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| In engineering, a '''truss''' is a [[architectural structure|structure]] comprising one or more triangular units constructed with straight members whose ends are connected at joints referred to as [[Vertex (geometry)|nodes]]. External forces and reactions to those forces are considered to act only at the nodes and result in forces in the members which are either [[tension (physics)|tensile]] or [[compression (physics)|compressive]] forces. Moments ([[torque]]s) are explicitly excluded because, and only because, all the joints in a truss are treated as [[Revolute joint|revolutes]].
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| A planar truss is one where all the members and nodes lie within a two dimensional plane, while a space truss has members and nodes extending into three dimensions. The top beams in a truss are called top chords and are generally in [[Compression (physics)|compression]], the bottom beams are called bottom chords and are generally in [[Tension (physics)|tension]], the interior beams are called webs, and the areas inside the webs are called panels.<ref>Ching, Frank. A Visual Dictionary of Architecture. 2nd ed. Hoboken, N.J.: Wiley, 2012. 277. Print. ISBN 9780470648858</ref>
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| [[File:RRTrussBridgeSideView.jpg|thumb|350px|[[Truss bridge]] for a single-track railway, converted to pedestrian use and pipeline support]]
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| == Etymology of truss ==
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| Truss is derived from Old French ''trousse'', around c.1200, which means "collection of things bound together."<ref>Reif, F., [http://www.etymonline.com/index.php?term=truss etymonline.com] (1965).</ref><ref>Oxford English Dictionary</ref> The term truss has often been used to describe any assembly of members such as a [[cruck]] frame<ref>Noble, Allen George. Traditional buildings a global survey of structural forms and cultural functions. London: I.B. Tauris ;, 2007. 115. ISBN 1845113055</ref><ref>Davies, Nikolas, and Erkki Jokiniemi. Dictionary of architecture and building construction. Amsterdam: Elsevier/Architectural Press, 2008. 394. ISBN 0750685026</ref> or couple of rafters<ref>Davies, Nikolas, and Erkki Jokiniemi. Architect's illustrated pocket dictionary. Oxford: Architectural Press, 2011. 121. ISBN 0080965377</ref><ref>Crabb, George. Universal Technological Dictionary Or Familiar Explanation of the Terms used in All Arts and Sciences...", Volume 1 London: 1823. Couples.</ref> but often means the engineering sense of "A truss is a single plane framework of individual structural member connected at their ends of forms a series of triangle (sic) to span a large distance."<ref>Shekhar, R. K. Chandra. Academic dictionary of civil engineering. Delhi: Isha Books, 2005. 431. ISBN 8182051908</ref>
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| == Characteristics of trusses ==
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| A truss consists of straight members connected at joints, traditionally termed '''panel points'''. Trusses are composed of triangles because of the structural stability of that shape and design. A triangle is the simplest geometric figure that will not change shape when the lengths of the sides are fixed.<ref name="ricker">{{cite book | last = Ricker | first = Nathan Clifford | title = A Treat on Design and Construction of Roofs| origyear = 1912 | url = http://books.google.com/books?id=b6oJAAAAIAAJ| accessdate = 2008-08-15 | year = 1912 | publisher = J. Wiley & Sons | location = New York | pages = 12}}</ref> In comparison, both the angles and the lengths of a four-sided figure must be fixed for it to retain its shape.
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| ===Planar truss===
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| [[File:Trusses 008.jpg|thumb|200px|right|Planar roof trusses]]
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| [[File:Santa croce, navata, capriate.JPG|thumb|The roof trusses of the [[basilica di Santa Croce]] ([[Florence]])]]
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| The simplest form of a truss is one single triangle. This type of truss is seen in a [[Framing (construction)|framed]] roof consisting of [[rafter]]s and a ceiling [[joist]],<ref name="maginnis">{{cite book|last=Maginnis|first=Owen Bernard|title=Roof Framing Made Easy|url=http://books.google.com/books?id=GJdBAAAAIAAJ|accessdate=2008-08-16|edition=2nd edition|year=1903|publisher=The Industrial Publication Company|location=New York|pages=9}}</ref> and in other mechanical structures such as [[bicycle frame|bicycles]] and aircraft. Because of the stability of this shape and the methods of analysis used to calculate the forces within it, a truss composed entirely of triangles is known as a simple truss.<ref name="hibbeler">{{cite book | last = Hibbeler | first = Russell Charles | title = Engineering Mechanics-Statics| origyear = 1974 | edition = 3rd edition | year = 1983 | publisher = Macmillan Publishing Co., Inc. | location = New York | isbn = 0-02-354310-8 | pages = 199–224}}</ref> The traditional diamond-shape bicycle frame, which utilizes two conjoined triangles, is an example of a simple truss.<ref>Wingerter, R., and Lebossiere, P., ''ME 354, Mechanics of Materials Laboratory: Structures'', University of Washington (February 2004), p.1</ref>
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| A planar truss lies in a single [[Plane (mathematics)|plane]].<ref name="hibbeler"/> Planar trusses are typically used in parallel to form roofs and bridges.
