Bridge Truss

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Contents 1 Design 2 Roadbed types 3 Truss types used in bridges 3.1 Allan truss 3.2 Bailey bridge 3.3 Baltimore truss 3.4 Bollman truss 3.5 Bowstring arch truss (Tied arch bridge) 3.6 Brown truss 3.7 Brunel Truss 3.8 Burr Arch Truss 3.9 Cantilevered truss 3.10 Fink truss 3.11 Howe truss 3.12 K truss 3.13 Kingpost truss 3.14 Lattice truss (Town's lattice truss) 3.15 Lenticular truss 3.16 Long truss 3.17 Parker (Camelback) truss 3.18 Pegram truss 3.19 Pennsylvania (Petit) truss 3.20 Post truss 3.21 Pratt truss 3.22 Queenpost truss 3.23 Truss arch 3.24 Waddell truss 3.25 Warren (non-polar) truss 3.26 Whipple Pratt truss 3.27 Vierendeel truss 4 Statics of trusses 5 Analysis of trusses 6.1 Design of members

Transcript of Bridge Truss

Page 1: Bridge Truss

Contents

1 Design2 Roadbed types3 Truss types used in bridges

3.1 Allan truss3.2 Bailey bridge3.3 Baltimore truss3.4 Bollman truss3.5 Bowstring arch truss (Tied arch bridge)3.6 Brown truss3.7 Brunel Truss3.8 Burr Arch Truss3.9 Cantilevered truss3.10 Fink truss3.11 Howe truss3.12 K truss3.13 Kingpost truss3.14 Lattice truss (Town's lattice truss)3.15 Lenticular truss3.16 Long truss3.17 Parker (Camelback) truss3.18 Pegram truss3.19 Pennsylvania (Petit) truss3.20 Post truss3.21 Pratt truss3.22 Queenpost truss3.23 Truss arch3.24 Waddell truss3.25 Warren (non-polar) truss3.26 Whipple Pratt truss3.27 Vierendeel truss

4 Statics of trusses5 Analysis of trusses6.1 Design of members6.2 Design of joints7. Force acting on truss bridges

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8. Reference

A truss bridge is a bridge composed of connected elements (typically straight) which may be stressed from tension,compression, or sometimes both in response to dynamic loads. Truss bridges are one of the oldest types of modern bridges. The basic types of truss bridges shown here have simple designs which could be easily analyzed by nineteenth and early twentieth century engineers. A truss bridge is economical to construct owing to its efficient use of materials.

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Design of Truss Bridges

A truss is constructed of a simple supporting lattice-work of triangles that support the beam or the span by adding rigidity. It increases the beam's ability to dissipate the compression and tension forces. The members of a truss are the chords or horizontals, verticals and diagonals, which will only act in compression or tension. Piles or pilings are the vertical members of a truss bridge. They are long columns of wood or steel driven into the ground to support vertical loads. The members are pinned together at the nodes where the straight members meet. This allows for some movement of the members without snapping.

Roadbed typesThe truss may carry its roadbed on top, in the middle, or at the bottom of the truss. Bridges with the roadbed at the top or the bottom are the most common as this allows both the top and bottom to be stiffened, forming a box truss. When the roadbed is atop the truss it is called a deck truss (an example of this was the I-35W Mississippi River bridge), when the truss members are both above and below the roadbed, it is called a through truss (an example of this application is the Pulaski Skyway), and where the sides extend above the roadbed but are not connected, a pony truss or half-through truss.Sometimes both the upper and lower chords support roadbeds, forming a double-decked truss. This can be used to separate rail from road traffic or to separate the two directions of automobile traffic and so avoiding the likelihood of head-on collisions.

Deck truss railroad bridge The four span through Pony truss bridge of reinforced concrete

Sky Gate Bridge R at Kansai International

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over the Erie Canal in Lockport, New York

trussGeneral Hertzog Bridge over theOrange River at Aliwal Northcarries vehicular traffic.

