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120-639: The Brooklyn Bridge is a hybrid cable-stayed / suspension bridge in New York City , spanning the East River between the boroughs of Manhattan and Brooklyn . Opened on May 24, 1883, the Brooklyn Bridge was the first fixed crossing of the East River. It was also the longest suspension bridge in the world at the time of its opening, with a main span of 1,595.5 feet (486.3 m) and

240-460: A 2-span or 3-span cable-stayed bridge, the loads from the main spans are normally anchored back near the end abutments by stays in the end spans. For more spans, this is not the case and the bridge structure is less stiff overall. This can create difficulties in both the design of the deck and the pylons. Examples of multiple-span structures in which this is the case include Ting Kau Bridge , where additional 'cross-bracing' stays are used to stabilise

360-505: A block fall. Construction on the suspension towers started in mid-1872, and by the time work was halted for the winter in late 1872, parts of each tower had already been built. By mid-1873, there was substantial progress on the towers' construction. The Brooklyn side's tower had reached a height of 164 feet (50 m) above mean high water (MHW), while the tower on the Manhattan side had reached 88 feet (27 m) above MHW. The arches of

480-445: A bridge between the then-separate cities of Brooklyn and New York had been suggested as early as 1800. At the time, the only travel between the two cities was by a number of ferry lines . Engineers presented various designs, such as chain or link bridges, though these were never built because of the difficulties of constructing a high enough fixed-span bridge across the extremely busy East River. There were also proposals for tunnels under

600-504: A cantilevered beam under a uniform load is given by: δ B = q L 4 8 E I ϕ B = q L 3 6 E I {\displaystyle {\begin{aligned}\delta _{B}&={\frac {qL^{4}}{8EI}}\\[1ex]\phi _{B}&={\frac {qL^{3}}{6EI}}\end{aligned}}} where The deflection at any point, x {\displaystyle x} , along

720-621: A contract with the Bodwell Granite Company, and delivered from Maine to New York by schooner. The Manhattan tower contains 46,945 cubic yards (35,892 m) of masonry, while the Brooklyn tower has 38,214 cubic yards (29,217 m) of masonry. There are 56 LED lamps mounted onto the towers. Each tower contains a pair of Gothic Revival pointed arches, through which the roadways run. The arch openings are 117 feet (36 m) tall and 33.75 feet (10.29 m) wide. The tops of

840-630: A deck 127 ft (38.7 m) above mean high water . The span was originally called the New York and Brooklyn Bridge or the East River Bridge but was officially renamed the Brooklyn Bridge in 1915. Proposals for a bridge connecting Manhattan and Brooklyn were first made in the early 19th century, which eventually led to the construction of the current span, designed by John A. Roebling . The project's chief engineer, his son Washington Roebling , contributed further design work, assisted by

960-457: A hybrid cable-stayed /suspension bridge design, with both vertical and diagonal suspender cables. Its stone towers are neo-Gothic , with characteristic pointed arches. The New York City Department of Transportation (NYCDOT), which maintains the bridge, says that its original paint scheme was "Brooklyn Bridge Tan" and "Silver", but other accounts state that it was originally entirely " Rawlins Red ". To provide sufficient clearance for shipping in

1080-573: A lawsuit in the United States District Court for the Southern District of New York against the cities of New York and Brooklyn. In 1879, an Assembly Sub-Committee on Commerce and Navigation began an investigation into the Brooklyn Bridge. A seaman who had been hired to determine the height of the span, testified to the committee about the difficulties that ship masters would experience in bringing their ships under

1200-444: A series of 24- watt LED lighting fixtures, referred to as "necklace lights" due to their shape. In addition, either 1,088, 1,096, or 1,520 galvanized steel wire suspender cables hang downward from the main cables. Another 400 cable stays extend diagonally from the towers. The vertical suspender cables and diagonal cable stays hold up the truss structure around the bridge deck. The bridge's suspenders originally used wire rope, which

1320-535: A series of brick slopes or "banks" was developed into a skate park , the Brooklyn Banks , in the late 1980s. The park uses the approach's support pillars as obstacles. In the mid-2010s, the Brooklyn Banks were closed to the public because the area was being used as a storage site during the bridge's renovation. The skateboarding community has attempted to save the banks on multiple occasions; after

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1440-422: A steel contract for the permanent cables still had not been awarded. There was disagreement over whether the bridge's cables should use the as-yet-untested Bessemer steel or the well-proven crucible steel . Until a permanent contract was awarded, the builders ordered 30 short tons (27 long tons) of wire in the interim, 10 tons each from three companies, including Washington Roebling's own steel mill in Brooklyn. In

1560-456: A structure containing trusses that run parallel to the roadway, each of which is 33 feet (10 m) deep. Originally there were six trusses, but two were removed during a late-1940s renovation. The trusses allow the Brooklyn Bridge to hold a total load of 18,700 short tons (16,700 long tons), a design consideration from when it originally carried heavier elevated trains. These trusses are held up by suspender ropes, which hang downward from each of

1680-518: A thickness of 2.5 feet (0.76 m) and weigh 46,000 pounds (21,000 kg) each. Each anchor plate is connected to the respective main cable by two sets of nine eyebars , each of which is about 12.5 feet (3.8 m) long and up to 9 by 3 inches (229 by 76 mm) thick. The chains of eyebars curve downward from the cables toward the anchor plates, and the eyebars vary in size depending on their position. The anchorages also contain numerous passageways and compartments. Starting in 1876, in order to fund

1800-633: A variety of loading and boundary conditions. A number of simple examples are shown below. The formulas expressed are approximations developed for long, slender, homogeneous, prismatic beams with small deflections, and linear elastic properties. Under these restrictions, the approximations should give results within 5% of the actual deflection. Cantilever beams have one end fixed, so that the slope and deflection at that end must be zero. The elastic deflection δ {\displaystyle \delta } and angle of deflection ϕ {\displaystyle \phi } (in radians ) at