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| The depth of a truss, or the height between the upper and lower [[Chord (truss construction)|chords]], is what makes it an efficient structural form. A solid [[girder]] or [[Beam (structure)|beam]] of equal strength would have substantial weight and material cost as compared to a truss. For a given [[Span (architecture)|span]], a deeper truss will require less material in the chords and greater material in the verticals and diagonals. An optimum depth of the truss will maximize the efficiency.<ref name="meriman">{{cite book|last=Merriman|first=Mansfield|title=American Civil Engineers' Pocket Book|origyear=192|url=http://books.google.com/books?id=AUVIAAAAIAAJ|accessdate=2008-08-16|year=1912|publisher=J. Wiley & Sons|location=New York|pages=785|quote=The Economic Depth of a Truss is that which makes the material in a bridge a minimum.}}</ref>
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| ===Space frame truss===
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| A [[space frame]] truss is a three-dimensional framework of members pinned at their ends. A [[tetrahedron]] shape is the simplest space truss, consisting of six members which meet at four joints.<ref name="hibbeler"/> Large planar structures may be composed from tetrahedrons with common edges and they are also employed in the base structures of large free-standing power line pylons
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| {{gallery
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| |File:Tetrahedron.png|Simple tetrahedron
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| |File:SpaceFrame02.png|Diagram of a planar space frame such as used for a roof
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| |File:Pylon-gorai.jpg|Three dimensionally trussed structure - [[Electricity pylon|Pylon]]
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| }}
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| ==Truss types==
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| [[File:Large Timber Howe Truss.jpg|thumb|right|A large timber [[Howe truss]] in a commercial building]]
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| :''For more truss types, see [[List of truss types]] or [[Truss bridge#Truss types used in bridges|Truss Bridge]].''
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| There are two basic types of truss:
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| * 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''.
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| * The ''parallel chord truss'', or ''flat truss'', gets its name from its parallel top and bottom chords. It is often used for floor construction.
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| 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 [[Truss connector plate|metal connector plates]].
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| ===Pratt truss===
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| [[File:pratt truss.png|top|100px|Pratt Truss]]
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| 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]; rtrieved 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 Tennessee Department of Transportation]; retrieved 2008-Feb-06</ref> The design uses vertical members for [[compression (physics)|compression]] and horizontal members to respond to [[Tension (physics)|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 continued popularity of the Pratt truss is probably due to the fact that the configuration of the members means that longer diagonal members are only in tension for gravity load effects. This allows these members to be used more efficiently, as slenderness effects related to [[buckling]] under compression loads (which are compounded by the length of the member) will typically not control the design. Therefore, for given planar truss with a fixed depth, the Pratt configuration is usually the most efficient under static, vertical loading.
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| The [[Southern Pacific Railroad]] bridge in [[Tempe, Arizona|Tempe]], [[Arizona]] is a 393 meter (1,291 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.
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| The [[Wright Flyer]] used a Pratt truss in its wing construction, as the minimization of compression member lengths allowed for lower [[aerodynamic drag]].<ref>http://www.arct.cam.ac.uk/personal-page/james/ichs/Vol%202%201221-1232%20Gasparini.pdf</ref>
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| {{-}}
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| ===Bowstring truss=== | |
| Named for their shape, bowstring trusses were first used for arched [[truss bridge]]s, often confused with [[tied-arch bridge]]s.
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| Thousands of bowstring trusses were used during [[World War II]] for holding up the curved roofs of aircraft hangars and other military buildings. Many variations exist in the arrangements of the members connecting the nodes of the upper arc with those of the lower, straight sequence of members, from nearly isosceles triangles to a variant of the Pratt truss.