Airport, Osaka,Japan, is the longest double-decked truss bridge in the world. It carries three lanes of automobile traffic on top and two of rail below over nine truss spans.

Truss types used in bridgesBridges are many times the best visible examples of truss use to the common person. There are many types of designs, many dating back hundreds of years. Below are some of the more common types and designs.

Allan truss

Allan Truss illustrated

Hampden Bridge showing the Allan truss designThe Allan Truss, designed by Percy Allan, is partly based on the Howe truss. TheHampden Bridge in Wagga Wagga, New South Wales, Australia, the first of the Allan truss bridges, was originally designed as a steel bridge. It was constructed with timber to reduce cost. In his design, Allan used Australian ironbark for its strength.[2] A similar bridge also designed by Percy Allen is the Victoria Bridge on Prince Street Picton, New South Wales. Also constructed of ironbark, the bridge is still in use today for pedestrian and light traffic.[citation needed]

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Bailey bridge

Bailey bridge over the Meurthe River, France.Designed for military use, the prefabricated and standardized truss elements may be easily combined in various configurations to adapt to the needs at the site. In the image at right, note the use of doubled prefabrications to adapt to the span and load requirements. In other applications the trusses may be stacked vertically.

Baltimore trussThe Baltimore truss is a subclass of the Pratt truss. A Baltimore truss has additional bracing in the lower section of the truss to prevent buckling in the compression members and to control deflection. It is mainly used for train bridges, boasting a simple and very strong design.

Bollman truss

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Bollman truss in Savage, Maryland. Built in 1869, moved to Savage in 1887. It is still in use today as a pedestrian bridge.

39°8 5.42″N′ 76°49 30.33″W′

The Bollman Truss Railroad Bridge at Savage, Maryland is the only surviving example of a revolutionary design in the history of American bridge engineering. The type was named for its inventor, Wendel Bollman, a self-educated Baltimore engineer. It was the first successful all-metal bridge design (patented in 1852) to be adopted and consistently used on a railroad. The design employswrought iron tension members and cast iron compression members. The use of multiple independent tension elements reduces the likelihood of catastrophic failure. The structure was also easy to assemble.The Wells Creek Bollman Bridge is the only other bridge designed by Wendel Bollman still in existence, but it is a Warren truss configuration.

Bowstring arch truss (Tied arch bridge)

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A tied arch bridge, in Pittsburgh, Pennsylvania. Note the stone pier in the background from the Wabash Bridge.The bowstring arch through truss bridge was patented in 1840 by Squire Whipple.[3] Thrust arches transform their vertical loads into a thrust along the arc of the arch. At the ends of the arch this thrust (at a downward angle away from the center of the bridge) may be resolved into two components, a vertical thrust equal to a proportion of the weight and load of the bridge section, and a horizontal thrust. In a typical arch this horizontal thrust is taken into the ground, while in a bowstring arch the thrust is taken horizontally by a chord member to the opposite side of the arch. This allows the footings to take only vertical forces, useful for bridge sections resting upon high pylons.

Brown truss

Brown truss illustrated. All interior vertical elements are under tension.This type of truss is particularly suited for timber structures that use iron rods as tension members.

Burr Arch Truss

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A covered bridge with a Burr Arch Truss structureThis combines an arch with a truss to form a structure both strong and rigid.

Cantilevered truss

Forth rail bridgeMost trusses have the lower chord under tension and the upper chord under compression. In a cantilever truss the situation is reversed, at least over a portion of the span. The typical cantilever truss bridge is a balanced cantilever, which enables the construction to proceed outward from a central vertical spar in each direction. Usually these are built in pairs until the outer sections may be anchored to footings. A central gap, if present, can then be filled by lifting a conventional truss into place or by building it in place using a traveling support.

Fink truss

Fink Truss (half span and cross section)The Fink truss was designed by Albert Fink of Germany in the 1860s. This type of bridge was popular with the Baltimore and Ohio Railroad. The Appomattox High Bridge on the Norfolk and Western Railroad included 21 Fink deck truss spans from 1869 until their replacement in 1886.

