In architecture and structural engineering, a truss is a structure comprising one or more triangular units constructed with straight slender members whose ends are connected at joints.

A plane truss is one where all the members and joints lie within a 2-dimensional plane, while a space truss has members and joints extending into 3 dimensions.

The Auckland Harbour Bridge from Watchman Island, west of it.

Truss bridge for a single track railway, converted to pedestrian use and pipeline support

History

The earliest trusses were made out of wood. The ancient Greeks used truss construction for their dwellings. In 1570 Andrea Palladio published I Quattro Libri dell'Architettura, which contained instructions for wooden trussed bridges.

Truss types

Support structure under the Auckland Harbour Bridge.

Pre fabricated steel bow string roof trusses built 1942 for war department properties in Northern Australia.

A metal plate-connected wood truss is a roof or floor truss whose wood members are connected with metal connector plates.

There are two basic types of truss. The pitched truss or common truss is characterized by its triangular shape. It is most often used for roof construction. Some common trusses are named according to their web configuration. The chord size and web configuration are determined by span, load and spacing. The parallel chord truss or flat truss gets its name from its parallel top and bottom chords. It is often used for floor construction. A combination of the two is a truncated truss, used in hip roof construction.

Bow string roof truss

Named for its distinctive shape, thousands of bow strings were used during World War II for aircraft hangars and other military buildings.

Vierendeel truss

A Vierendeel bridge; note the lack of diagonal elements in the primary structure and the way bending loads are carried between elements

A special truss is the Vierendeel truss, named after the Belgian engineer Arthur Vierendeel [1], who developed the design in 1896. The Vierendeel truss is a truss where the members are not triangulated but form rectangular openings, and is a frame with fixed joints that are capable of transferring and resisting bending moments. In this statically indeterminate structure the individual horizontal and vertical members are designed as beams. Diagonal bracing is omitted as the joints are designed to withstand the moments that occur at the ends of the members. Trusses of this type are used in some bridges (see Vierendeel bridge), and were also used in the frame of the Twin Towers of the World Trade Center[2]. By eliminating diagonal members, the creation of rectangular openings for windows and doors is simplified, since this truss can reduce or eliminate the need for compensating shear walls.

King post truss

King Post Truss

Main article: King post

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

Queen Post Truss

Main article: Queen post

The queen post truss, sometimes queenpost 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 centre which relies on beam action to provide mechanical stability. This truss style is only suitable for relatively short spans. ^[1]

Town's lattice truss

See Ithiel Town's lattice truss

Statics of trusses

A truss that is assumed to comprise of members that are connected by means of pin joints and which is supported at both ends by means of a 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 which may be subjected to an external load or force to remain static in space the following conditions are required to be true: the sum of all horizontal forces, and the sum of all vertical forces as well as the sum of all moments acting about the node need to equate to 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 composed entirely of triangles. In mathematical terms, we have the following necessary condition for stability:

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 2j equilibrium 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.

Some structures are built with more than this minimum number of truss members. Those structures may survive even when some of the members fail. They are called statically indeterminate structures, because their member forces also depend on the relative stiffness of the members, in addition to the equilibrium condition.

Analysis of trusses

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 the adjacent 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 matrix stiffness method, the flexibility method or the finite element method.

Forces in members

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 diagram
• Culmann diagram

Or the 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 (the bottom 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 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.

In addition to carrying the static forces, the members serve additional functions of stabilizing each other, preventing buckling. In the picture, the top chord is prevented from buckling by the presence of bracing and by the stiffness of the web members.

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.

A building under construction in Shanghai. The truss sections stabilize the building and will house mechanical floors.

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 / σ_y, where F is the force in the member, γ is a safety factor (typically 1.5 but depending on building codes) and σ_y 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.

Little Belt: a truss bridge in Denmark

See also

Wikimedia Commons has media related to:

trusses

Look up truss in
Wiktionary, the free dictionary.

