Truss

Overview

In architecture

and structural engineering

, a

comprising one or more triangular units constructed with straight members whose ends are connected at joints referred to as 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 tensile or compressive forces. Moments (torques) are explicitly excluded because, and only because, all the joints in a truss are treated as revolutes

.

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.

A truss consists of straight members connected at joints.

Architecture

Architecture is both the process and product of planning, designing and construction. Architectural works, in the material form of buildings, are often perceived as cultural and political symbols and as works of art...

and structural engineering

Structural engineering

Structural engineering is a field of engineering dealing with the analysis and design of structures that support or resist loads. Structural engineering is usually considered a specialty within civil engineering, but it can also be studied in its own right....

, a

**truss**is a structureArchitectural structure

An architectural structure is a free-standing, immobile outdoor constructed element. The structure may be temporary or permanent.Structures include buildings and nonbuilding structures . Examples of building structures include houses, town halls, libraries, and skyscrapers...

comprising one or more triangular units constructed with straight members whose ends are connected at joints referred to as nodes

Vertex (geometry)

In geometry, a vertex is a special kind of point that describes the corners or intersections of geometric shapes.-Of an angle:...

. 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 tensile or compressive forces. Moments (torques) are explicitly excluded because, and only because, all the joints in a truss are treated as revolutes

Revolute joint

A revolute joint is a one degree of freedom kinematic pair used in mechanisms. Revolute joints provide single-axis rotation function used in many places such as door hinges, folding mechanisms, and other uni-axial rotation devices. -See also:* Cylindrical joint* Kinematics* Degrees of freedom *...

.

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.

A truss consists of straight members connected at joints.

Unanswered Questions

Encyclopedia

In architecture

and structural engineering

, a

comprising one or more triangular units constructed with straight members whose ends are connected at joints referred to as 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 tensile or compressive forces. Moments (torques) are explicitly excluded because, and only because, all the joints in a truss are treated as revolutes

.

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.

roof consisting of rafter

s 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. The traditional diamond-shape bicycle frame, which utilizes two conjoined triangles, is an example of a simple 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 length, 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.

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. 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

There are two basic types of truss:

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

.

railway engineers, Caleb Pratt and his son Thomas Willis Pratt

. The design uses vertical members for compression and horizontal members 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. 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.

The Southern Pacific Railroad

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.

s, known as 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 Platt truss.

The

action to provide mechanical stability. This truss style is only suitable for relatively short spans.

Ithiel Town

designed

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 Belgian

engineer Arthur Vierendeel, 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 truss in buildings is that a large amount of the exterior envelope remains unobstructed and can be used for fenestration

and door openings. This is preferable to a braced-frame system, which would leave some areas obstructed by the diagonal braces.

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

:

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 , the truss is said to be statically determinate, because the (m+3) internal member forces and support reactions can then be completely determined by 2j equilibrium

equations, once we know the external loads

and the geometry of the truss. Given a certain number of joints, this is the minimum number of members, in the sense that if any member is taken out (or fails), then the truss as a whole fails. While the relation (a) is necessary, it is not sufficient for stability, which also depends on the truss geometry, support conditions and the load carrying capacity of the members.

Some structures are built with more than this minimum number of truss members. Those structures may survive even when some of the members fail. Their member forces depend on the relative stiffness

of the members, in addition to the equilibrium condition described.

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 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 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 direct stiffness method

, the flexibility method

or the finite element method.

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:

where the web consists of a series of separate members instead of a continuous plate. In the truss, the lower horizontal member (the

and 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

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.

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.

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

of the individual truss members. For members under tension the cross-sectional area A can be found using A = F × γ / σ

s) and σ

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.

. Based of 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.

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.

Architecture

Architecture is both the process and product of planning, designing and construction. Architectural works, in the material form of buildings, are often perceived as cultural and political symbols and as works of art...

and structural engineering

Structural engineering

Structural engineering is a field of engineering dealing with the analysis and design of structures that support or resist loads. Structural engineering is usually considered a specialty within civil engineering, but it can also be studied in its own right....