1920-489: A week after the Brooklyn Bridge opened, ferry crews reported a sharp drop in patronage, while the bridge's toll operators were processing over a hundred people a minute. However, cross-river ferries continued to operate until 1942. The bridge had cost US$ 15.5 million in 1883 dollars (about US$ 490,500,000 in 2023) to build, of which Brooklyn paid two-thirds. The bonds to fund the construction would not be paid off until 1956. An estimated 27 men died during its construction. Since

2040-679: Is a cable-stayed bridge with a more substantial bridge deck that, being stiffer and stronger, allows the cables to be omitted close to the tower and for the towers to be lower in proportion to the span. The first extradosed bridges were the Ganter Bridge and Sunniberg Bridge in Switzerland. The first extradosed bridge in the United States, the Pearl Harbor Memorial Bridge was built to carry I-95 across

2160-596: Is known for all x {\displaystyle x} . Where: If the beam is uniform and the deflection at any point is known, this can be calculated without knowing other properties of the beam. The formulas supplied above require the use of a consistent set of units. Most calculations will be made in the International System of Units (SI) or US customary units, although there are many other systems of units. Other units may be used as well, as long as they are self-consistent. For example, sometimes

2280-507: Is optimal for spans longer than cantilever bridges and shorter than suspension bridges. This is the range within which cantilever bridges would rapidly grow heavier, and suspension bridge cabling would be more costly. Cable-stayed bridges were being designed and constructed by the late 16th century, and the form found wide use in the late 19th century. Early examples, including the Brooklyn Bridge , often combined features from both

2400-417: Is slightly larger, measuring 172 by 102 feet (52 by 31 m) and located 78.5 feet (23.9 m) below high water, while the Brooklyn side's caisson measures 168 by 102 feet (51 by 31 m) and is located 44.5 feet (13.6 m) below high water. The caissons were designed to hold at least the weight of the towers which would exert a pressure of 5 short tons per square foot (49 t/m) when fully built, but

2520-400: Is the result of the study, of the experience, and of the knowledge of many men in many ages. It is not merely a creation; it is a growth. It stands before us today as the sum and epitome of human knowledge; as the very heir of the ages; as the latest glory of centuries of patient observation, profound study and accumulated skill, gained, step by step, in the never-ending struggle of man to subdue

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2640-554: Is usually calculated on the basis of the Euler–Bernoulli beam equation while that of a plate or shell element is calculated using plate or shell theory. An example of the use of deflection in this context is in building construction. Architects and engineers select materials for various applications. Beams can vary greatly in their geometry and composition. For instance, a beam may be straight or curved. It may be of constant cross section, or it may taper. It may be made entirely of

2760-608: The Penobscot Narrows Bridge , completed in 2006, and the Veterans' Glass City Skyway , completed in 2007. A self-anchored suspension bridge has some similarity in principle to the cable-stayed type in that tension forces that prevent the deck from dropping are converted into compression forces vertically in the tower and horizontally along the deck structure. It is also related to the suspension bridge in having arcuate main cables with suspender cables, although

2880-486: The Theodor Heuss Bridge (1958). However, this involves substantial erection costs, and more modern structures tend to use many more cables to ensure greater economy. Cable-stayed bridges may appear to be similar to suspension bridges , but they are quite different in principle and construction. In suspension bridges, large main cables (normally two) hang between the towers and are anchored at each end to

3000-465: The Virgin Mary next to an opening at the entrance. The vaults were closed for public use in the late 1910s and 1920s during World War I and Prohibition but were reopened thereafter. When New York magazine visited one of the cellars in 1978, it discovered a "fading inscription" on a wall reading: "Who loveth not wine, women and song, he remaineth a fool his whole life long." Leaks found within

3120-451: The live load of traffic crossing the bridge. The tension on the main cables is transferred to the ground at the anchorages and by downwards compression on the towers. In cable-stayed bridges, the towers are the primary load-bearing structures that transmit the bridge loads to the ground. A cantilever approach is often used to support the bridge deck near the towers, but lengths further from them are supported by cables running directly to

3240-406: The superposition principle . The change in length Δ L {\displaystyle \Delta L} of the beam, projected along the line of the unloaded beam, can be calculated by integrating the slope θ x {\displaystyle \theta _{x}} function, if the deflection function δ x {\displaystyle \delta _{x}}

3360-429: The Brooklyn Bridge has become an icon of New York City. Over the years, the bridge has been used as the location of various stunts and performances, as well as several crimes, attacks and vandalism. The Brooklyn Bridge is designated a National Historic Landmark , a New York City landmark , and a National Historic Civil Engineering Landmark . The Brooklyn Bridge, an early example of a steel-wire suspension bridge , uses

3480-454: The Brooklyn Bridge was considered mostly completed and was projected to open that June. Contracts for bridge lighting were awarded by February 1883, and a toll scheme was approved that March. There was substantial opposition to the bridge's construction from shipbuilders and merchants located to the north, who argued that the bridge would not provide sufficient clearance underneath for ships. In May 1876, these groups, led by Abraham Miller, filed

3600-455: The Brooklyn Bridge's truss system to be six to eight times as strong as he thought it needed to be. As such, the open truss structure supporting the deck is, by its nature, subject to fewer aerodynamic problems. However, due to a supplier's fraudulent substitution of inferior-quality wire in the initial construction, the bridge was reappraised at the time as being only four times as strong as necessary. The main span and side spans are supported by

