 Superstructure, 230,000,000 pounds, at 44 cents $10, 350. 000 
 
 River pier 3,500,000 
 
 New York pier 2, 300, 000 
 
 New Jersey anchorage 400, 000 
 
 New York anchorage 100, 000 
 
 Tracks, 4,000 linear feet, at $2.50 X 6 60, 000 
 
 Interest 2, 000, 000 
 
 Contingencies 1, 890, 000 
 
 20, 000, 000 
 
 Add 10 per cent 2, 000, 000 
 
 Total 22,000,000 
 
 Estimated cost of river pier, on basis of 60 feet diameter on top and 100 feet diameter 
 on bottom, ivith inclined sides. 
 
 Excavation, 1,178.100 cubic feet, at 27i cents $324, 000 
 
 Concrete, 38,733 cubic yards, at $6 232, 400 
 
 Steel, 3,000,000 pounds, at 3 cents 90, 000 
 
 Masonry, 8,600 cubic yards, at $15 129, 000 
 
 Cost of one cylinder 775, 400 
 
 Cost of pier, $775,400 x 4 cylinders 3, 101, 600 
 
 Add 10 per cent 310, 000 
 
 3, 411, 000 
 
 Test pier 89. 000 
 
 Total cost of river pier, say 3, 500, 000 
 
BRIDGE ACROSS THE HUDSON RIVER. 61 
 
 Detailed weight of New York and New Jersey bridge. 
 
 Suspended span, 720 feet c to c end pins : Pounds- 
 Top chords 2, 400, 000 
 
 End posts 1,900,000 
 
 Bottom chords 2, 900, 000 
 
 Web eyebars 1,500,000 
 
 Vertical posts and braces 800, 000 
 
 Pins 200, 000 
 
 Lateral system 700, 000 
 
 Stringers 2, 500, 000 
 
 Cross floor beams 1, 600, 000 
 
 14, 500, 000 
 
 Two cantilever arms : 
 
 Top chord eyebars 13, 400. 000 
 
 Web eyebars 7, 500, 000 
 
 Bottom chords 15, 800. 000 
 
 Pins 1,000,000 
 
 Web compression members 9, 000, 000 
 
 Lateral system 2, 800, 000 
 
 Stringers 5, 000, 000 
 
 Cross floor beams 4, 200, 000 
 
 Sundries 3,300,000 
 
 62, 000, 000 
 
 Two anchorage arms, 840 feet c to c end pins: 
 
 Eyebars 21, 200, 000 
 
 Bottom chords 21, 000, 000 
 
 Web compression members 34,000,000 
 
 Pins 2. 000, 000 
 
 Lateral system 3, 500, 000 
 
 Stringers 5, 500, 000 
 
 Cross floor beams 5, 000, 000 
 
 Sundries 3,300,000 
 
 9 95, 500, 000 
 
 Two center towers : 
 
 Eyebars 6, 900, 000 
 
 Tower vertical posts 24, 900, 000 
 
 Bottom chords 5,900.000 
 
 Lateral system 11, 600, 000 
 
 Stringers 1, 100, 000 
 
 Cross floor beams 1,900,000 
 
 Bedplates 5, 700, 000 
 
 58, 000, 000 
 
 Totals : 
 
 Suspended span 14, 500. 000 
 
 Two cantilever arms 62, 000, 000 
 
 Two anchorage arms 95, 500, 000 
 
 Two to wers 58, 000, 000 
 
 230, 000, 000 
 
 Appendix C. 
 
 STATEMENT OF MR. GUSTAV H. SCHWAB, CHAIRMAN SPECIAL COMMITTEE, CHAMBER 
 OF COMMERCE OF THE STATE OF NEW YORK, ON HUDSON RIVER BRIDGE. 
 
 New York, July 17, 1894. 
 Gentlemen : In accordance with your permission I avail myself of your courtesy 
 to present to you the views of the Chamber of Commerce of the State of New York 
 as represented by its special committee on the Hudson River bridge. 
 
62 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 The Chamber of Commerce ou December 7 last adopted the following resolutions: 
 
 "Resolved, That in the opinion of this Chamber the passage by Congress of any 
 Bill permitting the construction of a bridge across the Hudson, with piers in the 
 river bed, will be an obstruction to the commerce of this Port and an injury to the 
 entire country, particularly to the great West, whose products find an outlet through 
 the Erie Canal and the Hudson River. 
 
 "Resolved, That the Representatives in Congress from this State be requested to 
 strenuously oppose the passage of any Act which will permit the building of piers 
 or other obstructions in the river bed." 
 
 The objections urged by the chief commercial body of this city against the proposed 
 location of a pier or piers in the Hudson River between the pier-head lines, opposite 
 the city of New York, are the following: 
 
 The lower part of the Hudson River not only serves the purposes of river traffic 
 and of the accommodation of the enormous trade that finds its way from the great 
 West through the Erie Canal to tidewater, and from the brick, lumber, and stone 
 yards, manufactories and icehouses along the river, but this great river between 
 the New York side and the New Jersey shore furnishes such a harbor as can not be 
 found in any other part of the world. It provides the most varied kind of traffic — by 
 steamers, ferryboats, schooners, lighters, rafts, barges, large sailing vessels, and. 
 yachts — with accommodation, and renders it possible for the largest ocean steam- 
 ers to safely maneuver throughout its whole extent. Although at the present time 
 the piers accommodating ocean-steamship traffic do not extend much above the pro- 
 posed site of the New York and New Jersey bridge, it can not be doubted that with 
 the rapid growth of commerce and navigation of this port, the whole shore line 
 within the city limits of New York on the Hudson River will be ultimately taken up 
 in pier accommodations, as well as the opposite shore on the New Jersey side. This 
 appears a safe prediction, in view of the fact that thirty years ago the harbor ship- 
 ping of New York did not extend beyond Tenth street. At present it has reached 
 Seventieth street, and on the New Jersey side there are now plans in contemplation 
 and partly in execution for the building of piers as high as Eighty-sixth street. 
 
 In connection with this extension of harbor traffic it should be borne in mind that 
 ocean steamshipstendtogrow larger, and that the space required for their maneuver- 
 ing should therefore also be larger. It is for this reason that the East Riveris not used 
 for the handling of large transatlantic steamers, but that these steamers find their 
 docks on the North River, which is by far the most important part of the gre at harbor of 
 New York, the importance of which is shown by the fact that by a recent bill inCon- 
 gress the port of New York will now include Yonkers. The placing of ajpier or piers 
 in the river bed at any point between the pierhead lines will, inevitably, seriously 
 interfere with the maneuvering of these ocean steamers, as well as with harbor 
 traffic in general. The obstruction to harbor navigation and the great danger to 
 life involved in the construction of a pier or piers in the river bed must be patent to 
 anyone who has crossed the Hudson River in foggy, thick, or stormy weather. It 
 is to be feared that the placing of a pier almost in the center of the river will 
 result not only in an obstruction to the passage of ice in the winter months, but will 
 cause the formation of shoals around the abutments of such piers. 
 
 The current in the Hudson River opposite the city of New York does not pursue a 
 course parallel with the river banks, but runs diagonally across from shore to shore, 
 thereby causing thegreatest difficulty in handling tows and floats in the harbor. The 
 location of a pier in the river would greatly increase the difficulties aud dangers of 
 harbor navigation to those tows, and should a tow of canal boats or a steamer laden 
 with passengers on this crowded waterway have the misfortune to come into contact 
 with the abutments of these bridge piers, the serious consequences to life and prop- 
 erty can well be imagined. 
 
 The argument has been made in favor of the bill that the proposed pier is to be 
 placed in the anchorage grounds, and not in the main channel. If this is so, the 
 argument displays l^ck of information, for a pier placed in the anchorage grounds 
 would render a large part of such grounds useless. No vessel of any size could with 
 safety anchor within a circle of 2,400 feet in diameter of which the bridge pier would 
 be the center. 
 
 We believe that the existence of a natural rocky island, or islands, of the extent 
 of the proposed bridge pier, in the same location in the river would never be toler- 
 ated, and that millions of dollars would have been spent long ago to remove such 
 serious obstructions to navigation in the river and harbor, aud in view of the expend- 
 itures of the Government for the purpose of removing natural obstructions, the 
 deliberate erection of artificial barriers would appear to be the greatest folly 
 
 The reasons against the pier were so convincing upon the legislature of the State 
 of New York that the act giving a charter to the New York and New Jersey Bridge 
 Company insisted upon a singlAspan for this bridge. The company then appealed 
 to Congress for permission to plafi* a pier in the river ; the President, however, vetoed 
 the bill, in view of the danger to the commercial and navigation interests of the first 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 63 
 
 port of this country. As the bridge company represented in Congress that a span of 
 over 2,000 feet was a practical impossibility, your honorable Board was appointed by 
 the President to examine into the question thoroughly, whether a bridge could bo 
 built longer than 2,000 feet span, which, in this case, means a span over the entire 
 river, for if built for 2,100 or 2,300 feet it would still leave a dangerous obstruction 
 in the river between the pierhead lines, and would make thoNew Jersey shore intho 
 vicinity practically useless for dock purposes. This, then, is the question that comes 
 before your honorable Board, namely, whether a bridge can be built over tlie river 
 with a single span which would be practicable and not prohibitive in cost. 
 
 There is no rule by which the practicability as to cost can bo determined, but in 
 the view that a bridge with no pier in the river can bo built at a cost that is not 
 prohibitive the commercial and navigation interests of this port find themselves 
 supported by Mr. Thomas C. Clarke, the chief engineer of the New York and New 
 Jersey Bridge Company in his report to the company of March 15, 1892, submitted. to 
 the U. S. Senate on March 23, 1892. In this report Mr. Thomas C. Clarke, the chief 
 engineer of the New York and New Jersey Bridge Company, states as follows: 
 
 " I expect to be able to have plans and estimates of cost of the suspension-canti- 
 lever bridge, requiring no pier in the river between the pierhead lines, ready by 
 April 1st. * * * 
 
 ''I am now prepared to say that if they decide that thero shall be no pier in the 
 river, I can build you a bridge on the combined suspension-cantilever plan that sliall 
 be strong enough and stiff enough to carry trains at 20 miles an hour, and at a cost 
 that shall not be prohibitory." 
 
 These views of Mr. Thomas C. Clarke, chief engineer of the Noav York and New 
 Jersey Bridge Company, have the indorsement of Mr. W. A. Roebling, who has writ- 
 ten to me under date of June 21 last as follows: 
 
 "I am not familiar with the proposed designs for this work, but may say in gen- 
 eral that a cantilever with two spans of 2,000 feet each is considered feasible, and 
 that a suspension bridge with a single span of 3,000 feet is also feasible, with some 
 increase in cost. Such a span is within the carrying capacity of a commercial qual- 
 ity of steel wire." * * * 
 
 Mr. Roebling also states as follows: "I will close by saying that only two years 
 ago the promoters of the New York & New Jersey Bridge Co. had determined to 
 adhere to the suspension principle, in which I was consulted," " * * thus 
 amply corroborating the statements of the chief engineer of the New York and New 
 Jersey Bridge Company. 
 
 The Chamber of Commerce of the State of New York has retained Mr. William 
 Hildenbraud, recommended to them by Mr. W. A. Roebling, and one of his most 
 trustworthy assistants for many years, for the purpose. of presenting to you tech- 
 nical arguments in favor of a single span over the whole river, with its probable 
 cost, its practicability, and safety. 
 
 GUSTAV H. SCHWAB, 
 
 Chairman Special Committee on Hudson Hirer bridge, 
 
 Chamber of Commerce of the State of New York. 
 The Board of Engineers on Hudson River Bridge Span. 
 
 Appendix C 1 . 
 
 LETTER OF MR. W. HILDENBRAND TO MR. GUSTAV II. SCHWAB. 
 
 New York, July 12, 1S94. 
 
 Dear Sir: In answer to your question whether it be possible to construct a prac- 
 tical railroad bridge across the Hudson River at or near Sixty-ninth street without 
 a pier between pierhead lines, I do not hesitate to say yes, and beg to submit to you 
 the following data, which will demonstrate by figures that a suspension bridge of 
 over 3,000-foot span is not only an engineering possibility, but also will compare, 
 from a commercial point of view, not unfavorably with a cantilever bridge of 2,100- 
 foot span, as suggested by the New York and New Jersey Bridge Company. 
 