, a

**truss**is a structureArchitectural structure

An architectural structure is a free-standing, immobile outdoor constructed element. The structure may be temporary or permanent.Structures include buildings and nonbuilding structures . Examples of building structures include houses, town halls, libraries, and skyscrapers...

comprising one or more triangular units constructed with straight members whose ends are connected at joints referred to as nodes

Vertex (geometry)

In geometry, a vertex is a special kind of point that describes the corners or intersections of geometric shapes.-Of an angle:...

. 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 tensile or compressive forces. Moments (torques) are explicitly excluded because, and only because, all the joints in a truss are treated as revolutes

Revolute joint

A revolute joint is a one degree of freedom kinematic pair used in mechanisms. Revolute joints provide single-axis rotation function used in many places such as door hinges, folding mechanisms, and other uni-axial rotation devices. -See also:* Cylindrical joint* Kinematics* Degrees of freedom *...

.

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.

## Characteristics of Trusses

A truss consists of straight members connected at joints. 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. In comparison, both the angles and the lengths of a four-sided figure must be fixed for it to retain its shape.### Planar Truss

The simplest form of a truss is one single triangle. This type of truss is seen in a framedFraming (construction)

Framing, in construction known as light-frame construction, is a building technique based around structural members, usually called studs, which provide a stable frame to which interior and exterior wall coverings are attached, and covered by a roof comprising horizontal ceiling joists and sloping...

roof consisting of rafter

Rafter

A rafter is one of a series of sloped structural members , that extend from the ridge or hip to the downslope perimeter or eave, designed to support the roof deck and its associated loads.-Design:...

s and a ceiling joist

Joist

A joist, in architecture and engineering, is one of the horizontal supporting members that run from wall to wall, wall to beam, or beam to beam to support a ceiling, roof, or floor. It may be made of wood, steel, or concrete. Typically, a beam is bigger than, and is thus distinguished from, a joist...

. and in other mechanical structures such as bicycles

Bicycle frame

A bicycle frame is the main component of a bicycle, on to which wheels and other components are fitted. The modern and most common frame design for an upright bicycle is based on the safety bicycle, and consists of two triangles, a main triangle and a paired rear triangle...

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. The traditional diamond-shape bicycle frame, which utilizes two conjoined triangles, is an example of a simple truss.

A planar truss lies in a single plane

Plane (mathematics)

In mathematics, a plane is a flat, two-dimensional surface. A plane is the two dimensional analogue of a point , a line and a space...

. 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

Girder

A girder is a support beam used in construction. Girders often have an I-beam cross section for strength, but may also have a box shape, Z shape or other forms. Girder is the term used to denote the main horizontal support of a structure which supports smaller beams...

or beam

Beam (structure)

A beam is a horizontal structural element that is capable of withstanding load primarily by resisting bending. The bending force induced into the material of the beam as a result of the external loads, own weight, span and external reactions to these loads is called a bending moment.- Overview...

of equal strength would have substantial weight and material cost as compared to a truss. For a given span length, 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 frameSpace frame

A space frame or space structure is a truss-like, lightweight rigid structure constructed from interlocking struts in a geometric pattern. Space frames can be used to span large areas with few interior supports...

truss is a three-dimensional framework of members pinned at their ends. A tetrahedron

Tetrahedron

In geometry, a tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex. A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids...

shape is the simplest space truss, consisting of six members which 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

## Truss Types

- For more truss types, see List of truss types or Truss Bridge.

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

Metal connector plates

A truss connector plate is manufactured from ASTM A653/A653M, A591, A792/A792M, or A167 structural quality steel and is protected with zinc or zinc-aluminum alloy coatings or their stainless steel equivalent...

.

