Information about Truss
In architecture and structural engineering, a truss is a structure comprising one or more triangular units constructed with straight slender members whose ends are connected at joints.
A plane truss is one where all the members and joints lie within a 2-dimensional plane, while a space truss has members and joints extending into 3 dimensions.
A metal plate-connected wood truss is a roof or floor truss whose wood members are connected with metal connector plates.
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 special truss is the Vierendeel truss, named after the Belgian engineer Arthur Vierendeel [1], who developed the design in 1896. The Vierendeel truss is a truss 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. In this statically indeterminate structure the individual horizontal and vertical members are designed as beams. Diagonal bracing is omitted as the joints are designed to withstand the moments that occur at the ends of the members. Trusses of this type are used in some bridges (see Vierendeel bridge), and were also used in the frame of the Twin Towers of the World Trade Center[2]. By eliminating diagonal members, the creation of rectangular openings for windows and doors is simplified, since this truss can reduce or eliminate the need for compensating shear walls.
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 composed entirely of triangles. In mathematical terms, we have the following necessary condition for stability:
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. They are called statically indeterminate structures, because their member forces also depend on the relative stiffness of the members, in addition to the equilibrium condition.
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 frame.
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 the adjacent joints. Provided the members are long and slender, the moments transmitted through the joints are negligible and they can be treated as "hinges" 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 matrix stiffness method, the flexibility method or the finite element method.
The internal forces in the members of the truss can be calculated in a variety of ways including the graphical methods: Or the analytical Ritter method (method of sections).
In the Cremona method, first the external forces and reactions are drawn (to scale) forming a vertical line in the lower right side of the picture. This is the sum of all the force vectors and is equal to zero as there is mechanical equilibrium.
Since the equilibrium holds for the external forces on the entire truss construction, it also holds for the internal forces acting on each joint. For a joint to be at rest the sum of the forces on a joint must also be equal to zero. Starting at joint Aorda, the internal forces can be found by drawing lines in the Cremona diagram representing the forces in the members 1 and 4, going clockwise; VA (going up) load at A (going down), force in member 1 (going down/left), member 4 (going up/right) and closing with VA. As the force in member 1 is towards the joint, the member is under compression, the force in member 4 is away from the joint so the member 4 is under tension. The length of the lines for members 1 and 4 in the diagram, multiplied with the chosen scale factor is the magnitude of the force in members 1 and 4.
Now, in the same way the forces in members 2 and 6 can be found for joint C; force in member 1 (going up/right), force in C going down, force in 2 (going down/left), force in 6 (going up/left) and closing with the force in member 1.
The same steps can be taken for joints D, H and E resulting in the complete Cremona diagram where the internal forces in all members are known.
In a next phase the forces caused by wind must be considered. Wind will cause pressure on the upwind side of a roof (and truss) and suction on the downwind side. This will translate to asymmetrical loads but the Cremona method is the same. Wind force may introduce larger forces in the individual truss members than the static vertical loads.
The diagonal and vertical members form the truss web, and carry the shear force. Individually, they are also in tension and compression, the exact arrangement of forces depending on the type of truss and again on the direction of bending. In the truss shown above right, the vertical members are in tension, and the diagonals are in compression.
In addition to carrying the static forces, the members serve additional functions of stabilizing each other, preventing buckling. In the picture, the top chord is prevented from buckling by the presence of bracing and by the stiffness of the web members.
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 / σy, 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.
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A plane truss is one where all the members and joints lie within a 2-dimensional plane, while a space truss has members and joints extending into 3 dimensions.
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The Auckland Harbour Bridge from Watchman Island, west of it.
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Truss bridge for a single track railway, converted to pedestrian use and pipeline support
History
The earliest trusses were made out of wood. The ancient Greeks used truss construction for their dwellings. In 1570 Andrea Palladio published I Quattro Libri dell'Architettura, which contained instructions for wooden trussed bridges.Truss types
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Support structure under the Auckland Harbour Bridge.
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Pre fabricated steel bow string roof trusses built 1942 for war department properties in Northern Australia.
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.
Bow string roof truss
Named for its distinctive shape, thousands of bow strings were used during World War II for aircraft hangars and other military buildings.Vierendeel truss
)
A Vierendeel bridge; note the lack of diagonal elements in the primary structure and the way bending loads are carried between elements
King post truss
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Queen post truss
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Town's lattice truss
See Ithiel Town's lattice trussStatics of trusses
A truss that is assumed to comprise of members that are connected by means of pin joints and which is supported at both ends by means of a hinged joints or rollers is described as being statically determinate. Newton's Laws apply to the structure as a whole as well as to each node or joint. In order for any node which may be subjected to an external load or force to remain static in space the following conditions are required to be true: the sum of all horizontal forces, and the sum of all vertical forces as well as the sum of all moments acting about the node need to equate to zero. Analysis of these conditions at each node yields the magnitude of the forces in each member of the truss. These may be compression or tension forces.Trusses that are supported at more than two positions are said to be statically indeterminate and the application of Newton's Laws alone is not sufficient to determine the member forces.