 The design, as submitted to you, must be considered as a mere preliminary sug- 
 gestion which might undergo many changes if the problem bo worked out in detail, 
 but the calculations 6how what can be done, and I am confideut to say that the 
 weight of the metal and the cost as given will not be far from correct figures of 
 carefully prepared plans and estimates. 
 
 From a profile of the river, shown in a sketch of the proposed cantilever bridge, 
 published in the Scienti lie American of June 10, it appears that the distance between 
 pierhead lines is about 3,000 feet, consequently the length of a single-span bridge 
 S. Ex. 1 10 
 
64 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 was assumed to be 3,200 feet from center to center of towers, allowing 200 feet for 
 the width of the latter. 
 
 Most engineers will agree that the suspension principle is the only practical solu- 
 tion for a bridge of that length; hence, without trying any other kind of construc- 
 tion, all calculations are based on a design for a suspension bridge consisting of wire 
 cables and stiffened by a truss with three hinges. This is not the most economical 
 construction, but it was chosen for the purpose of showing the practicability and 
 economy of such a design, even under unfavorable conditions, and, on account of all 
 forces and strains being statically determinate, of easy comparison with a cantilever 
 or other structure. 
 
 A suspension bridge is never entirely rigid, because the contraction and expansion 
 of the cables under changes of temperature cause the floor to drop or rise to the 
 extent of several feet. An absolute stiffening of the floor against distortion under 
 one-sided loads would, therefore, be a waste of material, hence the stiffening girder 
 for this assumed design was constructed only with such rigidity that the simulta- 
 neous depression and rise of the floor under a one-sided load'would create no steeper 
 grade than 1| per cent, or about the same. as is caused. by the rise and fall in conse- 
 quence of extreme temperatures. Keeping these conditions in view, the following 
 are the principal features and dimensions of this bridge: 
 
 Total length from face to face of anchorage feet. .. 4, 900 
 
 Main span from center to center of towers do 3, 200 
 
 Width of tower at water 'line do 200 
 
 Width of tower at floor line, about do * 100 
 
 Eastern end span will consist of two independent truss bridges, each of 400-foot span. 
 Western end span will consist of three independent truss bridges, each of 266-foot 
 sjjan. 
 
 Deflections of cable: 
 
 Main span at 55° F feet ... 322 
 
 Main span at 0° do 319. 18 
 
 Main span at 110° do 324. 77 
 
 Rise and fall of cable and floor for a variation of 110° do 5. 59 
 
 Length of cable in main span at 55° F do 3, 285. 26 
 
 Length of cable from anchorage to anchorage do 5, 120 
 
 Deflection of back cable from a straight line connecting top of tower and 
 face of anchorage : 
 
 For dead load feet ... 9.8 
 
 For dead and live load do 7.2 
 
 Depression of center span when fully loaded : 
 
 Arising from the elongation of cable of 5,120 feet length do 4. 21 
 
 Arising from the change of deflection in back cable do .5 
 
 Total rise and fall of floor in center of bridge under extremes of tempera- 
 ture and load feet. . . 10. 3 
 
 Camber of floor at 55° F , do 8 
 
 Grade of floor at 55° F per cent. . 1 
 
 Grade of floor at 0° F do ... . 1. 35 
 
 Grade of floor at 1 10° F do ... . .66 
 
 Camber of floor at 110° and floor fully loaded feet. . . .62 
 
 From these figures it appears that the maximum grade of the floor is less than 
 1^ per cent, and that the floor, when fully loaded in the warmest weather, will 
 never sink below level. 
 
 The height of the towers will be determined by the following figures : 
 
 Feet 
 
 From high water to under side of bridge 150 
 
 Thickness of floor 8 
 
 Camber of floor 8 
 
 Bottom of cable above floor in center 2 
 
 Deflection of cable 322 
 
 Extra height of tower to support two or three tiers of cables 20 
 
 Total 510 
 
 The bridge is supposed to carry six railroad tracks, and the live load is assumed to 
 be 18,000 pounds per linear foot, covering the whole span from tower to tower. 
 
 If the moving load were but 4,500 pounds per linear foot, and one-half the span 
 be covered with the same, it can be shown that, without any sti Honing construc- 
 tion, the floor would doliect 6.01 feet at one quarter of the span and rise 5.23 feet at 
 the opposite quarter, making a total difference of 11.24 feet in 1,600 feet, or a grade 
 of 1.4 per cent. This is admissible; hence the stiffening girder must be calculated 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 G5 
 
 to resist a live load of 13,500 pounds per linear foot, and must be dimensioned to 
 deflect not over 6 feet in the quarter span. The span of the stiffening girder is 
 3,100 feet, and its height was assumed 80 feet, or one-fortieth of the span. 
 
 According to the theory of stiffening girders, as shown by Rankine, the loaded 
 half of the truss must be calculated for a uniformly distributed load of pounds 
 per foot, and the unloaded half for the same force, acting upward, deflecting the 
 girder thus : 
 
 Assuming a unit strain of 20,000 pounds per square inch the max. chord section is 
 1,266 square inches (= 633 square inches for one chord of each of two trusses); 
 the average weight of chords, 7,332 pounds per foot (= 1,833 pounds for one chord of 
 each of two trusses) ; the average weight of web members, 3,048 pounds per foot; 
 total, 10,380 pounds per linear foot. 
 
 Calculating the deflection of this truss, it wiil be found to be 4.58 feet, if the 
 elongation and contraetion of the web members and the separate moment of inertia 
 of each chord be neglected. The true deflection would therefore not exceed 6 feet. 
 
 The weight of the platform per double track is about the same as that of any 
 first-class railroad bridge, viz, 1,800 pounds per linear foot. 
 
 The floor beams will not reach across the six tracks in one span, but will be sup- 
 ported at two intermediate points; hence the total weight of the platform will be 
 5,400 pounds per linear foot. 
 
 The aggregate load to be sustained by the cables will be composed of the follow- 
 ing weights : 
 
 Pounds per 
 linear foot. 
 
 Moving load 18, 000 
 
 Weight of stiffening truss 10, 380 
 
 Weight of platform, 3,900 pounds steel and 1,500 wood 5, 400 
 
 Weight of projecting ends of floor beam 300 
 
 Weight of sway-bracing and intermediate floor-beam suspenders 810 
 
 Weight of wind cables and wind bracing 1, 240 
 
 Weight of suspenders 1, 110 
 
 Weight of cables 12, 500 
 
 9 
 
 Total 49,740 
 
 Total load on cable: 12,500 X 3,200 + 37,240 X 3,100 = 77,722 tons; tension in 
 cables at one-tenth deflections 104,613 tons; allowing a strain of 30 tons per 
 square inch, it requires 3,487 square inches or 74,570 No. 3 wires (diameter, 0.244 
 inch) which will weigh 12,000 pounds per foot. 
 
 Assuming 12 cables, 1 cable will consist of 6,220 wires and will have a diameter, 
 including wrapping, of 23 inches. With 14 cables the diameter of each would be 2l| 
 inches. 
 
 The size and number of cables may be varied according to individual opinion, but 
 the above size may be advisable for coinciding nearest with the cables of the New 
 York and Brooklyn bridge. The latter were designed to contain 6,308 wires, but 
 eventually were built of 5,400 wires of a heavier size. 
 
 There is no reason to assume that larger cables could not be made, but there can 
 certainly be no doubt about the successful construction of cables if a size be adopted 
 which is near the limit of the precedent given by the cables of the Brooklyn bridge. 
 
 The following sketches will illustrate the general design : 
 
 ( able making will require from 16 to 18 months, including the accessory work of 
 erecting "cradle" ropes and foot bridge. 
 
 The time consumed for making two of the Brooklyn bridge cables was 9 months, 
 bnt several methods applied there could be improved upon for shortening the time. 
 For instance, all cable wire was stored on one shore and taken across the river from 
 one side. It required from 7 to 8 minutes for the wire to travel across, while regu- 
 lating the same took only 2 to 2\ minutes; therefore, the time for strand making 
 can be shortened one-half if the wire wheel, instead of returning empty, would 
 take a wire across from the opposite shore. To "let off" and regulate one strand 
 required from 3 to 4 days' labor, and while this work went on strand making of the 
 Brooklyn bridge cables was interrupted. There is no particular reason for this, and 
 it is fully practical to make a new strand while another is regulated. In this way 
 the time of making cables is actually confined to the time of regulating strands 
 
 S. Ex. 12 5 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 Each of tho 12 cables will consist oithor of 19 or 37 strands, the former having 
 the advantage of quicker work, but dealing with great weights. Tho latter makes 
 it easier to handle tho strands, though it may take a little longer in regulat ing 
 them. Assuming 37 strands, and 3 days for regulating each strand, tho time of mak- 
 ing one cable without wrapping would be 111 days. 
 
 Two wrapping machines, working from the towers towards tho center, will wrap 
 about 20 feet per day, requiring 160 days for the whole span; but with a sufficient 
 number of ''squeezers" it would bo just as practical to employ 4 or more wrapping 
 machines and shorten tho time accordingly. If the time for wrapping the cable 
 bo reduced to 80 days, tho total time necessary for making 1 cable will be li»L work- 
 ing or 221 calendar days, which is less than 7^ months. Hence the above-stated 
 time of 16 or 18 months for tho whole operation of cable-making gives a liberal 
 allowance for contingencies and for tho erection of the auxiliary structures. Of 
 course it will be necessary to make arrangements for constructing all cables simul- 
 taneously, which can easily be done, provided the cables are not less than 3 or 4 feet 
 apart. 
 
 For attaching the suspendors and making connections between tho cables, cable 
 bands may be employed which are made in two parts, provided with heavy flanges, 
 and screwed up with three or more bolts in each flange. Tho cable bands of tho 
 Brooklyn bridge wero forged of one piece and screwed up with but one bolt; they 
 were perfectly tight when of correct size, but they had a tendency to slide when a 
 little too large. Bands made in two parts, as described, will never slide if properly 
 constructed, because tho number and size of the tightening bolts can be calculated 
 according to the requisite friction. 
 
 Tho unit strain of 60,000 pounds per square inch of cable wire was based on an 
 ultimato strength of 180,000 pounds. Much stronger wire, up to 300,000 pounds, can 
 be made, but that of 180,000 pounds seems preferable on account of its easy manu- 
 facture and cheap price. Tho limit of elasticity of this wire is 120,000 to 130,000 
 pounds, hence a maximum strain of 60,000 pounds, which rarely if ever occurs, is a 
 perfectly safe assumption. 
 
 The stiffening truss is subjected to reverse strains, hence a unit strain of 20,000 
 pounds per square inch is by many engineers considered equal to one of 40,000 
 pounds. 
 
 Whilo this may bo true if the opposito strains occur in rapid succession, namely, 
 at the rate of 5 to 20 and more times per second, as in car axles, it is, on tho other 
 hand, known from the experience with rails and continuous bridges that it is not 
 true if tho interval between the occurrence of tho different strains within the clastic 
 limit affords plenty of time for the recovery of the metal from the elastic deforma- 
 tions. But even it the strains were as high as 40,000 pounds, there could be no 
 objection to it if w r e adopt high-grade steel, of say 80,000 pounds ultimate strength 
 and 50,000 pounds elastic limit, considering that the maximum strain in the stiffen- 
 ing truss is based on an improbable assumption of load distribution, which may not 
 occur once in a lifetime. 
 
 Lastly, it may bo mentioned in justification of a high unit strain, that the stiffen- 
 ing truss is not a necessity, but merely a convenience; in other words, it could bo 
 dispensed with if a locomotive and train could ascend a 6 or 8 per cent grade ; hence 
 a rupture of tho truss would not endanger the safety of tho suspension bridge, but 
 would merely cause a temporary inconvenience. 
 