### Pratt Truss

The**Pratt truss**was patented in 1844 by two BostonBoston

Boston is the capital of and largest city in Massachusetts, and is one of the oldest cities in the United States. The largest city in New England, Boston is regarded as the unofficial "Capital of New England" for its economic and cultural impact on the entire New England region. The city proper had...

railway engineers, Caleb Pratt and his son Thomas Willis Pratt

Thomas Willis Pratt

Thomas Willis Pratt, born 1812 in Boston, Massachusetts, USA, was an American engineer. He is best known for his 1844 patent for the Pratt truss, which he designed with his father Caleb Pratt. He died in 1875.-References:...

. The design uses vertical members for compression and horizontal members 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. 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

Buckling

In science, buckling is a mathematical instability, leading to a failure mode.Theoretically, buckling is caused by a bifurcation in the solution to the equations of static equilibrium...

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

Southern Pacific Railroad

The Southern Pacific Transportation Company , earlier Southern Pacific Railroad and Southern Pacific Company, and usually simply called the Southern Pacific or Espee, was an American railroad....

bridge in Tempe

Tempe, Arizona

Tempe is a city in Maricopa County, Arizona, USA, with the Census Bureau reporting a 2010 population of 161,719. The city is named after the Vale of Tempe in Greece. Tempe is located in the East Valley section of metropolitan Phoenix; it is bordered by Phoenix and Guadalupe on the west, Scottsdale...

, Arizona

Arizona

Arizona ; is a state located in the southwestern region of the United States. It is also part of the western United States and the mountain west. The capital and largest city is Phoenix...

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

Wright Flyer

The Wright Flyer was the first powered aircraft, designed and built by the Wright brothers. They flew it four times on December 17, 1903 near the Kill Devil Hills, about four miles south of Kitty Hawk, North Carolina, U.S.The U.S...

used a Pratt truss in its wing construction, as the minimization of compression member lengths allowed for lower aerodynamic drag.

### Bowstring Truss

Named for their shape, bowstring trusses were first used for arched truss bridgeTruss bridge

A truss bridge is a bridge composed of connected elements which may be stressed from tension, compression, or sometimes both in response to dynamic loads. Truss bridges are one of the oldest types of modern bridges...

s, known as tied-arch bridges.

Thousands of bowstring trusses were used during World War II

World War II

World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...

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 Platt 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 center of the structure. The primary difference is the horizontal extension at the centre which relies on beamBeam (structure)

A beam is a horizontal structural element that is capable of withstanding load primarily by resisting bending. The bending force induced into the material of the beam as a result of the external loads, own weight, span and external reactions to these loads is called a bending moment.- Overview...

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, 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 Tattice Truss

American architectArchitect

An architect is a person trained in the planning, design and oversight of the construction of buildings. To practice architecture means to offer or render services in connection with the design and construction of a building, or group of buildings and the space within the site surrounding the...

Ithiel Town

Ithiel Town

Ithiel Town was a prominent American architect and civil engineer. One of the first generation of professional architects in the United States, Town made significant contributions to American architecture in the first half of the 19th century. He was high-strung, sophisticated, generous,...

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.### Vierendeel Truss

The**Vierendeel truss**is a truss where the members are not triangulated but form rectangular openings, and is a frameRigid frame

A rigid frame in structural engineering is the load-resisting skeleton constructed with straight or curved members interconnected by mostly rigid connections which resist movements induced at the joints of members. Its member can take bending moment,shear and axial loads....

with fixed joints that are capable of transferring and resisting bending moment

Bending Moment

A bending moment exists in a structural element when a moment is applied to the element so that the element bends. Moments and torques are measured as a force multiplied by a distance so they have as unit newton-metres , or pound-foot or foot-pound...

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 Belgian

Belgium

Belgium , officially the Kingdom of Belgium, is a federal state in Western Europe. It is a founding member of the European Union and hosts the EU's headquarters, and those of several other major international organisations such as NATO.Belgium is also a member of, or affiliated to, many...

engineer Arthur Vierendeel, 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 truss in buildings is that a large amount of the exterior envelope remains unobstructed and can be used for fenestration

Window

A window is a transparent or translucent opening in a wall or door that allows the passage of light and, if not closed or sealed, air and sound. Windows are usually glazed or covered in some other transparent or translucent material like float glass. Windows are held in place by frames, which...

and door openings. This is preferable to a braced-frame system, which would leave some areas obstructed by the diagonal braces.

