Acknowledgment: I would like to thank my teacher in my college who I have shared her classrooms and ideas over the semester. Her commitment and enthusiasm motivated me to write this report Last but not least, I wish to express my deepest gratitude to my family and my friends who encouraged me to begin and complete this report. Glossary: Vierendeel truss: Four parts of the truss; for example, this assumption means significant bending loads upon elements as in a vierendeel truss. Shear Force: the component of stress coplanar with a material cross section. Shear stress arises from the force vector component parallel to the cross section. Stiffness: intransigence, stubbornness, obstinacy, tenacity, obduracy, stiffness.
Abstract: 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. There are many different designs that all serve unique purposes and apply to different situations. Designs of bridges vary depending on the function of the bridge, the nature of the terrain where the bridge is constructed, the material used to make it and the funds available to build it. Bridges can be categorized in several different ways. Common categories include the type of structural elements used, by what they carry, whether they are fixed or movable, and by the materials used. Bridges may be classified by how the forces of tension, compression, bending, torsion and shear are distributed through their structure. Most bridges will employ all of the principal forces to some degree, but only a few will predominate. A Truss bridge is a bridge whose load-bearing superstructure is composed of a truss. This truss is a structure of connected elements forming triangular units. The connected elements (typically straight) 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. The basic types of truss bridges shown in this article have simple designs which could be easily analyzed by nineteenth and early twentieth century engineers. A truss bridge is economical to construct owing to its efficient use of materials.
A truss bridge is a bridge whose load-bearing superstructure is composed of a truss. This truss is composed of structural triangles joined together with pinned or riveted connection. This means that the truss is a structural of connected elements forming triangular units. This connection may be stressed from tension, compression or sometimes both in response to dynamics loads. The main piece or members may be stiff heavy struts, posts or thin flexible bars. Its ancestor is Beam Bridge. Its descendants are cantilever bridge, truss arch bridge, transporter bridge and lattice bridge. Its carries are pedestrians, pipelines, automobiles, trucks, light rail and heavy rail. Its span range is short to medium - not very long unless it’s continuous. Its materials are Timber, iron, steel, reinforced concrete and pressurised concrete. Its movable may be movable. A truss bridge is one of the oldest types of modern bridges. Old truss bridges were easy to be analyzed by nineteenth and early twentieth century engineers because of simple design. A truss bridge is economical and does not cost much money. Truss bridges were first use in United States in 1820. Early Truss bridges would typically use carefully fitted timbers for members taking compression and iron rods for tension members and constructed as a covered bridge to protect the structure. This topic deals with the design of truss bridges, design of members, design of joints, static of trusses, analysis of trusses and roadbed types.
Until the 19th century, bridges and indeed all structures were designed by methods familiar to Vitruvius and set out by him in De Architecture, written in the 1st century BC. The new engineering material, iron, as it became expensive enough for use in structures, called for new methods. The nature of a truss allows the analysis of the structure using a few assumptions and the applications of Newton’s law of motion according to the branch of physics known as statics. For purpose of analysis, trusses are assumed to be pin jointed where the straight components meet. This assumption means significant bending loads upon elements as in a vierendeel truss.
A common bridge design was the Warren truss bridge patented by James Warren and Willoughby Monzoni in 1848. The diagonal braces of this design point both towards and away from the midpoint of the bridge. Thus they experience both tension and compression stresses as a load, such as a trains, crosses from one end to the other. Similar to the above Warren Truss Bridge, the vertical supports at greater stability and strength. When building your toothpick bridge, be sure to include these vertical struts. It really makes a difference.
Subdividing your toothpick bridge using smaller pieces of toothpicks will reinforce your design. Be sure to select the best toothpicks as the quality will affect the strength of the toothpick bridge.
The Howe Truss Bridge (designed by William Howe) was patented in 1840. The advantages of the Howe Truss Bridge to the railroad companies of the era were that it was easy to prefabricate offsite and to ship by rail. When building your toothpick bridge using the Howe Truss, be sure to use crossing members to give it strength. Variations of this crossing member design are easily located on the internet.
As you can see, the Baltimore truss bridge is a simple modification to other standard truss bridges. The smaller struts have been added to increase the support and improve the load distribution across the structure. When building your toothpick bridge, be sure to glue the smaller struts perpendicular to the main cross beam.
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 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 labour. 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 pressurised 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.
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. 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.
'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 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 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.
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 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 direct stiffness method, the flexibility method or the finite element method.
The truss may carry its roadbed on top, in the middle, or at the bottom of the truss. Bridges with the roadbed at the top or the bottom are the most common as this allows both the top and bottom to be stiffened, forming a box truss. When the roadbed is atop the truss it is called a deck truss (an example of this was the I-35W Mississippi River bridge), when the truss members are both above and below the roadbed, it is called a through truss (an example of this application is the Pulaski Skyway), and where the sides extend above the roadbed but are not connected, a pony truss or half-through truss. Sometimes both the upper and lower chords support roadbeds, forming a double-decked truss. This can be used to separate rail from road traffic or to separate the two directions of automobile traffic and so avoiding the likelihood of head-on collisions.
We have talked about design of truss bridges, design of members, design of joints, static of trusses, analysis of trusses and roadbed types. In the first, there are three types of the design, first one is was the Warren truss bridge patented by James Warren and Willoughby Monzoni in 1848, the second is the warren Vertical support Similar to the first type, the third is Warren Subdivided and in this type we use smaller pieces of toothpicks, and there are many types else. A truss can be thought of as a beam where the web consists of a series of separate members instead of a continuous plate. A truss that is assumed to comprise members that are connected by means of pin joints and statics is important here.
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