 Tho following table gives the calculated weights and tho approximate cost of the 
 bridge : 
 
 Stiffening trusses, sway braces, and intermediate floor-beam suspenders, 
 
 11,190x3.100 = 17,345 tons at 4 cents $1, 387, 600 
 
 Floor construction, 4,200 X 3,200 = 6,720 tons at 3£ cents 436, 800 
 
 Towers, 26,330 tons at 4 J cents 2, 238, 000 
 
 Anchor chain and plates, 12,000 tons at 3} cents 840,000 
 
 Woodwork and track, 5,200 pounds at $24 124, 800 
 
 Cables, 12,000x5, 120 = 30,720 tons at 7 cents t, 300, 000 
 
 Wind cables and suspenders, 2, 350x3,200 = 3,760 tons at 8 cents 601, 600 
 
 East land span, consisting of two 400-foot span truss bridges, weighing 
 
 per foot, including floor, 13,950 pounds X 800 =5,580 tons at 4 cents 446, 100 
 
 One land pier, 146 feet high, 416 tons at 4 cents 33, 300 
 
 West land span, consisting of three 266-foot span truss bridges, weigh- 
 in-- per foot, including floor, 9,000 pounds X 800 = 3,600 tons at 4 cents. 288, 000 
 
 Two laud piers, 146 feet high, 468 tons at 4 cents 38,000 
 
 Anchorages 2, 500, 000 
 
 Total, 106,959 tons . 13, 234, 500 
 
 This is without the cost of foundations. In explanation of the cost of the anchor 
 ges, it may bo said that tho cables wero assumed to be anchored in rock for a depth 
 of 90 feet, and that tho masonry above the rock would rise 142 feet above high 
 
68 
 
 BRIDGE ACROSS THE HUDSON RIVER 
 
 water. For each anchorage a 15 by 20 foot shaft is supposed to be sunk in the rock, 
 widened at the bottom to 50 by 50, requiring about 3,500 cubic yards of excavation 
 and subsequent tilling with concrete. The resistance of the rock body surrounding 
 two of these shafts is at least 72,000 tons, and if a block of masonry containing 74,000 
 yards be added to it the total resistance will be 220,000 tons, against a maximum 
 pull of 104,600 tons in the cables. Assuming the cost of excavation at $3 per cubic 
 yard, filling with concrete at $6, and masonry at $14, the total cost of both anchor- 
 ages will be $2,198,000, or $2,500,000, allowing 15 per cent for contingencies. 
 
 The cost of making the Brooklyn bridge cables was 2.05 cents per pound. Wire 
 of the described quality can be bought at 4 or, at the outside, 4£ cents; hence, a 
 price of 6 to 6^ cents per pound for the finished cable would be about correct, while 
 1 cents was assumed in the estimate of cost. 
 
 The estimate must be considered as a liberal one in all items. 
 
 It has been mentioned that cables placed vertically over each other may be con- 
 nected in a way to form a suspended arch. This requires but little material for 
 stiffening purposes. No advantage was taken of this circumstance, though, if 
 adopted, it would considerably lighten the weight of the bridge. 
 
 Another reduction in the weight of the stiffening girder could be made by omitting 
 the center hinge and making the truss continuous. This would reduce its weight 
 nearly 10 per cent, but as the calculation of such a truss requires the introduction of 
 the elastic line, and could not be checked without considerable labor, I refrained 
 from discussing the same in this communication. 
 
 A comparison between a suspension bridge and the proposed cantilever bridge 
 must principally refer to the cost. Assuming the weight of the cantilever bridge to 
 bo about 116,000 tons, its cost at 4 cents per pound would be $9,280,000. To this 
 must be added the cost of 1,080-foot approach, because the suspension bridge is so 
 much longer from end to end. If constructed like the western land span, this cost 
 would amount to $440,000. 
 
 It appears from the published river profile that the foundation of the west canti- 
 lever tower must reach to 200 feet below water level, while that of the suspension 
 bridge tovrer would probably be less than 100 feet. This would make a difference 
 of at least $1,000,000 in favor of the suspension bridge if the lower portion of the 
 foundation were calculated at the same rate of cost as the upper portion. The end 
 abutments of the cantilever bridge will add $105,000, hence its total cost (exclusive 
 of foundations), as compared with the cost of a 3,200-foot span, will be $tf,280,000 -f 
 $440, 000 -f $1,000, 000 -f $105, 000 = $10,825, 000, or $2,409,500 less than a suspension 
 bridge of 3,200-foot span, supposing that the assumed weight of the cantilever bridge 
 be approximately correct. 
 
 There are some points tending to lower the cost of the suspension bridge or to 
 raise that of the cantilever, for instance, the erection of a suspension bridge after 
 the cables are finished, is much simpler and cheaper than the erection of a cantilever. 
 The latter requires two false works 810 feet long by 150 feet high, and the main 
 span must be erected from the towers toward the middle, while the superstructure 
 of a suspension bridge can, without false works, be erected simultaneously at many 
 places, as the cables form a bridge in themselves to work from at any point. 
 
 In regard to the safety factor, if assumed to be 3 in either design, it is relatively 
 of greater value for the suspension cables than for the cantilever truss, because the 
 latter is exposed to impacts while the cable is free from them. A rolling load of 
 18,000 pounds, on which the calculation of the suspension bridge was based, is an 
 excessive assumption, because the probability of a fully loaded floor decreases pro- 
 portionately w ith the length. 
 
 For a live load of 18,000 pounds per linear foot of bridge on a 2,100-foot span, one 
 of 15,000 pounds per linear foot would be a full equivalent for a span one-half longer. 
 This item alone would save $226,000 in the cost of cables and anchor chains, not to 
 mention the saving in the stiffening trusses and anchorages. 
 
 It should be noticed, also, that the estimated cost of the suspension bridge includes 
 contingencies, while no contingences were considered in the estimate of the canti- 
 lever. All these points taken into consideration, it is probable that the actual dif- 
 ference of cost between a cantilever bridge of 2,100-foot span, resting on a pier in 
 the middle of the river, and a suspension bridge of 3,200-foot span, without an inter- 
 mediate pier, may not exceed $2,000,000. 
 
 In the foregoing description I frequently used technical terms and mathematical 
 expressions which are probably of no interest to you, but as I understand that your 
 object is to submit this report to a board of expert engineers, familiar with the 
 science of bridge construction, I know they will find it easier to pass an opinion on 
 what I have endeavored to elucidate when the principles from which the data were 
 deduced are mentioned than if I had merely furnished a table of quantities. 
 
 Respectfully submitted, 
 
 W. HlLDENBKAND. 
 
 Gustav H. Schwab, Esq., 
 
 Chairman Special Committee Chamber of Commerce. 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 69 
 
 APPENDIX. — CALCULATION OF WIND BRACING. 
 
 Iii addition to the lateral system between the trusses two storm cables will be 
 stretched under the tloor from tower to tower : 
 
 These cables should be adjusted to a bearing, without initial strains, at 110°. The 
 contraction of the wire at zero will cause an initial strain of 20,800 pounds per 
 square inch, hence the strain in the cables will be a maximum if the greatest wind 
 would occur at the coldest weather. 
 
 If it be the strain per square inch of cable caused by the wind pressure, the total 
 
 strain in the cable resisting the wind force will be very nearly 20,800 -f- ^ an(1 * n tne 
 
 other cable 20,800— — , hence if t = 2 X 26,800 pounds, the strain in one cable will be 
 
 53,600 pounds per square inch, and in the other 0. 
 
 Assuming 150 feet to be the deflection of the cables in their normal position, and 
 allowing an extreme side deflection of the floor of 10 feet, the following table gives 
 the conditions of the cables at 0° F. : 
 
 Length of 
 cafle. 
 
 Deflection. 
 
 Tension 
 per square 
 iueh. 
 
 Pressure per 
 linear foot 
 of span, pro- 
 ducing the 
 tension per 
 square inch 
 in the preced- 
 ing column. 
 
 Total pres- 
 sure tor 
 entire span. 
 
 Feet. 
 
 3215. 76 
 3218.6 
 3221. 4 
 
 3216. 28 
 
 Feet. 
 
 Pounds. 
 
 Pounds. 
 
 Pounds. 
 
 150 
 160 
 
 uo 
 
 26, 800 
 52, 600 
 4, 220 
 
 3. 14 
 6.16 
 0.5 
 
 10, 048 
 19, 712 
 1,600 
 
 It follows, from these figures, that a strain of 52,600 pounds per square inch for a 
 side deflection of 10 feet from the normal position, will resist a wind pressure of 
 6.16 — 0.5 = 5.66 pounds per linear foot because the 0.5 pound arises from the pressure 
 of the opposite cable, and not from the wind, or a total pressure of 18,112 pounds. 
 
 The wind surface was approximated at 42.5 square feet per linear foot, and the 
 wind pressure at 30 pounds per linear foot; hence, the total pressure is 1,275 pounds 
 per linear foot extended over the whole middle span. Assuming a storm cable of 
 126 square inches section weighing 420 per foot, it will resist a pressure of 126 X 
 5.66 =713 pounds; hence, the truss chords and lateral system must resist 1,275 — 
 713=562 pounds per linear foot. 
 
 The weight of the horizontal-web system was computed at 434 pounds per linear 
 foot. The chord section for the wind truss will, therefore, be 337 square inches. 
 
 The deflection (at 20,000 pounds per square inch unit strain) of this wind truss in 
 the plane of the floor beam, and assumed as continuous, if calculated for a load of 
 562 pounds per linear foot, is greater than 10 feet; hence, v the chord section must bo 
 increased to reduce the deflection to 10 feet. It will be found that a chord section 
 of 466 square inches per truss complies with this condition, which reduces the unit 
 wind strain from 20,000 to 14,000 pounds per square inch. 
 
 On account of the center hinge (hinging the truss vertically) it will be necessary 
 to transmit the wind pressure to the towers by means of the bottom chord alone. 
 The section of one bottom chord of each of the two trusses in the quarter span ia 
 
70 
 
 BRIDGE ACROSS THE HUDSON RIVLR. 
 
 633 square inches, and in the center of the bridge will be about 270 square inches; 
 hence, it will be necessary to add 196 square inches extending over about 300 feet 
 each side from the center. 
 
 The wind strain in the quarter span will be found to be 2,585 tons. This is resisted 
 by a bottom-chord section of 633 square inches in each truss, to which should be 
 added 53 square inches extending over 700 feet on each side of the center. With 
 this increase of section, the maximum unit strain in the bottom chord would be 
 26,000 pounds, under the supposition of the improbable case that the greatest wind 
 strain would coincide with the maximum vertical distortion of the truss under a 
 one-sided load. The .additional weight, corresponding to the mentioned increase of 
 section in the bottom chord, amounts to 418 pounds per linear foot of bridge. 
 
 The floor beams, which are supposed to bo 30 feet apart, must resist the pressure 
 of tbo cables, amounting, to 126x6.16 = 776 pounds per linear foot, or of 23,280 pounds 
 per floor beam. This will require an increase of 1.16 square inches, or 370 pounds 
 of metal per floor beam, equal to 13 pounds per linear foot. 
 
 The total weight of the wind system, therefore, is : 
 
 Pounds per 
 linear foot. 
 
 Lateral- web system 434 
 
 Additional of bottom chords of trusses 418 
 
 Increase in floor beams 13 
 
 Storm cables 840 
 
 Total 1,705 
 
 In the original estimate of weight the total weight of wind bracing was calculated 
 to be 1,240 pounds per linear foot, based on the supposition of a continuous truss 
 which could transmit the wind pressure to the towers without requiring additional 
 chord sections. 
 
 The suspender weight was calculated for a unit strain of 20,000 pounds, while 
 40,000 pounds would be a moderate strain if the suspenders be constructed of wire 
 rope, reducing the assumed weight one-half. 
 
 The weight of wind bracing a*nd suspenders should therefore be corrected as follows : 
 
 1,705 + 555 = 2,260 lbs., costing 865 lbs. X 3,100 1,340 tons, at 4 cents = $107,260 
 
 840 + 555=1,395 lbs. X 3,200 2^232 tons, at 8 ceuts= 357^120 
 
 3,572 464,380 
 
 This is 188 tons and $137,000 less than given in the estimate on page 67. 
 
 The tower columns were calculated for a unit strain of 12 tons on top and 10 tons 
 at the bottom ; hence, no addition was made for wind strains, which are insignificant 
 compared with the direct strains from the weight of the bridge. 
 
 W. HlLDENBRAND. 
 
 Appendix C 2 . 
 
 STATEMENT OF MR. W. HlLDENBRAND TO THE BOARD OF ENGINEERS. 
 