• Andreini tessellations, the only 28 ways to fill 3D space with trusses that have identical joints everywhere
• Brown truss
• Geodesic dome, a truss in the shape of a sphere
• Girder
• Lattice bridge, using a truss form allowing lightweight components
• Mechanics of structures
• Serrurier truss, a truss form used for telescopes
• Space frame
• Stress:
  • Compressive stress
  • Tensile stress
• Structural steel
• Tensegrity truss, a truss where no compression member touches any other compression member
• Truss bridge
• Truss rod, a guitar part
• Vierendeel bridge

References

1. ^ http://www.dot.state.oh.us/se/coveredbridges/truss_types.htm

External links

• Historic Bridges of Michigan and Elsewhere With a focus on metal truss bridges, this site provides photos, information, maps, and links
• "Preventing Injuries and Deaths of Fire Fighters Due to Truss System Failures," National Institute for Occupational Safety and Health, Accessed September 13, 2007
• Classical Truss Theory
• An Introduction to Historic Truss Bridges
• truss bridge designer simulation (requires Java)
• Trusses in 20th-century architecture
• Vierendeel bridges (in Dutch)
• Residential trussed roofs Australia
• Structural Building Components Association
• Aluminum Truss Systems
• IsoTruss
• Truss Types Visual Guide at Structural Wiki. Line diagrams and names of 30+ truss types.

Truss bridge
Truss bridge for a single track railway, converted to pedestrian use and pipeline support
Ancestor:	Beam bridge
Related:	None
Descendant:	Cantilever bridge, truss arch bridge, transporter bridge, lattice bridge
Carries:	Pedestrians, pipelines, automobiles, trucks, light rail, heavy rail
Span range:	Short to medium
Material:	Timber, iron, steel, reinforced concrete, prestressed concrete
Movable:	May be movable - see movable bridge
Design effort:	Medium
Falsework required:	Depends upon length, materials, and degree of prefabrication

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. This type of bridge structure has a fairly simple design and is particularly cheap to construct owing to its efficient use of materials. For purposes of analysis most truss bridges may be considered to be pin jointed where the straight components meet. A more complex analysis may be required where rigid joints impose significant bending loads upon the elements.

Warren-type through truss bridge of the former Seaboard Air Line Railway. Located near the village of Willow, Florida. Abandoned by CSX since the mid-1980s.

In the bridge illustrated in the infobox at right, vertical members are in tension, lower horizontal members in tension, shear, and bending, outer diagonal and top members are in compression, while the inner diagonals are in tension. The central vertical member stabilizes the upper compression member, preventing it from buckling. If the top member is sufficiently stiff then this vertical element may be eliminated. If the lower chord (a horizontal member of a truss) is sufficiently resistant to bending and shear, the outer vertical elements may be eliminated, but with additional strength added to other members in compensation. The ability to distribute the forces in various ways has led to a large variety of truss bridge types. Some types may be more advantageous when wood is employed for compression elements while other types may be easier to erect in particular site conditions, or when the balance between labor, machinery and material costs have certain favorable proportions.

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, and the changing price of steel relative to that of labor have significantly influenced the design of modern bridges.

History in the United States

Bollman truss in Savage, Maryland (built 1869)

Because wood was so abundant, early truss bridges would typically use carefully fitted timbers for members taking compression and iron rods for tension members, usually constructed as a covered bridge to protect the structure. In 1820 a simple form of truss, Town's lattice truss was patented, and had the advantage of not requiring high labor skills nor much metal.

A few iron truss bridges were built in the United States before 1850. Bridges based on the Bollman truss (patented in 1852) were used successfully by the Baltimore and Ohio Railroad. Truss bridges became a common type of bridge to see built from the 1870s through the 1930s. Examples of these bridges still remain across the United States, but their numbers are dropping rapidly, as they are demolished and replaced with new structures. As metal slowly started to replace timber, wrought iron bridges in the U.S. started being built on a large scale in the 1870s. Bowstring truss bridges were a common truss design seen during this time, with their arched top chords. Companies like the Wrought Iron Bridge Company of Canton, Ohio and the King Bridge Company of Cleveland, Ohio became well-known companies, as they marketed their designs to different cities and townships. The bowstring truss design (photo) fell out of favor due to a lack of durability, and gave way to the Pratt truss design, which was stronger. Again, the bridge companies marketed their designs, with the Wrought Iron Bridge Company in the lead. As the 1880s and 1890s progressed, steel began to replace wrought iron as the preferred material. Other truss designs were used during this time, including the camel-back. By the 1910s, many states developed standard plan truss bridges, including steel Warren pony truss bridges. As the 1920s and 1930s progressed, some states, like Pennsylvania continued to build steel truss bridges, including massive steel through truss bridges for long spans. Other states, like Michigan, utilized standard plan concrete girder and beam bridges, and only a limited number of truss bridges were built.

