bridgeable, adj.bridgeless, adj.bridgelike, adj.
/brij/, n., v., bridged, bridging, adj.
1. a structure spanning and providing passage over a river, chasm, road, or the like.
2. a connecting, transitional, or intermediate route or phase between two adjacent elements, activities, conditions, or the like: Working at the hospital was a bridge between medical school and private practice.
3. Naut.
a. a raised transverse platform from which a power vessel is navigated: often includes a pilot house and a chart house.
b. any of various other raised platforms from which the navigation or docking of a vessel is supervised.
c. a bridge house or bridge superstructure.
d. a raised walkway running fore-and-aft.
4. Anat. the ridge or upper line of the nose.
5. Dentistry. an artificial replacement, fixed or removable, of a missing tooth or teeth, supported by natural teeth or roots adjacent to the space.
6. Music.
a. a thin, fixed wedge or support raising the strings of a musical instrument above the sounding board.
b. a transitional, modulatory passage connecting sections of a composition or movement.
c. (in jazz and popular music) the contrasting third group of eight bars in a thirty-two-bar chorus; channel; release.
7. Also, bridge passage. a passage in a literary work or a scene in a play serving as a movement between two other passages or scenes of greater importance.
8. Ophthalm. the part of a pair of eyeglasses that joins the two lenses and rests on the bridge or sides of the nose.
9. Also called bridge circuit. Elect. a two-branch network, including a measuring device, as a galvanometer, in which the unknown resistance, capacitance, inductance, or impedance of one component can be measured by balancing the voltage in each branch and computing the unknown value from the known values of the other components. Cf. Wheatstone bridge.
10. Railroads. a gantry over a track or tracks for supporting waterspouts, signals, etc.
11. Building Trades. a scaffold built over a sidewalk alongside a construction or demolition site to protect pedestrians and motor traffic from falling materials.
12. Metall.
a. a ridge or wall-like projection of fire brick or the like, at each end of the hearth in a metallurgical furnace.
b. any layer of partially fused or densely compacted material preventing the proper gravitational movement of molten material, as in a blast furnace or cupola, or the proper compacting of metal powder in a mold.
13. (in a twist drill) the conoid area between the flutes at the drilling end.
14. Billiards, Pool.
a. the arch formed by the hand and fingers to support and guide the striking end of a cue.
b. a notched piece of wood with a long handle, used to support the striking end of the cue when the hand cannot do so comfortably; rest.
15. transitional music, commentary, dialogue, or the like, between two parts of a radio or television program.
16. Theat.
a. a gallery or platform that can be raised or lowered over a stage and is used by technicians, stagehands, etc., for painting scenery (paint bridge), arranging and supporting lights (light bridge), or the like.
b. Brit. a part of the floor of a stage that can be raised or lowered.
17. Horol. a partial plate, supported at both ends, holding bearings on the side opposite the dial. Cf. cock1 (def. 10).
18. Chem. a valence bond illustrating the connection of two parts of a molecule.
19. a support or prop, usually timber, for the roof of a mine, cave, etc.
20. any arch or rooflike figure formed by acrobats, dancers, etc., as by joining and raising hands.
21. burn one's bridges (behind one), to eliminate all possibilities of retreat; make one's decision irrevocable: She burned her bridges when she walked out angrily.
22. to make a bridge or passage over; span: The road bridged the river.
23. to join by or as if by a bridge: a fallen tree bridging the two porches.
24. to make (a way) by a bridge.
25. Foundry. (of molten metal) to form layers or areas heterogeneous either in material or in degree of hardness.
26. (esp. of clothing) less expensive than a manufacturer's most expensive products: showing his bridge line for the fall season.
[bef. 1000; ME brigge, OE brycg; c. D brug, G Brücke; akin to ON bryggja pier]
Syn. 22. traverse, cross, vault. 23. link, connect.
/brij/, n. Cards.
a game derived from whist in which one partnership plays to fulfill a certain declaration against an opposing partnership acting as defenders. Cf. auction bridge, contract (def. 5).
[1885-90; earlier also sp. britch, biritch; of obscure orig; perh. < Turk bir one + üç three (one hand being exposed while the other three are concealed), but such a name for the game is not attested in Turkey or the Near East, from where it is alleged to have been introduced into Europe]

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Card game similar to whist.

Bridge is any one of several games, including games such as auction bridge and contract bridge, which retain the essential features of whist: Four players participate, two against two in partnership. They play with a 52-card pack, all cards of which are dealt face downward one at a time, clockwise. When play begins, the object is to win tricks, consisting of one card from each player in rotation. The players must, if able, contribute a card of the suit led, and the trick is won by the highest card. All tricks taken in excess of the first six tricks are known as odd tricks. Before play begins, a suit may be designated the trump suit, in which case any card in it beats any card of the other suits. In all types of bridge a certain number points are needed to win a game, and two games won by the same team allows them to win the rubber.
Structure that spans horizontally to allow pedestrians and vehicles to cross a void.

Bridge construction has always presented civil engineering with its greatest challenges. The simplest bridge is the beam (or girder) bridge, consisting of straight, rigid beams placed across a span (e.g., a tree trunk laid across a stream). Ancient Roman bridges are famous for their rounded arch form, which permitted spans much longer than those of stone beams and were more durable than wood. A modification of the arch bridge was the drawbridge, developed during medieval times. The lift bridge, another movable type, can change position to allow clearance for ships and boats. Suspension bridges (e.g., Brooklyn Bridge, Golden Gate Bridge) are capable of spanning great distances; their main support members are cables composed of thousands of strands of wire supported by two towers and anchored at each end, and the roadway is supported by vertical cables hung from the main cables. Other bridges include the truss bridge, popular (e.g., for railroad bridges) because it uses a relatively small amount of material to carry large loads, and the cantilever bridge, typically made with three spans, with the outer spans anchored down at the shore and the central span resting on the cantilevered arms.
(as used in expressions)
The Bridge
Bridges Calvin Blackman
Bridges Harry
Bridges Robert Seymour

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      card game derived from whist, through the earlier variants bridge whist and auction bridge. The essential features of all bridge games, as of whist, are that four persons play, two against two as partners; a standard 52-card deck of playing cards (playing card) is dealt out one at a time, clockwise around the table, so that each player holds 13 cards; and the object of play is to win tricks, each trick consisting of one card played by each player. Another feature is that one suit may be designated the trump suit (i.e., any card in that suit may take any card of the other suits), but the methods of designating the trump suit (or of determining that a deal will be played without trumps) differ in the various bridge games, as explained below.

      Since about 1896 bridge whist, auction bridge, and contract bridge have successively been the principal intellectual card games of the English-speaking countries. The third game of the series, contract bridge, spread throughout the world and in some respects constituted a social phenomenon unparalleled in the history of games. In addition to millions of casual players worldwide, there exist numerous national federations affiliated with the World Bridge Federation (WBF), which organizes international tournaments for more-serious competitors. Its largest affiliated member is the American Contract Bridge League (ACBL) with nearly 160,000 members.

      The arrival of personal computers and the Internet opened up new opportunities for instruction and play. In addition to being a venue for casual play, some Internet sites host tournaments recognized by ACBL and WBF at which participants can earn international master points.

The bridge games
      The first game of the series was originally called, simply, bridge, but it is now called bridge whist to distinguish it from the two later games. Upon its introduction to New York in 1893 and to London in 1894, it almost immediately supplanted whist in the card rooms of men's clubs, and before 1900 it was the favourite diversion of fashionable mixed gatherings. Bridge whist was itself supplanted with almost equal rapidity by auction bridge, which was introduced in England about 1904 and which became, from 1907 to 1928, the most universally popular card game theretofore known. Auction bridge had at least 15 million adherents when it was supplanted by contract bridge about 1930 and began to die out.

      In bridge, as in whist, there are four players in two partnerships, each player being dealt 13 cards. But in whist there is always a trump suit, determined by turning up the last card dealt to the dealer, and each player holds and plays his own hand. The principal innovations of bridge whist were: selection of the trump suit by the dealer or the dealer's partner after they saw their hands; the option of playing at no trump; the exposed dummy (the hand of dealer's partner), which was played by the dealer; a different method of scoring; and the right to double (the scoring values).

      In bridge whist, after the cards were dealt, the dealer could make the declaration (name any suit as trump, or decide to play without any trump), or he could transfer this duty to his partner. Before leading, the player on the dealer's left (eldest hand) could double or could pass that privilege to his partner; and if either doubled, dealer or his partner could redouble, and so the redoubling might continue indefinitely (except that many clubs placed a limit upon the number of redoubles).

      The player on the dealer's left then led. Dealer's partner, called the dummy, placed his entire hand faceup on the table in front of him, and dealer played both his own cards and dummy's, from each hand in proper turn. Otherwise play was as at whist.

      The side that won the majority of the tricks scored, for each odd trick (trick over six): if spades were trumps, 2 points; clubs, 4; diamonds, 6; hearts, 8; no trump, 12; these values doubled and redoubled as previously determined. The first side thus to score 30 or more points won game, and a fresh game was begun. The first side to win two games won rubber and received a 100-point bonus. Other bonuses, which did not count toward game, were awarded for a side holding three or more honours (ace, king, queen, jack, and 10) of the trump suit or, at no-trump declarations, three or more aces; for making slams (12 or 13 tricks won); and for chicane (a player's holding no card of the trump suit).

      The essential features added by auction bridge were that all four players bid for the right to name the trump suit and that the high bidder or his partner (not necessarily the dealer) became declarer and played the dummy's hand. In other respects the procedure at auction bridge underwent constant and frequent change.

      In its mechanics, contract bridge differs from auction bridge only in the scoring. At auction bridge, declarer's side scores toward game each odd trick that it wins, whether or not it contracted to win such a trick. At contract bridge, the odd tricks won by declarer cannot be scored toward game unless declarer's side previously contracted to win those tricks. Values of tricks, penalties, and premiums are higher in contract bridge than in auction bridge, and large bonuses are awarded for bidding and making slam contracts. See below Scoring (bridge).

How to play contract bridge
      The standard 52-card deck is used. The suits ranking downward in order are spades, hearts, diamonds, clubs; and the cards ranking downward in order are ace, king, queen, jack, 10, 9, 8, 7, 6, 5, 4, 3, 2.

      There are four players, two against two as partners, who face each other across the table. To determine partners, a pack may be spread facedown for each player to draw a card (not valid are any of the four cards at either end). The players drawing the two highest cards would then play as partners, the highest having choice of seats and cards (when two packs are used) and becoming the first dealer.

      If five or six wish to play in the same game, the draw establishes precedence: the player lowest in order of precedence sits out until the end of the first rubber, when he replaces the next lowest in the order. If two players draw cards of the same rank, the card of the higher-ranking suit takes precedence over the other.

      The player at dealer's left shuffles the cards. Preferably two packs are used so that one may be shuffled while the other is being dealt. Dealer transfers the shuffled pack to his right, where his opponent cuts it into two packets, each containing at least five cards. Dealer completes the cut.

      The rotation in contract bridge is always from player to player to the left. Dealer deals the cards in rotation, one at a time facedown, the first card to the player at his left and the last card to himself so that each player has 13 cards.

      The deal completed, each player in rotation beginning with the dealer has a chance to call. A call is a pass, a bid, a double, or a redouble. A pass signifies disinclination to contract to win any number of tricks. A bid contracts to win a specified number of odd tricks with a specified trump or at no trump. Thus, a bid of one heart assumes a contract to win seven tricks with hearts as trumps; a bid of one no trump, seven tricks with no trump suit. The highest possible bid is seven, a contract to win all 13 tricks.

      Each successive bid must overcall—that is, be higher than—any preceding bid. It must name a greater number of odd tricks, or the same number of odd tricks in a higher-ranking suit, with no trump as highest ranking. Thus, two no trump will overcall a bid of two in any suit but may be overcalled by three clubs or any higher bid.

      A player may double the last preceding bid if it was made by an opponent and has not previously been doubled. A player may redouble the last preceding bid if it was made by his own side, doubled by an opponent, and not previously redoubled. A bid may be overcalled as usual whether or not it has been doubled or redoubled.

      Each time a player's turn comes in rotation, he must make a call, and he may not change that call once it is made. A call out of rotation or a change of call is subject to penalty.

      The auction continues until any call is followed by three consecutive passes. If there was no bid, the next player in rotation deals. If any bid was made, the highest bid becomes the contract. The suit (if any) named in the contract becomes trump. The contractor who first named that suit (or no trump) becomes declarer, and his opponents become defenders. The auction is ended, and trick play commences.