Howe truss

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Jay Bridge showing the truss designThe relatively rare Howe truss, patented in 1840 by Massachusetts millwright William Howe, includes vertical members and diagonals that slope up towards the center, the opposite of the Pratt truss.[4] In contrast to the Pratt Truss, the diagonal web members are in compression and the vertical web members are in tension. Examples include Jay Bridge in Jay, New York, andSandy Creek Covered Bridge in Jefferson County, Missouri.

A large timber Howe truss in a commercial building

Howe truss illustrated - the diagonals are under compression under balanced loading King Post Truss

K trussA truss in the form of a K due to the orientation of the vertical member and two oblique members in each panel.

Kingpost trussOne of the simplest truss styles to implement, the king post consists of two angled supports leaning into a common vertical support.

Lattice truss (Town's lattice truss)

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Plank lattice truss of a covered bridgeThis type of bridge uses a substantial number of lightweight elements, easing the task of construction. Truss elements are usually of wood, iron, or steel.

Lenticular truss

Royal Albert Bridge under construction, 1859A lenticular truss bridge includes a lens-shape truss, with trusses between an upper arch that curves up and then down to end points, and a lower arch that curves down and then up to meet at the same end points. Where the arches extend above and below the roadbed, it is a lenticular pony truss bridge.One type of Lenticular truss consists of arcuate upper compression chords and lower eyebar chain tension links. The Royal Albert Bridge (United Kingdom) uses a single tubular upper chord. As the horizontal tension and compression forces are balanced these horizontal forces are not transferred to the supporting pylons (as is the case with most arch types). This in turn enables the truss to be fabricated on the ground and then to be raised by jacking as supporting masonry pylons are constructed. This truss has been used in the construction of a stadium[5], with the upper chords of parallel trusses supporting a roof that may be rolled back. TheSmithfield Street Bridge in Pittsburgh, Pennsylvania is another example of this type.An example of a lenticular pony truss bridge that uses regular spans of iron is the Turn-of-River Bridge designed and manufactured by the Berlin Iron Bridge Co..

Long truss

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HAER diagram of a Long TrussDesigned by Stephen H. Long in 1830; one surviving example is the Old Blenheim Bridge. The design resembles aHowe truss, but is entirely made of wood instead of a combination of wood and metal.[6]

Parker (Camelback) trussA Parker truss bridge is a Pratt truss design with a polygonal upper chord. A "camelback" is a subset of the Parker type, where the upper chord consists of exactly five segments. An example of a Parker truss is the Traffic Bridge in Saskatoon, Canada.

Pegram truss

Pegram TrussThe Pegram truss is a hybrid between the Warren and Parker trusses where the upper chords are all of equal length and the lower chords are longer than the corresponding upper chord. Because of the difference in upper and lower chord length, each panel was not square. The members which would be vertical in a Parker truss vary from near vertical in the center of the span to diagonal near each end (like a Warren truss). George H. Pegram, while the chief engineer of Edge Moor Iron Company in Wilmington, Delaware, patented this truss design in 1885.[7]

The Pegram truss consists of a Parker type design with the vertical posts leaning towards the center at an angle between 60 and 75°. The variable post angle and constant chord length allowed steel in existing bridges to be recycled into a new span using the Pegram truss design. This design also facilitated reassembly and permitted a bridge to be adjusted to fit different span lengths. There are ten remaining Pegram span bridges in the United States with seven in Idaho.

Pennsylvania (Petit) truss

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The Pennsylvania (Petit) truss is a variation on the Pratt truss.[8] An example of this truss type is the Schell Bridge in Northfield, Massachusetts.

Post truss

A Post trussA Post truss is a hybrid between a Warren truss and a double-intersection Pratt truss. Invented in 1863 by Simeon S. Post, it is occasionally referred to as a Post patent truss although he never received a patent for it.[9] The Ponakin Bridge and the Bell Ford Bridge are two examples of this truss.

