Bridges+notes

Bridges are technological tools that aim to solve the problem of crossing an obstacle in such a may as to cut down the effort and time needed to do so.
====Some of the benefits of bridges are: supplies can get across an obstacle or through difficult terrain in a shorter time. In economic terms, the cost of travel and trade falls and the financial benefits of increased social cohesion and sharing resources rise. Other longer-term payoffs from easier travel, with is crucially dependent on good bridges, come as a result of increased opportunities to share ideas. ====

**Arch Bridges **
==== The essence of an arch is that ideally there should be no tendency for it to bend, except under live loads. It should be purely in compression, and for that reason it can be made of materials such as, masonry, cast iron and concrete, that perform poorly in tension ==== ==== On the other hand, in a deck-stiffened arch, the deck is much thicker than the arch, because the deck is resisting any tendency to bend or buckle, leaving the arch chord to resist pure compression. In such a bridge, the deck can be very much thinner than a simple beam across the gap, because its weight is supported by the arch, and the arch can be very much thinner than a simple arch, because it is stiffened by the beam. ==== ==== In any structure, except a simple pier or column, it is impossible to have compression without tension. In the case of an arch, the tension is in the ground, which is therefore a member that costs nothing. If we take this argument further, it can prove that arch spans can be made longer than beam spans. Although the ground under an arch is in tension, the ground just outside the abutments is compressed by the thrust of the arch. Between the regions of tension and compression, the ground is subject to complicated mixtures of tension, compression and shear stresses. ==== ==== Although an arch is generally not under stress to make it bend, it has curvature designed in, because it is in a gravitational field. The amount of curvature at any point is designed so that the whole thing is perfectly balanced, neither tending to increase the curvature or to decrease it. The ideal shape is called the funicular, the exact shape of which depends on the weight distribution, so the funicular is not necessarily a simple mathematical curve such as a circle or a parabola. The arch and the suspension bridge are generally closer to the funicular or natural curve, than any other type. In this they imitate the path of projectiles, which also follow curved natural paths, and even light, which curves in a gravitational field. Nevertheless, although the cause, gravity, is the same for both arches and projectiles, the detailed reasons for the curvature are different. ==== ==== The forces comprise two distinct kinds – those pulling down (the weight of the section pulling down, and the load, if any) – and the forces from the sections on either side. In order to balance the downward forces, the forces from the side must not be exactly in line: the angle between them, repeated throughout the arch, is the reason for the curvature. ====

**Advantages of arches **
==== The entire arch is in compression. The compression is transferred into the abutments, and ultimately resisted by tension in the ground under the arch. The absence of tension in the arch means that it can sustain much greater spans than beams can achieve, and it can use materials that are not strong in tension, such as masonry and cast iron. ====

**Disadvantages of arches **
==== An arch cannot stand until it is complete. Therefore it must either rest on falsework (centring) until it is complete, or the two halves must be cantilevered from the springing, using cables. The cantilever method cannot be used for masonry arches or concrete arches. ====

The thrust of a big arch has a horizontal component, which the abutments must withstand without significant movement.
==== When spanning a road or a railway, the round arch must be wider than the railway or roadway in order to maintain clearance according to the loading gauge. ====

**Beam bridges **
==== The design is as simple as a single rigid 'beam', resting on supports at either end and unsupported in the middle. The weight of the beam, and of any traffic on it, is carried directly to the ground by the supports, often called 'piers' in the trade. ==== ==== <span style="font-family: Arial,sans-serif; font-size: 12pt;">The beam need not be of any particular shape and there are no other elements besides the piers to help dissipate the load. Hence the piers take the full weight of the load and are said to be in 'compression'. This means that they are being squashed by the forces at the top and bottom, and must be built from materials that can resist such forces without crumpling. ==== ==== <span style="font-family: Arial,sans-serif; font-size: 12pt;">The fact that the load tends to stress the beam itself - the top surface of the beam being shortened slightly and the bottom surface stretched - shows that the top is in ‘compression’ while the bottom is in 'tension'. ==== ==== <span style="font-family: Arial,sans-serif; font-size: 12pt;">The degree to which bridge components can withstand these opposing forces depends largely upon the material from which that bridge is made. Early beam bridges across streams were often made from stone 'clapper' slabs laid across the narrow gaps between piles of stones in the river bed itself. ==== ==== <span style="font-family: Arial,sans-serif; font-size: 12pt;">Stone is very strong under compression and is thus ideal as a material for the piers, but it is not strong under tension, cracking easily if given a sudden blow. Therefore, it is not ideal for use as a beam despite its apparent strength. In addition, stone slabs are very heavy and therefore difficult to maneuver into position. ==== ==== <span style="font-family: Arial,sans-serif; font-size: 12pt;">By contrast, wooden tree trunks or cut planks form a very strong beam when laid across a stream, despite their comparative lightness. Wood is able to carry both compression and tension equally well – wood is organic, after all, and heavy horizontal branches often carry similar loads to bridges themselves. Indeed, the longitudinal fibres within wood are designed to spread stresses within a tree without breaking. ====