Trick play
      The object of play is to win tricks. A trick consists of four cards, one played from the hand of each player in rotation. The first card played to a trick is the lead.

      The defender at declarer's left leads to the first trick. Declarer's partner then spreads his hand faceup before him on the table, grouped in suits with the trumps, if any, to his right; this player, and his hand, are the dummy. Declarer plays both his own cards and dummy's, but each in proper turn.

      Each player in rotation must follow suit to the card led (play a card of the same suit). A player unable to follow suit may play any card, including a trump, if desired. A trick is won by the highest card of the suit led or by the highest trump, if it contains any. One member of each side gathers in all tricks won by the partnership, turns them facedown, and keeps them separated sufficiently to make their number and sequence apparent. The winner of each trick leads to the next.

      When all 13 tricks have been played, the result is scored. The next dealer in rotation distributes the cards for a new deal.

      Each player is entitled to keep score; it is preferable for one member of each side to keep score. Scores are entered on a score sheet (U.S.) or bridge block (British): scores earned by the scorekeeper's side (conventionally designated “We”) are to the left of the vertical line, scores earned by the opponents (designated “They”) are to the right; below the horizontal line is the trick score, and above that line is the honour score.

      Provided declarer's side has at least fulfilled its contract, it scores bonus points, depending on the contract suit, for each trick over six. Diamonds and clubs score 20 points for each odd trick, spades and hearts score 30 points, and no trump scores 40 points for the first odd trick and 30 points for each additional odd trick.

      Such of these tricks as were included in the contract go in the trick score; the value of additional tricks (overtricks) goes in the honour score. If the contract was doubled, trick points scored below the line count twice their normal value, while overtricks count 100 each above the line if declarer's side was not vulnerable (a term explained below) and 200 points each if declarer's side was vulnerable. If the contract was redoubled, these values are again multiplied by two. A side fulfilling any doubled (redoubled) contract also receives a bonus of 50 (100) points on its honour score.

      When either side has scored 100 or more trick points below the line (whether they were scored in one or more deals), it wins a game. Another horizontal line is drawn across the score sheet, below the trick score, to signify the end of the game, and a new game is begun. Only trick scores count toward game; all other points score above the line.

      When either side has won two games, it wins the rubber and receives a bonus of 700 if its opponents have not won a game or 500 if its opponents have won a game. All the trick and honour points of each side are totaled, and the side with the higher total wins the difference from its opponents' score. For purposes of settlement or of keeping a running score, this difference is usually reduced to the nearest 100, a difference of 50 or more counting as 100 and a smaller portion of 100 being disregarded. After each rubber there may be a new draw for partners, seats, and deal.

      When a side has won a game, it is said to be vulnerable and is exposed to heavier undertrick penalties but receives larger bonuses for overtricks at doubled and redoubled contracts and for slams. Vulnerability also may be determined by rotation.

       Bridge: Undertrick penaltiesIf declarer fails to fulfill his contract, his opponents score for each trick by which he falls short (“goes down” or “is set”), as shown in the table (Bridge: Undertrick penalties).

      The ace, king, queen, jack, and 10 of the trump suit are honours. If any player holds four trump honours in his hand, his side scores 100 above the line; if any player holds all five trump honours, or all four aces at a no-trump contract, his side scores 150.

      For bidding and making a contract of six (small slam), a bonus of 500 is scored if not vulnerable, 750 if vulnerable. For a grand slam (all seven odd tricks) bid and made, the bonus is 1,000 if not vulnerable, 1,500 if vulnerable. A side bidding six and making seven scores only the small-slam bonus plus one overtrick. A side bidding seven and making only six has not fulfilled its contract, and its opponents score an undertrick penalty.

      If a player has to leave before a rubber is completed and no satisfactory substitute is available, a side having the only game scores 300 points; a side having the only partscore (trick score of less than 100) in an unfinished game scores 50.

The development of the game
      Bridge was probably born of three-hand whist games. Inveterate whist players, unwilling to forgo their game merely because there were only three available players, played a game called “dummy” (with one hand exposed) long before any bridge game was known or willingly played.

      The origin of bridge whist is not definitely known, but a similar game appeared in Constantinople before 1870, under the name khedive, and almost the same game had been played in Greece before that. Khedive, whose name had for some reason become biritch, was played on the French Riviera in the 1870s. A pamphlet titled Biritch; or, Russian Whist, was issued in London in 1887 and very nearly described bridge whist. There is a story that Ludovic Halévy (Halévy, Ludovic), in 1893, tried to persuade some whist-playing friends in Paris to play bridge with him, but they refused. In the same year, however, it was played at the Whist Club in New York City, and in 1894 Lord Brougham, penalized for failure to turn the last (trump) card in a whist game at London's Portland Club, apologized with the excuse that he forgot he was not playing bridge, “the finest card game ever introduced.”

      Whist players were prompt to deplore the arrival of bridge, almost unanimously asserting that whist, with all four hands hidden, was far more scientific than bridge. The fallacy of this soon became apparent, for exposure of the dummy provided clarity in thousands of situations in which the whist player had to guess blindly. This provided new opportunities for analysis and greatly stimulated the study of skillful play. By 1897 almost all the leading whist players had succumbed to the attractions of the new game, and even the whist authority “Cavendish” (Henry Jones (Jones, Henry)), who had refused for a period in 1897–98 to enter the Portland Club because whist had been all but abandoned there, was converted to bridge before his death in 1899.

      Bridge whist was the first game of the whist family to appeal to women as much as to men. It quickly became the favoured game of the fashionable world but did not supplant euchre and the other card games among the middle and lower classes, as auction bridge did later.

Development of auction bridge
      Several accounts of the origin of auction bridge have been advanced. It is probable that just as bridge whist developed from three-hand whist, auction bridge developed from three-hand bridge whist. A letter in the London Times, Jan. 16, 1903, signed by Oswald Crawfurd, describes “auction bridge for three players.” A book by “John Doe” (F. Roe), published in Allahabad, India, in 1904, presents three-hand auction bridge as an invention of Roe and two other members of the Indian civil service when, at an isolated post, they had no “fourth” for bridge whist. Experimental games in England and America apparently followed immediately on the publication of the Crawfurd letter, for by 1904 the best club players were turning to auction bridge. London's Portland Club adopted auction bridge in 1907, New York City's Whist Club and other American clubs in the two years following. By 1910 bridge whist was all but obsolete and auction bridge was virtually the only card game played by fashionable society and its emulators.

      The widespread appeal of auction bridge is attributable partly to the character of the game and partly to the social conditions into which it was born. The science of auction bridge, more complex and more nearly inexhaustible than that of any previous game, created a demand for large numbers of instructors in skillful play. The instructors, as a professional class, served as proselytizers. Concurrently, the rapid growth of the leisure class increased the demand for means for the entertainment of guests, and auction bridge was found to fill this need ideally. The gradual relaxation of church opposition to card playing, but not to gambling, stimulated acceptance of auction bridge, a game most often played without stakes and never for high stakes in the sense that gambling games are.

Development of contract bridge
      This game was developed almost concurrently with auction bridge but was slower to win popularity. At least as early as 1915, auction bridge players tried a variant in which one could score toward game only the odd tricks one had bid. The committee on laws of the Whist Club considered incorporation of this principle into the auction bridge laws in 1917 and again in 1920. They refrained in both instances because they thought such a difficult game would compromise the popularity of auction bridge.

      Harold S. Vanderbilt (see Vanderbilt Family) of New York was one of the expert auction bridge players who had experimented with contract bridge. While on a long sea voyage in 1926, Vanderbilt played Plafond, a French version of auction bridge. In the course of these games, he devised a new system of scoring values, multiplying auction bridge values five times or more; large slam bonuses; and the factor of vulnerability. (With minor changes this became and remains the contract bridge scoring system.)

      Until 1931 most casual players continued to play auction bridge. The publicity whereby contract bridge found its way to such players was supplied by another of the former auction bridge experts, Ely Culbertson (Culbertson, Ely) of New York. Culbertson established contract bridge as the leading card game and himself as its principal authority by a succession of tournament victories and by various maneuvers devised to publicize contract bridge and Culbertson personally. In 1930 Culbertson's teams won nearly every one of the principal American tournaments, then went to England and defeated three leading British teams. In the winter of 1931–32 Culbertson and his wife, Josephine Culbertson, played and defeated in a 150-rubber match one of the most prominent players among the former auction bridge authorities, Sidney S. Lenz. The progress of the match, called by American newspapers “the bridge battle of the century,” was featured for more than a month on their front pages. The unprecedented publicity made contract bridge a fad not only in the United States but also in South America and Europe.

      By 1935 the white heat of the fad had cooled. Nevertheless, the sales of books and playing cards for contract bridge increased steadily. By the start of the 21st century, bridge had become so commonplace that it was no longer a remarkable phenomenon and most newspapers in the United States and Great Britain carried regular columns. In particular, bridge was thriving in Europe, with many young players attracted to the game. In contrast, few young people were playing the game in the United States, although it remained popular with older generations. One of the main factors that has limited the growth of the game has been the small or nonexistent prizes awarded at tournaments. The only way to make a living from bridge has been to be hired by wealthy clients as a partner or teammate—“play for pay”—or through writing about the game. Another factor limiting the growth of bridge has been that, like chess, it is not very telegenic and requires considerable prior experience before a television viewer can appreciate the play.

      At the top level, bridge became much more scientific at the end of the 20th century, with experts having bidding-system notes that often ran to well over 100 pages in an attempt to cover all possible contingencies, and various unusual conventions and systems were developed. In the 1980s, forcing-pass methods were in vogue, especially in Poland (where they started), Australia, and New Zealand. An initial pass showed a good hand, usually at least 13 high-card points. Any other bid denied 13 points, and there was one call that indicated a very bad hand, normally 0–7 points. It was, of course, dangerous to have to open with no points, especially when vulnerable, but these systems gained popularity primarily because they put the opponents in unusual situations. Also, an opposing pair got to use its bidding system only if it dealt and opened immediately. Toward the end of the 1980s, these systems were banned from international play.

Duplicate and tournament bridge
      Bridge is played in three principal forms: rubber, Chicago, and duplicate. Rubber bridge is the simplest form for four players and is frequently played in casual games among friends. Chicago, or four-deal bridge, is most often used for small card parties in which several tables are used. Because a game of Chicago bridge involves only four deals, it is ideal for allowing each player to play with and against most of the other guests over the course of an evening. Duplicate bridge is played in all serious competitions and in official tournaments.

      The purpose of duplicate bridge is to eliminate, as nearly as possible, the element of luck from the game. After the usual deal and auction, the four players in playing their cards do not gather them up as tricks; instead, each shows the card he plays, then turns it down and keeps it on the table in front of him. After the result of the play has been ascertained and scored, the four hands in their original form are placed in a duplicate board, or tray, which is a rectangular container having four pockets, one for each hand. This board is then passed on to another table, where it is played by four other players. Thus, it is possible to compare results made with identical cards, the conclusion being that the pair making the higher score must have been more skillful.

      The result of each deal at duplicate contract bridge is first scored as in regular contract bridge, with these exceptions: there are no rubber bonuses, and, when declarer's side fulfills a game contract, it receives 300 points if not vulnerable, 500 points if vulnerable. For a trick score of less than 100 points, the bonus is 50 points regardless of vulnerability. The bonuses for honours held in one hand are not scored in match-point play.

      Dealer and vulnerability are assigned by the markings on the duplicate board. Sixteen such boards constitute a full set; although approximately 30 boards are usually played in one session, the series 17–32, 33–48, etc., are respectively identical to the 1–16. North is dealer on board 1, East on board 2, and so on in rotation. Neither side is vulnerable on boards 1, 8, 11, 14; North-South are vulnerable only on boards 2, 5, 12, 15, East-West on boards 3, 6, 9, 16, and both sides on boards 4, 7, 10, 13.

      Match-point scoring is used in all individual contests, most pair contests, and most team-of-four contests in which more than two teams compete. Each pair's (or team's) score for a board is compared with the scores made on that board by all other pairs that played precisely the same hands. A pair receives one match point for every such comparison in which it has the higher score, one-half match point for the same score. The pair or team amassing the most match points during the session is the winner.

      The European system of match-point scoring in team matches combines the total-point and match-point ideas. This system has been widely adopted in the United States. A team scores international match-points in proportion to its margin of victory on each board.

Bridge tournaments
      The idea of duplicate play achieved great popularity in the United States after Cassius M. Paine and J.L. Sebring patented the duplicate tray in 1891. Duplicate auction bridge became similarly popular in the 1920s, and championship tournaments were played regularly, but the game did not spread to Europe until contract bridge had arrived. The international matches between American and British teams in 1930 so stimulated interest that nearly all serious students of contract bridge took up duplicate play within the next two years. From 1934 until war or the threat of war interrupted them, national and European championships were held annually.