## Statics of Trusses

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 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 magnitudee may be compression or tension forces.Trusses that are supported at more than two positions are said to be statically indeterminate

Statically indeterminate

In statics, a structure is statically indeterminate when the static equilibrium equations are insufficient for determining the internal forces and reactions on that structure....

, 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

Mechanical equilibrium

A standard definition of static equilibrium is:This is a strict definition, and often the term "static equilibrium" is used in a more relaxed manner interchangeably with "mechanical equilibrium", as defined next....

:

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 , the truss is said to be statically determinate, because the (m+3) internal member forces and support reactions can then be completely determined by 2j equilibrium

Mechanical equilibrium

A standard definition of static equilibrium is:This is a strict definition, and often the term "static equilibrium" is used in a more relaxed manner interchangeably with "mechanical equilibrium", as defined next....

equations, once we know the external loads

Structural load

Structural loads or actions are forces, deformations or accelerations applied to a structure or its components.Loads cause stresses, deformations and displacements in structures. Assessment of their effects is carried out by the methods of structural analysis...

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

Stiffness is the resistance of an elastic body to deformation by an applied force along a given degree of freedom when a set of loading points and boundary conditions are prescribed on the elastic body.-Calculations:...

of the members, in addition to the equilibrium condition described.

## Analysis of Trusses

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 moments

Moment (physics)

In physics, the term moment can refer to many different concepts:*Moment of force is the tendency of a force to twist or rotate an object; see the article torque for details. This is an important, basic concept in engineering and physics. A moment is valued mathematically as the product of the...

transmitted through the joints are negligible and they can be treated as "hinge

Hinge

A hinge is a type of 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. Hinges may be made of flexible material or of moving components...

s" or 'pin-joints'. Every member of the truss is then in pure compression or pure tension – shear, bending moment, and other more complex stresses

Stress (physics)

In continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are a reaction to external forces applied on the body...

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

Structural analysis

Structural analysis is the determination of the effects of loads on physical structures and their components. Structures subject to this type of analysis include all that must withstand loads, such as buildings, bridges, vehicles, machinery, furniture, attire, soil strata, prostheses and...

of trusses of any type can readily be carried out using a matrix method such as the direct stiffness method

Direct stiffness method

As one of the methods of structural analysis, the direct stiffness method , also known as the displacement method or matrix stiffness method, is particularly suited for computer-automated analysis of complex structures including the statically indeterminate type...

, the flexibility method

Flexibility method

In structural engineering, the flexibility method is the classical consistent deformation method for computing member forces and displacements in structural systems...

or the finite element method.

### Forces in Members

On the right is a simple, statically determinate flat truss with 9 joints and (2 x 9) − 3 = 15 members. External loads are concentrated in the outer joints. Since this is a symmetricalSymmetry

Symmetry generally conveys two primary meanings. The first is an imprecise sense of harmonious or aesthetically pleasing proportionality and balance; such that it reflects beauty or perfection...

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

Force

In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

s in the members of the truss can be calculated in a variety of ways including the graphical methods:

- Cremona diagramCremona diagramThe Cremona diagram is a graphical method used in statics of trusses to determine the forces in members . The method was created by the Italian mathematician Luigi Cremona....
- CulmannCarl CulmannCarl Culmann was a German structural engineer.Born in Bad Bergzabern, Rhenish Palatinate, in modern-day Germany, Culmann's father, a pastor, tutored him at home before enrolling him at the military engineering school at Metz to prepare for entry to the École Polytechnique...

diagram - the analytical Ritter method (method of sections).

### Design of Members

A truss can be thought of as a beamBeam (structure)

A beam is a horizontal structural element that is capable of withstanding load primarily by resisting bending. The bending force induced into the material of the beam as a result of the external loads, own weight, span and external reactions to these loads is called a bending moment.- Overview...