In order for a truss with pin-connected members to be stable, it must be composed entirely of triangles. In mathematical terms, we have the following necessary condition for stability:
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. They are called statically indeterminate structures, because their member forces also depend on the relative stiffness of the members, in addition to the equilibrium condition.
Analysis of trusses
)
Cremona diagram for a plane truss
Because the forces in each of its two main girders are essentially planar, a truss is usually modelled as a two-dimensional plane frame. If there are significant out-of-plane forces, the structure must be modelled as a three-dimensional space frame.
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 the adjacent joints. Provided the members are long and slender, the moments transmitted through the joints are negligible and they can be treated as "hinges" 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 matrix stiffness method, the flexibility method 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 symmetrical truss with symmetrical vertical loads, it is clear to see that the reactions at A and B are equal, vertical and half the total load.The internal forces in the members of the truss can be calculated in a variety of ways including the graphical methods: Or the analytical Ritter method (method of sections).
In the Cremona method, first the external forces and reactions are drawn (to scale) forming a vertical line in the lower right side of the picture. This is the sum of all the force vectors and is equal to zero as there is mechanical equilibrium.
Since the equilibrium holds for the external forces on the entire truss construction, it also holds for the internal forces acting on each joint. For a joint to be at rest the sum of the forces on a joint must also be equal to zero. Starting at joint Aorda, the internal forces can be found by drawing lines in the Cremona diagram representing the forces in the members 1 and 4, going clockwise; VA (going up) load at A (going down), force in member 1 (going down/left), member 4 (going up/right) and closing with VA. As the force in member 1 is towards the joint, the member is under compression, the force in member 4 is away from the joint so the member 4 is under tension. The length of the lines for members 1 and 4 in the diagram, multiplied with the chosen scale factor is the magnitude of the force in members 1 and 4.
Now, in the same way the forces in members 2 and 6 can be found for joint C; force in member 1 (going up/right), force in C going down, force in 2 (going down/left), force in 6 (going up/left) and closing with the force in member 1.
The same steps can be taken for joints D, H and E resulting in the complete Cremona diagram where the internal forces in all members are known.
In a next phase the forces caused by wind must be considered. Wind will cause pressure on the upwind side of a roof (and truss) and suction on the downwind side. This will translate to asymmetrical loads but the Cremona method is the same. Wind force may introduce larger forces in the individual truss members than the static vertical loads.
Design of members
A truss can be thought of as a 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 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 force. Individually, they are also in tension and compression, the exact arrangement of forces depending on the type of truss and again on the direction of bending. In the truss shown above right, the vertical members are in tension, and the diagonals are in compression.
In addition to carrying the static forces, the members serve additional functions of stabilizing each other, preventing buckling. In the picture, the top chord is prevented from buckling by the presence of bracing and by the stiffness of the web members.
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.
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A building under construction in Shanghai. The truss sections stabilize the building and will house mechanical floors.
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 / σy, 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 of the bolt connections used in the joints, see also shear stress..jpeg'))
See also
- 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
- Girder
- Lattice bridge, using a truss form allowing lightweight components
- Mechanics of structures
- Serrurier truss, a truss form used for telescopes
- Space frame
- Stress:
- Compressive stress
- Tensile stress
- Structural steel
- Tensegrity truss, a truss where no compression member touches any other compression member
- Truss bridge
- Truss rod, a guitar part
- Vierendeel bridge
References
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 Health, Accessed September 13, 2007
- Classical Truss Theory
- An Introduction to Historic Truss Bridges
- truss bridge designer simulation (requires Java)
- Trusses in 20th-century architecture
- Vierendeel bridges (in Dutch)
- Residential trussed roofs Australia
- Structural Building Components Association
- Aluminum Truss Systems
Architecture is the art and science of designing buildings and structures. A wider definition often includes the design of the total built environment: from the macrolevel of town planning, urban design, and landscape architecture to the microlevel of construction details and,
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Structural engineering is a field of engineering that deals with the design of a structural system(s) with the purpose of supporting and resisting various loads. Though other disciplines touch on this field, a physical object or system is truly considered a part of structural
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An architectural structure is a free-standing, immobile outdoor construction.
The structure may be permanent. Typical examples include buildings and nonbuilding structures such as bridges, dams, electricity pylons, and radio masts.
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The structure may be permanent. Typical examples include buildings and nonbuilding structures such as bridges, dams, electricity pylons, and radio masts.
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The term ancient Greece refers to the periods of Greek history in Classical Antiquity, lasting ca. 750 BC[1] (the archaic period) to 146 BC (the Roman conquest). It is generally considered to be the seminal culture which provided the foundation of Western Civilization.
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Andrea Palladio (November 30, 1508 – August 19, 1580), was an Italian architect, widely considered the most influential person in the history of Western architecture.