3720-410: The Brooklyn side is shorter than the 1,567-foot (478 m) approach ramp from the Manhattan side. The approaches are supported by Renaissance-style arches made of masonry; the arch openings themselves were filled with brick walls, with small windows within. The approach ramp contains nine arch or iron- girder bridges across side streets in Manhattan and Brooklyn. Underneath the Manhattan approach,

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3840-585: The Brooklyn tower were completed by August 1874. The tower was substantially finished by December 1874 with the erection of saddle plates for the main cables at the top of the tower. However, the ornamentation on the Brooklyn tower could not be completed until the Manhattan tower was finished. The last stone on the Brooklyn tower was raised in June 1875 and the Manhattan tower was completed in July 1876. The saddle plates atop both towers were also raised in July 1876. The work

3960-507: The Donzère-Mondragon canal at Pierrelatte is one of the first of the modern type, but had little influence on later development. The steel-decked Strömsund Bridge designed by Franz Dischinger (1955) is, therefore, more often cited as the first modern cable-stayed bridge. Other key pioneers included Fabrizio de Miranda , Riccardo Morandi , and Fritz Leonhardt . Early bridges from this period used very few stay cables, as in

4080-453: The East River for the occasion. Officially, Emily Warren Roebling was the first to cross the bridge. The bridge opening was also attended by U.S. president Chester A. Arthur and New York mayor Franklin Edson , who crossed the bridge and shook hands with Brooklyn mayor Seth Low at the Brooklyn end. Abram Hewitt gave the principal address. It is not the work of any one man or of any one age. It

4200-629: The East River, but these were considered prohibitively expensive. German immigrant engineer John Augustus Roebling proposed building a suspension bridge over the East River in 1857. He had previously designed and constructed shorter suspension bridges, such as Roebling's Delaware Aqueduct in Lackawaxen, Pennsylvania , and the Niagara Suspension Bridge. In 1867, Roebling erected what became the John A. Roebling Suspension Bridge over

4320-403: The East River, the Brooklyn Bridge incorporates long approach viaducts on either end to raise it from low ground on both shores. Including approaches, the Brooklyn Bridge is a total of 6,016 feet (1,834 m) long when measured between the curbs at Park Row in Manhattan and Sands Street in Brooklyn. A separate measurement of 5,989 feet (1,825 m) is sometimes given; this is the distance from

4440-689: The East River. Following gradual deterioration, the Brooklyn Bridge was renovated several times, including in the 1950s, 1980s, and 2010s. The Brooklyn Bridge is the southernmost of the four toll-free vehicular bridges connecting Manhattan Island and Long Island , with the Manhattan Bridge , the Williamsburg Bridge , and the Queensboro Bridge to the north. Only passenger vehicles and pedestrian and bicycle traffic are permitted. A major tourist attraction since its opening,

4560-421: The Manhattan caisson reached a depth of 78.5 feet (23.9 m) with an air pressure of 35 pounds per square inch (240  kPa ), Washington deemed the sandy subsoil overlying the bedrock 30 feet (9.1 m) beneath to be sufficiently firm, and subsequently infilled the caisson with concrete in July 1872. Washington Roebling himself suffered a paralyzing injury as a result of caisson disease shortly after ground

4680-453: The Manhattan side was slightly different because it had to be installed at a greater depth. To protect against the increased air pressure at that depth, the Manhattan caisson had 22 layers of timber on its roof, seven more than its Brooklyn counterpart had. The Manhattan caisson also had fifty 4-inch-diameter (10 cm) pipes for sand removal, a fireproof iron-boilerplate interior, and different airlocks and communication systems. Proposals for

4800-567: The New York and Brooklyn Bridge was the only bridge across the East River at that time, it was also called the East River Bridge. Until the construction of the nearby Williamsburg Bridge in 1903, the New York and Brooklyn Bridge was the longest suspension bridge in the world, 20% longer than any built previously. Cable-stayed bridge A cable-stayed bridge has one or more towers (or pylons ), from which cables support

4920-547: The Ohio River between Cincinnati, Ohio , and Covington, Kentucky . In February 1867, the New York State Senate passed a bill that allowed the construction of a suspension bridge from Brooklyn to Manhattan. Two months later, the New York and Brooklyn Bridge Company was incorporated with a board of directors (later converted to a board of trustees). There were twenty trustees in total: eight each appointed by

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5040-585: The Quinnipiac River in New Haven, Connecticut, opening in June 2012. A cradle system carries the strands within the stays from the bridge deck to bridge deck, as a continuous element, eliminating anchorages in the pylons. Each epoxy-coated steel strand is carried inside the cradle in a one-inch (2.54 cm) steel tube. Each strand acts independently, allowing for removal, inspection, and replacement of individual strands. The first two such bridges are

5160-448: The base and 117 by 104 feet (36 by 32 m) at the top. Each anchorage weighs 60,000 short tons (54,000 long tons; 54,000 t). The Manhattan anchorage rests on a foundation of bedrock while the Brooklyn anchorage rests on clay. The anchorages both have four anchor plates , one for each of the main cables, which are located near ground level and parallel to the ground. The anchor plates measure 16 by 17.5 feet (4.9 by 5.3 m), with

5280-414: The beam), the δ x {\displaystyle \delta _{x}} and ϕ x {\displaystyle \phi _{x}} equations are identical to the δ B {\displaystyle \delta _{B}} and ϕ B {\displaystyle \phi _{B}} equations above. The deflection, at the free end B, of

5400-409: The bridge deck. A distinctive feature are the cables or stays , which run directly from the tower to the deck, normally forming a fan-like pattern or a series of parallel lines. This is in contrast to the modern suspension bridge , where the cables supporting the deck are suspended vertically from the main cable, anchored at both ends of the bridge and running between the towers. The cable-stayed bridge