      In the United States, championship tournaments at auction bridge were conducted by the American Whist League in 1924–35, the American Bridge League in 1927–37, and the U.S. Bridge Association in 1933–37. Also there was an annual team-of-four tournament for the Harold Vanderbilt Cup, the first trophy given (1928) for a national championship at contract bridge. In 1937 all came under the control of a new, consolidated association, the American Contract Bridge League (ACBL). Its membership grew from 9,000 in 1940 to more than 160,000 by the 21st century.

      Similar contests were held annually in Great Britain by the British Bridge League, founded in 1932, and European championships were conducted by the European Bridge League (EBL), founded the same year. These tournaments continued through 1937 and were resumed in 1946. At the annual tournament of the EBL held in Oslo, Norway, in 1958, the World Bridge Federation was formed to control the world championship matches as previously played and to conduct an Olympiad open to all continents and countries beginning in 1960 and renewable each four years thereafter. Teams in international competition have six players each, of whom four play at a time, plus a nonplaying captain. Twenty-nine nationals from every continent except Antarctica took part in the first World Bridge Olympiad, in Turin, Italy, which was won by the French team.

      In 2005 the governing bodies of bridge, chess, draughts ( checkers), and go formed the International Mind Sports Association. The aim was to engage in a dialogue with the International Olympic Committee and to try to organize the World Mind Games, or Intellympiad, to be held in the Olympic city directly after a Winter or Summer Games.

Laws of bridge
      As descendants of whist, the several bridge games have always had more detailed laws than those of any other nonathletic game except chess. The Portland Club of London and the Whist Club of New York became traditionally the lawmaking bodies for rubber auction bridge, the game played chiefly in clubs and private homes. With the rise of duplicate and tournament bridge in the 1930s and '40s, the ACBL and the European Bridge League became predominant in lawmaking.

      The Portland Club adopted a code of laws for bridge whist in 1895, the Whist Club a different code in 1897. The Whist Club's laws were revised in 1902, the Portland Club's never. In 1909 the Portland Club published the first code of laws for auction bridge (revised 1914, 1924, 1928), and in 1910 the Whist Club published its first auction bridge laws (revised 1912, 1913, 1915, 1917, 1920, 1926). After 1910 auction bridge was never officially played under identical laws in Great Britain and elsewhere. Under the American laws, a bid of (for example) three in any suit would overcall a bid of two in any suit. Under British laws, a bid of one no trump, worth 12 points, would overcall a bid of five spades, worth 5 × 2 = 10 points. The American principle prevailed and by 1930 had become universal.

      The scoring values were changed several times in both countries. At first the scoring was as it had been in bridge whist. Then for a time the game was called royal auction because the spade suit had alternative values: a player might bid either spades, worth two points per trick, or royal spades (in the United States often called “lilies”), worth nine points per trick. The same suit would be trumps in either case, but the declarer's profit or risk would depend on which scoring value he had established by his bid. The count for a chicane was dropped after the first few years.

      The first laws of contract bridge were published by the Knickerbocker Whist Club of New York in 1927, but when later in the same year the Whist Club issued a code, the Knickerbocker laws were withdrawn. The Portland Club issued a code in 1929. In 1932 representatives of the Portland and Whist clubs met and agreed on the first international code, to which the Commission Française du Bridge subscribed. Since then, except for a 1941 American code (published 1943) issued unilaterally because the European correspondents were at war when it was written, every code has been international, and the revisions of 1948 and 1949 were promulgated by the ACBL and the EBL, to which the Whist Club and the Portland Club had ceded their claims of prerogative. In turn, these organizations, along with representative bodies from South America, deferred to the newly formed World Bridge Federation (WBF) in 1958. The most recent WBF rules for traditional rubber bridge were adopted in 1993, for duplicate contract bridge in 1997, and for play over the Internet in 2001.

Strategy of contract bridge
      The object in contract bridge is to score as many points as possible and to permit the opponents to score as few points as possible. The strategy employed by the best players in pursuit of this object embraces a technique that in complexity approaches the technique of chess, as well as a scope for deductive analysis, psychology, alertness, and mental ascendancy over one's opponents. Thus it is an art, which can hardly be taught or even described. The best players of the game (like the best players of bridge whist and auction bridge before them) combine unusual aptitude, interest amounting virtually to obsession, and experience derived from constant play with and against their peers.

      Nevertheless, the general rules, called systems, enable the casual player to emulate the expert standard in most cases. In whist, the progenitive game, the science was meagre; in bridge whist it improved; in auction bridge the best players were competent but the literature of the game never reflected the best practices; in contract bridge the most popular systems, if strictly followed, have produced nearly 90 percent efficiency.

      The factors in the systems of contract bridge bidding and play are:
● 1. Valuation. The player who bids accepts danger; if unable to fulfill his contract, he will be subject to penalties. Therefore, he must be able to estimate the trick-taking power of his hand.
● 2. Information. Bridge is essentially a partnership game. Each partner must inform his partner as to the nature and strength of the hand he holds. Assuming such information has been given and received, one partner should be able to decide the best contract for the combined hands.
● 3. Strategy. A bid defeats its own purposes if the information it gives is more valuable to the opponents than to the bidder's partner. Therefore, ideally, each bid should be designed to inform the bidder's partner only to the extent necessary while withholding information from the opponents.

      Only a few general principles can be stated for the play of the cards, but to the extent possible they have been exhaustively treated in the literature of the several bridge games. The ethics of the game permit information to be given only by the card led or the card played to a trick. Convention has endowed certain plays with meanings generally understood.

Bidding systems
      Bidding systems have preoccupied the student of bridge since the earliest appearance of contract bridge. The first system proposed was that of Harold S. Vanderbilt, who created the game that became successful as contract bridge. The Vanderbilt Club system provided that a player with a strong hand bid one club, the lowest bid; his partner with a weak hand would bid one diamond and with a strong hand would make some other bid. Despite its technical excellence, the Vanderbilt Club system was not widely accepted. The most successful system of the first 20 years of contract bridge was devised by Ely Culbertson (Culbertson, Ely) of New York. The Culbertson system required a player to value his hand by a schedule of high-card combinations called honour tricks and then to bid in accordance with established requirements based on the number of honour tricks held and the length of the player's suits.

      Despite competition from other systems advanced by those who had been the principal authorities in auction bridge (the official system), by leading players such as Phillip Hal Sims (the Sims system), and by leading teams such as the Four Aces (the Four Aces system), all during the early 1930s, the Culbertson system was paramount throughout the world until the late 1940s.

      In 1949 Charles H. Goren (Goren, Charles H.) of Philadelphia popularized a method of valuation called the point count, an extension of similar methods proposed as early as 1904 but not previously made applicable to more than a fraction of the many hands a bridge player might hold. In other respects Goren's system was similar to or identical with the methods advocated by Culbertson and the Four Aces.

      Hundreds of different bidding systems have been proposed for contract bridge, and at all times several dozen systems are in use. Some of these are modifications of the Goren system, or they are substantially the same as the Goren system with the addition of a few special bidding conventions; others are radically different. Bidding systems can be divided into two main groups: natural systems, in which the bidder usually has strength in any suit he bids, and artificial systems, in which most bids are signals designed to show the general strength of the bidder's hand but do not necessarily promise any strength in the suit bid. (Goren wrote the Goren system section of the bridge article for the 1963 printing of the 14th edition of Encyclopædia Britannica; see the Britannica Classic: .)

Slam bidding
      When a partnership has been able to ascertain that it has at least 33 points in the combined hands plus an adequate trump suit, the only thing that remains is to make certain that the opponents are unable to cash two quick tricks. For this purpose control-showing bids are used. Three systems are most popular: the Blackwood convention, the Gerber convention, and cue bidding.

Blackwood convention
      In this convention, devised in 1934 by Easley Blackwood (Blackwood, Easley) of Indianapolis, Ind., a bid of four no trump asks partner to show his total number of aces. A response of five clubs shows no aces (or all four aces); five diamonds shows one ace; five hearts shows two aces; five spades shows three aces. After aces have been shown, the four no-trump bidder may ask for kings by bidding five no trump. The responder now shows kings as he showed aces in response to the four no-trump bid, by bidding six clubs with no kings, six diamonds with one king, and so forth.

Gerber convention
      This was devised in 1938 by John Gerber of Houston, Texas. An unnecessary bid of four clubs, when the bid could not possibly have a natural meaning (such as opener bids one no trump, responder bids four clubs) asks partner to show the number of his aces. A response of four diamonds shows no aces, four hearts shows one ace, and so forth. If the asking hand desires information about kings, he bids five clubs (or, by partnership agreement, the next higher suit over his partner's ace-showing response; thus, if the responding hand has bid four hearts over four clubs to show one ace, a call of four spades would ask him to show kings and he would reply four no trump to show no kings, five clubs to show one king, and so forth).

Cue bidding
      The individual method of ace showing (cue bidding) is used when both partners have shown strength or when the trump suit has been agreed on. For example, opener bids two spades, responder bids three spades; a bid of four clubs by opener now would show the ace of clubs (or a void) and would invite responder to show an ace if he had one.

      The card led against declarer is selected so as to give information to the leader's partner. Certain conventional meanings of leads were established during the bridge whist period and, with slight changes, persisted in contract bridge.

      In winning or attempting to win a trick to which some other player led, a defender plays the lowest card in an unbroken sequence of high cards; as, the 10 from Q-J-10-8.

      A standard defender's signal is the high-low, or come-on: the play or discard of an unnecessarily high card, followed if possible by a lower card of the same suit on a subsequent trick. This denotes a desire to have that suit led.

      There are many other signals and conventions in defenders' play. These do not violate the spirit of the game if they are known to the opponents. Declarer need not observe any system in the selection of cards, for he has no partner to inform.

Bridge problems
      Proficiency at the play of the cards in bridge is enhanced by study of double-dummy problems (in which the location of all unplayed cards is known). Putting such knowledge to practical use has been much better accomplished in contract bridge than in any of its predecessor games. For example, a prime problem at whist was the “Great Vienna Coup,” with which the expert whist players had difficulty even when they could see all four hands. Execution of this and similarly difficult plays is commonplace among contract bridge players far below the highest rank.

      Most double-dummy problems embrace the squeeze (so named by Sidney S. Lenz of New York, because it reminded him of a maneuver in baseball), in which a player has winning cards in two or three suits but is forced to discard one of them. The throw-in play and the trump pickup (generic terms for the group of plays that included the grand coup of whist) are other favourite themes of problem constructors.

The Whitfeld six
 The most famous of all double-dummy problems was proposed by W.H. Whitfeld, a mathematician at the University of Cambridge, in 1885 and is called the Whitfeld six because each hand has six cards. Whist players of the day could make nothing of it, and, despite the advancement in the science of card playing, it would cause trouble even to most experienced contract bridge players. See figure—>.

The Vienna coup
 The characteristic of the Vienna coup is that a high card must be played early, apparently establishing a card in an opponent's hand but actually subjecting him to a squeeze that could not have been effected had the high card remained unplayed. See figure—>.

Albert H. Morehead Phillip Alder

Additional Reading
Alan Truscott and Dorothy Truscott, The New York Times Bridge Book: An Anecdotal History of the Development, Personalities, and Strategies of the World's Most Popular Card Game (2002), is an excellent introduction to the game. The American Contract Bridge League series by Audrey Grant, which includes The Spade Series: An Introduction to Duplicate Bridge (1990, reissued 1997), The Club Series: Bidding (1990, reissued 1998), The Diamond Series: Play of the Hand (1999, reissued 2002), and The Heart Series: Introduction to Bridge Defense (1997, reissued 2002), is a comprehensive course. Eddie Kantar, Bridge for Dummies (1997), gives a comprehensive introduction to the game using modern bidding methods.Phillip Alder

▪ electrical instrument
 in electrical measurement, instrument for measuring electrical quantities. The first such instrument, invented by British mathematician Samuel Christie and popularized in 1843 by Sir Charles Wheatstone, (Wheatstone, Sir Charles) measures resistance by comparing the current flowing through one part of the bridge with a known current flowing through another part. The Wheatstone bridge has four arms, all predominantly resistive. A bridge can measure other quantities in addition to resistance, depending upon the type of circuit elements used in the arms. It can measure inductance, capacitance, and frequency with the proper combination and arrangement of inductances and capacitances in its arms.

 structure that spans horizontally between supports, whose function is to carry vertical loads. The prototypical bridge is quite simple—two supports holding up a beam—yet the engineering problems that must be overcome even in this simple form are inherent in every bridge: the supports must be strong enough to hold the structure up, and the span between supports must be strong enough to carry the loads. Spans are generally made as short as possible; long spans are justified where good foundations are limited—for example, over estuaries with deep water.