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I Quattro Libri dell'Architettura (The Four Books of Architecture) was published in 1570, in four volumes written by the architect Andrea Palladio (1508-1580), whose name is identified with an architectural movement named after him known as Palladian architecture.
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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.
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hip is the bony projection of the femur which is known as the greater trochanter, and the overlying muscle and fat. The hip joint is the joint between the femur and acetabulum of the pelvis and its primary function is to support the weight of the body in both static
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Allied powers:
Soviet Union
United States
United Kingdom
China
France
...et al. Axis powers:
Germany
Japan
Italy
...et al.
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Soviet Union
United States
United Kingdom
China
France
...et al. Axis powers:
Germany
Japan
Italy
...et al.
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Motto
Eendracht maakt macht (Dutch)
L'union fait la force" (French)
Einigkeit macht stark
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Eendracht maakt macht (Dutch)
L'union fait la force" (French)
Einigkeit macht stark
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Arthur Vierendeel (April 10, 1852 – November 8, 1940) was a Belgian civil engineer born in Leuven.
He obtained an MSc in engineering in 1874 at the Katholieke Universiteit Leuven.
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He obtained an MSc in engineering in 1874 at the Katholieke Universiteit Leuven.
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A rigid frame in structural engineering is the load-resisting skeleton constructed with straight or curved members interconnected by mostly rigid connections.It can resists moments at joints.Its member can take bending moment,shear and axial loads.
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A Vierendeel bridge is a bridge employing a Vierendeel truss. Such trusses do not have the usual trianglular voids seen in a pin–joint truss bridge, rather employing rectangular openings and rigid connections in the elements, which (unlike a conventional truss) must
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World Trade Center in New York City (sometimes informally referred to as the WTC or the Twin Towers) was a complex of seven buildings in Lower Manhattan, mostly designed by American architect Minoru Yamasaki and engineer Leslie Robertson and developed by the Port
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A king post (or king-post) is a central vertical supporting post extending vertically from a crossbeam to the apex of a triangular truss. The king post connects the apex of the truss with its base, holding up the tie beam at the base of the truss.
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A king post (or king-post) is a central vertical supporting post extending vertically from a crossbeam to the apex of a triangular truss. The king post connects the apex of the truss with its base, holding up the tie beam at the base of the truss.
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beam is a structural element that carries load primarily in bending (flexure). Beams generally carry vertical gravitational forces but can also be used to carry horizontal loads (i.e. loads due to an earthquake or wind).
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Ithiel Town
Personal information
Name Ithiel Town
Nationality American
Birth date September 3 1784
Birth place Thompson, Connecticut
Date of death May 13 1844 (aged 61)
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Personal information
Name Ithiel Town
Nationality American
Birth date September 3 1784
Birth place Thompson, Connecticut
Date of death May 13 1844 (aged 61)
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Stability can refer to:
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- Aircraft flight Stability (aircraft)
- Atmospheric stability, a measure of the turbulence in the ambient atmosphere
- BIBO stability (Bounded Input, Bounded Output stability), in signal processing and control theory, part of electrical
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mechanical equilibrium is:
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- A system is in mechanical equilibrium when the sum of the forces, and torque, on each particle of the system is zero,
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Structural loads are forces applied to a component of a structure or to the structure as a unit.
In structural design, assumed loads are specified in national and local design codes for types of structures, geographic locations, and usage.
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In structural design, assumed loads are specified in national and local design codes for types of structures, geographic locations, and usage.
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In statics, a structure is statically indeterminate when the static equilibrium equations are not sufficient for determining the internal forces and reactions on that structure.
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Stiffness is the resistance of an elastic body to deflection or deformation by an applied force. It is an extensive material property.
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Definition
The stiffness k of a body that deflects a distance δ under an applied force P is..... Click the link for more information.
space frame is a truss-like, lightweight rigid structure constructed from interlocking struts in a geometric pattern. Space frames usually utilize a multidirectional span, and are often used to accomplish long spans with few supports.
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- Principle of Moments redirects here. For the Robert Plant album, see The Principle of Moments. See also Moment (mathematics) for a more abstract concept of moments that evolved from this concept of physics.
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A hinge is a type of bearing that connects two solid objects, typically allowing only a limited angle of rotation between them. Hinges may be made of flexible material or of moving components. In biology, many joints function as hinges.
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Stress is a measure of force per unit area within a body. It is a body's internal distribution of force per area that reacts to external applied loads. Stress is often broken down into its shear and normal components as these have unique physical significance.
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Structural analysis comprises the set of physical laws and mathematics required to study and predict the behavior of structures. The subjects of structural analysis are engineering artifacts whose integrity is judged largely based upon their ability to withstand loads; they
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In structural engineering, the matrix stiffness method (or simply stiffness method, also known as Direct stiffness method) is a matrix method that makes use of the members' stiffness relations for computing member forces and displacements in structures.
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In structural engineering, the flexibility method is the classical consistent deformation method for computing member forces and displacements in structural systems.
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