5520-411: The bridge when it was completed. Another witness, Edward Wellman Serrell , a civil engineer, said that the calculations of the bridge's assumed strength were incorrect. The Supreme Court decided in 1883 that the Brooklyn Bridge was a lawful structure. The New York and Brooklyn Bridge was opened for use on May 24, 1883. Thousands of people attended the opening ceremony, and many ships were present in

5640-473: The bridge's maintenance, the New York City government made the large vaults under the bridge's Manhattan anchorage available for rent, and they were in constant use during the early 20th century. The vaults were used to store wine, as they were kept at a consistent 60 °F (16 °C) temperature due to a lack of air circulation. The Manhattan vault was called the "Blue Grotto" because of a shrine to

5760-405: The cable-stayed and suspension designs. Cable-stayed designs fell from favor in the early 20th century as larger gaps were bridged using pure suspension designs, and shorter ones using various systems built of reinforced concrete . It returned to prominence in the later 20th century when the combination of new materials, larger construction machinery, and the need to replace older bridges all lowered

5880-562: The cable-stayed bridge are balanced so that the supporting towers do not tend to tilt or slide and so must only resist horizontal forces from the live loads. The following are key advantages of the cable-stayed form: There are four major classes of rigging on cable-stayed bridges: mono , harp , fan, and star . There are also seven main arrangements for support columns: single , double , portal , A-shaped , H-shaped , inverted Y and M-shaped . The last three are hybrid arrangements that combine two arrangements into one. Depending on

6000-473: The caissons were over-engineered for safety. During an accident on the Brooklyn side, when air pressure was lost and the partially-built towers dropped full-force down, the caisson sustained an estimated pressure of 23 short tons per square foot (220 t/m) with only minor damage. Most of the timber used in the bridge's construction, including in the caissons, came from mills at Gascoigne Bluff on St. Simons Island, Georgia . The Brooklyn side's caisson, which

6120-465: The cities of New York (now Manhattan) and Brooklyn to subscribe to $ 5 million in capital stock , which would fund the bridge's construction. Roebling was subsequently named the chief engineer of the work and, by September 1867, had presented a master plan. According to the plan, the bridge would be longer and taller than any suspension bridge previously built. It would incorporate roadways and elevated rail tracks, whose tolls and fares would provide

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6240-462: The city destroyed the smaller banks in the 2000s, the city government agreed to keep the larger banks for skateboarding. When the NYCDOT removed the bricks from the banks in 2020, skateboarders started an online petition . In the 2020s, local resident Rosa Chang advocated for the 9-acre (3.6 ha) space under the Manhattan approach to be converted into a recreational area known as Gotham Park. Some of

6360-603: The closest support and is given by: x 1 = L 2 − a 2 3 {\displaystyle x_{1}={\sqrt {\frac {L^{2}-a^{2}}{3}}}} The elastic deflection (at the midpoint C) on a beam supported by two simple supports, under a uniform load (as pictured) is given by: δ C = 5 q L 4 384 E I {\displaystyle \delta _{C}={\frac {5qL^{4}}{384EI}}} where The deflection at any point, x {\displaystyle x} , along

6480-460: The closest support, is given by: δ max = F a ( L 2 − a 2 ) 3 / 2 9 3 L E I {\displaystyle \delta _{\text{max}}={\frac {Fa\left(L^{2}-a^{2}\right)^{3/2}}{9{\sqrt {3}}LEI}}} where This maximum deflection occurs at a distance x 1 {\displaystyle x_{1}} from

6600-693: The combination of technologies created a stiffer bridge. John A. Roebling took particular advantage of this to limit deformations due to railway loads in the Niagara Falls Suspension Bridge . The earliest known surviving example of a true cable-stayed bridge in the United States is E.E. Runyon's largely intact steel or iron Bluff Dale Suspension bridge with wooden stringers and decking in Bluff Dale, Texas (1890), or his weeks earlier but ruined Barton Creek Bridge between Huckabay, Texas and Gordon, Texas (1889 or 1890). In

6720-571: The cross-section, and M {\displaystyle M} is the internal bending moment in the beam. If, in addition, the beam is not tapered and is homogeneous , and is acted upon by a distributed load q {\displaystyle q} , the above expression can be written as : E I   d 4 w ( x ) d x 4 = q ( x ) {\displaystyle EI~{\frac {\mathrm {d} ^{4}w(x)}{\mathrm {d} x^{4}}}=q(x)} This equation can be solved for

6840-403: The curb at Centre Street in Manhattan. The main span between the two suspension towers is 1,595.5 feet (486.3 m) long and 85 feet (26 m) wide. The bridge "elongates and contracts between the extremes of temperature from 14 to 16 inches". Navigational clearance is 127 ft (38.7 m) above mean high water (MHW). A 1909 Engineering Magazine article said that, at the center of

6960-404: The delay in steel deliveries. Despite Edgemoor's assurances that the contract would be fulfilled, the deliveries still had not been completed by November 1881. Brooklyn mayor Seth Low , who became part of the board of trustees in 1882, became the chairman of a committee tasked to investigate Edgemoor's failure to fulfill the contract. When questioned, Edgemoor's president stated that the delays were

7080-572: The design, the columns may be vertical or angled or curved relative to the bridge deck. A side-spar cable-stayed bridge uses a central tower supported only on one side. This design allows the construction of a curved bridge. Far more radical in its structure, the Puente del Alamillo (1992) uses a single cantilever spar on one side of the span, with cables on one side only to support the bridge deck. Unlike other cable-stayed types, this bridge exerts considerable overturning force upon its foundation and

7200-402: The end, it was decided to use number 8 Birmingham gauge (approximately 4 mm or 0.165 inches in diameter) crucible steel, and a request for bids was distributed, to which eight companies responded. In January 1877, a contract for crucible steel was awarded to J. Lloyd Haigh , who was associated with bridge trustee Abram Hewitt , whom Roebling distrusted. The spinning of the wires required