 New York, July 20, 1S94. 
 Gentlemen: I beg to submit to you herewith a modified plan and estimate for a 
 suspension bridge across the Hudson River at Sixtieth street. It differs from my 
 former design, offered to the inspection of your honorable Board on .July 17 by the 
 chairman of the special committee of the Chamber of Commerce, in being adapted 
 to the correct profile of the river and complying with your instructions as to unit 
 strains in different parts of the superstructure and the admissiblo pressure on the 
 foundation : 
 
 The following are the principal data of this* plan: 
 
 Total length of bridge feet.. 4, 310 
 
 Span from ceiiter to center of towers do. 3, 310 
 
 Width of towers at base do . . . 180 
 
 Clear, span between piers (=elear waterway between pierhead lines). do. 3. 130 
 
 Width of tower at high water, center to center of columns do. 131.5 
 
 Length of tower at high water, center to center of columns do. 340 
 
 Width of. tower at floor line do. . . 100 
 
 Wi (1 1 li of tower at top do. .. 70 
 
 Clear span of cable in middle span do. . . 3, 240 
 
 1 Reflection of cable at 55° F do . . . 400 
 
 1 )ellection of cable at 0° F do. . . 397. 63 
 
 1 Reflection of cable at 110° F do. . . 402. 30 
 
 Lengths of cable in center span at 55° do. ... 3, 369. 1 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 71 
 
 do... 0.3 
 
 Lengths of west back cable feet . . 1, 611. 7 
 
 Lengths of east back cable do . . . 903. 2 
 
 Total lengths of cable, anchorage to anchorage do. . . 5, 884 
 
 Rise and fall of cable for a difference of temperature of from ()°-110 o . . .do. . . 4. 67 
 Deflection of west back cable from a straight line connecting top of tower 
 and anchor pin : 
 
 For dead load feet. . 32. 1 
 
 For dead and live load do. 21. 6 
 
 Deflection of east back cable from a straight line connecting top of tower 
 and face of anchorage : 
 
 For dead load feet . . 8 
 
 For dead and live load do . . . 5. 3 
 
 Depression of center span when fully loaded arising — 
 
 Feet. 
 
 From elongation of center cable 1.77~ 
 
 From elongation of west back cable 0. 85 
 
 From elongation of east back cable 0.47 
 
 From change of deflection in west back cable, causing the 
 
 saddle to move forward 0. 92 
 
 The same of the east back ( able 0. 06 J 
 
 (This depression could be reduced one-half if the cables w r ere connected 
 
 with the land piers by suspenders and held down.) 
 Total rise and fall in center of bridge under extremes of temperatures and 
 
 loads , feet.. 10.97 
 
 Camber of floor at 55° F do. . . 9 
 
 Grade of floor at 55° F per cent. . 1. 11 
 
 Gradeof llooratO°F. (camber 11.37 , less contraction of tower = 0.19). do. . . 1.38 
 Grade of floor at 110 3 F. (camber — 6.7 -f elongation of tower = 0. 19). do. .. 0.85 
 Camber of floor at 110° if fully loaded (0.4 -f- elongation of tower) . . .feet. . 0. 59 
 
 These figures show that the floor will never sink below level and that the maximum 
 grade is less than H per cent. It should also be noticed that this grade extends 
 only over a few feet near the towers, and diminishes rapidly when a train proceeds 
 toward the center of the bridge. 
 
 The height of the towers is : 
 
 Feet. 
 
 From high water to under side of bridge 150 
 
 Thickness of floor 8 
 
 Camber of floor #. 9 
 
 Bottom of cable above floor 2 
 
 Deflection of cable at 55° 400 
 
 Extra height for the support of two tiers of cables 40 
 
 Total 589 
 
 The live load was assumed to be 18,000 pounds per linear foot. The unit strain in 
 stiffening trusses does not exceed 15,000 per square inch for reversed stresses. The 
 unit strain in the cables was restricted to 50,000 pounds per square inch for wire 
 having an ultimate strength of 180,000 pounds. The stiffening truss was calculated 
 to resist a live load of 18,000 pounds per linear foot, covering one-half of the span, 
 while the opposite half be unloaded. 
 
 It will require a moving load of 2,400 pounds per linear foot to deflect the dead 
 mass of the bridge (without regard to any stiffening) 3.8 feet in one-quarter span 
 and raise it 3.7 feet in the opposite quarter. 
 
 This distortion of the floor causes a grade of less than 1 per cent. Hence this 
 stiffening girder was calculated for a moving load of 15,000 pounds. 
 
 To comply with this condition and not to strain the metal above 15,000 pounds per 
 square inch, the height of the truss was chosen to be 120 feet giving the following- 
 dimensions : 
 
 Maximum chord, section of either top or bottom chords square inches. 1, 395 
 
 Average weight of both chords pounds per linear foot. 8,000 
 
 Average weight of web svtem do 4,220 
 
 Total do ....12,280 
 
 It will be found that the deflection of this truss for a load of 15,000 pounds per 
 linear foot is 2.35 feet if the elongations and contractions of the web members be 
 neglected; hence its true deflection will about coincide with the distortion of the 
 cable under a load of 2,400 pounds per linear foot. 
 
72 
 
 BRIDGE ACROSS THE HUDSON RIVE 1 ?. 
 
 The intermediate floor-beam suspenders and cross-bracings were calculated for a 
 local load of 200 tons, in addition to the dead weight on each suspender. 
 
 < 30 X 30 X 30 > 
 
 I I I I I T T T T I T T T T 
 
 T T 
 
 20$ t. 209 t. 
 
 Allowing a unit strain of 20,000 pounds per square inch, the weight of these parts 
 will be 1,332 pounds per linear foot. 
 
 The question was investigated whether there was an appreciable inclination of 
 the floor beams if three tracks on one side of the axis of the bridge were fully 
 loaded in. one-half of the spans, and if the opposite three tracks were loaded in the 
 other half of *<4io span. For instance, a load of 9,000 pounds per linear foot on the 
 three right-hand tracks will depress the right end of the floor beams 1.37 feet and 
 the left end 0.53 foot. The same load on the left three tracks in the opposite half 
 span will raise the right ends of the former floor beams 0.53 foot, and will depress 
 the left ends 1.35 feet; hence, the greatest inclination of a floor beam is 1.68 feet in 
 100 feet, which is hardly noticeable. 
 
 The two suspenders of one floor beam wore calculated with a unit strain of 50,000 
 pounds per square inch for the dead load, plus 600 tons, assuming six 100-ton loco- 
 motives to meet on one floor beam. 
 
 The estimated weight is 776 pounds per linear foot. The aggregate load to be sus- 
 tained by the cable is : 
 
 Pounds per 
 linear foot. 
 
 Moving load 18.000 
 
 Stiffening trusses 12, 280 
 
 Platform 5,400 
 
 Projecting ends of floor beams 300 
 
 Intermediate floor-beam suspenders and sway braces 1, 340 
 
 Lateral wind bracing 860 
 
 Storm cables 840 
 
 Suependers 780 
 
 Cables 13,000 
 
 52, 800 
 
 Total load on cables, 39, 800x3,210 + 13,000x3,240=84,939 tons. 
 Tension in cable at one-eighth deflection, 94,960 tons. 
 
 Allowing 25 tons strain per square inch, it requires 3,800 square inches, or 81,270 
 No. 3 wires (0.244 inch diameter). 
 
 Dividing the number of wires into 16 cables, one cable will contain 5,080 wires 
 and will have a diameter of 20| inches. 
 
 The tension in the east anchor chain will bo 94,700 tone. The tension in the 
 west anchor chain will be 88,500 tons; average tension, 91,600 tons; requiring 9,160 
 square inches and weighing 39,700 pounds per linear foot. 
 
 Tons. 
 
 Total weight of anchor chain for a length of 510 feet 10, 120 
 
 Weight of anchor plates 1, 580 
 
 11, 700 
 
BRIDGE ACROSS THE HUDSON" RIVER. 73 
 
 The towers were calculated for the combined maximum load and wind strains at 
 12 tons per square inch. 
 
 Tons. 
 
 Weight on top of tower (requiring 7,080 square inches) 84,940 
 
 Weight of tower 15, 110 
 
 Weight of land truss resting on tower 1, 400 
 
 Wind strains 1, 350 
 
 Pressure at base of tower, 102,800 tons, requiring 8,566 square inches. Average 
 section, 7,823 square inches. 
 
 Weight per linear foot, 52,150 pounds. 
 Total weight of two towers, 579 feet high, 30,200 tons. 
 
 The pressure on the rock foundation of the east tower will be 247,380 tons, and 
 the buoyancy of the pier cylinder 90,250; hence the foundation must contain 15,713 
 square feet in order to resist a pressure of 157,130 tons. 
 
 This area can be procured by sinking eight cylinders of 50 feet diameter, filled 
 with concrete, one for each tower column. The total mass of foundation work will 
 amount to 2,081,300'cubic feet. The pressure on the west tower is less, owing to the 
 light inclination of the back cable, hence concrete-filled cylinders of 47 feet diame- 
 ter will answer the conditions of the foundation. 
 
 The total pressure is 137,710 tons, requiring a foundation mass of 1,958,600 cubic 
 feet. 
 
 The east land pier, supporting two independent 400-foot truss bridges, requires a 
 foundation mass of 100,400 cubic feet, requiring four cylinders of 20 feet diameter. 
 As regards the pressure on the foundation, the cylinders might be smaller, but as 
 they must be sunk to a depth of about 80 feet, a smaller diameter seems not to be 
 advisable. No land spans were designed for the west side, as the west tower coin- 
 cides with the position of the west end abutment of the cantilever bridge; hence, 
 whatever construction be used for this approach would be common for both designs. 
 
 The west anchorage is entirely in rock 200 feet below the surface, requiring 13,200 
 cubic yards of rock excavation, 9,000 cubic yards of concrete filling, and 25,000 
 cubic yards of masonry. 
 
 Estimating the rock excavation at $4, the filling at $6, and the masonry at $14 per 
 cubic yard, the cost of this anchorage will be $456,000. 
 
 The east anchorage is also partially in rock, which according to the contour of 
 the rock strata will probably be found at a depth of 30 to 35 feet below high water. 
 It requires, therefore, 6,800 cubic yards of rock excavation and filling, 80,000 cubic 
 yards of earth excavation, and 80,000 cubic yards of masonry. 
 
 Estimating rock excavation at $3, earth excavation at 50 cents, concrete filling at 
 $6, and masonry at $14, the cost of this anchorage will be $1,221,000. 
 
 The following is the calculated weight and estimated cost of the bridge: 
 
 Stiffening truss, 12,280 x 3,210= 19,710 tons at 4 cents $1, 576. 700 
 
 Platform, 4,200 x 3,310=6,950 tons, at 3£ cents 451, 800 
 
 Intermediate floor-beam suspenders and sway bracing, 1,340x3,210 = 
 
 2,150 tons, at 4 cents 172. 000 
 
 Towers, 30,200 tons, at 4£ cents 2, 576, 000 
 
 Woodwork and track, 4,310 feet, at $24 103, 400 
 
 Anchor chains and plates, 11,700 tons, at 3^- cents 81!>. 000 
 
 Cables, 13,000 X 5,884 = 38,250 tons, at 7 cents 5, 354, 400 
 
 Wind laterals and additional weight in bottom chord and floor beams, 
 
 860 X 3,210 = 1,380 tons, at 4 cents 110, 400 
 
 Storm cables, 840 X 3,210 = 1,350 tons, at 8 cents 235, 700 
 
 Suspenders, 780 X 3,210= 1,250 tons, at 8 cents 200. 300 
 
 East land span, 13,950 X 800 = 5,580 tons, at 4 cents 446. 400 
 
 East land pier, 150 feet high =420 tons, at 4 cents 33, 600 
 
 Anchorages 1, 760, 000 
 
 Total superstructure, 118,940 tons 13, 830, 700 
 
 Total foundation mass = 4,140,000 cubic feet, estimated at 50 cents, will 
 
 amount to 2, 070. 000 
 
 Total bridge, 4,310 feet long 15, 900, 700 
 
 The proposed cantilever bridge is but 4,120 feet long, and if its weight, as assumed 
 in my former report be correct, and the foundation be calculated on the same basis, 
 its cost would be about $12,665,000, or $3,235,000 less than a single span suspension 
 bridge. 
 