Pratt trussA Pratt truss includes vertical members and diagonals that slope down towards the center, the opposite of the Howe truss.[4] It can be subdivided, creating Y- and K-shaped patterns. The Pratt Truss was invented in 1844 by Thomas and Caleb Pratt. This truss is practical for use with spans up to 250 feet and was a common configuration for railroad bridges as truss bridges moved from wood to metal. They are statically determinate bridges, which lends themselves well to long spans.

Pratt truss illustrated - the interior diagonals are under tension under balanced loading and vertical elements under compression. If pure tension elements are used in the diagonals (such as eyebars) then crossing elements may be needed near the center to accept concentrated live loads as they traverse the span.

Queenpost truss

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Queen Post TrussThe queenpost truss, sometimes queen post or queenspost, is similar to a king post truss in that the outer supports are angled towards the center of the structure. The primary difference is the horizontal extension at the center which relies on beam action to provide mechanical stability. This truss style is only suitable for relatively short spans.[10]

Truss arch

A truss arch may contain all horizontal forces within the arch itself, or alternatively may be either a thrust arch consisting of a truss, or of two arcuate sections pinned at the apex. The latter form is common when the bridge is constructed as cantilever segments from each side as in the Navajo Bridge.

Waddell truss

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Waddell "A" truss (1898 bridge)Patented 1894 (U.S. Patent 529,220) its simplicity eases erection at the site. It was intended to be used as a railroad bridge.

Warren (non-polar) truss

Warren truss illustrated – some of the diagonals are under compression and some under tensionThe Warren truss was patented in 1848 by its designers James Warren and Willoughby Theobald Monzani, and consists of longitudinal members joined only by angled cross-members, forming alternately inverted equilateral triangle-shaped spaces along its length, ensuring that no individual strut, beam, or tie is subject to bending or torsional straining forces, but only to tension or compression. Loads on the diagonals alternate between compression and tension (approaching the center), with no vertical elements, while elements near the center must support both tension and compression in response to live loads. This configuration combines strength with economy of materials and can therefore be relatively light. It is an improvement over the Neville truss which uses a spacing configuration of isosceles triangles.

Whipple Pratt truss

Bridge L-158A whipple truss is usually considered a subclass of the Pratt truss because the diagonal members are designed to work in tension. The main characteristic of a whipple truss is that the tension members are elongated, usually thin, at a shallow angle and cross two or more bays (rectangular sections defined by the vertical members).An example of a Pratt Truss bridge is the Fair Oaks Bridge in Fair Oaks, California

Vierendeel truss

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A Vierendeel bridgeThe Vierendeel truss, unlike common pin-jointed trusses, imposes significant bending forces upon its members — but this in turn allows the elimination of many diagonal elements. While rare as a bridge type this truss is commonly employed in modern building construction as it allows the resolution of gross shear forces against the frame elements while retaining rectangular openings between columns. This is advantageous both in allowing flexibility in the use of the building space and freedom in selection of the building's outer curtain wall, which affects both interior and exterior styling aspects

Statics of trusses

A truss that is assumed to comprise members that are connected by means of pin joints, and which is supported at both ends by means of hinged joints or rollers, is described as being statically determinate. Newton's Laws apply to the structure as a whole, as well as to each node or joint. In order for any node that may be subject to an external load or force to remain static in space, the following conditions must hold: the sums of all (horizontal and vertical) forces, as well as all moments acting about the node equal zero. Analysis of these conditions at each node yields the magnitude of the forces in each member of the truss. These may be compression or tension forces.Trusses that are supported at more than two positions are said to be statically indeterminate, and the application of Newton's Laws alone is not sufficient to determine the member forces.In order for a truss with pin-connected members to be stable, it must be entirely composed of triangles. In mathematical terms, we have the following necessary condition forstability:

where m is the total number of truss members, j is the total number of joints and r is the number of reactions (equal to 3 generally) in a 2-dimensional structure.When m = 2j − 3, the truss is said to be statically determinate, because the (m+3) internal member forces and support reactions can then be completely determined by 2jequilibrium equations, once we know the external loads and the geometry of the truss. Given a certain number of joints, this is the minimum number of members, in the sense that if any member is taken out (or fails), then the truss as a whole fails. While the relation (a) is necessary, it is not sufficient for stability, which also depends on the truss geometry, support conditions and the load carrying capacity of the members.