7320-472: The fault of another contractor, the Cambria Iron Company , who was manufacturing the eyebars for the bridge trusses; at that point, the contract was supposed to be complete by October 1882. Further complicating the situation, Washington Roebling had failed to appear at the trustees' meeting in June 1882, since he had gone to Newport, Rhode Island . After the news media discovered this, most of

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7440-399: The final total was thought to be about 2,500 men in total. In spite of this, only a few workers were paralyzed. At its final depth, the caisson's air pressure was 21 pounds per square inch (140 kPa). The Manhattan side's caisson was the next structure to be built. To ensure that it would not catch fire like its counterpart had, the Manhattan caisson was lined with fireproof plate iron. It

7560-400: The fire was called, delayed construction for several months, since the holes in the caisson had to be repaired. On March 6, 1871, the repairs were finished, and the caisson had reached its final depth of 44.5 feet (13.6 m); it was filled with concrete five days later. Overall, about 264 individuals were estimated to have worked in the caisson every day, but because of high worker turnover ,

7680-578: The following month. Washington Roebling , John Roebling's 32-year-old son, was then hired to fill his father's role. Tammany Hall leader William M. Tweed also became involved in the bridge's construction because, as a major landowner in New York City, he had an interest in the project's completion. The New York and Brooklyn Bridge Company—later known simply as the New York Bridge Company—was actually overseen by Tammany Hall, and it approved Roebling's plans and designated him as chief engineer of

7800-411: The forces of nature to his control and use. Though Washington Roebling was unable to attend the ceremony (and rarely visited the site again), he held a celebratory banquet at his house on the day of the bridge opening. Further festivity included the performance by a band, gunfire from ships, and a fireworks display. On that first day, a total of 1,800 vehicles and 150,300 people crossed the span. Less than

7920-425: The four main cables. Crossbeams run between the trusses at the top, and diagonal and vertical stiffening beams run on the outside and inside of each roadway. An elevated pedestrian-only promenade runs in between the two roadways and 18 feet (5.5 m) above them. It typically runs 4 feet (1.2 m) below the level of the crossbeams, except at the areas surrounding each tower. Here, the promenade rises to just above

8040-455: The four main cables. Each drum had a capacity of 60,000 feet (18,000 m) of wire. The first experimental wire for the main cables was stretched between the towers on May 29, 1877, and spinning began two weeks later. All four main cables were being strung by that July. During that time, the temporary footbridge was unofficially opened to members of the public, who could receive a visitor's pass; by August 1877 several thousand visitors from around

8160-513: The free end in the example image: A (weightless) cantilever beam, with an end load, can be calculated (at the free end B) using: δ B = F L 3 3 E I ϕ B = F L 2 2 E I {\displaystyle {\begin{aligned}\delta _{B}&={\frac {FL^{3}}{3EI}}\\[1ex]\phi _{B}&={\frac {FL^{2}}{2EI}}\end{aligned}}} where Note that if

8280-403: The function that mathematically describes the slope of the deflected shape of the member under that load. Standard formulas exist for the deflection of common beam configurations and load cases at discrete locations. Otherwise methods such as virtual work , direct integration , Castigliano's method , Macaulay's method or the direct stiffness method are used. The deflection of beam elements

8400-436: The ground. This can be difficult to implement when ground conditions are poor. The main cables, which are free to move on bearings in the towers, bear the load of the bridge deck. Before the deck is installed, the cables are under tension from their own weight. Along the main cables smaller cables or rods connect to the bridge deck, which is lifted in sections. As this is done, the tension in the cables increases, as it does with

8520-475: The headaches were blinding. Once the caisson had reached the desired depth, it was to be filled in with vertical brick piers and concrete. However, due to the unexpectedly high concentration of large boulders atop the riverbed, the Brooklyn caisson took several months to sink to the desired depth. Furthermore, in December 1870, its timber roof caught fire, delaying construction further. The "Great Blowout", as

8640-417: The intricacies of cable construction. She spent the next 11 years helping supervise the bridge's construction, taking over much of the chief engineer's duties, including day-to-day supervision and project management. After the caissons were completed, piers were constructed on top of each of them upon which masonry towers would be built. The towers' construction was a complex process that took four years. Since

8760-419: The kilogram-force ( k g f {\displaystyle \mathrm {kgf} } ) unit is used to measure loads. In such a case, the modulus of elasticity must be converted to k g f m 2 {\displaystyle \mathrm {\frac {kgf}{m^{2}}} } . Building codes determine the maximum deflection, usually as a fraction of the span e.g. 1/400 or 1/600. Either

8880-481: The last of the main cables' wires went over the river. After the suspender wires had been placed, workers began erecting steel crossbeams to support the roadway as part of the bridge's overall superstructure. Construction on the bridge's superstructure started in March 1879, but, as with the cables, the trustees initially disagreed on whether the steel superstructure should be made of Bessemer or crucible steel. That July,

9000-657: The latter's wife, Emily Warren Roebling . Construction started in 1870 and was overseen by the New York Bridge Company, which in turn was controlled by the Tammany Hall political machine. Numerous controversies and the novelty of the design prolonged the project over thirteen years. After opening, the Brooklyn Bridge underwent several reconfigurations, having carried horse-drawn vehicles and elevated railway lines until 1950. To alleviate increasing traffic flows, additional bridges and tunnels were built across

9120-563: The legislators passed a law authorizing the allotment with the condition that the cities would buy the stock of Brooklyn Bridge's private stockholders. Work proceeded concurrently on the anchorages on each side. The Brooklyn anchorage broke ground in January 1873 and was subsequently substantially completed in August 1875. The Manhattan anchorage was built in less time, having started in May 1875, it