 If the cantilever bridge was calculated, as I understand it was, for a unit strain 
 of 20,000 pounds per square inch of metal, I beg to draw the attention of your hon- 
 orable Board to the fact that this circumstance puts the comparison between the two 
 
74 
 
 BRIDGE ACROSS THE HUDSON RIVEu. 
 
 bridges on two different bases. According to Cooper's specifications, soft steel would 
 not reach a strength of over 60,000 per square inch, and medium steel would have 
 an average strength of 64,000 pounds, hence a strain of 20,000 per square inch 
 is equal to a factor of not over 3.2. The steel wire of which the cables of the suspen- 
 sion bridge are to be made will have a minimum strength of 180,000 pounds, hence 
 a unit strain of 50,000 pounds is equal to a safety factor of 3.6. If this factor be 
 placed at only 3.2, as in the cantilever bridge, the admissible unit strain would be 
 56,000 pounds and the saving in the cost of cables $600,000, and in towers and 
 anchorages $180,000. 
 
 In regard to employing a unit strain of 20,000 pounds for the stiffening truss, as 
 assumed in my first report, it seems at lirst sight high on account of working in 
 compression as well as in tension, which induced your honorable Board to restrict 
 this strain to 15,000 pounds per square inch. Personally I believe that a strain of 
 20,000 will give ample safety, because the reverse strains will occur only at long 
 intervals. But even with a strain of 15,000 the weight of the stiffening construction 
 could easily be reduced 1,800 to 2,000 pounds per linear foot by connecting each pair of 
 cables in a vertical plane in a way to form a suspended arch. The saving of weight 
 in the superstructure, cables, towers, anchorages, and foundation work would, in that 
 case, amount to at least $1,600,000, reducing the difference of cost between the two 
 designs, cantilever and suspension bridge, to about $1,500,000. 
 
 Respectfully submittted. 
 
 W. HlLDENBRAND. 
 
 To the Board op Engineers, 
 
 New Yorlc and New Jersey Bridge. 
 
 Appendix D. 
 
 NORTH RIVER BRIDGE TO HOBOKEN. 
 [Designed by G. Lindenthal, Chief Engineer.] 
 GENERAL. 
 
 Location. — It is shown on the attached map, Exhibit A. Under the charter the 
 company could locate the bridge anywhere over the Hudson River between the Bat- 
 tery and the northern New York City limit. The location at Hoboken was advised 
 by the principal railroad interests as the most direct entrance into New York. It 
 has also the advantage of accommodating local travel to Hoboken and Jersey City 
 Heights, the revenue from which will be a large item. 
 
 From a purely engineering point of view a location farther up, where the rocky 
 bluffs are close to the water's edge, would have been preferable. It would have 
 cheapened the construction of the bridge (with a single span under the charter) by 
 several million dollars. The managers of the company, however, considered the 
 business advantages of locating at Hoboken, and the larger revenue therefrom as 
 far outweighing the cheaper cost of construction on a location farther north. 
 
 The location was approved by the Secretary of War December 29, 1891. 
 
 The New York anchorage for this location had to bo placed at the intersection of 
 Twenty-third street and Tenth avenue, where the borings indicated the rock at 22 
 feet below the surface. It is the old. natural river shore. From this line towards 
 the river is made ground, and the rock dips rapidly, reaching a depth of 190 feet at 
 the foot of Twenty-second street, where the New York tower is located. 
 
 Rocky bottom (whether solid or bowlders is not definitely known yet), overlaid 
 with sandy clay, containing smaller bowlders to a depth of 26 feet, is found to exist 
 for the New Jersey anchorage. The New Jersey tower will require less than one- 
 half the depth of the New York tower for a foundation. 
 
 The river between pierhead lines is here 2,740 feet wide. The New Jersey tower 
 is located close to the New Jersey pierhead line. The New York tower is located 
 150 feet back of the New York pierhead line, to shorten the New York end span, 
 and to avoid.deoper foundations. The resulting span is 3,100 feet center to center 
 of towers. 
 
 The total length of the bridge between anchorages is 6,800, and including the 
 anchorages, 7,340 feet. 
 
 Capacity of bridge. — It is based on tho view that the bridge must derive its largest 
 business from suburban traffic at low rates. Tho passenger travel to distant points, 
 together with the freight traffic likely to go over the bridge, would not pay on the 
 investment. 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 75 
 
 The bridge, as a lateral outlet for the masses, must have a largo track capacity, 
 on which the company has been at great pains to get the advice and estimates of, 
 railroad managers familiar with the situation. 
 
 It is not necessary to give here the estimate of the number of trains capable of 
 handling over the bridge, but only to explain that the in and out going tracks will 
 be connected by loops at the New York terminus to avoid switching and delay, and 
 to save the costly space for a switching station. As far as the Now York passenger 
 terminus is concerned, it will be as for a 4-track railroad doubled on itself. 
 
 A switching and cleaning yard will bo provided in the New Jersey meadows. 
 
 The number of tracks over the bridge will be 8, namely, 2 tracks for suburban 
 tra vel, 2 tracks for through passenger and express trains, 2 tracks for freight, and 2 
 tracks for electrical railroads. 
 
 During certain hours in the morning and evening the freight tracks will be avail- 
 able also for suburban business. 
 
 The suburban loaded trains coming in the morning will turn around the loop and 
 go back empty to their respective yards. The reverse process will take place in the 
 evening hours. 
 
 Since the largest growth of business will come from the suburban traffic, the 
 structure is so designed as to permit of an addition of 6 rapid-transit tracks on a 
 second deck. 
 
 The anchorages and towers will be constructed for a capacity of 14 tracks, as 
 shown below. All other parts of the structure will be erected for a capacity of 8 
 tracks. 
 
 The additional cost of the heavier anchorages and towers is such a small percent- 
 age (about 9 per cent) of the total cost of the structure that it cuts no figure in the 
 large cost of the entire undertaking. 
 
 Following is a brief description of the salient features, and of the dimensions and 
 quantities of material in the structure: 
 
 (1) Anchorages. — Pull on each anchorage. 
 
 From dead load, 8 tracks (15 tons per linear foot of superstructure), 58,000 tons. 
 From the assumed live load (12 tons per linear foot of bridge on 8 tracks), 46,000 
 tons. Total, 104,000 tons. 
 
 Provision is made for a future increase to 14 railroad tracks, for which the pull 
 from dead load (19 tons per linear foot of suspended superstructure) would be 73,000 
 tons, and for live load (18 tons per linear foot of bridge), extreme limit, 65,000 tons. 
 Total, 138,000 tons, maximum. 
 
 Total net section of anchorage steel bars (60,000 ultimate average strength) in 
 each anchorage, 10,000 square inches. 
 # 
 
 Anchor platforms of steel, 90 feet below the pavement. 
 
 Weight of masonry and rock, and filling of stone, gravel, and sand, of each 
 
 anchorage tons . . 480, 000 
 
 Assumed coefficient of friction for masonry on foundation 0. 60 
 
 Minimum resistance of anchorages against sliding tons.. 288, 000 
 
 Total bearing area of anchor platform and anchor chains against masonry 
 
 in each anchorage ... square feet. . 17, 000 
 
 (For quantities, see estimate below.) 
 
 Quantities in each anchorage (to grade line). 
 
 Excavation cubic yards. . 30, 000 
 
 Concrete masonry do 96, 000 
 
 Ashlar granite facing cubic feet. . 440, 000 
 
 Filling for weight, rock, gravel, sand, and tamped earth cubic yards.. 160, 000 
 
 Steel in anchors and anchor bars tons.. 6, 200 
 
 Asphaltum for metal bearings cubic feet.. 1, 000 
 
 Note. — The structure above the grade line of the anchorage is a building with an 
 open court or yard over the tracks— this building to contain way station (for elec- 
 trical cars), accessible by elevators from the street, the upper part to contain offices 
 (for renting purposes) with their windows out upon the inclosed space or court. 
 
 The outside of this building corresponds in architecture with the base of the 
 anchorage, but the weight of the building is not considered (in the above given 
 weight) as a part of the anchorage. 
 
 (2) Towers. — The tower bases are hollow, of masonry, reaching 40 feet below high 
 water and extending 30 feet above high water. 
 
 The construction of the tower foundation on New Jersey side, 90 feet down to rock, 
 is by the usual pneumatic method, using a wooden caisson, 175 by 335 feet, with 
 two hollow spaces, each 90 feet square, where there is no pressure from the steel col- 
 umns, the air chamber, after reaching firm bearing, to be filled with packed sand and 
 gravel, and with concrete where necessary. 
 
76 
 
 BRIDGE ACROSS THE HUDSON RIVER 
 
 The wooden caisson is of cellular construction; one-third of the section consists 
 of gravel and sand filling. 
 
 Bearing area, 40,000 square feet. 
 
 Pressure on foundation 80,000 tons from tower base, after deducting displacement; 
 76,500 tons superstructure and steel tower, complete lor 14 tracks; 61,000 tons 
 
 extreme live load from 14 tracks; total, 217,500 tons. 
 
 Tons. 
 
 Pressure, per square foot 5. 425 
 
 From wind pressure of 3,000 tons on tower, on lee side 200 
 
 Maximum (per square foot) 5. 625 
 
 From dead load alone (per square foot) 3. 92 
 
 Maximum pressure on timber, 80 pounds per square inch. 
 
 The New York tower foundation, 190 feet down to rock, is of a different construc- 
 tion. An open, braced caisson, or cofferdam, with lower edge conforming to con- 
 tour of rock, as obtained by borings all around, 350 by 180 inside, of wood and 
 iron, 10 feet thick, filled with gravel, is first sunk and the inside dredged out down 
 to rock, which is leveled off with concrete in bags, and finely broken stone, below 
 water A hollow-spaced wooden crib, 345 feet by 175 feet and 150 feet deep, is built 
 up lioating inside the caisson. Two large hollow spaces, 75 feet square, enlarging 
 towards the top to 90 feet square, are spared out in the center of each half tower, 
 where there is no pressure from the steel columns. Masonry below water is also 
 built with hollow spaces. The whole mass of foundation is calculated to iloat 
 during construction, so that all masonry can be done above water till the whole 
 settles down evenly upon the leveled foundation. All hollow spaces in the wooden 
 crib are then tilled with gravel and sand, and in the masonry, with concrete. 
 
 Maximum pressure on rock foundations: New York tower, 130,000 tons, tower 
 base, after deducting displacement; 75,000 tons, superstructure and steel tower; 
 61,000 tons, extreme live load. Total pressure, 267,500 tons on 50,000 square feet, or 
 5.35 tons per square foot; from extreme wind pressure, 0.26; maximum pressure, 
 5.61 tons per square foot; from dead load alone, 4.13 tons per square foot; maxi- 
 mum pressure on timber, 80 pounds per square inch. 
 
 Each steel tower has 16 columns, with a total cross section of hard steel (100,000 
 pounds ultimate per square inch*). At the top, 16x515 square inches =^,240 square 
 inches. At the base, 16x580 square inches— 9,280 square inches. 
 
 Diameter of columns, 8 feet at top; 9 feet at bottom. 
 
 (For quantities, see estimate below.) 
 
 Pounds. 
 
 Compression per square inch of steel from dead load of only 8 tracks, and 
 
 from maximum bending moment 12, 500 
 
 From maximum live load of only 8 tracks 9, 600 
 
 Total 22, 100 
 
 From dead load in the future of 14 tracks and from maximum bending 
 
 moment 15, 300 
 
 From maximum live load of 14 tracks 14, 400 
 
 Possible maximum total 29,700 
 
 The elastic limit of the 100,000 pound steel is 60,000 pounds. Buckling strength of 
 steel columns is 54,400 pounds per square inch. 
 
 With 16 trains of ordinary size (600 tons each) on the bridge, the total compres- 
 sion per square inch in the tower columns will not exceed 13,500 pounds per square 
 inch for 8 tracks superstructure. 
 
 For 14 tracks superstructure the total compression from dead and live load will 
 rarely reach 17,000 pounds per square inch. 
 
 The above considered maximum compression of 29,700 pounds per square inch 
 may never occur in the life of the bridge. It would require a live load of 122,000 
 tons, equal to about 3,000 loaded freight cars. 
 