 All major bridges are built with the public's money. Therefore, bridge design that best serves the public interest has a threefold goal: to be as efficient, as economical, and as elegant as is safely possible. Efficiency is a scientific principle that puts a value on reducing materials while increasing performance. Economy is a social principle that puts value on reducing the costs of construction and maintenance while retaining efficiency. Finally, elegance is a symbolic or visual principle that puts value on the personal expression of the designer without compromising performance or economy. There is little disagreement over what constitutes efficiency and economy, but the definition of elegance has always been controversial.

 Modern designers have written about elegance or aesthetics since the early 19th century, beginning with the Scottish engineer Thomas Telford (Telford, Thomas). Bridges ultimately belong to the general public, which is the final arbiter of this issue, but in general there are three positions taken by professionals. The first principle holds that the structure of a bridge is the province of the engineer and that beauty is fully achieved only by the addition of architecture. The second idea, arguing from the standpoint of pure engineering, insists that bridges making the most efficient possible use of materials are by definition beautiful. The third case holds that architecture is not needed but that engineers must think about how to make the structure beautiful. This last principle recognizes the fact that engineers have many possible choices of roughly equal efficiency and economy and can therefore express their own aesthetic ideas without adding significantly to materials or cost.

      Generally speaking, bridges can be divided into two categories: standard overpass bridges or unique-design bridges over rivers, chasms, or estuaries. This article describes features common to both types, but it concentrates on the unique bridges because of their greater technical, economic, and aesthetic interest.

The elements of bridge design

Basic forms
      There are six basic bridge forms: the beam, the truss, the arch, the suspension, the cantilever, and the cable-stay.

 The beam bridge is the most common bridge form. A beam carries vertical loads by bending. As the beam bridge bends, it undergoes horizontal compression on the top. At the same time, the bottom of the beam is subjected to horizontal tension. The supports carry the loads from the beam by compression vertically to the foundations.

 When a bridge is made up of beams spanning between only two supports, it is called a simply supported beam bridge. If two or more beams are joined rigidly together over supports, the bridge becomes continuous.

 A single-span truss bridge is like a simply supported beam because it carries vertical loads by bending. Bending leads to compression in the top chords (or horizontal members), tension in the bottom chords, and either tension or compression in the vertical and diagonal members, depending on their orientation. Trusses are popular because they use a relatively small amount of material to carry relatively large loads.

  The arch bridge carries loads primarily by compression, which exerts on the foundation both vertical and horizontal forces. Arch foundations must therefore prevent both vertical settling and horizontal sliding. In spite of the more complicated foundation design, the structure itself normally requires less material than a beam bridge of the same span.

  A suspension bridge carries vertical loads through curved cables in tension. These loads are transferred both to the towers (tower), which carry them by vertical compression to the ground, and to the anchorages, which must resist the inward and sometimes vertical pull of the cables. The suspension bridge can be viewed as an upside-down arch in tension with only the towers in compression. Because the deck is hung in the air, care must be taken to ensure that it does not move excessively under loading. The deck therefore must be either heavy or stiff or both.

  A beam is said to be cantilevered when it projects outward, supported only at one end. A cantilever bridge is generally made with three spans, of which the outer spans are both anchored down at the shore and cantilever out over the channel to be crossed. The central span rests on the cantilevered arms extending from the outer spans; it carries vertical loads like a simply supported beam or a truss—that is, by tension forces in the lower chords and compression in the upper chords. The cantilevers carry their loads by tension in the upper chords and compression in the lower ones. Inner towers carry those forces by compression to the foundation, and outer towers carry the forces by tension to the far foundations.

  Cable-stayed bridges carry the vertical main-span loads by nearly straight diagonal cables (cable) in tension. The towers transfer the cable forces to the foundations through vertical compression. The tensile forces in the cables also put the deck into horizontal compression.

      The four primary materials used for bridges have been wood, stone, iron, and concrete. Of these, iron has had the greatest effect on modern bridges. From iron, steel is made, and steel is used to make reinforced and prestressed concrete. Modern bridges are almost exclusively built with steel, reinforced concrete, and prestressed concrete.

wood and stone
       wood is relatively weak in both compression and tension, but it has almost always been widely available and inexpensive. Wood has been used effectively for small bridges that carry light loads, such as footbridges. Engineers now incorporate laminated wooden beams and arches into some modern bridges.

      Stone is strong in compression but weak in tension. Its primary application has been in arches (arch), piers (pier), and abutments.

iron and steel
      The first iron (iron processing) used during the Industrial Revolution was cast iron, which is strong in compression but weak in tension. wrought iron, on the other hand, is as strong in compression as cast iron, but it also has much greater tensile strength. steel is an even further refinement of iron and is yet stronger, superior to any iron in both tension and compression. Steel can be made to varying strengths, some alloys being five times stronger than others. The engineer refers to these as high-strength steels.

       concrete is an artificial stone made from a mixture of water, sand, gravel, and a binder such as cement. Like stone, it is strong in compression and weak in tension. Concrete with steel bars embedded in it is called reinforced concrete. Reinforcement allows for less concrete to be used because the steel carries all the tension; also, the concrete protects the steel from corrosion and fire.

      Prestressed concrete is an important variation of reinforced concrete. A typical process, called post-tensioned prestressing, involves casting concrete beams with longitudinal holes for steel tendons—cables or bars—like reinforced concrete, but the holes for the tendons are curved upward from end to end, and the tendons, once fitted inside, are stretched and then anchored at the ends. The tendons, now under high tension, pull the two anchored ends together, putting the beam into compression. In addition, the curved tendons exert an upward force, and the designer can make this upward force counteract much of the downward load expected to be carried by the beam. Prestressed concrete reduces the amount of steel and concrete needed in a structure, leading to lighter designs that are often less expensive than designs of reinforced concrete.

Beam bridges
      All bridges need to be secure at the foundations and abutments. In the case of a typical overpass beam bridge with one support in the middle, construction begins with the casting of concrete footings for the pier and abutments. Where the soil is especially weak, wooden or steel piles (pile) are driven to support the footings. After the concrete piers and abutments have hardened sufficiently, the erection of a concrete or steel superstructure begins. Steel beams (beam) are generally made in a factory, shipped to the site, and set in place by cranes. For short spans, steel beams are usually formed as a single unit. At the site, they are placed parallel to each other, with temporary forms between them so that a concrete deck can be cast on top. The beams usually have metal pieces welded on their top flanges, around which the concrete is poured. These pieces provide a connection between beam and slab, thus producing a composite structure.

      For longer spans, steel beams are made in the form of plate girders (girder). A plate girder is an I beam consisting of separate top and bottom flanges welded or bolted to a vertical web. While beams for short spans are usually of a constant depth, beams for longer spans are often haunched—that is, deeper at the supports and shallower at mid-span. Haunching stiffens the beam at the supports, thereby reducing bending at mid-span.

Arch bridges
      Arches (arch) are normally fabricated on-site. After the building of abutments (and piers, if the bridge is multiarch), a falsework is constructed. For a concrete arch, metal or wooden falsework and forms hold the cast concrete and are later removed. For steel arches, a cantilevering method is standard. Each side of an arch is built out toward the other, supported by temporary cables above or by falsework below until the ends meet. At this point the arch becomes self-supporting, and the cables or falsework are removed.

Suspension bridges (suspension bridge)
  When bridges requiring piers (pier) are built over a body of water, foundations are made by sinking caissons (caisson) into the riverbed and filling them with concrete. Caissons are large boxes or cylinders that have been made from wood, metal, or concrete. In the case of suspension bridges, towers are built atop the caissons. The first suspension-bridge towers were stone, but now they are either steel or concrete. Next, the anchorages are built on both ends, usually of reinforced concrete with embedded steel eyebars to which the cables (cable) will be fastened. An eyebar is a length of metal with a hole (or “eye”) at the ends. Cables for the first suspension bridges were made of linked wrought-iron eyebars; now, however, cables are generally made of thousands of steel wires (wire) spun together at the construction site. Spinning is done by rope pulleys that carry each wire across the top of the towers to the opposite anchorage and back. The wires are then bundled and covered to prevent corrosion. When the cables are complete, suspenders are hung, and finally the deck is erected—usually by floating deck sections out on ships, hoisting them with cranes, and securing them to the suspenders.

Cantilever bridges
      Like suspension bridges, steel cantilever bridges generally carry heavy loads over water, so their construction begins with the sinking of caissons and the erection of towers and anchorages. For steel cantilever bridges, the steel frame is built out from the towers toward the centre and the abutments. When a shorter central span is required, it is usually floated out and raised into place. The deck is added last.

      The cantilever method for erecting prestressed concrete bridges consists of building a concrete cantilever in short segments, prestressing each succeeding segment onto the earlier ones. Each new segment is supported by the previous segment while it is being cast, thus avoiding the need for falsework.

Cable-stayed bridges
 Construction of cable-stayed bridges usually follows the cantilever method. After the tower is built, one cable and a section of the deck are constructed in each direction. Each section of the deck is prestressed before continuing. The process is repeated until the deck sections meet in the middle, where they are connected. The ends are anchored at the abutments.

Performance in service
      Bridges are designed, first, to carry their own permanent weight, or dead load; second, to carry traffic, or live loads; and, finally, to resist natural forces such as winds or earthquakes.

Live load and dead load
      The primary function of a bridge is to carry traffic loads: heavy trucks, cars, and trains. Engineers must estimate the traffic loading. On short spans, it is possible that the maximum conceivable load will be achieved—that is to say, on spans of less than 30 metres (100 feet), four heavy trucks may cross at the same time, two in each direction. On longer spans of a thousand metres or more, the maximum conceivable load is such a remote possibility (imagine the Golden Gate Bridge with only heavy trucks crossing bumper-to-bumper in each direction at the same time) that the cost of designing for it is unreasonable. Therefore, engineers use probable loads as a basis for design.

      In order to carry traffic, the structure must have some weight, and on short spans this dead load weight is usually less than the live loads. On longer spans, however, the dead load is greater than live loads, and, as spans get longer, it becomes more important to design forms that minimize dead load. In general, shorter spans are built with beams, hollow boxes, trusses, arches, and continuous versions of the same, while longer spans use cantilever, cable-stay, and suspension forms. As spans get longer, questions of shape, materials, and form become increasingly important. New forms have evolved to provide longer spans with more strength from less material.

Forces of nature
      Dead and live weight are essentially vertical loads, whereas forces from nature may be either vertical or horizontal. wind causes two important loads, one called static and the other dynamic. Static wind load is the horizontal pressure that tries to push a bridge sideways. Dynamic wind load gives rise to vertical motion, creating oscillations in any direction. Like the breaking of an overused violin string, oscillations are vibrations that can cause a bridge to fail. If a deck is thin and not properly shaped and supported, it may experience dangerous vertical or torsional (twisting) movements.

      The expansion and contraction of bridge materials by heat and cold have been minimized by the use of expansion joints in the deck along with bearings at the abutments and at the tops of piers. Bearings allow the bridge to react to varying temperatures without causing detrimental stress to the material. In arches, engineers sometimes design hinges to reduce stresses caused by temperature movement.

      Modern bridges must also withstand natural disasters such as tropical cyclones (tropical cyclone) and earthquakes (earthquake). In general, earthquakes are best withstood by structures that carry as light a dead weight as possible, because the horizontal forces that arise from ground accelerations are proportional to the weight of the structure. (This phenomenon is explained by the fundamental Newtonian law of force equals mass times acceleration.) For cyclones, it is generally best that the bridge be aerodynamically designed to have little solid material facing the winds, so that they may pass through or around the bridge without setting up dangerous oscillations.

The history of bridge design (civil engineering)
      Modern bridges, the focus of this article, began with the introduction of industrially produced iron (iron processing). They have evolved over the past 200 years as engineers have come to understand better the new possibilities inherent first in cast iron, then in wrought iron and structural steel, and finally in reinforced and prestressed concrete. These materials have led to bridge designs that have broken completely with the designs in wood or stone that characterized bridges before the Industrial Revolution.

      Industrial strength has been an important factor in the evolution of bridges. Great Britain, the leading industrialized country of the early 19th century, built the most significant bridges of that time. Likewise, innovations arose in the United States from the late 19th century through the mid-20th century and in Japan and Germany in subsequent decades. Switzerland, with its highly industrialized society, has also been a fertile ground for advances in bridge building.