9240-616: The level of the crossbeams, connecting to a balcony that slightly overhangs the two roadways. The path is generally 10 to 17 feet (3.0 to 5.2 m) wide. The iron railings were produced by Janes & Kirtland , a Bronx iron foundry that also made the United States Capitol dome and the Bow Bridge in Central Park . Each of the side spans is reached by an approach ramp. The 971-foot (296 m) approach ramp from

9360-452: The lowest bid for Bessemer steel, but at Hewitt's direction, the contract was awarded to Haigh. A subsequent investigation discovered that Haigh had substituted inferior quality wire in the cables. Of eighty rings of wire that were tested, only five met standards, and it was estimated that Haigh had earned $ 300,000 from the deception. At this point, it was too late to replace the cables that had already been constructed. Roebling determined that

9480-410: The main cables and support the deck. By May 1878, the main cables were more than two-thirds complete. However, the following month, one of the wires slipped, killing two people and injuring three others. In 1877, Hewitt wrote a letter urging against the use of Bessemer steel in the bridge's construction. Bids had been submitted for both crucible steel and Bessemer steel; John A. Roebling's Sons submitted

9600-411: The manufacture of large coils of it which were galvanized but not oiled when they left the factory. The coils were delivered to a yard near the Brooklyn anchorage. There they were dipped in linseed oil , hoisted to the top of the anchorage, dried out and spliced into a single wire, and finally coated with red zinc for further galvanizing. There were thirty-two drums at the anchorage yard, eight for each of

9720-449: The masonry blocks were heavy, the builders transported them to the base of the towers using a pulley system with a continuous 1.5-inch (3.8 cm)-diameter steel wire rope, operated by steam engines at ground level. The blocks were then carried up on a timber track alongside each tower and maneuvered into the proper position using a derrick atop the towers. The blocks sometimes vibrated the ropes because of their weight, but only once did

9840-531: The mayors of New York and Brooklyn, as well as the mayors of each city and the auditor and comptroller of Brooklyn. The company was tasked with constructing what was then known as the New York and Brooklyn Bridge. Alternatively, the span was just referred to as the "Brooklyn Bridge", a name originating in a January 25, 1867, letter to the editor sent to the Brooklyn Daily Eagle . The act of incorporation, which became law on April 16, 1867, authorized

9960-504: The means to pay for the bridge's construction. It would also include a raised promenade that served as a leisurely pathway. The proposal received much acclaim in both cities, and residents predicted that the New York and Brooklyn Bridge's opening would have as much of an impact as the Suez Canal , the first transatlantic telegraph cable or the first transcontinental railroad . By early 1869, however, some individuals started to criticize

10080-413: The midpoint C of a beam, loaded at its center, supported by two simple supports is then given by: δ C = F L 3 48 E I {\displaystyle \delta _{C}={\frac {FL^{3}}{48EI}}} where The maximum elastic deflection on a beam supported by two simple supports, loaded at a distance a {\displaystyle a} from

10200-552: The newspapers called for Roebling to be fired as chief engineer, except for the Daily State Gazette of Trenton, New Jersey , and the Brooklyn Daily Eagle . Some of the longstanding trustees, including Henry C. Murphy , James S. T. Stranahan , and William C. Kingsley , were willing to vouch for Roebling, since construction progress on the Brooklyn Bridge was still ongoing. However, Roebling's behavior

10320-492: The poorer wire would leave the bridge only four times as strong as necessary, rather than six to eight times as strong. The inferior-quality wire was allowed to remain and 150 extra wires were added to each cable. To avoid public controversy, Haigh was not fired, but instead was required to personally pay for higher-quality wire. The contract for the remaining wire was awarded to the John A. Roebling's Sons, and by October 5, 1878,

10440-436: The process, it was determined that the main span would have to be raised from 130 to 135 feet (40 to 41 m) above MHW, requiring several changes to the overall design. In June 1869, while conducting these surveys, Roebling sustained a crush injury to his foot when a ferry pinned it against a piling . After amputation of his crushed toes, he developed a tetanus infection that left him incapacitated and resulted in his death

10560-467: The project, saying either that the bridge was too expensive, or that the construction process was too difficult. To allay concerns about the design of the New York and Brooklyn Bridge, Roebling set up a "Bridge Party" in March 1869, where he invited engineers and members of U.S. Congress to see his other spans. Following the bridge party in April, Roebling and several engineers conducted final surveys. During

10680-522: The project. Construction of the Brooklyn Bridge began on January 2, 1870. The first work entailed the construction of two caissons, upon which the suspension towers would be built. The Brooklyn side's caisson was built at the Webb & Bell shipyard in Greenpoint, Brooklyn , and was launched into the river on March 19, 1870. Compressed air was pumped into the caisson, and workers entered the space to dig

10800-547: The pylons; Millau Viaduct and Mezcala Bridge , where twin-legged towers are used; and General Rafael Urdaneta Bridge , where very stiff multi-legged frame towers were adopted. A similar situation with a suspension bridge is found at both the Great Seto Bridge and San Francisco–Oakland Bay Bridge where additional anchorage piers are required after every set of three suspension spans – this solution can also be adapted for cable-stayed bridges. An extradosed bridge

10920-517: The relative price of these designs. Cable-stayed bridges date back to 1595, where designs were found in Machinae Novae , a book by Croatian - Venetian inventor Fausto Veranzio . Many early suspension bridges were cable-stayed construction, including the 1817 footbridge Dryburgh Abbey Bridge , James Dredge 's patented Victoria Bridge, Bath (1836), and the later Albert Bridge (1872) and Brooklyn Bridge (1883). Their designers found that