 The temperature strains in the cable do not affect the towers, but the towers 
 themselves are exposed to bending strains from temperature differences in the col- 
 umns, exposed to the heat of the sun, and others being in the shade. The computed 
 deflection of tower tops from this cause, for differences of 30° P., is 2 inches. 
 
 The deilection of tower tops lengthwise with bridge from difference of load effects 
 will not exceed 8.1 inches. 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 77 
 
 Quantities in Neiv Jersey tower base (00 feet below high water). 
 
 Excavation cubic yards. . 105, 000 
 
 Timber M . . 20, 000 
 
 Irou tons . . 460 
 
 Concrete below water cubic yards.. 3,000 
 
 Gravel and sand tilling do 40, 000 
 
 Masonry of hard-burned brick. 
 
 Concrete and granite facing and coping cubic yards.. 50, 000 
 
 Quantities in Neiv York tower base and cofferdam (192 feet below high water). 
 
 Excavation cubic yards . . 3G0, 000 
 
 Timber M . . 65, 000 
 
 Iron tons.. 2,340 
 
 Concrete under water cubic yards. . 1, 000 
 
 Broken stone do 3, 000 
 
 Gravel tilling do 180,000 
 
 Masonry, tbo same as for other tower do 56, 000 
 
 Weight of steel for each tower: 
 
 Sixteen columns, with base plates and cable bearings tons.. 7, 220 
 
 Lattice, horizontal, wind, and longitudinal bracing do . . . 4, 060 
 
 Cable chambers on top and upper bracing between towers do. . . 040 
 
 One tower do.. . 12,220 
 
 Two towers do. . . 24, 440 
 
 Quantities for each pedestal : 
 
 Excavation cubic yards . . 2, 000 
 
 Masonry, concrete, with granite facing and coping do 1, 200 
 
 Steel columns, with bracing and vertical anchorage tons.. 170 
 
 (3) Cables. — The 4 cables are computed with a factor of safety of 3 for a dead 
 load of 15 tons per linear foot, and for a moving load of 12 tons per linear foot, 
 covering the entire bridge. Maximum total load, 27 tons for 8 tracks. 
 
 In ordinary operation the moving load will rarely reach 3,000 tons for the middle 
 span on all 8 tracks. 
 
 The 4 cables are composed of pin-connected wire links. Each wire link is made 
 up to accurate length of parallel wires looped around flanged steel shoes, bored out 
 to tit the pins. The pins are 16 inches diameter and hollow. The steel wire is 
 No. 3, Birmingham gftuge (0.259 diameter), and has an ultimate strength of 180,000 
 pounds per square inch (9,600 pounds per wire). 
 
 Wire links have the advantage of accurate work and close inspection in the shop, 
 quick erection, and testing to destruction, so their accurate value may be known. 
 Wire links permit also of variations in the cable section, as needed. 
 
 The length of the wire links varies from 50 feet at the center to 54 feet at the 
 towers. 
 
 The horizontal panel length is 50 feet throughout. 
 
 The links contain from 400 to 800 wires each, according to position in the cable, 
 and on the pins. 
 
 The vertical distance of the cables is 55 feet from center to center throughout, 
 i. e., the upper and lower cable have the same curvature. 
 
 Each cable is composed of 3 chains, one above the other, coupled vertically at 
 the pins. The vertical couplings consist of one-half inch steel plates between 
 links, sufficiently strong transversely to transmit the increment of the web strains 
 into the chains of the cable. 
 
 The middle chain has alternately 9 and 10 links, and the upper and lower chains 
 have each alternately 7 and 8 links. 
 
 Total number of wires in each cable : At the tower, 18,400; solid metal section, 
 975 square inches ; ultimate strength, 87,700 tons. At the dip, 16,900 ; solid metal sec- 
 tion, 890 square inches; ultimate strength, 80,000 tons. 
 
 The dip of the cables is one-tenth of the span, 310 feet. 
 
 The cables are so arranged that for an addition of 6 tracks (to a total of 14) the 
 wires in each cable can be increased in the future up to 25,000 by the addition of 
 wire links. 
 
 The chains of wire links are surrounded by a water-tight removable shell (or 
 envelope) of corrugated steel (one-eighth inch thick) 9 feet in diameter, as a pro- 
 tection against the weather. 
 
 The bracing between the cables is of rolled steel. 
 
 The verticals consist of two latticed 20-inch eyebars, varying in cross section for 
 one member from 140 to 80 square inches. 
 
78 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 The diagonals consist of sets of adjustable rods, from 2 to 3 inches square, with 
 screw ends fitting into eyebar saddles, having their bearings on the cable pins of the 
 middle chain. The aggregate section of the square rods varies for one member from 
 206 to 92 square inches. 
 
 The average weight per linear foot of each suspended rib, including wire links, 
 steel shoes, pins, and steel envelope, is 7,200 pounds; bracing between cables, 1,300 
 pounds; total net weight of one rib average per linear foot, 8,500 pounds. 
 
 Conrpared with one of the four arch ribs of St. Louis bridge: Steel tube flanges, 
 635 pounds average per linear foot; web, 285 pounds average per linear foot; total, 
 920 pounds. 
 
 Or, compared with one of the six arch ribs of the Harlem bridge : Flanges, 850 
 pounds average ; web, 190 pounds average ; total, 1,040 pounds. 
 
 In the St. Louis bridge the web is 30 per cent of the total weight of the rib ; in 
 the Washington bridge, 19 per cent, and in the North River bridge only 15 per cent 
 of the total weight of the rib. 
 
 The two ribs can resist a bending moment of 1,600,000 foot tons before the perma- 
 nent tension in the upper cables from the dead load would be nullified. (Wire-link 
 cables can not take compression, and overstraining from bending is next to impos- 
 sible). 
 
 Calculation shows that to produce this bending moment trains, would be required 
 side by side, 1,200 feet long, aggregating 10,800 tons moving over the bridge. 
 
 It would be next to impossible to bring such a load and such an extraordinary 
 assemblage of double-headed trains upon the bridge. 
 
 The assistance of the stiffening trusses is here entirely disregarded, also that part 
 of the live load directly absorbed by the cables by reason of their deflection. 
 
 The calculated maximum deflection, at one quarter the span, from this extreme 
 load is 2.4 feet. In every-day operation the load effects and deflection will probably 
 not reach 10 per cent of this extreme. 
 
 The suspended ribs, with a depth of one fifty-sixth of the span, are therefore stiff 
 and strong enough to resist deformation, without stiffening trusses, from the heaviest 
 moving load, and being in stable equilibrium are more rigid than the compression 
 ribs with fixed ends of the St. Louis arch bridge with a depth of one forty-fourth of 
 the span, which are in unstable equilibrium and subject to compression and tension 
 alternately. 
 
 The suspended ribs are assumed to be hinged at their ends in the a- chorages and 
 on the towers. This assumption is severely carried out in the construction. The 
 exact equivalent for the hinge on the towers is a toggle joint, made of short wire 
 links. 
 
 The diagonals of the cable bracing during erection remain loose. After erection 
 of complete superstructure, and with the cables therefor in perfect equilibrium 
 from dead load, equally divided upon the four cables, the diagonals are adjusted 
 and receive a slight initial tension. 
 
 The cable bearings on the towers are fixed, i. e., can not slide, but they can accom- 
 modate themselves to the hinge movement of the toggle joint. The bending strains 
 in the towers (from the difference of temperature, and from load effects in the 
 cables) are allowed for. 
 
 The temperature strains in the cables are relatively small. The steel envelopes 
 protect the wires against the direct rays of the sun and against uneven heating. 
 
 The bending moments from live load in the long end spans (having a dip of g^) 
 
 would be greater than in the middle span. 
 
 To reduce them to the same limit, the end spans are in the middle provided with 
 anchor columns, reaching to masonry pedestals below. These columns bear no part 
 of the dead load. They are counterwoighted in the pedestals in such manner as to 
 be affected only by an excessive concentrated live load, in which case a positive or 
 negative reaction (of -J- 6,000 tons, according to position of live load) is produced 
 and accurately known. The computation of the bending strains is thereby much 
 facilitated. 
 
 (Note. — This is the present arrangement, but a change to a fixed hinge, as more 
 economical still, is under consideration). 
 
 The weight per linear foot of the suspended structure in the end spans is brought 
 within the same limits as for the middle span. 
 
 The position of the anchorages and lengths of end spans are dictated by local con- 
 ditions. If the anchorages could have been placed nearer to the lowers it would 
 have reduced cost of bridge very much, as shown below. 
 
 The arch ribs are cradled 6.5 per cent, i. e., inclined toward each other. They are 
 160 feet apart on top of towers and 120 feet at the middle of span, 
 
 No wind bracing is required between the cradled cables. 
 
 The suspenders are of bundled steel wire ropes, 35 square inches solid section. 
 Maximum tension, with 14 tracks, on one suspender, 700 tone. 
 
BRIDGE ACROSS THE HUDSON RIVER. 79 
 
 Assuming E == 29,000,000, the middle span would deflect under the assumed maxi- 
 mum load of 12 tons per linear toot, which may never occur. 
 
 From elongation of cables in middle span inches.. 48 
 
 From bending of towers do 21 
 
 From -j- 65 c F., as a maximum, affecting only the middle span do 21.7 
 
 Maximum deflection do 90.7 
 
 Normal camber 15 feet=180.0 iuches for middle temperature at + 50° F. 
 
 Pounds per 
 square inch. 
 
 Tension in the cable wires from dead load alone 32, 500 
 
 From temperature bending moment 6, 200 
 
 From full live load (12 tons per linear foot) 2G, 000 
 
 Maximum at center of span 64, 700 
 
 Maximum from bending moment at the quarter 65,000 
 
 Lowest elastic limit of 180,000 pounds steel wire assumed at 85, 000 
 
 But more likely to run up to 120,000 
 
 The maximum dellection, at the quarter from one-sided loading, of 29 inches is 
 equal to a change of six-tenths per cent in the grade on the middle span. 
 
 Track platform and wind girders. — The panels are 50 feet long. Stringers placed 
 directly under the rails, which rest on wooden block cushions between steel guard 
 rails, open on the sides to let cinder and snow fall through; no wooden ties at all 
 are used. 
 
 The space between steel guard rails is stretched over with a taut wire netting, 
 weighing 2± pounds per square foot. 
 
 Stringers and floor beams, 5 feet deep, dimensioned for locomotives weighing 150 
 tons with tendor. 
 
 The lower floor beam carries 8 tracks, and has 3 intermediate supports from a 
 cross arch above, for which it acts as the tension member between arch footings. 
 
 The cross arch is 65 feet high and placed at every panel point. It acts also as 
 cross bracing between the lower and upper wind trusses. 
 
 The cross arch is further to carry an upper floor beam for a second deck of 6 
 rapid-transit tracks to be added when needed in the future. 
 
 On top of the cross arch is the promenade, 20 feet wide with wooden flooring. 
 
 The lower wind truss is in the plane of the lower floor for 8 tracks. The upper 
 wind truss is placed below the promenade. Both are 115 wide, center to center of 
 chords, equal to one-twenty-sixth of the distance between the towers. 
 
 Both wind trussed have the same chord sections (180 square inches each for 100,000 
 pounds steel) from end to end (anchorage to anchorage). 
 
 The wind trusses are proportioned as horizontal continuous girders of uniform 
 chord section, with a consequent great saving of metal for the chords. Their ends 
 in the towers can slide and adjust themselves to temperature changes, but are 
 arranged to resist vertical and horizontal bending moments at the towers. 
 
 The ends of the wind trusses at the anchorages are firmly anchored into the 
 masonry, to also resist end-bending moments. 
 
 The assumed wind pressure is 2,400 pounds per linear foot of superstructure. 
 
 Maximum stress in chord -|- 36,000 pounds per square inch and maximum stress 
 in diagonals -f- 30,000 pounds per square inch from maximum wind pressure. 
 
 The chord sections of the horizontal wind trusses are utilized also in two vertical 
 stiffening trusses, in connection with the floor system and cross arches, as an aid in 
 distributing the concentrated train loads upon the braced cables, although not nec- 
 essary, as stated above. 
 