Early wood and stone bridges
The ancient world

Beam bridges
 The first bridges were simply supported beams (beam), such as flat stones or tree trunks laid across a stream. For valleys and other wider channels—especially in East Asia and South America, where examples can still be found—ropes made of various grasses and vines tied together were hung in suspension for single-file crossing. Materials were free and abundant, and there were few labour costs, since the work was done by slaves, soldiers, or natives who used the bridges in daily life.

      Some of the earliest known bridges are called clapper bridges (from Latin claperius, “pile of stones”). These bridges were built with long, thin slabs of stone to make a beam-type deck and with large rocks or blocklike piles of stones for piers. Postbridge in Devon, England, an early medieval clapper bridge, is an oft-visited example of this old type, which was common in much of the world, especially China.

Roman arch bridges
      The Romans (ancient Rome) began organized bridge building to help their military campaigns. Engineers and skilled workmen formed guilds that were dispatched throughout the empire, and these guilds spread and exchanged building ideas and principles. The Romans also discovered a natural cement, called pozzolana, which they used for piers in rivers.

  Roman bridges are famous for using the circular arch form, which allowed for spans much longer than stone beams and for bridges of more permanence than wood. Where several arches were necessary for longer bridges, the building of strong piers (pier) was critical. This was a problem when the piers could not be built on rock, as in a wide river with a soft bed. To solve this dilemma, the Romans developed the cofferdam, a temporary enclosure made from wooden piles (pile) driven into the riverbed to make a sheath, which was often sealed with clay. Concrete was then poured into the water within the ring of piles. Although most surviving Roman bridges were built on rock, the Sant'Angelo Bridge in Rome stands on cofferdam foundations built in the Tiber River more than 1,800 years ago.

 The Romans built many wooden bridges, but none has survived, and their reputation rests on their masonry bridges. One beautiful example is the bridge over the Tagus River at Alcántara, Spain. The arches, each spanning 29 metres (98 feet), feature huge arch stones (voussoirs) weighing up to eight tons each. Typical of the best stone bridges, the voussoirs at Alcántara were so accurately shaped that no mortar was needed in the joints. This bridge has remained standing for nearly 2,000 years. Another surviving monument is the Pont du Gard (Gard, Pont du) aqueduct near Nîmes in southern France, completed in AD 14. This structure, almost 270 metres (900 feet) long, has three tiers of semicircular arches, with the top tier rising more than 45 metres (150 feet) above the river. The bottom piers form diamond-shaped points, called cutwaters, which offer less resistance to the flow of water.

Asian (Asia) cantilever and arch bridges
      In Asia, wooden cantilever bridges were popular. The basic design used piles driven into the riverbed and old boats filled with stones sunk between them to make cofferdam-like foundations. When the highest of the stone-filled boats reached above the low-water level, layers of logs were crisscrossed in such a way that, as they rose in height, they jutted farther out toward the adjacent piers. At the top, the Y-shaped, cantilevering piers were joined by long tree trunks. By crisscrossing the logs, the builders allowed water to pass through the piers, offering less resistance to floods than with a solid design. In this respect, these designs presaged some of the advantages of the early iron bridges.

      In parts of China many bridges had to stand in the spongy silt of river valleys. As these bridges were subject to an unpredictable assortment of tension and compression, the Chinese created a flexible masonry-arch bridge. Using thin, curved slabs of stone, the bridges yielded to considerable deformation before failure.

      In the Great Stone Bridge in Chao-chou, Hopeh (Hebei) Province, China, built by Li Ch'un between 589 and 618, the single span of 37 metres (123 feet) has a rise of only 7 metres (23 feet) from the abutments to the crown. This rise-to-span ratio of 1:5, much lower than the 1:2 ratio found in semicircular arches, produced a large thrust against the abutments. To reduce the weight, the builders made the spandrels (walls between the supporting vault and deck) open. The Great Stone Bridge thus employed a form rarely seen in Europe prior to the mid-18th century, and it anticipated the reinforced-concrete designs of Robert Maillart (Maillart, Robert) in the 20th century.

 After the fall of the Roman Empire, progress in European (Europe) bridge building slowed considerably until the Renaissance. Fine bridges sporadically appeared, however. Medieval bridges are particularly noted for the ogival, or pointed arch. With the pointed arch the tendency to sag at the crown is less dangerous, and there is less horizontal thrust at the abutments. Medieval bridges served many purposes. Chapels and shops were commonly built on them, and many were fortified with towers and ramparts. Some featured a drawbridge, a medieval innovation. The most famous bridge of that age was Old London Bridge (London Bridge), begun in the late 12th century under the direction of a priest, Peter of Colechurch, and completed in 1209, four years after his death. London Bridge was designed to have 19 pointed arches, each with a 7.2-metre (24-foot) span and resting on piers 6 metres (20 feet) wide. There were obstructions encountered in building the cofferdams, however, so that the arch spans eventually varied from 4.5 to 10.2 metres (15 to 34 feet). The uneven quality of construction resulted in a frequent need for repair, but the bridge held a large jumble of houses and shops and survived more than 600 years before being replaced.

      A more elegant bridge of the period was the Saint-Bénézet Bridge at Avignon, France. Begun in 1177, part of it still stands today. Another medieval bridge of note is Monnow Bridge in Wales, which featured three separate ribs of stone under the arches. Rib construction reduced the quantity of material needed for the rest of the arch and lightened the load on the foundations.

The Renaissance and after

Stone arch bridges
 During the Renaissance, the Italian (Italy) architect Andrea Palladio (Palladio, Andrea) took the principle of the truss, which previously had been used for roof supports, and designed several successful wooden bridges with spans up to 30 metres (100 feet). Longer bridges, however, were still made of stone. Another Italian designer, Bartolommeo Ammannati (Ammannati, Bartolommeo), adapted the medieval ogival arch by concealing the angle at the crown and by starting the curves of the arches vertically in their springings from the piers (pier). This elliptical shape of arch, in which the rise-to-span ratio was as low as 1:7, became known as basket-handled and has been adopted widely since. Ammannati's elegant Santa Trinità Bridge (1569) in Florence, with two elliptical arches, carried pedestrians and later automobiles until it was destroyed during World War II; it was afterward rebuilt with many of the original materials recovered from the riverbed. Yet another Italian, Antonio da Ponte (Ponte, Antonio da), designed the Rialto Bridge (1591) in Venice, an ornate arch made of two segments with a span of 27 metres (89 feet) and a rise of 6 metres (21 feet). Antonio overcame the problem of soft, wet soil by having 6,000 timber piles driven straight down under each of the two abutments, upon which the masonry was placed in such a way that the bed joints of the stones were perpendicular to the line of thrust of the arch. This innovation of angling stone or concrete to the line of thrust has been continued into the present.

      By the middle of the 18th century, bridge building in masonry reached its zenith. Jean-Rodolphe Perronet (Perronet, Jean), builder of some of the finest bridges of his day, developed very flat arches supported on slender piers. His works included the Pont de Neuilly (1774), over the Seine (Seine River), the Pont Sainte-Maxence (1785), over the Oise (Oise River), and the beautiful Pont de la Concorde (Concorde, Pont de la) (1791), also over the Seine. In Great Britain (United Kingdom), William Edwards built what many people consider the most beautiful arch bridge in the British Isles—the Pontypridd Bridge (1750), over the Taff in Wales, with a lofty span of 42 metres (140 feet). In London the young Swiss engineer Charles Labelye, entrusted with the building of the first bridge at Westminster (Westminster, City of), evolved a novel and ingenious method of sinking the foundations, employing huge timber caissons that were filled with masonry after they had been floated into position for each pier. The 12 semicircular arches of portland stone, rising in a graceful camber over the river, set a high standard of engineering and architectural achievement for the next generation and stood for a hundred years.

      Also in London, John Rennie (Rennie, John), engaged by private enterprise in 1811, built the first Waterloo Bridge, whose level-topped masonry arches were described by the Italian sculptor Antonio Canova (Canova, Antonio, marchese d'Ischia) as “the noblest bridge in the world.” It was replaced by a modern bridge in 1937–45. Rennie subsequently designed the New London Bridge (London Bridge) of multiple masonry arches. Completed in 1831, after Rennie's death, it was subsequently widened and was finally replaced in the 1960s.

Timber truss bridges
 In the 18th century, designs with timber, especially trusses (truss), reached new span lengths. In 1755 a Swiss builder, Hans Grubenmann, used trusses to support a covered timber bridge with spans of 51 and 58 metres (171 and 193 feet) over the Rhine at Schaffhausen. Many timber truss bridges were built in the United States. One of the best long-span truss designs was developed by Theodore Burr, of Torrington, Connecticut, and based on a drawing by Palladio; a truss strengthened by an arch, it set a new pattern for covered bridges in the United States. Burr's McCall's Ferry Bridge (1815; on the Susquehanna River near Lancaster, Pennsylvania) had a record-breaking span of 108 metres (360 feet). Another successful design was the “lattice truss,” patented by Ithiel Town in 1820, in which top and bottom chords were made of horizontal timbers connected by a network of diagonal planks.

      Early trusses were built without precise knowledge of how the loads are carried by each part of the truss. The first engineer to analyze correctly the stresses in a truss was Squire Whipple (Whipple, Squire), an American who designed hundreds of small truss bridges and published his theories in 1869. Understanding precisely how loads were carried led to a reduction in materials, which by then were shifting from wood and stone to iron and steel.

Sir Hubert Shirley-Smith David P. Billington Philip N. Billington

iron and steel bridges, 1779–1929

Early designs
      During the Industrial Revolution the timber and masonry tradition was eclipsed by the use of iron (iron processing), which was stronger than stone and usually less costly. The first bridge built solely of iron spanned the River Severn (Severn, River) near Coalbrookdale, England. Designed by Thomas Pritchard and built in 1779 by Abraham Darby (Darby, Abraham), the Ironbridge, constructed of cast-iron pieces, is a ribbed arch whose nearly semicircular 30-metre (100-foot) span imitates stone construction by exploiting the strength of cast iron in compression. In 1795 the Severn region was wracked by disastrous floods, and the Ironbridge, lacking the wide flat surfaces of stone structures, allowed the floodwaters to pass through it. It was the only bridge in the region to survive—a fact noted by the Scottish engineer Thomas Telford (Telford, Thomas), who then began to create a series of iron bridges that were judged to be technically the best of their time. The 1814 Craigellachie Bridge, over the River Spey (Spey, River) in Scotland, is the oldest surviving metal bridge of Telford's. Its 45-metre (150-foot) arch has a flat, nearly parabolic profile made up of two curved arches connected by X-bracing. The roadway has a slight vertical curve and is supported by thin diagonal members that carry loads to the arch.

      The use of relatively economical wrought iron freed up the imaginations of designers, and one of the first results was Telford's use of chain suspension cables to carry loads by tension. His eyebar cables consisted of wrought-iron bars of 6 to 9 metres (20 to 30) feet with holes at each end. Each eye matched the eye on another bar, and the two were linked by iron pins. The first of these major chain-suspension bridges and the finest of its day was Telford's Menai Bridge, over the Menai Strait in northwestern Wales. At the time of its completion in 1826, its 174-metre (580-foot) span was the world's longest. In 1893 its timber deck was replaced with a steel deck, and in 1940 steel chains replaced the corroded wrought-iron ones. The bridge is still in service today.

Railway (railroad) bridges
      The rise of the locomotive as a mode of transportation during the 19th century spurred the design of new bridges and bridge forms strong enough to handle both the increased weight and the dynamic loads of trains. The most significant of these early railway bridges was Robert Stephenson (Stephenson, Robert)'s Britannia Bridge, also over the Menai Straits. Completed in 1850, Stephenson's design was the first to employ the hollow box girder. The hollow box gave the deck the extra stiffness of a truss, but it was easier to build and required less engineering precision—at the cost, however, of extra material. The wrought-iron boxes through which the trains ran were originally to be carried by chain suspension cables, but, during the building, extensive theoretical work and testing indicated that the cables were not needed; thus the towers stand strangely useless. For the Royal Albert Bridge (1859) over the River Tamar (Tamar, River) at Saltash, England, designer Isambard Kingdom Brunel (Brunel, Isambard Kingdom) used a combination of tubular arch and chain cable. The arches rise above the deck and, in conjunction with the chain suspenders, gives the bridge in profile what appear to be a set of eyes. The bridge at Saltash also carries trains, and its two main spans of 136.5 metres (455 feet) are comparable in length to the Britannia's 138-metre (460-foot) spans.