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| ===King post truss===
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| {{main|King post}}
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| [[File:king post truss.png|left|100px|King Post Truss]]
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| One of the simplest truss styles to implement, the '''king post''' consists of two angled supports leaning into a common vertical support.
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| [[File:queen post truss.png|left|100px|Queen Post Truss]]
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| 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>
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| {{-}}
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| ===Lenticular truss===
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| [[File:Waterville Bridge in Swatara State Park HAER 462-14.jpg|thumb|The [[Waterville Bridge]] in [[Swatara State Park]] in Pennsylvania is a lenticular truss]]
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| Lenticular trusses, patented in 1878 by William Douglas, have the top and bottom chords of the truss arched, forming a lens shape. A [[lenticular pony truss bridge]] is a bridge design that involves a lenticular truss extending above and below the roadbed.
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| ===Town's lattice truss===
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| {{main|Lattice truss bridge}}
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| [[File:lattice truss.png|left|100px|Lattice Truss]]
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| American [[architect]] [[Ithiel Town]] designed '''Town's Lattice Truss''' as an alternative to heavy-timber bridges. His design, [[patented]] in 1820 and 1835, uses easy-to-handle planks arranged diagonally with short spaces in between them.
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| {{-}}
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| {{anchor|Vierendeel Truss}}
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| ===Vierendeel truss===
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| [[File:Grammene-vierendeelbridge 20030618.jpg|thumb|A [[Vierendeel bridge]]; note the lack of diagonal elements in the primary structure]]
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| {{see also|Arthur Vierendeel|Vierendeel bridge}}
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| The '''Vierendeel truss''' is a structure 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. As such, it does not fit the strict definition of a truss; 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 structure was named after the 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. Its use for bridges is rare due to higher costs compared to a triangulated truss.
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| The utility of this type of structure in buildings is that a large amount of the exterior envelope remains unobstructed and can be used for [[window|fenestration]] and door openings. This is preferable to a braced-frame system, which would leave some areas obstructed by the diagonal braces.
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| {{-}}
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| ==Statics of trusses==
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| 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 indeterminate#Statically determinate|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 compression or tension forces.
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| 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.
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| 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 [[mechanical equilibrium|stability]]:
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| :<math> m \ge 2j - r \qquad \qquad \mathrm{(a)} </math>
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| 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.
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| 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.
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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.
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| ==Analysis of trusses==
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| [[File:cremonadiagram.jpg|thumbnail|right|Cremona diagram for a plane truss]]
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| 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.
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| 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.
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| [[Structural analysis]] of trusses of any type can readily be carried out using a matrix method such as the [[direct stiffness method]], the [[flexibility method]] or the [[finite element]] method.
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| <!-- Yes, this was redundant. Feel free to merge these paragraphs together and delete the redundant stuff. -->
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| ===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 [[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.
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| The internal [[force]]s in the members of the truss can be calculated in a variety of ways including the graphical methods:
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| * ''[[Cremona diagram]]''
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| * ''[[Carl Culmann|Culmann]] diagram''
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| * ''the analytical ''Ritter'' method ([[Structural_analysis#Method_of_Sections|method of sections]]).
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| ===Design of members===
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| 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 [[compression (physics)|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.
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| 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 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.
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| [[File:Shanghai Shimao Plaza Construction.jpg|thumb|right|A building under construction in [[Shanghai]]. The truss sections stabilize the building and will house [[mechanical floor]]s.]]
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| 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 [[bridge]]s.
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| Once the force on each member is known,
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| 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>
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| The members under compression also have to be designed to be safe against buckling.
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| 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.
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| 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.
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| 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.
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| 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.
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| ===Design of joints===
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| 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]]. Based on the needs of the project, truss internal connections (joints) can be designed as rigid, semi rigid, or hinged. Rigid connections can allow transfer of bending moments leading to development of secondary bending moments in the members.
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| ==Applications==
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| ===Post frame structures===
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| Component connections are critical to the structural integrity of a framing system. In buildings with large, clearspan wood trusses, the most critical connections are those between the truss and its supports. In addition to gravity-induced forces (a.k.a. bearing loads), these connections must resist shear forces acting perpendicular to the plane of the truss and uplift forces due to wind. Depending upon overall building design, the connections may also be required to transfer bending moment.
