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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 A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such as ...
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, trusses typically comprise five or more triangular units constructed with straight members whose ends are connected at joints referred to as ''
nodes In general, a node is a localized swelling (a "knot") or a point of intersection (a Vertex (graph theory), vertex). Node may refer to: In mathematics *Vertex (graph theory), a vertex in a mathematical graph *Vertex (geometry), a point where two ...
''. 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 In physics, tension is described as the pulling force transmitted axially by the means of a string, a rope, chain, or similar object, or by each end of a rod, truss member, or similar three-dimensional object; tension might also be described as t ...
or
compressive In continuum mechanics, stress is a physical quantity. It is a quantity that describes the magnitude of forces that cause deformation. Stress is defined as ''force per unit area''. When an object is pulled apart by a force it will cause elonga ...
. 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 truss In architecture and structural engineering, a space frame or space structure ( 3D truss) is a rigid, lightweight, truss-like structure constructed from interlocking struts in a geometric pattern. Space frames can be used to span large areas wi ...
has members and nodes that extend into
three dimensions Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called ''parameters'') are required to determine the position of an element (i.e., point). This is the informal ...
. The top beams in a truss are called ''top chords'' and are typically in compression, 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'', or from graphic statics (see
Cremona diagram The Cremona diagram, also known as the Cremona-James Clerk Maxwell, Maxwell method, is a graphical method used in statics of trusses to determine the forces in members (graphic statics). The method was developed by the Italian mathematician Luigi ...
) ''polygons''.


Etymology

''Truss'' derives from the Old French word ''trousse'', from around 1200, which means "collection of things bound together". The term ''truss'' has often been used to describe any assembly of members such as a cruck frame or a couple of rafters. One engineering definition is: "A truss is a single plane framework of individual structural member icconnected at their ends of forms a series of triangle icto span a large distance".


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. The joint at which a truss is designed to be supported is commonly referred to as the Munter Point.


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 utilizes two conjoined triangles, is an example of a simple truss.


Planar truss

A planar truss lies in a single
plane Plane(s) most often refers to: * Aero- or airplane, a powered, fixed-wing aircraft * Plane (geometry), a flat, 2-dimensional surface Plane or planes may also refer to: Biology * Plane (tree) or ''Platanus'', wetland native plant * Planes (gen ...
. 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 Beam may refer to: Streams of particles or energy *Light beam, or beam of light, a directional projection of light energy **Laser beam *Particle beam, a stream of charged or neutral particles **Charged particle beam, a spatially localized grou ...
of equal strength would have substantial weight and material cost as compared to a truss. For a given
span Span may refer to: Science, technology and engineering * Span (unit), the width of a human hand * Span (engineering), a section between two intermediate supports * Wingspan, the distance between the wingtips of a bird or aircraft * Sorbitan es ...
, 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 In architecture and structural engineering, a space frame or space structure ( 3D truss) is a rigid, lightweight, truss-like structure constructed from interlocking struts in a geometric pattern. Space frames can be used to span large areas with ...
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. File:Tetrahedron.png, Simple tetrahedron File:SpaceFrame02.png, Diagram of a space frame such as used for a roof File:Pylon-gorai.jpg, This
electrical pylon A transmission tower, also known as an electricity pylon or simply a pylon in British English and as a hydro tower in Canadian English, is a tall structure, usually a steel lattice tower, used to support an overhead power line. In electrical ...
is a three-dimensional truss structure


Types

: ''For more truss types, see truss types used in bridges.'' 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 In vertebrate anatomy, hip (or "coxa"Latin ''coxa'' was used by Celsus in the sense "hip", but by Pliny the Elder in the sense "hip bone" (Diab, p 77) in medical terminology) refers to either an anatomical region or a joint. The hip region is ...
roof construction. A metal plate-connected wood truss is a roof or floor truss whose wood members are connected with
metal connector plates A truss connector plate, or gang plate, is a kind of tie. Truss plates are light gauge metal plates used to connect prefabricated light frame wood trusses. They are produced by punching light gauge galvanized steel to create teeth on one side. T ...
.