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Some structures are built with more than this minimum number of truss members. Those structures may survive even when some of the members fail. Their member forces depend on the relative stiffness of the members, in addition to the equilibrium condition described.

Analysis of trusses

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Cremona diagram for a plane truss

Because the forces in each of its two main girders are essentially planar, a truss is usually modelled as a two-dimensional plane frame. If there are significant out-of-plane forces, the structure must be modelled as a three-dimensional space.The analysis of trusses often assumes that loads are applied to joints only and not at intermediate points along the members. The weight of the members is often insignificant compared to the applied loads and so is often omitted. If required, half of the weight of each member may be applied to its two end joints. Provided the members are long and slender, the moments transmitted through the joints are negligible and they can be treated as "hinges" or 'pin-joints'. Every member of the truss is then in pure compression or pure tension – shear, bending moment, and other more complex stresses are all practically zero. This makes trusses easier to analyze. This also makes trusses physically stronger than other ways of arranging material – because nearly every material can hold a much larger load in tension and compression than in shear, bending, torsion, or other kinds of force.Structural analysis of trusses of any type can readily be carried out using a matrix method such as the direct stiffness method, theflexibility method or the finite element method.

Forces in members

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On the right is a simple, statically determinate flat truss with 9 joints and (2 x 9) − 3 = 15 members. External loads are concentrated in the outer joints. Since this is a symmetrical truss with symmetrical vertical loads, it is clear to see that the reactions at A and B are equal, vertical and half the total load.The internal forces in the members of the truss can be calculated in a variety of ways including the graphical methods:Cremona diagramCulmann diagramthe analytical Ritter method (method of sections).

Design of members

A truss can be thought of as a beam where the web consists of a series of separate members instead of a continuous plate. In the truss, the lower horizontal member (thebottom chord) and the upper horizontal member (the top chord) carry tension and compression, fulfilling the same function as the flanges of an I-beam. Which chord carries tension and which carries compression depends on the overall direction of bending. In the truss pictured above right, the bottom chord is in tension, and the top chord in compression.The diagonal and vertical members form the truss web, and carry the shear force. Individually, they are also in tension and compression, the exact arrangement of forces is depending on the type of truss and again on the direction of bending. In the truss shown above right, the vertical members are in tension, and the diagonals are in compression.

A building under construction in Shanghai. The truss sections stabilize the building and will house mechanical floors.In addition to carrying the static forces, the members serve additional functions of stabilizing each other, preventing buckling. In the picture to the right, the top chord is prevented from buckling by the presence of bracing and by the stiffness of the web members.

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The inclusion of the elements shown is largely an engineering decision based upon economics, being a balance between the costs of raw materials, off-site fabrication, component transportation, on-site erection, the availability of machinery and the cost of labor. In other cases the appearance of the structure may take on greater importance and so influence the design decisions beyond mere matters of economics. Modern materials such as prestressed concrete and fabrication methods, such as automated welding, have significantly influenced the design of modern bridges.Once the force on each member is known, the next step is to determine the cross section of the individual truss members. For members under tension the cross-sectional area A can be found using A = F × γ / σy, where F is the force in the member, γ is a safety factor (typically 1.5 but depending on building codes) and σy is the yield tensile strength of the steel used.The members under compression also have to be designed to be safe against buckling.The weight of a truss member depends directly on its cross section—that weight partially determines how strong the other members of the truss need to be. Giving one member a larger cross section than on a previous iteration requires giving other members a larger cross section as well, to hold the greater weight of the first member—one needs to go through another iteration to find exactly how much greater the other members need to be. Sometimes the designer goes through several iterations of the design process to converge on the "right" cross section for each member. On the other hand, reducing the size of one member from the previous iteration merely makes the other members have a larger (and more expensive) safety factor than is technically necessary, but doesn't require another iteration to find a buildable truss.The effect of the weight of the individual truss members in a large truss, such as a bridge, is usually insignificant compared to the force of the external loads.