11040-423: The river, and the two ends were spliced to form a traveler, a lengthy loop of wire connecting the towers, which was driven by a 30 horsepower (22 kW) steam hoisting engine at ground level. The wire was one of two that were used to create a temporary footbridge for workers while cable spinning was ongoing. The next step was to send an engineer across the completed traveler wire in a boatswain's chair slung from

11160-423: The roadways. Each main cable measures 15.75 inches (40.0 cm) in diameter and contains 5,282 parallel, galvanized steel wires wrapped closely together in a cylindrical shape. These wires are bundled in 19 individual strands, with 278 wires to a strand. This was the first use of bundling in a suspension bridge and took several months for workers to tie together. Since the 2000s, the main cables have also supported

11280-658: The same material (homogeneous), or it may be composed of different materials (composite). Some of these things make analysis difficult, but many engineering applications involve cases that are not so complicated. Analysis is simplified if: In this case, the equation governing the beam's deflection ( w {\displaystyle w} ) can be approximated as: d 2 w ( x ) d x 2 = M ( x ) E ( x ) I ( x ) {\displaystyle {\frac {\mathrm {d} ^{2}w(x)}{\mathrm {d} x^{2}}}={\frac {M(x)}{E(x)I(x)}}} where

11400-450: The second derivative of its deflected shape with respect to x {\displaystyle x} ( x {\displaystyle x} being the horizontal position along the length of the beam) is interpreted as its curvature, E {\displaystyle E} is the Young's modulus , I {\displaystyle I} is the area moment of inertia of

11520-418: The sediment until it sank to the bedrock. As one sixteen-year-old from Ireland, Frank Harris , described the fearful experience: The six of us were working naked to the waist in the small iron chamber with the temperature of about 80 degrees Fahrenheit: In five minutes the sweat was pouring from us, and all the while we were standing in icy water that was only kept from rising by the terrific pressure. No wonder

11640-400: The self-anchored type lacks the heavy cable anchorages of the ordinary suspension bridge. Unlike either a cable-stayed bridge or a suspension bridge, the self-anchored suspension bridge must be supported by falsework during construction and so it is more expensive to construct. Deflection (engineering) The deflection distance of a member under a load can be calculated by integrating

11760-515: The space under the Manhattan approach reopened in May 2023 as a park called the Arches; this was followed in November 2024 by another 15,000-square-foot (1,400 m) section of parkland. The Brooklyn Bridge contains four main cables, which descend from the tops of the suspension towers and help support the deck. Two are located to the outside of the bridge's roadways, while two are in the median of

11880-717: The span doubles, the deflection increases eightfold. The deflection at any point, x {\displaystyle x} , along the span of an end loaded cantilevered beam can be calculated using: δ x = F x 2 6 E I ( 3 L − x ) ϕ x = F x 2 E I ( 2 L − x ) {\displaystyle {\begin{aligned}\delta _{x}&={\frac {Fx^{2}}{6EI}}(3L-x)\\[1ex]\phi _{x}&={\frac {Fx}{2EI}}(2L-x)\end{aligned}}} Note: At x = L {\displaystyle x=L} (the end of

12000-487: The span of a center loaded simply supported beam can be calculated using: δ x = F x 48 E I ( 3 L 2 − 4 x 2 ) {\displaystyle \delta _{x}={\frac {Fx}{48EI}}\left(3L^{2}-4x^{2}\right)} for 0 ≤ x ≤ L 2 {\displaystyle 0\leq x\leq {\frac {L}{2}}} The special case of elastic deflection at

12120-843: The span of a uniformly loaded cantilevered beam can be calculated using: δ x = q x 2 24 E I ( 6 L 2 − 4 L x + x 2 ) ϕ x = q x 6 E I ( 3 L 2 − 3 L x + x 2 ) {\displaystyle {\begin{aligned}\delta _{x}&={\frac {qx^{2}}{24EI}}\left(6L^{2}-4Lx+x^{2}\right)\\[1ex]\phi _{x}&={\frac {qx}{6EI}}\left(3L^{2}-3Lx+x^{2}\right)\end{aligned}}} Simply supported beams have supports under their ends which allow rotation, but not deflection. The deflection at any point, x {\displaystyle x} , along

12240-437: The span of a uniformly loaded simply supported beam can be calculated using: δ x = q x 24 E I ( L 3 − 2 L x 2 + x 3 ) {\displaystyle \delta _{x}={\frac {qx}{24EI}}\left(L^{3}-2Lx^{2}+x^{3}\right)} The deflection of beams with a combination of simple loads can be calculated using

12360-475: The span, the height above MHW could fluctuate by more than 9 feet (2.7 m) due to temperature and traffic loads, while more rigid spans had a lower maximum deflection . The side spans, between each suspension tower and each side's suspension anchorages, are 930 feet (280 m) long. At the time of construction, engineers had not yet discovered the aerodynamics of bridge construction, and bridge designs were not tested in wind tunnels . John Roebling designed

12480-512: The spar must resist the bending caused by the cables, as the cable forces are not balanced by opposing cables. The spar of this particular bridge forms the gnomon of a large garden sundial . Related bridges by the architect Santiago Calatrava include the Puente de la Mujer (2001), Sundial Bridge (2004), Chords Bridge (2008), and Assut de l'Or Bridge (2008). Cable-stayed bridges with more than three spans involve significantly more challenging designs than do 2-span or 3-span structures. In

12600-427: The strength limit state (allowable stress) or the serviceability limit state (deflection considerations among others) may govern the minimum dimensions of the member required. The deflection must be considered for the purpose of the structure. When designing a steel frame to hold a glazed panel, one allows only minimal deflection to prevent fracture of the glass. The deflected shape of a beam can be represented by