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 tensionTension (mechanics)

In physics, tension is the magnitude of the pulling force exerted by a string, cable, chain, or similar object on another object. It is the opposite of compression. As tension is the magnitude of a force, it is measured in newtons and is always measured parallel to the string on which it applies...

and compression, fulfilling the same function as the flange

Flange

A flange is an external or internal ridge, or rim , for strength, as the flange of an iron beam such as an I-beam or a T-beam; or for attachment to another object, as the flange on the end of a pipe, steam cylinder, etc., or on the lens mount of a camera; or for a flange of a rail car or tram wheel...

s of an I-beam

I-beam

-beams, also known as H-beams, W-beams , rolled steel joist , or double-T are beams with an - or H-shaped cross-section. The horizontal elements of the "" are flanges, while the vertical element is the web...

. Which chord carries tension and which carries compression depends on the overall direction of bending

Bending

In engineering mechanics, bending characterizes the behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element. The structural element is assumed to be such that at least one of its dimensions is a small fraction, typically...

. 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 shearShearing (physics)

Shearing in continuum mechanics refers to the occurrence of a shear strain, which is a deformation of a material substance in which parallel internal surfaces slide past one another. It is induced by a shear stress in the material...

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.

In addition to carrying the static forces, the members serve additional functions of stabilizing each other, preventing buckling

Buckling

In science, buckling is a mathematical instability, leading to a failure mode.Theoretically, buckling is caused by a bifurcation in the solution to the equations of static equilibrium...

. 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.

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

Prestressed concrete

Prestressed concrete is a method for overcoming concrete's natural weakness in tension. It can be used to produce beams, floors or bridges with a longer span than is practical with ordinary reinforced concrete...

and fabrication methods, such as automated weld

Weld

Weld most commonly refers to a joint formed by welding.Weld may also refer to:-People:* Weld family, an extended family of New England** Theodore Dwight Weld** Tuesday Weld* Weld-Blundell family* Cecil Weld-Forester, 1st Baron Forester...

ing, have significantly influenced the design of modern bridge

Bridge

A bridge is a structure built to span physical obstacles such as a body of water, valley, or road, for the purpose of providing passage over the obstacle...

s.

Once the force on each member is known,

the next step is to determine the cross section

Cross section (geometry)

In geometry, a cross-section is the intersection of a figure in 2-dimensional space with a line, or of a body in 3-dimensional space with a plane, etc...

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 codeBuilding code

A building code, or building control, is a set of rules that specify the minimum acceptable level of safety for constructed objects such as buildings and nonbuilding structures. The main purpose of building codes are to protect public health, safety and general welfare as they relate to the...

s) and σ

_{y}is the yield tensile strengthTensile strength

Ultimate tensile strength , often shortened to tensile strength or ultimate strength, is the maximum stress that a material can withstand while being stretched or pulled before necking, which is when the specimen's cross-section starts to significantly contract...

of the steel used.

The members under compression also have to be designed to be safe against buckling.

The weight of a truss member depends directly on its cross section—that weight partially determines how strong the other members of the truss need to be.

Giving one member a larger cross section than on a previous iteration requires giving other members a larger cross section as well, to hold the greater weight of the first member—one needs to go through another iteration to find exactly how much greater the other members need to be.

Sometimes the designer goes through several iterations of the design process to converge on the "right" cross section for each member. On the other hand, reducing the size of one member from the previous iteration merely makes the other members have a larger (and more expensive) safety factor than is technically necessary, but doesn't require another iteration to find a buildable truss.

The effect of the weight of the individual truss members in a large truss, such as a bridge, is usually insignificant compared to the force of the external loads.

### Design of Joints

After determining the minimum cross section of the members, the last step in the design of a truss would be detailing of the bolted joints, e.g., involving shear of the bolt connections used in the joints, see also shear stressShear stress

A shear stress, denoted \tau\, , is defined as the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section...

. Based of 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.