 The cable ribs are so rigid that the aid of the vertical trusses amounts to only 10 
 per cent; i. e.. 00 per cent of the deforming effect from moving load goes into the arch 
 ribs and 10 per cent into the stiffening trusses for equal values of deflection. 
 
 Erection. — The construction of the anchorages and the erection of the steel Lowers 
 oiler no new features, except large size. 
 
 All steel work, except wire loops, can be done with existing plant. The plant for 
 making wire loops will be simple and not expensive. There will be 9,300 wire links, 
 and it is estimated that on one machine two links can be furnished per day on an 
 average, which would require sixteen mouths on ten machines for the 9,300 links 
 required. 
 
 As for manufacturing capacity of wire, there are several large works equipped 
 for it, and one of them offers to alone furnish all the wire (over 40,000 tons) in one 
 year without extra effort. 
 
 The links will average 4 tons each, and the cost of making the links is estimated 
 at live-eighths cent per pound, including oiling. (The wires will not be galvanized). 
 
 The erection of the superstructure will be similar to that for the Brooklyn bridge, 
 S. Ex. 1 11 
 
80 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 i. c, without false works. First, a temporary footbridge of wire ropes over the 
 towers, strong enough to carry one set of wire links of permanent cables. 
 
 Then, erection of first wire links, suspended temporarily from the footbridge 
 above, alternating one and two links, commencing at each tower, toward center 
 and anchorage, respectively, until first set of wire links is connected up from anchor- 
 age to anchorage for each side. Thereon all following wire links are erected and 
 pushed upon the pins wi-thout further support from the footbridge. The wire ropes 
 of temporary footbridge are used afterwards for the suspenders. 
 
 The wire links, being all made in the shop to exact length, the same as eyebars, 
 the erection of the cables can proceed without regard to the weather and without 
 delay from adjustment; 160 erecting gangs, if needed, can be employed at one time 
 simultaneously in the erection of the four cables, which can be completed in less 
 than ten months. 
 
 The erection of the other parts of the superstructure is the same as for Brooklyn 
 bridge. 
 
 It is immaterial what form the cables assume during erection. The adjustment of 
 the diagonal bracing between the cables and of stiffening trusses takes place only 
 after the entire superstructure down to the rails is in place. 
 
 The time of construction is estimated at four years, namely, two years for anchor- 
 ages and tower bases, nine months for steel towers, and fifteen months for cables 
 and superstructure. 
 
 Weights of superstructure, 6,800 feet long, between anchorages: 
 
 (1) 8 tracks: 
 
 100-pound rails on wooden blocks. 
 Steel guard rails and wire netting. 
 
 Tons. 
 
 200 pounds per linear foot of track 5,440 
 
 (2) Floor construction, per panel of 50 feet : 
 
 Tons. 
 
 8 pairs of stringers 88 
 
 1 cross arch, with suspended floor beam, including verticals 
 
 for stiffening trusses 73 
 
 2 sets of hanger eyebars fo^ cable suspenders 7 
 
 4 wind chords 65 
 
 Horizontal wind bracing (average) 12 
 
 Stringers and hand rail for promenade 7 
 
 Diagonals of stiffening trusses (average) 8 
 
 Total per panel 260 
 
 Tons. 
 
 Per linear foot of bridge, 5.2 tons 35,360 
 
 (3) Suspenders of wire ropes 1, 900 
 
 (4) Two cable ribs: 
 
 Cables with pins, shoes, couplings, and shell 48, 960 
 
 Bracing between cables * 8, 840 
 
 57, 800 
 
 Weight of superstructure, metal 95, 060 
 
 Weight of superstructure, niefcal and track 100, 500 
 
 Average dead load of superstructure, per linear foot of— . . 
 
 Metal 13.95 
 
 Track 80 
 
 Flooring of promenade > 
 
 Telegraph wires \ 
 
 15. 00 
 
 °g — ^^'=1.875 tons dead load per linear foot of track, which is the same as 
 
 for a 400-foot Whipple truss span. 
 Total amount of steel in — 
 
 Tons 
 
 Anchorages 12, 400 
 
 Towers 24, 780 
 
 Superstructure 95,060 
 
 132, 240 
 
 iqo 04.0 
 
 Weight of steel per linear foot of entire bridge, 7,340 feet long: =18.02 
 Ions, or 2.25 tons per linear foot of track. 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 81 
 
 The addition of six rapid-transit tracks (for a live load of 1 ton per linear foot of 
 track), whenever needed in the future, will require 17,500 tons wire links and 
 10,200 tons of other steel work, 27,700 tons, total addition, at a cost of $2,500,000. 
 
 If the bridge had been located at souie point north, Avhere the rocky binds come 
 close to the river, the length would have been reduced to about 5,500 feet, a saving 
 iu length of over 1,800 feet. 
 
 For suspension spans of 3,000 feet, a difference of 200 feet more or less spau does 
 not greatly affect the cost per running foot. 
 
 The cost of bridge would have been reduced : 
 
 (1) In the anchorages, on account of the natural rock bluffs, at least $1, 000, 000 
 
 (2) In the towers, probably nothing. 
 
 (3) In the superstructure, 1,800 feet shorter, about 2, 200, 000 
 
 3, 200, 000 
 
 Hence the bridge for eight tracks would then have cost only about $17,800,000. 
 
 There is, however, an offset of 1,800 feet approaches against such saving, which, at 
 $400 a linear foot, would cost $720,000, thus making the saving only about •$2,480,000. 
 
 Six per cent interest thereon would have amounted to $148,800 yearly. 
 
 The location at Hoboken holds out the certainty of greater revenue, from local 
 traffic alone, by ten times the amount of the interest on the saving in cost of a shorter 
 and cheaper location further north. 
 
 The cost of the land, of the approaches, and of the terminal station are greater 
 than the cost of the bridge. There is, further, the interest account during construc- 
 tion and the legal and administration expenses. 
 
 July 18, 1894. G. L. 
 
 Appendix E. 
 
 THEORY OF THE CONTINUOUS STIFFENING TRUSS WITH ENDS ANCHORED DOWN BUT 
 NOT FIXED IN A VERTICAL PLANE. 
 
 The ends of this stiffening truss are free to change their direction, but not their 
 elevation, in a vertical plane, and the truss is continuous from end to end. The 
 theory of this truss has been published for a considerable number of years in 
 standard engineering works, and its principal formulas only will be given without 
 detailed denionstjation : 
 
 The moving load will be taken as passing on the span from the left end A 
 Reference will be made to Fig. 1 in the analysis and the following notation will be 
 employed : 
 
 Length of stiffening truss between centers of end supports / (feet) 
 
 Moving load per linear foot w 
 
 Uniform upward pull (supposed to bo distributed over I) per linear foot p 
 
 Reaction of truss at A (upward under conditions taken) R 
 
 Reaction of truss at B (downward under conditions taken) R 1 
 
 Tho coordinate of x or X\ will be measured from A as an origin positive toward 
 C, the center of the span. In general, bending moments will be represented by M 
 and shears by S. 
 
 In this case all the moving load is carried to the cable through the suspenders; 
 hence the two reactions R and R 1 will be equal and opposite in direction. 
 
 S. Ex. 12 6 
 
82 BRIDGE ACROSS THE HUDSON RIVER. 
 
 The equations of condition for equilibrium are: 
 
 R + p l —wxj + R* — (1) 
 
 £of pP + R l l— i wx, a = (2) 
 
 R+Ri = (3) 
 
 Equation (1) at once gives: 
 
 WX\ 
 
 V= I ( 4 ) 
 
 Then from equations (2) and (3) : 
 
 B = -B'=~!(i_*') (5) 
 
 The bending moment at any section distant x (never greater than Xi) from A is: 
 
 M = Bx-(«-j>)f (l-*) (6) 
 
 Heuce there is always a point of contra-flexure at the head of the moving load. 
 
 M has its maximum value for x = ^. 
 
 2 
 
 Hence : 
 
 Mi = wxS fl-*S (7) 
 
 Mi has its maximum value for Xi = ~ I. 
 
 o 
 
 Hence : 
 
 TV/T 4 Wl 2 /Q\ 
 
 M max=27 8 (8) 
 
 The unloaded part of the span acts aa a beam simply supported at its ends and 
 carrying an upward load of uniform intensity p = Hence its greatest bending 
 
 moment at center will be : 
 
 - M '=^ J 0-*') 2 (9) 
 
 2 
 
 This has its maximum for x { =-^l. 
 
 o 
 
 Hence : 
 
 -M = 4 wP . (10) 
 
 max 27 8 
 
 If any given length of load, as ivx l} move over the span, there will be a point of 
 contra-flexure at each extremity of it, and the greatest bendiug moment it produces 
 (i. e., at its center) will be given in general by equation (7), or by equation (8) if 
 
 2 
 
 its length is — I. The range of the maximum downward bending moment given by 
 
 o 
 
 equation (8) is the middle third of the span, while the same maximum, as an upward 
 moment, equation (10), occurs at the one-third points only. 
 
 The shear at any section distant x (less than x { ) from A (figure 1), is: 
 
 = R+ px — wx = w(l — Q 1 — -' (11) 
 
BRIDGE ACROSS THE PIUDSON RIVER. 83 
 
 When x=0 (i. e., at the end of the span) the shear is equal to the reaction R. 
 The greatest shear is found by making x=0 and X\ = ^ in equation (11) : — S max = 
 
 ~. When x is greater thanf 1 , the shear S becomes negative and takes its inaxi- 
 o 2 
 
 mum at the head of the load, or for x = Xi : 
 
 S==— ™* A — ^)=Ri (12) 
 
 Equations (11) and (12) give the shear when the load wxi occupies any position 
 on the span, provided x and X\ are measured from either end of that loading. 
 The shear in tho unloaded portion of the span (I — x { ) is: 
 
 S = -Ri-M'-*) = '-fi{ (*-*-) - 2 ( 1_ l) (I3) 
 
 This expression attains its maximum values for x — l and x=x i} as it then becomes 
 equal to R or R 1 ; it also becomes zero for x = $ (I 
 
 THEORY OP THE CENTER HINGED STIFFENING TRUSS. 
 
 There will be given in this appendix only such a concise statement of the theory 
 of the center-hinged stiffening truss as the purposes of this report require, but 
 within those limits it will be complete. Those purposes are satisfactorily served by 
 considering tho question as a problem in statics, in which tho effects resulting from 
 the deformation of the cablo, the elastic stretching of the suspenders, and the elas- 
 tic deflection of tho truss, all under the moving load, are ignored. A complete 
 analysis of tho influences of these separate assumptions exerted upon the results 
 obtained would be out of place here, although the effect of the stretching of tho 
 suspenders is illustrated at tho end of this appendix, but it may bo stated that the 
 resultant effect is to confer upon the cable an increased facility of adjustment in 
 form to tho requirements of a'varying moving load, and hence, an enhanced capac- 
 ity to receive such moving load directly through the suspenders without 
 action of the truss. The variations from tho exact treatment which involves tho 
 consideration of plastic deformation of tho members named results in formulae 
 which, as the mathematical theory of tho combined elastic action of cables and 
 beams show, give greater bending'moments and shears in the stiffening truss over 
 the greater part of the span than those which actually exist. All estimates of 
 material for tho members affected will consequently bo on the safe side. The 
 influence of the elevation or depression of the cablo as a whole, due either to a 
 variation in temperature or to elastic extension, is eliminated by the center hinge. 
 
 The moving load will be taken on the left half truss A C, and the same notation 
 as that given below fig. 1 in tho preceding section will bo used. 
 
 Case I. 
 
 In this case tho moving load w will bo taken as passing on tho truss from A and 
 its variable length measured from that point will be represented by x\. 
 
 Inasmuch as the pull exerted on the truss by the suspenders is upward and as there 
 is no moving load on B C, it is clear that the reaction R 1 at B must bo downward in 
 direction and that an equal downward reaction must bo exerted by the half truss A 
 CouBC at C, the hinge point at tho center of the span. That downward reaction 
 at C is a part of the requisite portion of tho moving load w X\ determined by the 
 
 simple principle of the lever applied toAC= s as a span, while tho other part of 
 
84 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 that portion is carried directly to A without exerting any pull on the suspenders, and, 
 consequently, without stressing the cable. The part transferred to C (equal to the 
 downward reaction at 13) is evidently less than that transferred to A, except in the 
 case of the moving load covering the half span, when they are equal. From this 
 reasoning it follows that the total upward pull on the suspenders is less than the 
 moving load iv Xibj the excess of the part transferred to C, but both these differ- 
 ences disappear when the moving load covers the half span. 
 