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, Caleb Pratt and his son
Thomas Willis Pratt Thomas Willis Pratt, (born 1812, Boston, Massachusetts) was an American engineer. He is best known for his 1844 patent for the Pratt truss, which he designed with his father, Caleb Pratt. Pratt also surveyed the route of the Providence and Worces ...
. 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. 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 given planar truss with a fixed depth, the Pratt configuration is usually the most efficient under static, vertical loading. The
Southern Pacific Railroad The Southern Pacific (or Espee from the railroad initials- SP) was an American Class I railroad network that existed from 1865 to 1996 and operated largely in the Western United States. The system was operated by various companies under the ...
bridge in Tempe, Arizona is a 393 meter (1,291 foot) long truss bridge built in 1912. The structure is composed of nine Pratt truss spans of varying lengths. The bridge is still in use today. The Wright Flyer used a Pratt truss in its wing construction, as the minimization of compression member lengths allowed for lower
aerodynamic drag In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding fl ...
.


Bowstring truss

Named for their shape, bowstring trusses were first used for arched truss bridges, often confused with
tied-arch bridge A tied-arch bridge is an arch bridge in which the outward horizontal forces of the arch(es) caused by tension at the arch ends to a foundation are countered by equal tension of its own gravity plus any element of the total deck structure such grea ...
s. 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 post truss

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 Beam may refer to: Streams of particles or energy *Light beam, or beam of light, a directional projection of light energy **Laser beam *Particle beam, a stream of charged or neutral particles **Charged particle beam, a spatially localized grou ...
action to provide mechanical stability. This truss style is only suitable for relatively short spans.


Lenticular truss

Lenticular trusses, patented in 1878 by William Douglas (although the
Gaunless Bridge Gaunless Bridge was a railway bridge on the Stockton and Darlington Railway. It was completed in 1823 and is one of the first railway bridges to be constructed of iron and the first to use an iron truss. It is also of an unusual lenticular trus ...
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.


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.


Vierendeel truss

The Vierendeel truss is a structure 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. As such, it does not fit the strict 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 Arthur Vierendeel (10 April 1852 – 8 November 1940) was a civil engineer born in Leuven, Belgium. He had a career as a university professor, and civil engineer. The structure known as the Vierendeel truss is named after him. Biography He o ...
,Vierendeel bruggen
/ref> who developed the design in 1896. Its use for bridges is rare due to higher costs compared to a triangulated truss. 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 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 In statics and structural mechanics, a structure is statically indeterminate when the static equilibrium equations force and moment equilibrium conditions are insufficient for determining the internal forces and Reaction (physics), reactions on tha ...
. 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, we have the following necessary condition for stability of a simple truss: : m \ge 2j - r \qquad \qquad \mathrm 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 2''j'' 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. Their member forces depend on the relative
stiffness Stiffness is the extent to which an object resists deformation in response to an applied force. The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is. Calculations The stiffness, k, of a b ...
of the members, in addition to the equilibrium condition described.


Analysis

Because the forces in each of its two main girders are essentially planar, a truss is usually modeled as a two-dimensional plane frame. However if there are significant out-of-plane forces, the structure must be modeled 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; alternatively, half of the weight of each member may be applied to its two end joints. Provided that the members are long and slender, the moments transmitted through the joints are negligible, and the junctions can be treated as "
hinge A hinge is a mechanical bearing that connects two solid objects, typically allowing only a limited angle of rotation between them. Two objects connected by an ideal hinge rotate relative to each other about a fixed axis of rotation: all other ...
s" or "pin-joints". Under these simplifying assumptions, every member of the truss is then subjected to pure compression or pure tension forces – shear, bending moment, and other more-complex stresses are all practically zero. Trusses are physically stronger than other ways of arranging structural elements, because nearly every material can resist a much larger load in tension or compression than in shear, bending, torsion, or other kinds of force. These simplifications make trusses easier to analyze.
Structural analysis Structural analysis is a branch of Solid Mechanics which uses simplified models for solids like bars, beams and shells for engineering decision making. Its main objective is to determine the effect of loads on the physical structures and thei ...
of trusses of any type can readily be carried out using a matrix method such as the
direct stiffness method As one of the methods of structural analysis, the direct stiffness method, also known as the matrix stiffness method, is particularly suited for computer-automated analysis of complex structures including the statically indeterminate type. It is a ...
, the flexibility method, or the finite element method.