      Among the most important railway bridges of the latter 19th century were those of Gustave Eiffel (Eiffel, Gustave). Between 1867 and 1869 Eiffel constructed four viaducts (viaduct) of trussed-girder design along the rail line between Gannat and Commentry, west of Vichy in France. The most striking of these, at Rouzat, features wrought-iron towers that for the first time visibly reflect the need for lateral stiffness to counter the influence of horizontal wind loads. Lateral stiffness is achieved by curving the towers out at the base where they meet the masonry foundations, a design style that culminated in Eiffel's famous Parisian tower of 1889.

      Eiffel also designed two major arch bridges that were the longest-spanning structures of their type at the time. The first, the 1877 Pia Maria Bridge over the Duoro River near Oporto, Portugal, is a 157-metre (522-foot), crescent-shaped span that rises 42 metres (140 feet) at its crown. Again, a wide spreading of the arches at their base gives this structure greater lateral stiffness. The crowning achievement of the crescent-arch form in the 19th century was represented by the completion in 1884 of Eiffel's 162-metre (541-foot) Garabit Viaduct over the Truyère River near Saint-Flour, France. Unlike the bridge at Duoro, the Garabit arch is separated visually from the thin horizontal girder. Both arches were designed with hinges at their supports so that the crescent shape widens from points at the supports to a deep but light truss at the crown. The hinged design served to facilitate construction and also to produce the powerful visual image intended by Eiffel.

Suspension bridges (suspension bridge)
      In the United States, engineer John Roebling (Roebling, John Augustus) established a factory in 1841 for making rope out of iron wire, which he initially sold to replace the hempen rope used for hoisting cars over the portage railway in central Pennsylvania. Later Roebling used wire ropes as suspension cables for bridges, and he developed the technique for spinning the cables in place rather than making a prefabricated cable that needed to be lifted into place. In 1855 Roebling completed a 246-metre- (821-foot-) span railway bridge over the Niagara River in western New York state. Wind loads were not yet understood in any theoretical sense, but Roebling recognized the practical need to prevent vertical oscillations. He therefore added numerous wire stays, which extended like a giant spiderweb in various directions from the deck to the valley below and to the towers above. The Niagara Bridge confounded nearly all the engineering judgment of the day, which held that suspension bridges could not sustain railway traffic. Although the trains were required to slow down to a speed of only five kilometres (three miles) per hour and repairs were frequent, the bridge was in service for 42 years, and it was replaced only because newer trains had become too heavy for it.

      Roebling's Cincinnati Bridge (now called the John A. Roebling Bridge) over the Ohio River was a prototype for his masterful Brooklyn Bridge (see below Steel: Suspension bridges (bridge)). When this 317-metre- (1,057-foot-) span, iron-wire cable suspension bridge was completed in 1866, it was the longest spanning bridge in the world. Roebling's mature style showed itself in the structure's impressive stone towers and its thin suspended span, with stays radiating from the tower tops to control deck oscillations from wind loads.

Railway bridges
      Between the American Civil War and World War I, railroads (railroad) reached their peak in the United States and elsewhere, increasing the need for bridges that could withstand these heavier loads. New processes for making steel gave rise to many important bridges, such as the Eads Bridge over the Mississippi River at St. Louis, the Forth Bridge over the Firth of Forth in Scotland, the Hell Gate Bridge and Bayonne Bridge in New York City, and the Sydney Harbour Bridge in Australia.

      The 1874 Eads Bridge was the first major bridge built entirely of steel, excluding the pier foundations. Designed by James Buchanan Eads (Eads, James B.), it has three arch spans, of which the two sides are each 151 metres (502 feet) and the middle is 156 metres (520 feet). The Eads bridge was given added strength by its firm foundations, for which pneumatic caissons (caisson), instead of cofferdams (cofferdam), were used for the first time in the United States. Another innovation carried out by Eads, based on a proposal by Telford, was the construction of arches by the cantilevering method. The arches were held up by cables supported by temporary towers above the piers, all of which were removed when the arches became self-supporting.

      The Forth Bridge over the Firth of Forth in Scotland, designed by Benjamin Baker (Baker, Sir Benjamin), has two cantilevered spans of 513 metres (1,710 feet), which made it the world's longest bridge upon its completion in 1890. The steel structure rises 103 metres (342 feet) above the masonry piers. Although from an approaching standpoint it appears dense and massive, in profile it exhibits a surprising lightness. Baker designed the bridge with an artist's temperament. In his writings he criticized the Britannia Bridge for its towers, which Stephenson admitted had been left in place only in case the bridge needed suspension chains and not out of structural necessity. The Forth Bridge, on the other hand, is pure structure; nothing has been added for aesthetic appearance that does not have a structural function. For more than a century the bridge has carried a railway, and indeed it was one of the last great bridges built for that purpose in the 19th century.

      The Hell Gate Bridge, completed by Gustav Lindenthal (Lindenthal, Gustav) in 1916, also had an aesthetic intention. It was made to look massive by its stone towers and by the increased spacing of the two chords at the support, yet structurally the towers serve no purpose; the lower chord of the arch is actually hinged at the abutments, and all of the load is carried to the foundations by that lower chord. Nevertheless, the bridge has an imposing presence, and its arch of 293 metres (978 feet) was the world's longest at the time.

      Similar in arch form to Hell Gate is the 1931 Bayonne Bridge, designed by Lindenthal's former associate, Othmar Ammann (Ammann, Othmar Herman). Spanning the Kill van Kull between Staten Island, New York, and Bayonne, New Jersey, the Bayonne Bridge, though longer than the Hell Gate Bridge at 496 metres (1,652 feet), is significantly lighter. The main span for the Hell Gate required 39 million kg (87 million pounds) of steel, compared with 17 million kg (37 million pounds) for the Bayonne. Part of the reason is the lower live loads; for the Hell Gate, train loading was taken at 36,000 kg per metre (24,000 pounds per foot) of bridge length, whereas for the Bayonne the car loading was 10,000 kg per metre (7,000 pounds per foot). But the decrease is also due to an effort to make the arch more graceful as well as more economical. Massive-looking stone-faced abutments were designed for the sake of appearance but then were never built, leaving a rather useless tangle of light steel latticework at the abutments. Nevertheless, from a distance the Bayonne Bridge shows a lightness and delicacy that bespeaks structural integrity.

      Across the world in Sydney Harbour, New South Wales, Australia, Sir Ralph Freeman (Freeman, Sir Ralph) designed a steel arch bridge with a span of 495 metres (1,650 feet) that was begun in 1924 and completed in 1932. Because of the deep waters in the harbour, temporary supports were impractical, so the steel arch was assembled by cantilevering out from each bank and meeting in the middle. A high-strength silicon steel was used, making it the heaviest steelwork of its kind. The Sydney Harbour Bridge is a two-hinged arch, with its deck 52 metres (172 feet) above the water. It carries four railroad tracks, a roadway 17 metres (57 feet) wide, and two walkways. On each bank it is supported by a pair of large stone towers that, like those of the Hell Gate, disguise the fact that almost the entire load is carried by the lower arch chord.

Suspension bridges (suspension bridge)
      John Roebling (Roebling, John Augustus) died in 1869, shortly after work began on the Brooklyn Bridge, but the project was taken over and seen to completion by his son, Washington Roebling (Roebling, Washington Augustus). Technically, the bridge overcame many obstacles through the use of huge pneumatic caissons, into which compressed air was pumped so that men could work in the dry; but, more important, it was the first suspension bridge on which steel wire was used for the cables (cable). Every wire was galvanized (galvanizing) to safeguard against rust, and the four cables, each nearly 40 cm (16 inches) in diameter, took 26 months to spin back and forth over the East River. After many political and technical difficulties and at least 27 fatal accidents, the 479-metre- (1,595-foot-) span bridge was completed in 1883 to such fanfare that within 24 hours an estimated quarter-million people crossed over it, using a central elevated walkway that John Roebling had designed for the purpose of giving pedestrians a dramatic view of the city.

      By the turn of the 20th century, the increased need for passage from Manhattan to Brooklyn over the East River resulted in plans for two more long-span, wire-cable, steel suspension bridges, the Williamsburg and Manhattan bridges (Manhattan Bridge). The Williamsburg Bridge, designed by L.L. Buck with a span of just over 480 metres (1,600 feet), became the longest cable-suspension span in the world upon completion in 1903. Its deck truss is a bulky lattice structure with a depth of 12 metres (40 feet), and the towers are of steel rather than masonry. The truss in effect replaced Roebling's stays as stiffeners for the deck. The 1909 Manhattan Bridge has a span of 441 metres (1,470 feet). Its fixed steel towers spread laterally at the base, and a 7.4-metre- (24.5-foot-) deep truss is used for the deck. Of greater significance than the deck construction, however, was the first application of deflection theory, during the design of these two bridges, in calculating how the horizontal deck and curved cables worked together to carry loads. First published in 1888 by the Austrian academic Josef Melan, deflection theory explains how deck and cables deflect together under gravity loads, so that, as spans become longer and the suspended structure heavier, the required stiffness of the deck actually decreases. Deflection theory especially influenced design in the 1930s, as engineers attempted to reduce the ratio of girder depth to span length in order to achieve a lighter, more graceful, appearance without compromising safety. Up to 1930, no long-span suspension bridge had a ratio of girder depth to span length that was higher than 1:84.

      Ralph Modjeski (Modjeski, Ralph)'s Philadelphia-Camden Bridge (now called the Benjamin Franklin Bridge), over the Delaware River, is another wire-cable steel suspension bridge; when completed in 1926, it was the world's longest span at 525 metres (1,750 feet). However, it was soon exceeded by the Ambassador Bridge (1929) in Detroit and the George Washington Bridge (1931) in New York. The Ambassador links the United States and Canada over the Detroit River. Because of heavy traffic on the river, a wide clearance was necessary. The steel suspension bridge designed by Jonathan Jones has a span of 555 metres (1,850 feet) and a total length, including approach spans, of more than 2,700 metres (9,000 feet). The design of the Ambassador Bridge originally called for using heat-treated steel wires for the cables. Normally wires were cold-drawn, a method in which steel is drawn through successively smaller holes in dies, reducing its diameter yet raising its ultimate tensile strength. Extensive laboratory tests showed that heat-treated wires had a slightly higher ultimate strength, but during the construction of the Ambassador Bridge several of them broke, and, to the contractors' credit, all the cables spun thus far were immediately replaced with cold-drawn wire. The example illustrates the limitations of laboratory testing as opposed to studies of actual working conditions.

  The George Washington Bridge, a steel suspension bridge designed by Ammann (Ammann, Othmar Herman), was significant first for its span length of 1,050 metres (3,500 feet) and second for its theoretical innovations. After studying deflection theory, Ammann concluded that no stiffness was needed in the deck at all, as it would be stabilized by the great weight of the bridge itself. Indeed, the George Washington Bridge is the heaviest single-span suspension bridge built to date, and its original ratio of girder depth to span was an astonishing 1:350. Originally the 191-metre- (635-foot-) high towers were to have a masonry facade, but a shortage of money during the Great Depression precluded this, and the steel framework stands alone. Ammann designed the bridge to carry a maximum of 12,000 kg per metre (8,000 pounds per foot), even though the maximum conceivable load on the bridge was estimated at 69,000 kg per metre (46,000 pounds per foot), thus illustrating the principle that longer bridges need not be designed for maximum load. In 1962 the addition of a second deck for traffic resulted in the construction of a deck truss, giving the bridge its current ratio of girder depth to span of 1:120.

concrete bridges

Early bridges
      During the 19th century, low-cost production of iron and steel, when added to the invention of portland cement in 1824, led to the development of reinforced concrete. In 1867 a French gardener, Joseph Monier (Monier, Joseph), patented a method of strengthening thin concrete flowerpots by embedding iron wire mesh into the concrete. Monier later applied his ideas to patents for buildings and bridges. In 1879 another Frenchman, François Hennebique (Hennebique, François), set out to fireproof a metal-frame house in Belgium, and his decision to cover the iron beams with concrete led him to develop a structural system wherein the metal bars (replacing iron beams) carried tension and the concrete carried compression. By the end of the century reinforced concrete had become an economical substitute for stone, since it was generally cheaper to produce concrete than to quarry stones. In addition to its price and load-carrying advantages, reinforced concrete could be molded into a variety of shapes, allowing for much aesthetic expression on the part of the engineer without significantly increasing materials or cost.