Design of joints

After determining the minimum cross section of the members, the last step in the design of a truss would be detailing of the bolted joints, e.g., involving shear of the bolt connections used in the joints, see also shear stress.

Forces Acting on Truss Bridges

There are two major forces that act on bridges: compression and tension. The compression force bears down on an object to shorten or compress it, while tension is the directly opposing force that lengthens and stretches the object. A spring is a good example of a simple mechanism that works with both forces.

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Compression pushes the coils together, thus shortening the spring and tension pulls the coils further apart, lengthening the spring.Compression & Tension Forces

Compression and tension are seen in a bridge in the road deck, which shortens on top as traffic weight loads bear down directly on it, pushing down with weight and gravity. The compression on the upper side of the decking causes the underside to go into tension and stretch. The diagonals and horizontal members of a truss transfer the forces to the pilings. At these points, most of the downward load or weight of compression applied to the structure is dissipated or transferred into the earth. Dissipation means to spread the force out or transfer it to a larger area so that no one point bears the entire concentrated focus of the force.Construction Strength Of Truss Bridges

Truss bridges are designed so that compression and tension don't cause the structure to fail by snapping or buckling. If the compression force overcomes the bridge's ability to handle the stress, it will buckle, and if the tension forces overwhelm the structure, its members may snap. The truss bridge designs ensure that these forces are dissipated or transferred through the members and away from the structure.

Other Forces Acting On Truss Bridges

Other forces, such as torsion, resonance and seismic forces from earthquakes cause stresses on bridges in different ways. Torsion is a rotational or twisting force produced during storms with high hurricane or near hurricane strength winds. Truss construction allows the winds to blow through both the substructure and the superstructure of the road deck so that torsion is minimized.

Resonance refers to standing waves that can run back and forth through a bridge causing it to fail through fatigue. Fatigue refers to the repeated bending up and down of horizontal members causing them to fail. A simple example is a wire bent up and down repeatedly so that one area heats up due to friction, weakens, stretches and finally breaks. When an army marches across a bridge, the soldiers are ordered to "break step" so that the cadence is broken and wave forms cannot set up. The simple truss construction disperses forces through the members so that no single member can be overstressed in this manner.

Seismic waves caused by earthquakes move through the ground and perturb the surface in all three dimensions. Waves move back and forth, up and down and from side to side and it's very difficult for any structure to resist this kind of punishment. Truss bridges are just as vulnerable as any other structure to this kind of failure. Railroads have replaced almost all truss bridges in areas prone to seismic disturbance

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Reference

Historical American Engineering Record (1976). "Trusses: A Study by the Historical American Engineering Record" (pdf). National Park Service. Retrieved 2008-07-20.

Bridge Basics - A Spotter's Guide to Bridge Design - from Pghbridges.com - Illustrates many of the various types of truss arrangements used in bridges.

Historic Bridges of Michigan and Elsewhere - Many photos of truss bridges are available on this informative and mainly truss-focused bridge website.

Historic Bridges of Iowa - An illustrated list of different architectural bridge types found in Iowa, USA. Many of these are truss bridges.

Historic Bridges of the U.S. - An enormous database of historic bridges. Over 17,400 truss bridges are listed here.

Iron and Early Steel Bridges of Ohio - A comprehensive inventory of all remaining truss bridges in Ohio. Includes maps, photos, and invites visitor assistance in identifying extant or demolished bridges.

Matsuo Bridge Company: Bridge Types - Truss

structurae.de The Structurae database on bridges.