12720-420: The time and was first called "caisson disease" by the project physician, Andrew Smith. Between January 25 and May 31, 1872, Smith treated 110 cases of decompression sickness, while three workers died from the disease. When iron probes underneath the Manhattan caisson found the bedrock to be even deeper than expected, Washington Roebling halted construction due to the increased risk of decompression sickness. After

12840-441: The towers are located 159 feet (48 m) above the floor of each arch opening, while the floors of the openings are 119.25 feet (36.35 m) above mean water level, giving the towers a total height of 278.25 feet (84.81 m) above mean high water. The towers rest on underwater caissons made of southern yellow pine and filled with cement. Inside both caissons were spaces for construction workers. The Manhattan side's caisson

12960-411: The towers. That has the disadvantage, unlike for the suspension bridge, that the cables pull to the sides as opposed to directly up, which requires the bridge deck to be stronger to resist the resulting horizontal compression loads, but it has the advantage of not requiring firm anchorages to resist the horizontal pull of the main cables of the suspension bridge. By design, all static horizontal forces of

13080-545: The trustees decided to award a contract for 500 short tons (450 long tons) of Bessemer steel to the Edgemoor (or Edge Moor) Iron Works, based in Philadelphia , to be delivered by 1880. The trustees later passed another resolution for another 500 short tons (450 long tons) of Bessemer steel. However, by February 1880 the steel deliveries had not started. That October, the bridge trustees questioned Edgemoor's president about

13200-529: The twentieth century, early examples of cable-stayed bridges included A. Gisclard's unusual Cassagnes bridge (1899), in which the horizontal part of the cable forces is balanced by a separate horizontal tie cable, preventing significant compression in the deck, and G. Leinekugel le Coq's bridge at Lézardrieux in Brittany (1924). Eduardo Torroja designed a cable-stayed aqueduct at Tempul in 1926. Albert Caquot 's 1952 concrete-decked cable-stayed bridge over

13320-647: The vault's spaces necessitated repairs during the late 1980s and early 1990s. By the late 1990s, the chambers were being used to store maintenance equipment. The bridge's two suspension towers are 278 feet (85 m) tall with a footprint of 140 by 59 feet (43 by 18 m) at the high water line. They are built of limestone , granite , and Rosendale cement . The limestone was quarried at the Clark Quarry in Essex County, New York . The granite blocks were quarried and shaped on Vinalhaven Island, Maine , under

13440-494: The wire, to ensure it was safe enough. The bridge's master mechanic, E.F. Farrington, was selected for this task, and an estimated crowd of 10,000 people on both shores watched him cross. A second traveler wire was then stretched across the span, a task that was completed by August 30. The temporary footbridge, located some 60 feet (18 m) above the elevation of the future deck, was completed in February 1877. By December 1876,

13560-441: The world had used the footbridge. The visitor passes ceased that September after a visitor had an epileptic seizure and nearly fell off. As the wires were being spun, work also commenced on the demolition of buildings on either side of the river for the Brooklyn Bridge's approaches; this work was mostly complete by September 1877. The following month, initial contracts were awarded for the suspender wires, which would hang down from

13680-520: Was broken for the Brooklyn tower foundation. His debilitating condition left him unable to supervise the construction in person, so he designed the caissons and other equipment from his apartment, directing "the completion of the bridge through a telescope from his bedroom." His wife, Emily Warren Roebling , not only provided written communications between her husband and the engineers on site, but also understood mathematics , calculations of catenary curves, strengths of materials, bridge specifications, and

13800-501: Was built first, originally had a height of 9.5 feet (2.9 m) and a ceiling composed of five layers of timber, each layer 1 foot (0.30 m) tall. Ten more layers of timber were later added atop the ceiling, and the entire caisson was wrapped in tin and wood for further protection against flooding. The thickness of the caisson's sides was 8 feet (2.4 m) at both the bottom and the top. The caisson had six chambers: two each for dredging , supply shafts, and airlocks . The caisson on

13920-471: Was considered suspect among the younger trustees who had joined the board more recently. Construction on the bridge itself was noted in formal reports that Murphy presented each month to the mayors of New York and Brooklyn. For example, Murphy's report in August 1882 noted that the month's progress included 114 intermediate cords erected within a week, as well as 72 diagonal stays, 60 posts, and numerous floor beams, bridging trusses, and stay bars. By early 1883,

14040-411: Was dangerous: by 1876, three workers had died having fallen from the towers, while nine other workers were killed in other accidents. In 1875, while the towers were being constructed, the project had depleted its original $ 5 million budget. Two bridge commissioners, one each from Brooklyn and Manhattan, petitioned New York state lawmakers to allot another $ 8 million for construction. Ultimately,

14160-412: Was launched from Webb & Bell's shipyard on May 11, 1871, and maneuvered into place that September. Due to the extreme underwater air pressure inside the much deeper Manhattan caisson, many workers became sick with "the bends"— decompression sickness —during this work, despite the incorporation of airlocks (which were believed to help with decompression sickness at the time). This condition was unknown at

14280-485: Was mostly completed in July 1876. The anchorages could not be fully completed until the main cables were spun, at which point another 6 feet (1.8 m) would be added to the height of each 80-foot (24 m) anchorage. The first temporary wire was stretched between the towers on August 15, 1876, using chrome steel provided by the Chrome Steel Company of Brooklyn. The wire was then stretched back across

14400-433: Was replaced in the 1980s with galvanized steel made by Bethlehem Steel . The vertical suspender cables measure 8 to 130 feet (2.4 to 39.6 m) long, and the diagonal stays measure 138 to 449 feet (42 to 137 m) long. Each side of the bridge contains an anchorage for the main cables. The anchorages are trapezoidal limestone structures located slightly inland of the shore, measuring 129 by 119 feet (39 by 36 m) at

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