### 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 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.

## See also

- Andreini tessellationConvex uniform honeycombIn geometry, a convex uniform honeycomb is a uniform tessellation which fills three-dimensional Euclidean space with non-overlapping convex uniform polyhedral cells.Twenty-eight such honeycombs exist:* the familiar cubic honeycomb and 7 truncations thereof;...

s, the only 28 ways to fill 3D space with trusses that have identical joints everywhere - Brown trussBrown trussA Brown truss is a type of bridge truss, used in covered bridges. It is noted for its economical use of materials and is named after the inventor, Josiah Brown Jr., of Buffalo, New York, who patented it July 7, 1857 as US patent 17,722.-Description:...
- Geodesic domeGeodesic domeA geodesic dome is a spherical or partial-spherical shell structure or lattice shell based on a network of great circles on the surface of a sphere. The geodesics intersect to form triangular elements that have local triangular rigidity and also distribute the stress across the structure. When...

, a truss in the shape of a sphere - GirderGirderA girder is a support beam used in construction. Girders often have an I-beam cross section for strength, but may also have a box shape, Z shape or other forms. Girder is the term used to denote the main horizontal support of a structure which supports smaller beams...
- List of truss types
- Mechanics of structures
- Serrurier trussSerrurier trussA Serrurier truss is used in telescope tube assembly construction. The design was created in 1935 by engineer Mark U. Serrurier when he was working on the Mt. Palomar Hale telescope. The design solves the problem of truss flexing by supporting the primary objective mirror and the secondary mirror...

, a truss form used for telescopes - Space frameSpace frameA space frame or space structure is a truss-like, lightweight rigid structure constructed from interlocking struts in a geometric pattern. Space frames can be used to span large areas with few interior supports...
- Stress:
- Compressive stress
- Tensile stress

- Structural steelStructural steelStructural steel is steel construction material, a profile, formed with a specific shape or cross section and certain standards of chemical composition and mechanical properties...
- Tensegrity trussTensegrityTensegrity, tensional integrity or floating compression, is a structural principle based on the use of isolated components in compression inside a net of continuous tension, in such a way that the compressed members do not touch each other and the prestressed tensioned members delineate the...

, a truss where no compression member touches any other compression member - Truss bridgeTruss bridgeA truss bridge is a bridge composed of connected elements which may be stressed from tension, compression, or sometimes both in response to dynamic loads. Truss bridges are one of the oldest types of modern bridges...
- Truss rodTruss rodThe truss rod is part of a guitar or banjo used to stabilize and adjust the lengthwise forward curvature , of the neck. Usually it is a steel rod that runs inside the neck and has a bolt that can be used to adjust its tension...

, a guitarGuitarThe guitar is a plucked string instrument, usually played with fingers or a pick. The guitar consists of a body with a rigid neck to which the strings, generally six in number, are attached. Guitars are traditionally constructed of various woods and strung with animal gut or, more recently, with...

part - Timber roof trussesTimber roof trusses-King post trusses:King post truss A roof truss that is mostly wooden with two principal rafters, a tie beam and a central vertical King post. The simplest of trusses...

## External links

- Historic Bridges of Michigan and Elsewhere With a focus on metal truss bridges, this site provides photos, information, maps, and links
- "Preventing Injuries and Deaths of Fire Fighters Due to Truss System Failures," National Institute for Occupational Safety and HealthNational Institute for Occupational Safety and HealthThe National Institute for Occupational Safety and Health is the United States’ federal agency responsible for conducting research and making recommendations for the prevention of work-related injury and illness. NIOSH is part of the Centers for Disease Control and Prevention within the U.S...

, Accessed September 13, 2007 - Classical Truss Theory
- An Introduction to Historic Truss Bridges
- Truss bridge designer simulation (requires Java)
- Web-based 2D Truss Analysis Program (requires Flash)
- Web-based 3D Truss Analysis Program (requires Flash)
- Trusses in 20th-century architecture
- Structural Building Components Association
- American Lenticular Truss Bridges