Truss
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Reverted edits by [[Special:Contributions/61.9.6.243|61.9.6.243]] to last version by Bobo192 (using [[WP:HG|Huggle]])
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[[Image:RRTrussBridgeSideView.jpg|thumb|350px|[[Truss bridge]] for a single track railway, converted to pedestrian use and pipeline support]]
In [[architecture]] and [[structural engineering]], a '''truss''' is a [[architectural structure|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.
== Truss types ==
[[Image:Bow-string-truss.jpg|thumb|245px|Pre fabricated steel bow string roof trusses built 1942 for war department properties in Northern [[Australia]].]]
[[Image:Truss Dachstuhl.jpg|thumb|245px|Roof truss in a side building of [[Cluny Abbey]], [[France]].]]
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 (roofing)|hip]] roof construction. A metal plate-connected wood truss is a roof or floor truss whose wood members are connected with [[metal connector plates]].
===Pratt truss===
[[Image:pratt truss.png|left|100px|Vierendeel Truss]]
The '''Pratt truss''' was patented in [[1844]] by two [[Boston]] railway engineers<ref>''[http://www.heritage.nsw.gov.au/07_subnav_01_2.cfm?itemid=5056556 Bethanga Bridge]'' at the [http://www.heritage.nsw.gov.au NSW Heritage Office]; retrieved 2008-Feb-06</ref>; Caleb Pratt and his son [[Thomas Willis Pratt]]<ref>''[http://www.tdot.state.tn.us/bridges/historybridges.htm A Brief History of Covered Bridges in Tennessee]'' at the [http://www.tdot.state.tn.us Tenessee Department of Transportation]; retrieved 2008-Feb-06</ref>. The design uses vertical beams for [[compression]] and horizontal beams to respond to [[tension]]. What is remarkable about this style is that it remained popular even as wood gave way to iron, and even still as iron gave way to steel.<ref>''[http://www.sha.state.md.us/keepingcurrent/maintainRoadsBridges/bridges/OPPE/historicBridges/V-Pratt.pdf The Pratt Truss]'' courtesy of the [http://www.sha.state.md.us Maryland Department of Transportation]; retrieved 2008-Feb-6</ref>
The [[Southern Pacific Railroad]] bridge in [[Tempe, Arizona|Tempe]], [[Arizona]] is a 393 meter (1291 foot) long truss bridge built in [[1912]]<ref>''[http://www.tempe.gov/museum/Tempe_history/properties/hps228.htm Tempe Historic Property Survey]'' at the [http://www.tempe.gov/museum/ Tempe Historical Museum]; retrieved 2008-Feb-06</ref>. The structure is composed of nine Pratt truss spans of varying lengths. The bridge is still in use today.
===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.
===King post truss===
[[Image:king post truss.png|left|100px|King Post Truss]]
{{main|King post}}
One of the simplest truss styles to implement, the '''king post''' consists of two angled supports leaning into a common vertical support.
[[Image:queen post truss.png|left|100px|Queen Post Truss]]
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 (structure)|beam]] action to provide mechanical stability. This truss style is only suitable for relatively short spans. <ref>[http://www.dot.state.oh.us/se/coveredbridges/truss_types.htm Covered Bridge's Truss Types<!-- Bot generated title -->]</ref>
===Town's lattice truss===
[[Image:lattice truss.png|left|100px|King Post Truss]]
{{main|Lattice truss bridge}}
American [[architect]] [[Ithiel Town]] designed '''Town's Lattice Truss''' as an alternative to heavy-timber bridges. His design, [[patented]] in 1835, uses easy-to-handle planks arranged diagonally with short spaces in between them.
===Vierendeel truss===
[[Image:vierendeel truss.png|left|100px|Vierendeel Truss]]
[[Image:Grammene-vierendeelbridge 20030618.jpg|thumb|245px|A [[Vierendeel bridge]]; note the lack of diagonal elements in the primary structure and the way bending loads are carried between elements]]
{{see|Vierendeel bridge}}
The '''Vierendeel truss''' is a truss where the members are not triangulated but form rectangular openings, and is a [[Rigid frame|frame]] with fixed joints that are capable of transferring and resisting [[bending moment]]s. Regular trusses comprise members that are commonly assumed to have pinned joints with the implication that no moments exist at the jointed ends. This style of truss was named after the [[Belgium|Belgian]] engineer [[Arthur Vierendeel]]<ref>[http://users.telenet.be/karel.roose/vierendeel/vierendeel.html Vierendeel bruggen<!-- Bot generated title -->]</ref>, who developed the design in [[1896]]
The beauty of this type of truss is that there is no diagonal bracing, the creation of rectangular openings for windows and doors is simplified and in cases the need for compensating shear walls is reduced or eliminated.
After being damaged by the impact of plane hitting the building parts of the framed curtain walls of the Twin Towers of the [[World Trade Center]] resisted collapse by Vierendeel action displayed by the remaining portions of the frame. <!-- dead link <ref>http://www.pubs.asce.org/ceonline/ceonline02/0502feat.html</ref> -->.
