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# maths report.docx

truss anaysis

truss anaysis

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### maths report.docx

1. 1. Introduction A truss is a meeting of individuals together with beams, related with the aid of using nodes, that creates an inflexible shape. In engineering, a truss is a shape that "includes -pressure individuals most effective, wherein the individuals are prepared in order that the assemblage as an entire behaves as a unmarried object”. A "-pressure member" is a structural aspect wherein pressure is carried out to most effective points. Although this rigorous definition permits the individuals to have any form related in any solid configuration, trusses normally include 5 or extra triangular gadgets built with immediately individuals whose ends are related at joints known as nodes. In this commoncontext, outside forces and reactions to the ones forces are taken into considerationto behave mosteffective on the nodes and bring about forces withinside the individuals which can be both tensile or compressive. Forimmediately individuals, moments (torques) are explicitly excluded because, and most effective because, all of the joints in a truss are handled as revolutes, as is essential for the hyperlinks to be -pressure individuals. A planar truss is one wherein all individuals and nodes lie inside a - dimensional plane, even as a area truss has individuals and nodes that amplify into 3 dimensions.The pinnacle beams in a truss are known as pinnacle chords and are normally in compression,the lowest beams are known as backside chords,and are normally in tension. The indoors beams are known as webs, and the regions withinside the webs are known as panels, or from picture statics (see Cremona diagram) polygons.
2. 2. Typical detail of a steel truss, which is considered as a revolute joint
3. 3. Characteristics A truss includes typically (however now no longer necessarily) immediately contributors related at joints, historically termed panel points. Trusses are typically (however now no longer necessarily composedof triangles due to the structural balance of that form and design.A triangle is the best geometric discernin an effortto now no longer extrade form while the lengths of the edges are constant. In comparison,each the angles and the lengths of a four- sided discernneed to be constant for it to keep its form. The joint at which a truss is designed to be supported is usually called the Munter Point Simple truss: The handiest shape of a truss is one unmarried triangle. This form of truss is visible in a framed roof such as rafters and a ceiling joist, and in different An Egyptian ship with a rope truss, the oldest known use of trusses. Trusses did not come into common use until the Roman era.
4. 4. mechanical systems inclusive of bicycles and aircraft. Because of the stableness of this form and the strategies of evaluation used to calculate the forces inside it, a truss composedcompletelyof triangles is called a easy truss. However, a easy truss is regularly describedextra restrictively through stressful that it could be built thru successive additionof pairs of participants, every related to 2 current joints and to every different to shape a brand new joint, and this definition does now no longer require a easy truss to incorporate simplest triangles. The conventional diamond-form bicycle body, which makes use of conjoined triangles, is an instance of a easy truss. Planar truss A planar truss lies in a unmarried plane. Planar trusses are generally utilised in parallel to shape roofs and bridges. The intensity of a truss, or the peak among the higher and decrease chords, is what makes it an green structural shape. A stable girder or beam of identical energy could have tremendous weight and cloth fee in comparison to a truss. For a given span, a deepertruss would require much less cloth withinside the chords and more cloth withinside the verticals and diagonals. A most reliable intensity of the truss will maximise the efficiency. Space body truss A area body truss is a 3-dimensional framework of participants pinned at their ends. A tetrahedron form is the handiest area truss, such as six participants that meet at 4 joints. Large planar systems can be composed from tetrahedrons with not unusual place edges,and they're additionally hired withinside the base systems of massive free-status electricity line pylons.
5. 5. Diagram of a space frame such as used for a roof
6. 6. Types For more truss types, see truss types used in bridges. There are two basic types of truss: • The pitched truss, or commontruss, is characterised by its triangular shape. It is mostoften used for roof construction. Some commontrusses are named according to their "web configuration". The chord size and web configuration are determined by span, load and spacing. This electrical pylon is a three- dimensional truss structure
7. 7. • The parallel chord truss, or flat truss, gets its name from its parallel top and bottom chords. It is often used for floorconstruction. A combination of the two is a truncated truss, used in hip roof construction. A metal plate-connected wood truss is a roof or floortruss whose wood members are connected with metal connectorplates. Pratt truss The Pratt truss was patented in 1844 by two Bostonrailway engineers, Caleb Pratt and his son Thomas Willis Pratt. The design uses vertical members forcompressionand diagonal members to respond to tension. The Pratt truss designremained popular as bridge designers switched from wood to iron, and from iron to
8. 8. 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 slendernesseffects related to buckling under compressionloads (which are compoundedby the length of the member)will typically not control the design. Therefore, forgiven planar truss with a fixed depth, the Pratt configuration is usually the most efficientunder 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 composedof 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 minimisation of compressionmemberlengths allowed for lower aerodynamic drag. Octet truss Truss members are made up of all equivalent equilateral triangles. The minimum compositionis two regular tetrahedrons along with an octahedron. They fill up three dimensional space in a variety of configurations. King post truss One of the simplesttruss styles to implement, the king post consists of two angled supports leaning into a common vertical support. The queen post truss, sometimesqueen-postor queens-post,is similar to a king post truss in that the outer supports are angled towards the centre of the structure. The primary difference is the horizontal extension at the centre which relies on beam action to provide mechanical stability. This truss style is only suitable for relatively short spans.
9. 9. Warren truss Truss members form a series of equilateral triangles, alternating up and down. Vierendeel truss A Vierendeel bridge, which lacks diagonal elements in the primary structure The Vierendeeltruss 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 commonlyassumed to have pinned joints, with the implication that no moments exist at the jointed ends. This style of structure was named after the Belgian engineerArthur Vierendeel,who developed the designin 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
10. 10. door openings. In some applications this is preferable to a braced-frame system, which would leave some areas obstructed by the diagonal braces. Applications Post frame structures Component connections are vital to the structural integrity of a framing system. In homes with massive, clean span timber trusses, the maximum vital connections are the ones among the truss and it is supports. In addition to gravity-caused forces (a.k.a. bearing loads), those connections ought to face up to shear forces performing perpendicular to the aircraft of the truss and uplift forces because of wind. Depending upon general constructing design, the connections can also be required to switch bending moment. Wood posts permitthe fabrication of strong, direct, but cheaperconnections among massive trusses and walls. Exact information for submit-to-truss connections range from clothier to clothier, and can be encouraged with the aid of using submit type. Solid-sawn wood and glulam posts are commonly notched to shape a truss bearing surface. The truss is rested at the notches and bolted into place. A unique plate/bracket can be delivered to growth connection load switch capabilities. With mechanically-laminated posts,the truss might also additionally relaxation on a shortened outer-ply or on a A see through truss in a skyscraper
11. 11. shortened inner-ply. The later state of affairs locations the bolts in double shear and is a totally powerful connection.
12. 12. calculation of truss forces made by program that use matrix Gauss solving method
13. 13. A creative use of truss A proper ship which can stand on its legs to install wind mills in deep ocean. The legs are trusses which can support 60000 tons of load.The ship can be raised to height of 60 m from water surface.