Roadbed types

The four span through truss General Hertzog Bridge over the Orange River at Aliwal North carries vehicular traffic.

Deck truss railroad bridge over the Erie Canal

Pony truss bridge of reinforced concrete

The 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, 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.

The double-decked First Bridge at Wuhan, China carries four lanes of automobile traffic on top, two of rail below over nine truss spans

Truss types used in bridges

Some truss types are applicable to the construction of floor and roof structures and pylons as well as bridges.

Some stub sections for various truss types employed in bridges follow - can you can assist by adding text ?

Bailey bridge

Bailey bridge over the Meurthe River, France.

Main article: Bailey bridge

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 truss

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Bollman truss

Bollman truss in Savage, Maryland (built 1869)

Main article: Bollman Truss Railroad Bridge

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 to be adopted and consistently used on a railroad. The design employs wrought iron tension members and cast iron compression members. The use of multiple independent tension elements reduces the likelihood of catastrophic failure and 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)

A tied arch bridge, in Pittsburgh, Pennsylvania

Main article: Tied arch bridge

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

Main article: Brown truss

This type of truss is particularly suited for timber structures that use iron rods as tension members.

Brown truss illustrated. All interior vertical elements are under tension.

Brunnel Truss

See Lenticular truss below

Burr Arch Truss

Main article: Burr Arch Truss

Cantilevered truss

Firth of Forth rail bridge

Main article: Cantilever bridge

Most 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

Howe truss

The relatively rare Howe truss includes vertical members and diagonals that slope up towards the center, the opposite of the Pratt truss.^[1]

Howe truss illustrated - the diagonals are under compression under balanced loading

This short section requires expansion.

Kingpost truss

King Post Truss

Main article: King post

One 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)

Plank lattice truss of a covered bridge

Main article: Lattice truss bridge

This 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, 1859

Main article: Royal Albert Bridge

The Lenticular truss was developed by the famous 19th century engineer Isambard Kingdom Brunel for use in railway bridges. It consists of an arcuate tubular upper compression chord and lower eyebar chain tension links. 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.

Parker (Camelback) truss

This short section requires expansion.

Pennsylvania (Petit) truss

An example of this truss type is the Schell Bridge in Northfield, Massachusetts.

This short section requires expansion.

Pratt truss

A Pratt truss includes vertical members and diagonals that slope down towards the center, the opposite of the Howe truss.^[1] It can be subdivided, creating Y- and K-shaped patterns.

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.

This short section requires expansion.

Queenpost truss

Queen Post Truss

Main article: Queen post

The 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 centre which relies on beam action to provide mechanical stability. This truss style is only suitable for relatively short spans. ^[2]

Truss arch

Main article: Truss arch bridge

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.

Waddel truss

Waddel "A" truss (1898 bridge)

Main article: John Alexander Low Waddell

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

The Warren truss consists of diagonals that alternate between compression and tension (approaching the center), with no vertical elements. Elements near the center must support both tension and compression in response to live loads.

Warren truss illustrated - some of the diagonals are under compression and some under tension

Whipple Pratt truss

This short section requires expansion.

Vierendeel truss

Main article: Vierendeel bridge

A Vierendeel bridge

The 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.

Wichert truss

This short section requires expansion.

External links

Wikimedia Commons has image media such as pictures and art related to:

Through truss bridges

Truss drawings

A Russian truss bridge by Lavr Proskuryakov. Early colour photograph, taken ca. 1912.

• 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 the U.S. - An enormous database of historic bridges. Over 1000 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
• Historic Bridges of Iowa - An illustrated list of different architectural bridge types found in Iowa, USA. Many of these are truss bridges.
• structurae.de The Structurae database on bridges.

See also

References

Bridge-related articles
Types of bridges	Moveable bridge · Beam bridge · Cantilever bridge · Arch bridge · Suspension bridge · Cable-stayed bridge · Truss bridge · Visual index to various types
Lists of Bridges	Notable bridges · By length · Longest suspension bridge spans · Largest cable-stayed bridges · Longest cantilever bridges · Arch bridges · Bridge disasters