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| Wood posts enable the fabrication of strong, direct, yet inexpensive connections between large trusses and walls. Exact details for post-to-truss connections vary from designer to designer, and may be influenced by post type. Solid-sawn timber and glulam posts are generally notched to form a truss bearing surface. The truss is rested on the notches and bolted into place. A special plate/bracket may be added to increase connection load transfer capabilities. With mechanically-laminated posts, the truss may rest on a shortened outer-ply or on a shortened inner-ply. The later scenario places the bolts in double shear and is a very effective connection.
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| ==Gallery==
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| <gallery>
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| Image:80ft Double Chorded Heavy Timber Truss.JPG|Double chorded heavy timber truss with 80 foot clear span.
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| Image:HK_Bank_of_China_Tower_View.jpg|The [[Bank of China Tower, Hong Kong|Hong Kong Bank of China Tower]] 中銀大廈 (香港) has an externally visible truss structure.
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| Image:HK_HSBC_Main_Building_2008.jpg|The [[HSBC Main Building, Hong Kong]] has an externally visible truss structure.
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| Image:Below Auckland Harbour Bridge Hossen27.jpg|Support structure under the [[Auckland Harbour Bridge]].
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| Image:Auckland Harbour Bridge Watchman.jpg|The [[Auckland Harbour Bridge]] from [[Watchman Island]], west of it.
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| Image:The Little Belt Bridge (1935).jpeg|[[Little Belt Bridge|''Little Belt'']]: a truss [[bridge]] in [[Denmark]]
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| Image:Bow-string-truss.jpg|[[Pre-fabricated]] steel bow string roof trusses built in 1942 for war department properties in Northern [[Australia]].
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| Image:Truss Dachstuhl.jpg|Roof truss in a side building of [[Cluny Abbey]], [[France]].
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| File:Queen-post-truss.png|A section through a Queen post roof truss, see [[Timber roof truss]]
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| File:Woodlands mall3 texas.jpg|A space truss carrying a floor in [[The Woodlands Mall]].
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| File:Elledningsstolpe2_lund.jpg|[[Electricity pylon]]
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| </gallery>
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| == See also ==
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| * [[Convex uniform honeycomb|Andreini tessellation]]s, the only 28 ways to fill 3D space with trusses that have ''identical'' joints everywhere
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| * [[Brown truss]]
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| * [[Geodesic dome]], a truss in the shape of a sphere
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| * [[Girder]]
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| * [[List of truss types]]
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| * [[Structural mechanics]]
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| * [[Serrurier truss]], a truss form used for telescopes
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| * [[Space frame]]
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| * Stress:
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| ** [[Compressive stress]]
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| ** [[Tensile stress]]
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| * [[Structural steel]]
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| * [[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 ? -->
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| * [[Truss bridge]]
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| * [[Truss rod]], a [[guitar]] part
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| *[[Timber roof truss]]
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| == References ==
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| {{reflist}}
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| == External links ==
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| {{wiktionary|truss}}
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| {{commons category|trusses}}
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| * [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
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| * [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
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| * [http://urban.arch.virginia.edu/~km6e/arch324/content/lectures/lec-18/review-of-17.html Classical Truss Theory]
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| * [http://www.historicbridges.org/info/intro/index.htm An Introduction to Historic Truss Bridges]
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| * [http://www.jhu.edu/virtlab/bridge/truss.htm Truss bridge designer simulation] (requires Java)
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| * [http://www.nexote.net/nexote/Structural%20Analysis%20Notebook/default.asp Web-based 2D Truss Analysis Program] (requires Flash)
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| * [http://www.nexote.net/nexote/3D%20Truss%20Analysis%20Notebook/default.asp Web-based 3D Truss Analysis Program] (requires Flash)
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| * [http://www.people.cornell.edu/pages/jo24/comments/truss.html Trusses in 20th-century architecture]
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| * [http://www.sbcindustry.com Structural Building Components Association]
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| * [http://www.historycooperative.org/journals/sia/30.1/boothby.html American Lenticular Truss Bridges]
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| * [http://minera-rooftrusses.com/trusses_shapes.html A guide to spans and names of shapes of roof trusses aka trussed rafters]
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| * [http://design.medeek.com/calculator/calculator.pl Residential Roof Truss Designer with Load Analysis]
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| {{Wood products}}
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| [[Category:Structural system]]
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| [[Category:Architectural elements]]
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| [[Category:Mechanics]]
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| [[Category:Airship technology]]
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| [[Category:Trusses| ]]
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