==Statics of trusses==
[[Image:Below Auckland Harbour Bridge Hossen27.jpg|thumb|245px|Support structure under the [[Auckland Harbour Bridge]].]]
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 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 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 forces, all 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 for [[stability]]:
:<math> m \ge 2j - r \qquad \qquad \mathrm{(a)} </math>
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 <math> m=2j - 3</math>, the truss is said to be ''statically determinate'', because the (''m''+3) internal member forces and support reactions can then be completely determined by 2''j'' [[mechanical equilibrium|equilibrium]] equations, once we know the external [[structural load|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 depend on the relative [[stiffness]] of the members, in addition to the equilibrium condition described.
==Analysis of trusses==
[[Image:cremonadiagram.jpg|thumbnail|right|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 [[moment (physics)|moments]] transmitted through the joints are negligible and they can be treated as "[[hinge]]s" or 'pin-joints'. Every member of the truss is then in pure compression or pure tension – shear, bending moment, and other more complex [[stress (physics)|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.
<!-- Yes, this was redundant. Feel free to merge these paragraphs together and delete the redundant stuff. -->
===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 [[symmetry|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 [[force]]s in the members of the truss can be calculated in a variety of ways including the graphical methods:
* ''[[Cremona diagram]]''
* ''[[Carl Culmann|Culmann]] diagram''
Or the analytical ''Ritter'' method ([[Structural analysis#Mechanics of materials methods|method of sections]]).
===Design of members===
[[Image:Auckland Harbour Bridge Watchman.jpg|right|thumb|350px|The [[Auckland Harbour Bridge]] from [[Watchman Island]], west of it.]]
A truss can be thought of as a [[beam (structure)|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 (mechanics)|tension]] and [[physical compression|compression]], fulfilling the same function as the [[flange]]s 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 [[shearing (physics)|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.
[[Image:Shanghai Shimao Plaza Construction.jpg|thumb|left|200px|A building under construction in [[Shanghai]]. The truss sections stabilize the building and will house [[mechanical floor]]s.]]
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 [[weld]]ing, have significantly influenced the design of modern [[bridge]]s.
Once the force on each member is known,
the next step is to determine the [[cross section (geometry)|cross section]] of the individual truss members. For members under tension the cross-sectional area ''A'' can be found using ''A'' = ''F'' × γ / σ<sub>''y''</sub>, where ''F'' is the force in the member, γ is a [[safety factor]] (typically 1.5 but depending on [[building code]]s) and σ<sub>y</sub> is the [[yield]] [[tensile strength]] of the steel used.<br>
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 joint]]s, e.g., involving shear of the bolt connections used in the joints, see also [[shear stress]].
[[Image:The Little Belt Bridge (1935).jpeg|thumb|500px|none|center|[[Little Belt Bridge|''Little Belt'']]: a truss [[bridge]] in [[Denmark]]]]
== See also ==
{{commonscat|trusses}}
{{wiktionary|truss}}
* [[Convex uniform honeycomb|Andreini tessellation]]s, 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]]
* [[Mechanics of structures]]
* [[Serrurier truss]], a truss form used for telescopes
* [[Space frame]]
* Stress:
** [[Compressive stress]]
** [[Tensile stress]]
* [[Structural steel]]
* [[Tensegrity|Tensegrity truss]], a truss where no compression member touches any other compression member <!-- ... um, some of them have little clusters of tension truses, where no cluster touches any other cluster. Is there a better definition ? -->
* [[Truss bridge]]
* [[Truss rod]], a [[guitar]] part
== References ==
{{reflist}}
== External links ==
* [http://pcnate.com/bridges/index.htm Historic Bridges of Michigan and Elsewhere] With a focus on metal truss bridges, this site provides photos, information, maps, and links
* [http://www.cdc.gov/niosh/docs/2005-132/ "Preventing Injuries and Deaths of Fire Fighters Due to Truss System Failures,"] ''[[National Institute for Occupational Safety and Health]]'', Accessed September 13, 2007
* [http://urban.arch.virginia.edu/~km6e/arch324/content/lectures/lec-18/review-of-17.html Classical Truss Theory]
* [http://www.historicbridges.org/info/intro/index.htm An Introduction to Historic Truss Bridges]
* [http://www.jhu.edu/virtlab/bridge/truss.htm truss bridge designer simulation] (requires Java)
* [http://www.people.cornell.edu/pages/jo24/comments/truss.html Trusses in 20th-century architecture]
* [http://users.telenet.be/karel.roose/vierendeel/vierendeel.html Vierendeel bridges (in Dutch)]
* [http://www.builderbill-diy-help.com/roof-truss.html Residential trussed roofs Australia]
* [http://www.sbcindustry.com Structural Building Components Association]
* [http://www.bridgeart.net/wiki/Category:Truss_types_visual_guide Truss Types Visual Guide] at Structural Wiki. Line diagrams and names of 30+ truss types.
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