Forces in members

Illustrated is a simple,
statically determinate In statics and structural mechanics, a structure is statically indeterminate when the static equilibrium equations force and moment equilibrium conditions are insufficient for determining the internal forces and Reaction (physics), reactions on tha ...
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, the reactive forces at A and B are vertical, equal, and half the total load. The internal
force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a p ...
s in the members of the truss can be calculated in a variety of ways, including graphical methods: *
Cremona diagram The Cremona diagram, also known as the Cremona-James Clerk Maxwell, Maxwell method, is a graphical method used in statics of trusses to determine the forces in members (graphic statics). The method was developed by the Italian mathematician Luigi ...
* Culmann diagram * Ritter analytical method ( method of sections)


Design of members

A truss can be thought of as a
beam Beam may refer to: Streams of particles or energy *Light beam, or beam of light, a directional projection of light energy **Laser beam *Particle beam, a stream of charged or neutral particles **Charged particle beam, a spatially localized grou ...
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 stress. 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. In addition to carrying the static forces, the members serve additional functions of stabilizing each other, preventing buckling. In the adjacent 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. 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 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 stress of the bolt connections used in the joints. 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.


Applications


Post frame structures

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. 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 Glued laminated timber, commonly referred to as glulam, is a type of structural engineered wood product constituted by layers of dimensional lumber bonded together with durable, moisture-resistant structural adhesives so that all of the grain ru ...
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.


Gallery

File:Bank of china night.jpg, The Hong Kong Bank of China Tower has an externally visible truss structure File:HK HSBC Main Building 2008.jpg, The HSBC Main Building, Hong Kong has an externally visible truss structure File:Below Auckland Harbour Bridge Hossen27.jpg, Support structure under the Auckland Harbour Bridge File:Auckland Harbour Bridge Watchman.jpg, The Auckland Harbour Bridge seen from
Watchman Island Watchman Island is a tiny sandstone island in the Waitemata Harbour of Auckland, New Zealand. It lies approximately 600 metres north of the Herne Bay suburb. History The island is known to Tāmaki Māori iwi as Matungaegae, and was the si ...
to its west File:The Little Belt Bridge (1935).jpeg, '' Little Belt Bridge'': a truss bridge in Denmark File:Bow-string-truss.jpg,
Pre-fabricated Prefabrication is the practice of assembling components of a structure in a factory or other manufacturing site, and transporting complete assemblies or sub-assemblies to the construction site where the structure is to be located. The term is u ...
steel bow string roof trusses built in 1942 for war department properties in Northern Australia File:Truss Dachstuhl.jpg, Roof truss in a side building of
Cluny Abbey Cluny Abbey (; , formerly also ''Cluni'' or ''Clugny''; ) is a former Benedictine monastery in Cluny, Saône-et-Loire, France. It was dedicated to Saint Peter. The abbey was constructed in the Romanesque architectural style, with three churches ...
, France File:Queen-post-truss.png, A section through a queen post timber roof truss File:Woodlands mall3 texas.jpg, A space truss carrying a floor in The Woodlands Mall File:Elledningsstolpe2 lund.jpg,
Electricity pylon A transmission tower, also known as an electricity pylon or simply a pylon in British English and as a hydro tower in Canadian English, is a tall structure, usually a steel lattice tower, used to support an overhead power line. In electrical ...
File:Inside wboylston old stone church.jpg, Timber roof truss File:Temporary bridge made of Truss.jpg, Modern temporary bridge made of Bailey bridge truss panels in Montreal
Québec Quebec ( ; )According to the Government of Canada, Canadian government, ''Québec'' (with the acute accent) is the official name in Canadian French and ''Quebec'' (without the accent) is the province's official name in Canadian English is ...
File:Three dimensional truss construction Unic Rotarex®.jpg, alt=Three dimensional truss construction, Three dimensional truss construction File:Kratownica statycznie wyznaczalna - obciążenia.svg, Example of calculation truss forces made by program that use matrix Gauss solving method


See also

* Lattice tower * 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 *
Structural mechanics Structural mechanics or Mechanics of structures is the computation of deformations, deflections, and internal forces or stresses (''stress equivalents'') within structures, either for design or for performance evaluation of existing structures. It ...
* Serrurier truss, a truss form used for telescopes * Stress: ** Compressive stress ** Tensile stress *
Structural steel Structural steel is a category of steel used for making construction materials in a variety of shapes. Many structural steel shapes take the form of an elongated beam having a profile of a specific cross section. Structural steel shapes, sizes, ...
* Tensegrity truss, a truss where no compression member touches any other compression member * Truss rod, a guitar part


References


External links


Truss Calculator
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