      The most prolific designers first using reinforced concrete were Hennebique and the German engineer G.A. Wayss, who bought the Monier patents. Hennebique's Vienne River Bridge at Châtellerault, France, built in 1899, was the longest-spanning reinforced arch bridge of the 19th century. Built low to the river—typical of many reinforced-concrete bridges whose goal of safe passage across a small river is not affected by heavy boat traffic—the Châtellerault bridge has three arches, the centre spanning just over 48 metres (160 feet). In 1904 the Isar River Bridge at Grünewald, Germany, designed by Emil Morsch for Wayss's firm, became the longest reinforced-concrete span in the world at 69 metres (230 feet).

      The longest-spanning concrete arches of the 1920s were designed by the French engineer Eugène Freyssinet (Freyssinet, Eugène). In his bridge over the Seine (Seine River) at Saint-Pierre-du-Vauvray (1922), two thin, hollow arches rise 25 metres (82 feet) at mid-span and are connected by nine crossbeams. The arches curve over the deck, which is suspended by thin steel wires lightly coated with mortar and hanging down in a triangular formation. The 131-metre (435-foot) span, then a record for reinforced concrete, thus has a light appearance. The bridge was destroyed during World War II but was rebuilt in 1946 using the same form.

      In 1930 Freyssinet completed his most renowned work, the Plougastel Bridge over the Elorn Estuary near Brest, France. This bridge featured three 176-metre (585-foot) hollow-box arch spans, then the longest concrete spans in the world. Because of the great scale of this structure, Freyssinet studied the creep, or movement under stress, of concrete. This led him to his general idea for prestressing (see below Prestressed concrete (bridge)).

      In 1943 the Plougastel was eclipsed in length by the Sandö Bridge over the Ångerman River (Angerman River) in Sweden. The Sandö Bridge is a thin, single-ribbed, reinforced-concrete arch with a span of 260 metres (866 feet), rising 39 metres (131 feet) above the river.

Maillart's innovations
      Swiss engineer Robert Maillart (Maillart, Robert)'s use of reinforced concrete, beginning in 1901, effected a revolution in structural art. Maillart, all of whose main bridges are in Switzerland, was the first 20th-century designer to break completely with the masonry tradition and put concrete into forms technically appropriate to its properties yet visually surprising. For his 1901 bridge over the Inn River at Zuoz, he designed a curved arch and a flat roadway connected by longitudinal walls that turned the complete structure into a hollow-box girder with a span of 37.5 metres (125 feet) and with hinges at the abutments and the crown. This was the first concrete hollow-box to be constructed. The arch at Zuoz is thickened at the bottom, and all of the load to the abutments is carried at these thick points. The walls near the abutments, therefore, are technically superfluous. For his 1905 bridge over the Vorderrhein at Tavanasa, with a span of 50 metres (167 feet), Maillart cut out the spandrel walls to achieve a technically superior form that was also visually new. As at Zuoz, the concrete arches of the Tavanasa bridge were connected by hinges to both abutments and to each other at the crown, thus allowing the arch to rise freely without internal stress when the temperature rose and to drop when the temperature went down. By contrast, Hennebique's bridge at Châtellerault did not have hinges, and the arches cracked severely at the abutments and crown. The Tavanasa bridge was unfortunately destroyed by an avalanche in 1927.

      Maillart's Valtschielbach Bridge of 1926, a deck-stiffened arch with a 43-metre (142-foot) span, demonstrated that the arch can be extremely thin as long as the deck beam is stiff. The arch at Valtschielbach increases in thickness from a mere 23 cm (9 inches) at the crown to just over 28 cm (11 inches) at the supports. Thin vertical slabs, or cross-walls, connect the arch to the deck, allowing the deck to stiffen the arch and thus permitting the arch to be thin. Such technical insight revealed Maillart's deep understanding of how to work with reinforced concrete—an understanding that culminated in a series of masterpieces beginning with the 1930 Salginatobel Bridge, which, as with the others already mentioned, is located in the Swiss canton of Graubünden. The form of the Salginatobel Bridge is similar to the Tavanasa yet modified to account for a longer central span of 89 metres (295 feet), which is needed to cross the deep ravine below. Maillart's hollow-box, three-hinged arch design not only was the least costly of the 19 designs proposed but also was considered by the district engineer to be the most elegant. The stone abutments of earlier Maillart bridges were dispensed with at Salginatobel, as the rocky walls of the ravine that meet the arch are sufficient to carry the load.

      Other notable bridges by Maillart are the bridge over the Thur at Felsegg (1933), the Schwandbach Bridge near Hinterfultigen (1933), and the Töss River footbridge near Wulflingen (1934). The Felsegg bridge has a 68-metre (226-foot) span and features for the first time two parallel arches, both three-hinged. Like the Salginatobel Bridge, the Felsegg bridge features X-shaped abutment hinges of reinforced concrete (invented by Freyssinet), which were more economical than steel hinges. The Schwandbach Bridge, with a span of 37 metres (123 feet), is a deck-stiffened arch with a horizontally curved roadway. The true character of reinforced concrete is most apparent in this bridge, as the inner edge of the slab-arch follows the horizontal curve of the highway, while the outer edge of the arch is straight. Vertical trapezoidal cross-walls integrate the deck with the arch, and the result is one of the most acclaimed bridges in concrete. The Töss footbridge is a deck-stiffened arch with a span of 37.5 metres (125 feet). The deck is curved vertically at the crown and countercurved at the riverbanks, integrating the structure into the setting.

      Maillart's great contribution to bridge design was that, while he kept within the traditional discipline of engineering, always striving to use less material and keep costs down, he continually played with the forms in order to achieve maximum aesthetic expression. Some of his last bridges—at Vessy, Liesberg, and Lachen—illustrate his mature vision for the possibilities of structural art. Over the Arve River at Vessy in 1935, Maillart designed a three-hinged, hollow-box arch in which the thin cross-walls taper at mid-height, forming an X shape. This striking design, giving life to the structure, is both a natural form and a playful expression. Also in 1935, a beam bridge over the Birs River at Liesberg employed haunching of the beams, a tapering outward at the base of the thin columns, and a curved top edge becoming less deep near the abutments. For a skewed railway overpass at Lachen in 1940, Maillart used two separate three-hinged arches that sprang from different levels of the abutment, creating a dynamic interplay of shapes.

Eugène Freyssinet (Freyssinet, Eugène)
      The idea of prestressing concrete was first applied by Freyssinet in his effort to save the Le Veurdre Bridge over the Allier River near Vichy, France. A year after its completion in 1910, Freyssinet noted the three-arch bridge had been moving downward at an alarming rate. A flat concrete arch, under its own dead load, generates huge compressive forces that cause the structure to shorten over time and, hence, move eventually downward. This “creep” may eventually cause the arch to collapse. Freyssinet's solution was to jack apart the arch halves at the crown, lifting the arch and putting the concrete into additional compression against the abutments and then casting new concrete into the spaces at the crown. By 1928, experience with the Le Veurdre Bridge led Freyssinet to propose the more common method of prestressing, using high-strength steel to put concrete into compression.

      Freyssinet's major prestressed works came after the reinforced-concrete Plougastel Bridge and included a series of bridges over the Marne River following World War II. The Luzancy Bridge (1946), with a span of 54 metres (180 feet), demonstrates the lightness and beauty that can be achieved using prestressed concrete for a single-span beam bridge.

      The first major bridge made of prestressed concrete in the United States, the Walnut Lane Bridge (1950) in Philadelphia, was designed by Gustave Magnel and features three simply supported girder spans with a centre span of 48 metres (160 feet) and two end spans of 22 metres (74 feet). Although it was plain in appearance, a local art jury responsible for final approval found that the slim lines of the bridge were elegant enough not to require a stone facade.

Ulrich Finsterwalder
      During the years after World War II, a German engineer and builder, Ulrich Finsterwalder, developed the cantilever method of construction with prestressed concrete. Finsterwalder's Bendorf Bridge over the Rhine (Rhine River) at Koblenz, Germany, was completed in 1962 with thin piers and a centre span of 202 metres (673 feet). The double cantilevering method saved money through the absence of scaffolding in the water and also by allowing for reduced girder depth and consequent reduction of material where the ends of the deck meet in the centre. The resulting girder has the appearance of a very shallow arch, elegant in profile. Another fine bridge by Finsterwalder is the Mangfall Bridge (1959) south of Munich, a high bridge with a central span of 106 metres (354 feet) and two side spans of 89 metres (295 feet). The Mangfall Bridge features the first latticed truss walls made of prestressed concrete, and it also has a two-tier deck allowing pedestrians to walk below the roadway and take in a spectacular view of the valley. Finsterwalder successfully sought to show that prestressed concrete could compete directly with steel not only in cost but also in reduction of depth.

Christian Menn
      The technical and aesthetic possibilities of prestressed concrete were most fully realized in Switzerland with the bridges of Christian Menn. Menn's early arch bridges were influenced by Maillart, but, with prestressing, he was able to build longer-spanning bridges and use new forms. The Reichenau Bridge (1964) over the Rhine, a deck-stiffened arch with a span of 98 metres (328 feet), shows Menn's characteristic use of a wide, prestressed concrete deck slab cantilevering laterally from both sides of a single box. For the high, curving Felsenau Viaduct (1974) over the Aare River in Bern, spans of up to 154 metres (512 feet) were built using the cantilever method from double piers. The trapezoidal box girder, only 11 metres (36 feet) wide at the top, haunches at the supports and carries an 26-metre- (85-foot-) wide turnpike. More impressive yet is the high, curving Ganter Bridge (1980), crossing a deep valley in the canton of Valais. The Ganter is both a cable-stayed and a prestressed cantilever girder bridge, with the highest column rising 148 metres (492 feet) and with a central span of 171 metres (571 feet). The form is unique: the cable-stays are flat and covered by thin concrete slabs, making the bridge look very much like a Maillart bridge upside-down.

steel bridges after 1931
Long-span suspension bridges (suspension bridge)
 The success of the George Washington Bridge—especially its extremely small ratio of girder depth to span—had a great influence on suspension bridge design in the 1930s. Its revolutionary design led to the building of several major bridges, such as the Golden Gate (Golden Gate Bridge) (1937), the Deer Isle (1939), and the Bronx-Whitestone (1939). The Golden Gate Bridge, built over the entrance to San Francisco Bay under the direction of Joseph Strauss (Strauss, Joseph B), was upon its completion the world's longest span at 1,260 metres (4,200 feet); its towers rise 224 metres (746 feet) above the water. Deer Isle Bridge in Maine, U.S., was designed by David Steinman (Steinman, David Barnard) with only plate girders to stiffen the deck, which was 7.5 metres (25 feet) wide yet had a central span of 324 metres (1,080 feet). Likewise, the deck for Othmar Ammann (Ammann, Othmar Herman)'s Bronx-Whitestone Bridge in New York was originally stiffened only by plate girders; its span reached 690 metres (2,300 feet). Both the Deer Isle and the Bronx-Whitestone bridges later oscillated in wind and had to be modified following the Tacoma Narrows disaster.

Tacoma Narrows
  In 1940 the first Tacoma Narrows Bridge opened over Puget Sound in Washington state, U.S. Spanning 840 metres (2,800 feet), its deck, also stiffened by plate girders, had a depth of only 2.4 metres (8 feet). This gave it a ratio of girder depth to span of 1:350, identical to that of the George Washington Bridge. Unfortunately, at Tacoma Narrows, just four months after the bridge's completion, the deck tore apart and collapsed under a moderate wind. At that time bridges normally were designed to withstand gales of 190 km (120 miles) per hour, yet the wind at Tacoma was only 67 km (42 miles) per hour. Motion pictures taken of the disaster show the deck rolling up and down and twisting wildly. These two motions (resonance), vertical and torsional, occurred because the deck had been provided with little vertical and almost no torsional stiffness. Engineers had overlooked the wind-induced failures of bridges in the 19th century and had designed extremely thin decks without fully understanding their aerodynamic behaviour. After the Tacoma bridge failed, however, engineers added trusses to the Bronx-Whitestone bridge, cable-stays to Deer Isle, and further bracing to the stiffening truss at Golden Gate. In turn, the diagonal stays used to strengthen the Deer Isle Bridge led engineer Norman Sollenberger to design the San Marcos Bridge (1951) in El Salvador with inclined suspenders, thus forming a cable truss between cables and deck—the first of its kind.

Lessons of the disaster
  The disaster at Tacoma caused engineers to rethink their concepts of the vertical motion of suspension bridge decks under horizontal wind loads. Part of the problem at Tacoma was the construction of a plate girder with solid steel plates, 2.4 metres (8 feet) deep on each side, through which the wind could not pass. For this reason, the new Tacoma Narrows Bridge (1950), as well as Ammann's 1,280-metre- (4,260-foot-) span Verrazano Narrows Bridge (Verrazano-Narrows Bridge) in New York (1964), were built with open trusses for the deck in order to allow wind passage. The 1,140-metre- (3,800-foot-) span Mackinac Bridge in Michigan, U.S., designed by Steinman, also used a deep truss; its two side spans of 540 metres (1,800 feet) made it the longest continuous suspended structure in the world at the time of its completion in 1957.

