Truss

A truss is an assembly of members such as beams, connected by nodes, that creates a rigid structure.

In engineering, a truss is a structure that "consists of two-force members only, where the members are organized so that the assemblage as a whole behaves as a single object". A two-force member is a structural component where force is applied to only two points. Although this rigorous definition allows the members to have any shape connected in any stable configuration, architectural trusses typically comprise five or more triangular units constructed with straight members whose ends are connected at joints referred to as nodes.

In this typical context, external forces and reactions to those forces are considered to act only at the nodes and result in forces in the members that are either tensile or compressive. For straight members, moments (torques) are explicitly excluded because, and only because, all the joints in a truss are treated as revolutes, as is necessary for the links to be two-force members.

A planar truss is one where all members and nodes lie within a two-dimensional plane, while a space frame has members and nodes that extend into three dimensions. The top beams in a truss are called top chords and are typically in compression, and the bottom beams are called bottom chords and are typically in tension. The interior beams are called webs, and the areas inside the webs are called panels,Ching, Frank. A Visual Dictionary of Architecture. 2nd ed. Hoboken, N.J.: Wiley, 2012. 277. Print. or from graphic statics (see Cremona diagram) polygons.Bow R. H., Economics of construction in relation to framed structures. Spon, London, 1873

Etymology Truss derives from the Old French word trousse, from around 1200 AD, which means "collection of things bound together".Reif, F., etymonline.com (1965).Oxford English Dictionary The term truss has often been used to describe any assembly of members such as a cruck frameNoble, Allen George. Traditional buildings a global survey of structural forms and cultural functions. London: I.B. Tauris; 2007. 115. Davies, Nikolas, and Erkki Jokiniemi. Dictionary of architecture and building construction. Amsterdam: Elsevier/Architectural Press, 2008. 394. or a couple of rafters.Davies, Nikolas, and Erkki Jokiniemi. Architect's illustrated pocket dictionary. Oxford: Architectural Press, 2011. 121. Crabb, George. Universal Technological Dictionary Or Familiar Explanation of the Terms used in All Arts and Sciences...", Volume 1 London: 1823. Couples.

Characteristics

A truss consists of typically (but not necessarily) straight members connected at joints, traditionally termed panel points. Trusses are typically (but not necessarily) 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. In comparison, both the angles and the lengths of a four-sided figure must be fixed for it to retain its shape.

Simple truss

The simplest form of a truss is one single triangle. This type of truss is seen in a framed roof consisting of rafters and a ceiling joist, and in other mechanical structures such as 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. However, a simple truss is often defined more restrictively by demanding that it can be constructed through successive addition of pairs of members, each connected to two existing joints and to each other to form a new joint, and this definition does not require a simple truss to comprise only triangles. The traditional diamond-shape bicycle frame, which uses two conjoined triangles, is an example of a simple truss.Wingerter, R., and Labossiere, P., ME 354, Mechanics of Materials Laboratory: Structures, University of Washington (February 2004), p.1

Planar truss

A planar truss lies in a single plane. Planar trusses are typically used in parallel to form roofs and bridges.

The depth of a truss, or the height between the upper and lower chords, is what makes it an efficient structural form. A solid girder or beam of equal strength would have substantial weight and material cost as compared to a truss. For a given 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.

Space frame truss 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 that meet at four joints. 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.

Types For more truss types, see truss types.

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

Warren truss

Truss members form a series of equilateral triangles, alternating up and down.

Octet truss Truss members are made up of all equivalent equilateral triangles. The minimum composition is two regular tetrahedrons along with an octahedron. They fill up three-dimensional space in a variety of configurations.

Pratt truss

The Pratt truss was patented in 1844 by two Boston railway engineers,Bethanga Bridge at the NSW Heritage Office; retrieved 2008-Feb-06 Caleb Pratt and his son Thomas Willis Pratt.A Brief History of Covered Bridges in Tennessee at the Tennessee Department of Transportation; retrieved 2008-Feb-06 The design uses vertical members for compression and diagonal members to respond to tension. The Pratt truss design remained popular as bridge designers switched from wood to iron, and from iron to steel.The Pratt Truss courtesy of the Maryland Department of Transportation; retrieved 2008-Feb-6 This 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 a given planar truss with a fixed depth, the Pratt configuration is usually the most efficient under static, vertical loading.

The Southern Pacific Railroad bridge in Tempe, Arizona, is a truss bridge built in 1912.Tempe Historic Property Survey at the Tempe Historical Museum; retrieved 2008-Feb-06 The structure, still in use today, consists of nine Pratt truss spans of varying lengths.

The Wright Flyer used a Pratt truss in its wing construction, as the minimization of compression member lengths allowed for lower aerodynamic drag.Dario Gasparini, Case Western Reserve University. The Wright Brothers and the Pratt Truss, presentation slides

Town's lattice truss

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, to form a lattice.

Bowstring truss

Named for their shape, bowstring trusses were first used for arched truss bridges, often confused with tied-arch bridges.

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.

King and queen post trusses

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

The queen post truss, sometimes queenpost or queenspost, is similar to a king post truss in that the outer supports are angled towards the centre 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.

An application of the queen post truss, once common on freight and passenger railroad vehicles – especially ones with wooden bodies – is an inversion of the design applied to bridges. Originally deployed on cars with wood frames (and on some very early steel frame cars with shallow sills) to provide strength to resist vertical deflection, the truss made the car stronger and/or lighter than the alternatives available at the time. The design was superseded when stronger, cheaper steels became available and steel centre sills were incorporated.

Lenticular truss

Lenticular trusses, patented in 1878 by William Douglas (although the Gaunless Bridge of 1823 was the first of the type), 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.

Vierendeel structure

The members of a Vierendeel structure are not triangulated but form rectangular openings. The structure has a frame with fixed joints that are capable of transferring and resisting bending moments. As such, it does not fit the definition of a truss, since it contains non-two-force members: 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,Vierendeel bruggen who developed the design in 1896. It is rarely used for bridges because of higher costs compared to a triangulated truss, but in buildings it has the advantage that a large amount of the exterior envelope remains unobstructed and it can therefore be used for windows and door openings. In some applications this is preferable to a braced-frame system, which would leave some areas obstructed by the diagonal braces.

Statics

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 and 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 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 does not need to be entirely composed of triangles. In mathematical terms, the following necessary condition for stability of a simple truss exists:

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.