<span style="font-family: Arial,sans-serif; font-size: 12pt;">Of course, wood is not as hard wearing as stone and needs replacing relatively often.
==== <span style="font-family: Arial,sans-serif; font-size: 12pt;">Most simple beam bridges have been made from wooden planks, laid on stone pier supports. Relatively recently, materials have been developed that are stronger, weight for weight, than wood, and we will be looking at some of these later in this module. These days, bridges carrying the huge weights of trains across small roads are almost always beam bridges made from steel. They are very robust and stable, and often do not require any intermediate pier. ==== ==== <span style="font-family: Arial,sans-serif; font-size: 12pt;">For a wider crossing, however, a series of intermediate piers may be needed, effectively forming several 'mini' beam bridges. Such a structure can form a hugely long bridge over, say, a valley floor, a fairly shallow lake or an estuary. ==== ==== <span style="font-family: Arial,sans-serif; font-size: 12pt;">This latter solution does produce a significant new obstacle to shipping, however. Several major bridges of this type have been catastrophically struck by ships, often in foggy conditions. ====

==== <span style="font-family: Arial,sans-serif; font-size: 12pt;">All beams tend to 'sag' between the piers and 'hog' over the piers themselves. This results from the downward forces of the load and the upward forces at the pier supports. The greater the span or the load, the greater the tendency towards sagging and hogging. ==== ==== <span style="font-family: Arial,sans-serif; font-size: 12pt;">The longer a beam is, the weaker it becomes. The greater length gives more weight and more leverage for that weight - increasing the 'bending moment' (see the module on beam calculations for more detail on this). ==== ==== <span style="font-family: Arial,sans-serif; font-size: 12pt;">This is why the bridge tends to sag more in the centre. It is rather as if you were holding a piece of A4 paper out towards someone else. The paper is much more likely to bend if you place a weight on it or hold it by its corner rather than at its centre. Both the weight and the unsupported length of an object make it more likely to sag. ====

**<span style="font-family: Arial,sans-serif;">Cable-Stayed Bridges **
==== <span style="font-family: Arial,sans-serif;">The cable-stayed bridge is related to the cantilever bridge. The cables are in tension, and the deck is in compression. The spans can be constructed as cantilevers until they are joined at the centre. A big difference between cantilever bridges and cable-stayed bridges is that the former usually have a suspended span, and the latter do not. ==== ==== <span style="font-family: Arial,sans-serif;">A cable stayed-bridge lacks the great rigidity of a trussed cantilever, and the continuous beam compensates for this to some extent. Indeed, while a long cable-stayed span is under construction, there may be great concern about possible oscillations, until the cantilevers are joined. ====

**<span style="font-family: Arial,sans-serif;">Advantages of cable-stayed bridges **
==== <span style="font-family: Arial,sans-serif;">The two halves may be cantilevered out from each side. There is no need for anchorages to sustain strong horizontal forces, because the spans are self-anchoring. They can be cheaper than suspension bridges for a given span. Many asymmetrical designs are possible. ====

**<span style="font-family: Arial,sans-serif;">Disadvantages of cable-stayed bridges **
==== <span style="font-family: Arial,sans-serif;">In the longer sizes, the cantilevered halves are very susceptible to wind induced oscillation during construction. The cables require careful treatment to protect them from corrosion. ====

**<span style="font-family: Arial,sans-serif;">Cantilever Bridges **
==== <span style="font-family: Arial,sans-serif;">A cantilever differs from the arch and the beam in that the attachment points are not necessarily at opposite ends. The cantilever is rather like a bracket, projecting out into space. The two forces almost always act in opposite directions. ==== ==== <span style="font-family: Arial,sans-serif;">As with the beam, the bending stresses and shear stresses vary throughout the structure. A cantilever is really a large bracket, held rigidly at one end. ==== ==== <span style="font-family: Arial,sans-serif;">Most cantilever bridges have two cantilevers, with a beam suspended between their free ends. The largest cantilever bridges are made of steel, though medium sized ones are sometimes in pre-stressed concrete. ==== ==== <span style="font-family: Arial,sans-serif;">The cantilevers can be maintained in position in two different ways. Firstly, they can be supported by pivots or hinges at the balance point, with the fixed end held in place at the abutment; secondly they can be supported at the balance point by a tower with a base so wide that no practical load can tip the structure. The central part of the Forth railway bridge is of the second type, which is why it has a wider tower than the outer parts. Most cantilevers are of the first type. In the first type there are two ways of holding the structure in position. One is to make the anchored span so heavy that no practical load at the free end can tip the structure. The other is to fix the anchored end to the ground. The outer ends of the Forth railway bridge are high up on masonry piers, which cannot withstand tension. The steel structures therefore have heavy weights attached, which hang down inside the piers. These weights are so heavy that the spans cannot be tipped by any likely load. ====