      The 972-metre- (3,240-foot-) span Severn Bridge (1966), linking southern England and Wales over the River Severn (Severn, River), uses a shallow steel box for its deck, but the deck is shaped aerodynamically in order to allow wind to pass over and under it—much as a cutwater allows water to deflect around piers with a greatly reduced force. Another innovation of the Severn Bridge was the use of steel suspenders from cables to deck that form a series of Vs in profile. When a bridge starts to oscillate in heavy wind, it tends to move longitudinally as well as up and down, and the inclined suspenders of the Severn Bridge act to dampen the longitudinal movement. The design ideas used on the Severn Bridge were repeated on the Bosporus Bridge (1973) at Istanbul and on the Humber Bridge (1981) over the River Humber (Humber, River) in England. The Humber Bridge in its turn became the longest-spanning bridge in the world, with a main span of 1,388 metres (4,626 feet).

Truss bridges
      Although trusses are used mostly as secondary elements in arch, suspension, or cantilever designs, several important simply supported truss bridges have achieved significant length. The Astoria Bridge (1966) over the Columbia River in Oregon, U.S., is a continuous three-span steel truss with a centre span of 370 metres (1,232 feet), and the Tenmon Bridge (1966) at Kumamoto, Japan, has a centre span of 295 metres (984 feet).

      In 1977 the New River Gorge Bridge, the world's longest-spanning steel arch, was completed in Fayette county, West Virginia, U.S. Designed by Michael Baker, the two-hinged arch truss carries four lanes of traffic 263 metres (876 feet) above the river and has a span of 510 metres (1,700 feet).

Cable-stayed bridges
German designs (Germany)
      Beginning in the 1950s, with the growing acceptance of cable-stayed bridges, there came into being a type of structure that could not easily be classified by construction material. Cable-stayed bridges offered a variety of possibilities to the designer regarding not only the materials for deck and cables (cable) but also the geometric arrangement of the cables. Early examples, such as the Strömsund Bridge in Sweden (1956), used just two cables fastened at nearly the same point high on the tower and fanning out to support the deck at widely separated points. By contrast, the Oberkasseler Bridge, built over the Rhine River in Düsseldorf, Germany, in 1973, used a single tower in the middle of its twin 254-metre (846-foot) spans; the four cables were placed in a harp or parallel arrangement, being equally spaced both up the tower and along the centre line of the deck. The Bonn-Nord Bridge in Bonn, Germany (1966), was the first major cable-stayed bridge to use a large number of thinner cables instead of relatively few but heavier ones—the technical advantage being that, with more cables, a thinner deck might be used. Such multicable arrangements subsequently became quite common. The box girder deck of the Bonn-Nord, as with most cable-stayed bridges built during the 1950s and '60s, was made of steel. From the 1970s, however, concrete decks were used more frequently.

U.S. designs (United States)
      Cable-stayed bridges in the United States reflected trends in both cable arrangement and deck material. The Pasco-Kennewick Bridge (1978) over the Columbia River in Washington state supported its centre span of 294 metres (981 feet) from two double concrete towers, the cables fanning down to the concrete deck on either side of the roadway. Designed by Arvid Grant in collaboration with the German firm of Leonhardt and Andra, its cost was not significantly different from those of other proposals with more conventional designs. The same designers produced the East End Bridge across the Ohio River between Proctorville, Ohio, and Huntington, West Virginia, in 1985. The East End has a major span of 270 metres (900 feet) and a minor span of 182 metres (608 feet). The single concrete tower is shaped like a long triangle in the traverse direction, and the cable arrangement is of the fan type; but, while the Pasco-Kennewick Bridge has two parallel sets of cables, the East End has but one set, fanning out from a single plane at the tower into two planes at the composite steel and concrete deck, so that, as one moves from pure profile to a longitudinal view, the cables do not align visually.

 The Sunshine Skyway Bridge (1987), designed by Eugene Figg and Jean Mueller over Tampa Bay in Florida, has a main prestressed-concrete span of 360 metres (1,200 feet). It, too, employs a single plane of cables, but these remain in one plane that fans out down the centre of the deck. The longest cable-stayed bridge in the United States is Dames Point Bridge (1987), designed by Howard Needles in consultation with Ulrich Finsterwalder and crossing the St. Johns River in Jacksonville, Florida. The main span at Dames Point is 390 metres (1,300 feet), with side spans of 200 metres (660 feet). From H-shaped towers (tower) of reinforced concrete, two planes of stays in harp formation support reinforced-concrete girders. The towers are carefully shaped to avoid a stiff appearance.

Japanese (Japan) long-span bridges
      In the 1970s the Japanese, working primarily with steel, began to build a series of long-span bridges using several forms that by the year 2000 included many of the world's longest spans.

Ōsaka Harbour
      In 1974 the Minato Bridge, linking the city of Ōsaka with neighbouring Amagasaki, became one of the world's longest-spanning cantilever truss bridges, at 502 metres (1,673 feet). In 1989 two other impressive and innovative bridges were completed for the purpose of carrying major highways over the port facilities of Ōsaka Harbour. The Konohana suspension bridge carries a four-lane highway on a slender, steel box-beam deck only 3 metres (10 feet) deep. The bridge is self-anchored—that is, the deck has been put into horizontal compression, like that on a cable-stayed bridge, so that there is no force of horizontal tension pulling from the ground at the anchorages. Spanning 295 metres (984 feet), it is the first major suspension bridge to use a single cable. The towers are delta-shaped, with diagonal suspenders running from the cable down the centre of the deck. On the same road as the Konohana is the Ajigawa cable-stayed bridge, with a span of 344 metres (1,148 feet) and an elegantly thin deck just over three metres deep.

Island bridges
      The Kanmon Bridge (1975), linking the islands of Honshu and Kyushu over the Shimonoseki Strait, was the first major island bridge in Japan. At about this time the Honshu-Shikoku Bridge Authority was formed to connect these two main islands with three lines of bridges and highways. Completed in 1999, the Honshu-Shikoku project was the largest in history, building 6 of the 20 largest spanning bridges in the world as well as the first major set of suspension bridges to carry railroad traffic since John Roebling's Niagara Bridge. The Authority conducted most of the design work itself; unlike projects in other countries, it is not usually possible to identify individual designers for Japanese bridges.

 The first part of the project, completed in 1988, is a route connecting the city of Kojima, on the main island of Honshu, to Sakaide, on the island of Shikoku. The Kojima-Sakaide route has three major bridge elements, often referred to collectively as the Seto Ōhashi (Seto Great Bridge) (“Seto Great Bridge”): the Shimotsui suspension bridge, with a suspended main span of 940 metres (3,100 feet) and two unsuspended side spans of 230 metres (760 feet); the twin 420-metre- (1,380-foot-) span cable-stayed Hitsuishijima and Iwakurojima bridges; and the two nearly identical Bisan-Seto suspension bridges, with main spans of 990 metres (3,250 feet) and 1,100 metres (3,610 feet). The striking towers of the cable-stayed Hitsuishijima and Iwakurojima bridges were designed to evoke symbolic images from Japanese culture, such as the ancient Japanese helmet. The side spans of the two Seto bridges, being fully suspended, give a visual unity to these bridges that is missing from the Shimotsui bridge, where the side spans are supported from below. The double deck of the entire bridge system is a strong 13-metre- (43-foot-) deep continuous truss that carries cars and trucks on the top deck and trains on the lower deck.

      The Kojima-Sakaide route forms the middle of the three Honshu-Shikoku links. The eastern route, between Kōbe (Honshu) and Naruto (Shikoku), has only two bridges: the 1985 Ohnaruto suspension bridge and the 1998 Akashi Kaikyō (Akashi Strait) suspension bridge. The Akashi Kaikyō Bridge, now the world's longest suspension bridge, crosses the strait with a main span of 1,991 metres (6,530 feet) and side spans of 960 metres (3,150 feet). Its two 297-metre (975-foot) towers, made of two hollow steel shafts in cruciform section connected by X-bracing, are the tallest bridge towers in the world. The two suspension cables are made of a high-strength steel developed by Japanese engineers for the project. In January 1995 an earthquake that devastated Kōbe had its epicentre almost directly beneath the nearly completed Akashi Kaikyō structure; the bridge survived undamaged, though one tower shifted enough to lengthen the main span by almost one metre.

      The western Honshu-Shikoku route links Onomichi (Honshu) with Imabari (Shikoku). One of the major structures is the Ikuchi cable-stayed bridge, with a main span of 490 metres (1,610 feet). The two towers of the Ikuchi Bridge are delta-shaped, with two inclined planes of fan-arranged stays. Also on the Onomichi-Imabari route is the 1979 Ohmishima steel arch bridge, whose 297-metre (975-foot) span made it the longest such structure in the Eastern Hemisphere. But the single most significant structure on the route is the 1999 Tatara cable-stayed bridge, whose main span of 890 metres (2,920 feet) makes it the longest of its type in the world—34 metres (112 feet) longer than the 1995 Normandy Bridge in France. The twin towers of the Tatara Bridge, 220 metres (720 feet) high, have elegant diamond shapes for the lower 140 metres; the upper 80 metres consist of two parallel linked shafts that contain the cables.

David P. Billington Philip N. Billington

Additional Reading
David P. Billington, The Tower and the Bridge: The New Art of Structural Engineering (1983), traces the history of structures since the Industrial Revolution and emphasizes a series of individual engineers who were structural artists. David J. Brown, Bridges (1993), chronicles bridge building from its beginnings to future projects, with discussions of the world's most important bridges, some of which were failures. Eric DeLony (ed.), Landmark American Bridges (1993), contains elegantly illustrated presentations of large and small bridges built in the United States from the late 18th century to the post-World War II era, with a time line encapsulating the history of bridges from 1570 to the present. C.M. Woodward, A History of the St. Louis Bridge (1881), on the Eads Bridge, is still the most complete work ever published on one bridge, a classic work for both the nontechnical reader and the engineer. David McCullough, The Great Bridge (1972, reissued 1982), narrates the political and human history of the building of the Brooklyn Bridge. David P. Billington, Robert Maillart's Bridges (1979), gives substantial details of the major works of this bridge designer and builder.Fritz Leonhardt, Bridges: Aesthetics and Design (1984), provides a substantial general discussion and includes a wide selection of striking photographs of old and new bridges. A finely illustrated nontechnical text by Hans Wittfoht, Building Bridges (1984), centers on both the design and the construction of bridges. M.S. Troitsky, Planning and Design of Bridges (1994), focuses on the selection of bridge type and preliminary design. Walter Podolny, Jr., and John B. Scalzi, Construction and Design of Cable-Stayed Bridges, 2nd ed. (1986), treats the modern bridge form and provides substantial technical detail, although the nontechnical reader will understand much of the text. Christian Menn, Prestressed Concrete Bridges, trans. and ed. by Paul Gauvreau (1990; originally published in German, 1986), a technical work primarily for engineers, provides historical coverage and deals elegantly with the many complex issues in bridge design. Louis G. Silano (ed.), Bridge Inspection and Rehabilitation (1993), is a compendium of practical information.Early works on bridge design and construction still widely available include Henry Grattan Tyrrell, History of Bridge Engineering (1911), a fine, nontechnical sweep through history from ancient bridges to early reinforced concrete arches; Wilbur J. Watson, Bridge Architecture (1927), exploring the collaboration between engineers and architects and focusing on early 20th-century designs, and A Decade of Bridges, 1926–1936 (1937), with a narrower scope; Charles S. Whitney, Bridges: A Study in Their Art, Science, and Evolution (1929, reprinted as Bridges: Their Art, Science, and Evolution, 1983), a nontechnical work; and Elizabeth B. Mock (Elizabeth B. Kassler), The Architecture of Bridges (1949), the first major book on bridges to give a modern viewpoint.David P. Billington

      in stringed musical instruments, piece of elastic wood that transmits the vibrations of the string to the resonating body. Bridges are of two kinds. In the pressure bridge, the string is fastened at one end to a tuning peg or a wrest pin and at the other to a pin or a tailpiece; it passes over the bridge (or bridges), which may be glued to the soundboard (as in the piano) or held in position solely by the pressure of the strings (as in the violin). In the tension bridge, one end of the string is fastened to a tuning peg or wrest pin and the other to the bridge itself, which is glued to the soundboard (as in the guitar and the lute).

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Universalium. 2010.


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