 The forces acting on the entire truss A 13 are, then, the upward reaction R (at A), 
 the downward reaction R 1 (at B), the upward pull pi, and the downward-moving 
 load w X\ } and it is necessary for equilibrium that their sum shall be zero. 
 
 Hence : 
 
 2>l-\-R — wxi — R!=0 (14) 
 
 Because the truss is hinged at the point C, moments of the same forces acting on 
 each half, and about C as a center, must be equal to zero. 
 Hence : 
 
 8 + 2 ~ wx > (^-)-° { 
 8" 2 j 
 
 By placing the two equations (15) equal to each other 
 
 R = w Xi—^—R 1 (16) 
 
 The substitution of this value of R in equation (14) will give: 
 
 By the combination of the second of equations (15) and equation (17) : 
 
 B'=^ (18) 
 
 By placing this value of R 1 in equation (16) : 
 
 R=WXl (i_|i) : d9) 
 
 The value of R 1 from equation (18) placed in the second of equations (15) will 
 yield : 
 
 „- 2tv2C l (20^ 
 
 P— p 
 
 Those values of R l , R, and p, in which x v must never exceed £ I, will enable all 
 moments and shears to bo immediately written. 
 
 The expression for the bending moment at any point x (not greater than x t ) from 
 tho point of support A is : 
 
 M 
 
 In order to determine what position of loading must be taken so that the maxi- 
 mum bending moment will exist at any desired section distant x from the point of 
 support A, the first derivative of M in respect to Xi (x being considered constant) 
 must be put equal to zero and then solved for X\ : 
 
 d M < 3X& 3xiX |^ 2x^x^ ? __ n 
 
 3Z— 2x 
 
 (22) 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 85 
 
 By placing the value of X\ in equation (21) : 
 
 Equation (23) will give the greatest possible bending moment in the half truss 
 A C at any point indicated or located by the coordinate x which will never exceed 
 I 
 
 -Tp The corresponding length ot loading from A will be given bya?i in equation (22). 
 The greatest bending moment in the half truss A C can be found by placing 
 ^ x = 0, then solving this ( 
 there is a simple procedure. 
 
 *Pj^ x - 0, then solving this equation for x and placing its value in equation (23) ; but 
 
 Let X\ be considered constant in equation (21), then if there will be located 
 
 the section of the greatest bending for any given length of loading x, : 
 
 dM. i s 3#i\ s2xr „ \ ) 
 
 ♦'•^^ (t- 1 ) (24) 
 2xi 8 
 P ~~ 1 
 
 If this value of x be placed in equation (22) there will result: 
 
 Equation (25) is satisfied, for: 
 
 ^ = .395---<* (26) 
 
 Or, the greatest bending moment in the span occurs when 0.395 of its length is 
 covered with the moving load. 
 
 If j is taken from equation (26) and placed in equation (24) : 
 
 x =.234 1 (27) 
 
 Equation (27) thus locates the section of greatest bonding in the span. 
 By placing £ = .234 I in equation (23), that maximum moment becomes: 
 
 wl 1 
 
 M ■ =.018825 — wF-=: .1506 -« (28) 
 
 max o 
 
 The half truss B C is simply supported at each end and carries the uniform upward 
 load p por linear foot; hence it will be bent upward with the negative moment: 
 
 This expression evidently has its maximum value when X\. — 
 
 a 
 
 Hence : 
 
 M 
 
 max 
 
 =-tG 1 -») ^ 
 
 I 
 
 In these expressions neither x t norx can ever exceed 
 
86 
 
 BRIDGE ACROSS THE HUDSON RIVER. 
 
 With the value x = — I : 
 4 
 
 max g 8 64 " W 
 
 The shear at any section located by the coordinate x (never exceeding x x ) is: 
 
 S=j>« + B— , ra = ^g"-' + «*, (>-§■)- «*. 
 ... S =, ra ( 2 ^- 1 ) + W x,(l-^ (31) 
 
 In order to; determine the greatest shear at any point or section x the same pro- 
 cedure employed lor the moment must be followed: 
 
 dS = 4««, 3x, =0 . % _P (82 ) 
 
 rfxi Z 3Z — 4z v y 
 
 This value of sc, placed in equation (31) gives: 
 
 ^="\m£=m-*\ (33) 
 
 The value Si in equation (33) gives the greatest shear in the half truss at any sec- 
 tion x. 
 
 The form of equation (33) shows that the maximum of all the values of Si will be 
 found by making x = 0; hence: 
 
 S ma* = T ' (34) 
 
 By making x = in equation (32) it appears that the length of moving load 
 required to produce the maximum shear is : 
 
 *i=! (35) 
 
 This value of X\ placed in equation (19) shows that the maximum shear is equal to 
 the maximum reaction R. 
 
 The preceding equations have been so written that an upward shear is positive 
 and a downward shear negative. If Si be placed equal to zero, by using equation 
 (33): 
 
 The second value indicates nothing useful, but the first value (^^) shows that the 
 
 shear is always upward over that quarter of the span nearest A, and downward or 
 negative over that quarter adjacent to C. The greatest negative shears will 
 obviously occur at the head of the moving load, and they will be given by making 
 x=x } in equation (31); 
 
 _S,='i|L 2 (?£'-|) (37) 
 
 For a maximum : 
 
 x,=^an.l-S, = -'| 
 The preceding reasoning shows that the maximum negative shears will he given hy 
 equation (37) in which X\ must have values hetween -| and^ only; but that the maxi- 
 mum positive shears will he given hy equation (33), in which x must have values hetween 
 
 x = and x= \ only. 
 
 4 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 87 
 
 Since forxi^-^, IV = l( ^ and }) = ™ , the expression for the shear in the half 
 truss B C (or in the half truss A C fully loaded) will bo: 
 
 S 1 == w 
 
 G-f) <*» 
 
 By increasing r from to \ in equation (38) there will result the positivo shears 
 
 a 
 
 iii iho right half of B C and the negative shears in the left half of B C. 
 
 Case II. 
 
 In this case a moving load of length varying from to A will be supposed to be 
 
 placed on tlie span and to extend from the center C to any point distant ^ - \ _ 
 
 from C. All notation will remain as in Case I. 
 
 The equations of condition for equilibrium corresponding to equations (14) and 
 ( 15) now become : 
 
 jri-f ^ _ w {1 _ jbA— Ri = (39) 
 
 + 2-2 (2-^)" = °1 
 
 pi- R 1 / 
 8-2- =0 
 
 (40) 
 
 The two equations (10) give: 
 
 „ W/ i \ 2 
 
 R = l\2~ x - R ' (41) 
 
 The substitutions of R from equation (41) and pi from the second of equations 
 (40) in equation (24) give: 
 
 R, -l(l*^) (t + §) ( 42 > 
 
 By placing this value of R 1 in equation (41) : 
 
 w si \ si 3x, \ 
 *=2\2- x V2--TJ ( 43 > 
 
 The same value of R 1 in the second of equations (40) : 
 
 2w s I 
 
 2w s I \ sx\ 1 \ 
 
 (44) 
 
 The reactions R and R 1 will evidently have their greatest values when X\ = 0: 
 
 R =Ri =^ (45) 
 
 max max 8 
 
 The greatest values of two bending moments must be determined — i. e., one at 
 that extremity of the moving load at the distance X\, from A, fig. 2, and the other 
 at any point of A C with that half span entirely covered with the moving load. 
 The expression for the moment at any point x between the end A and aj is : 
 
 M=Rx+ i G-*.) f f 0- f0+?(? +1) 1 m 
 
 The form of this expression shows it to bo a maximum for x = x x : 
 
 M, = h'Xi I (J-*)' (47) 
 
88 ' BRIDGE ACROSS THE HUDSON RIVER. 
 
 In order to find a maximum : 
 
 dM 
 
 Hence Xi 
 
 Which placed in equation (47) 
 
 Mi 
 
 wf 27 
 8 "512 
 
 0527 
 
 wl 1 
 
 (48) 
 
 If the moving load covers the whole of the half span A C, the moment at any 
 point x will he, since then p = 1 ~\ 
 
 M- = (,-^ 2 (^-x) = ^(^-x) 
 
 (49) 
 
 This is the maximum for# = 
 
 M ] 
 
 125 w l 
 
 64" 
 
 (50) 
 
 The bending in the right half of the span is given by equations (29) and (30) in 
 the preceding case. 
 
 The general expression for the upward (positive) shear in the unloaded portion Xi 
 of £he left half, A C, of the span is : 
 
 For the greatest value of S, always x = X\: 
 
 (51) 
 (52) 
 
 The shears in each half of the span with the left half, A C, fully loaded, have been 
 given in the preceding case by equation (38). 
 
 EFFECT OF CHANGES OF LENGTHS OF THE SUSPENDERS ON THE DISTRIBUTIVE FUNC- 
 TION OF THE STIFFENING GIRDER. 
 
 The suspenders are lengthened or shortened by changes of temperature ; they are 
 lengthened by the live load; their increment of length due to either cause are pro- 
 
 
 
 Fig.3. 
 
 i 
 i 
 
 
 
 - C — -f 
 
 ^ — i 
 
 1 
 
 k \ \~ 
 
 
 -i<fe 
 
 
 r s 
 
 i 
 
 
 i - 
 
 
 portional to their length ; these increments are, therefore, ordinates of parabolas. 
 
 Referring to fig. 3, whore A C B represents the cable, acb the stiffening girder, and 
 Aa,B6, the towers, if the increments of length of the suspenders, due to a rise of tern- 
 
BRIDGE ACROSS THE HUDSON RIVER. 
 
 89 
 
 peraturc, be plotted downward from lino a b, they will give the parabolic arc a ( Oi ; 
 supposing that the towers expand in the same proportion as the suspenders, the 
 curve «] Oi becomes a o 2 and represents, in position, the deflected line of the girder, 
 this line is similar to the curve of deflection due to a uniform rate of loading, and 
 has a slight convexity upward, showing that no disturbance has taken place in the 
 distributive action of the girder, except a slight relief of duty for the loaded part, 
 and a slight increase of duty for the unloaded part, of the girder. Owing, however, 
 to the greater bulk of material in the tower, its temperature and rate of expansion 
 will be less than for the suspenders; if a s represents the difference due to this 
 cause, then the curve, a o 2 drops to the position s o 3 , and «So 3 becomes the line of 
 deflection of the girder, showing that in the immediate vicinity of the towers the 
 suspenders are partly relieved of their duty, and that a part of the load is carried 
 directly to the tower by the girder. 
 
 A similar construction for a fall of temperature, to the right of the figure, shows 
 the effect on the girder to be slight deflection downward with the convexity of the 
 curve downward, indicating a slight increase of duty for the loaded part of the 
 girder and a slight decrease for the unloaded part, owing to the difference of con- 
 traction b t of the tower, the deflected line of the girder will be b T m>, showing that 
 the duty of the suspenders in the immediate vicinity of the tower has been increased. 
 
 The effect of the elastic elongation of the suspenders due to the live load is exactly 
 the same as it is for a rise of temperature, except that owing to the fact that the 
 tower contracts instead of expanding, the disturbing effects in the vicinity of the 
 tower is increased in warm weather and decreased in cold weather. 
 
 The ill effects on the girders and suspenders arising from these disturbances are 
 avoided by omitting the suspenders for a short distance next to the towers. 
 
 c 
 
NEW YORK & NEW JERSEY BRIDGE. 
 PROFILE OF HUDSON RIVER ON LINE "A" 
 BETWEEN 59™ & 60™ STS. PRODUCED 
 
 SEx t3- 53 ; 
 
|-;jl!;ill!f;[[lii[tH 
 
 Pt#A/ Of Prl/D&f 
 
 /?/>/><?/ astso u/vaf/? /7c r or Cbv&ttss frr&orto Jva/s7-/S9* 
 
 Srwt 300/'/' " / /M 
 
 \ ■ !» A, A, *L — d.. «t. i U — »l. ,i „ 
 
 g E , /2. 53 3 
 
I 
 
Sketch of Towers 
 
 SEx 53