**<span style="font-family: Arial,sans-serif;">Advantages of cantilevers **
==== <span style="font-family: Arial,sans-serif;">Building out from each end enables construction to be done with little disruption to navigation below. The span can be greater than that of a simple beam, because a beam can be added to the cantilever arms. Cantilever bridges are very common over roads. Because the beam is resting simply on the arms, thermal expansion and ground movement are fairly simple to sustain. The supports can be simple piers, because there is no horizontal reaction. Cantilever arms are very rigid, because of their depth. ====

**<span style="font-family: Arial,sans-serif;">Disadvantages of cantilevers **
==== <span style="font-family: Arial,sans-serif;">Like beams, they maintain their shape by the opposition of large tensile and compressive forces, as well as shear, and are therefore relatively massive. Truss construction is used in the larger examples to reduce the weight. ====

<span style="font-family: Arial,sans-serif;">The cable of a suspension bridge is in tension, enabling it to be much narrower and cheaper than an arch of the same span.
==== <span style="font-family: Arial,sans-serif;">With the deck high above the floppy cables, this looks unstable, and it is. This construction can be used only for spans that are short enough for a stiff deck to transmit lateral forces to the anchorages. Some early iron trusses were made like this, one advantage being that the top chord of a truss is in compression, and has to be thick, and so it may as well carry the deck, especially for railways. ====

<span style="font-family: Arial,sans-serif;">And the deck is there to carry the traffic.
==== <span style="font-family: Arial,sans-serif;">The deck has also to possess enough local rigidity in bending and torsion to prevent undue flexure as vehicles pass. Locally, around each vehicle, it acts as a beam with rather diffuse supports, namely the hangers for some distance in each direction. This same rigidity must be sufficient to help in the task of preventing undesirable amplitudes of oscillation. Some hangers are provided with small devices that help to damp oscillations in them. ==== ==== <span style="font-family: Arial,sans-serif;">Before the invention of steel, many suspension bridges were based on wrought iron eye-bars, resting on masonry towers. The invention of the steel wire cable, spun in place, changed everything. Though the great Brooklyn bridge had masonry towers, steel became the normal material for a long period, until concrete became a popular alternative. ====

**<span style="font-family: Arial,sans-serif;">Advantages of suspension bridges **
==== <span style="font-family: Arial,sans-serif;">The main sustaining members, the cables or chains, are purely in tension, and are not required to be rigid, so they can be only as thick as needed to resist the tension. The towers are almost purely in compression, so their design is relatively simple. ====

**<span style="font-family: Arial,sans-serif;">Disadvantages of suspension bridges **
==== <span style="font-family: Arial,sans-serif;">They are only as rigid as the deck structure, which in older structures was usually of truss construction. This makes them generally unsuitable for railway traffic. Great attention is required in the design stage to deal with aerodynamic loads and, in the smaller sizes, periodic loads applied by pedestrians. During construction, the cables and towers may be susceptible to wind induced oscillations. The anchorages must sustain very strong horizontal forces as well as vertical ones. Constructing the cables or chains across the gap can be a lengthy process. ====

**<span style="font-family: Arial,sans-serif;">Truss bridges **
==== <span style="font-family: Arial,sans-serif;">A truss bridge is a bridge <span style="font-family: Arial,sans-serif;">composed of connected elements (typically straight) which may be stressed from tension <span style="font-family: Arial,sans-serif; text-align: -webkit-auto;">, <span class="apple-converted-space" style="font-family: Arial,sans-serif; text-align: -webkit-auto;"> compresion <span style="font-family: Arial,sans-serif; text-align: -webkit-auto;">, or sometimes both in response to dynamic loads. Truss bridges are one of the oldest types of modern bridges. The basic types of truss <span style="font-family: Arial,sans-serif;">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. ==== ==== <span style="font-family: Arial,sans-serif;">The nature of a truss allows the analysis of the structure using a few assumptions and the application of Newton`s laws of motion according to the branch of physics known as statics. For purposes of analysis, trusses are assumed to be pin jointed where the straight components meet. This assumption means that members of the truss (chords, verticals and diagonals) will act only in tension or compression. ====

====<span style="background-color: white; font-family: Arial,sans-serif;">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, and the changing price of steel relative to that of labor have significantly influenced the design of modern bridges. ====