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What You Might Need to Build a Bridge

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Introduction

 

Throughout this website, most of the diagrams adhere to the convention that red represents compression, blue represents tension, and green represents the effect of gravity, expressed as weight.

In this panel we find a list of the set of parts that you might need to build a structure. Please note that in many actual structures the means of attaching the parts to each may transfer forces and bending moments in such a way that the parts are not "pure" examples of their primary type.

A Kit of Parts for Bridges, Comprising

Struts, Ties, Attachments, Cables, Beams, Towers and Piers,

Foundations and the Earth,

Communication, Skill, Knowledge, Discipline, Courage, Money,

and Funiculars

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Gravity, Weight and Funiculars

Gravity is not something that you would think to include in a kit of parts, but as it cannot be removed from earthly structures, we may as well include it in our list. In fact, without gravity, much of our structural work would not be needed at all. The structure of space craft and space-stations is very much lighter than that of earth-bound objects. We see this too in very small plants and animals, and in those which live in water, especially the smallest. Watching tiny creatures such as daphnia, one sees that gravity little direct part in their structure or behaviour, and they seem to float along like spacecraft.

Elephant.jpg (50246 bytes)CraneflyKX.jpg (107235 bytes)Galileo explained why large and small structures are not similar; he pointed out that area, related to strength against forces, is proportional to length squared, and volume, related to weight, is proportional to length cubed, so they don't change with size in the same way. The two pictures here, showing an elephant, a plant, and a crane fly, illustrate this clearly. It is no surprise that the largest animals that have ever lived on this planet live in the sea. Why do you think the largest land animals died out long ago, while the largest sea animals are still here?

If you don't think of gravity as a legitimate component of a bridge, consider some bridge spans that were displaced by the great New Orleans flood of 2014. Why did they move? They moved because they received an up thrust from the floodwater, counteracting some of the weight, and allowing the flow of water to move them. Any bridge section that is a hollow box or tube, or is concave below, could be subject to this problem, indeed, concrete ships have been considered in the past. The solution is to provide holes in the beams to allow air to escape and water to enter, and in the case of closed boxes, for the water to enter. There must also be adequate provision for water to escape quickly enough as the flood waters recede, to prevent the possibility of a span failing under the weight of trapped water, when supported at each end.

Gravity dams too, can experience upthrust if water seeps into cracks underneath. The up thrust reduces the effective weight of the dam above the cracks, upsetting the balance of forces that has been calculated to hold the dam in place. Numerous dams have failed because of up thrust

Why is up thrust from water so dangerous? After all, any statically supported object experiences an up thrust which is exactly equal to its weight. The difference between the up thrust from weight and the hydrostatic up thrust is that the latter is constant when the object moves, whereas the support thrust is generated by deformation of the support. Therefore, when a reservoir is filled, a gravity dam is pushed horontally by the water, and the base near the wetted face will press less heavily on the substrate. The reduction in the forces stops when the deformation of the substrate has been reduced to the right point. But if water gets under the dam, no matter how much the dam and substrate move or deform, the pressure of the water remains the same - it never stops pushing up, like a never-tiring sumo wrestler. It can happen that a dam that safely holds back the water when completely connected to the substrate can fail to do so if a large enough area below it is wetted.

The diagram below shows an object, with its weight shown by the green arrow. 

Representing the size and direction of a force by the length and direction of an arrow is often very convenient. The arrow represents a quantity called a vector. Mathematical treatment of vectors does not actually require the drawing: it simply calculates with the quantities themselves, often in the form of their components in three orthogonal directions. In this context orthogonal means at right angles. But in writing equations we can often write the vectors as entire entities, without thinking about their parts, as long as we use the correct rules, which are an extension of the usual rules of arithmetic. For example, 1 + 1 can be 2, or 0, or anything between, because forces may not be in the same direction. Vector algebra gets it right for you. On the other hand, there are simple diagrammatical constructions that enable the calculations to be done in a visually intuitive way, which can be helpful in learning.

We have drawn the weight as if acts at a single point, called the centre of gravity, but in fact each part of the object is pulled down individually, so that if the object lies on a surface, the bottom layer is supporting the rest of the object, while the top layer supports hardly anything. When you look at a bridge, imagine that every part is being pulled down by the force of gravity. But gravity isn't always an adversary: in a cantilever bridge, we use the weight of one arm to balance the weight of the other arm and its load. And the sheer weight of a span can be used to hold it down without the need for bolts, rivets or welds.

Funiculars

The list at the top of the page includes funiculars. Whenever you build something that is supported in two or more places, a funicular exists. It is not a component that you can make or buy: it is an idea. A dynamic equivalent would be the racing line on a motor-racing circuit, or the ideal path on a downhill ski-racing piste. Other examples are a great circle route between places on the earth, and the routes taken by light through adjacent refracting substances. You can build structures without thinking about funiculars at all, but it is important nonetheless. It is important because deviating from it incurs a penalty, just like deviating from the racing line on a race-track, or from a great circle in long distance flying.

The funicular for any part is the shape that the part should have in order that the forces in it should be pure compression or pure tension, with no tendency to bend. It is an idealisation for real structures, because when live loads occur, the line moves far more than the structure. In fact, in materials which cannot resist tension, there are strict rules about the position of the funicular. In some structures, such as beams, the funicular is not a useful idea, as it is so far from the structure.

Although there is a penalty for deviation from the funicular, it is one that we are often willing to pay, because the funicular shape is often extremely inconvenient. A house with funicular floors would be weird and totally impractical. On the other hand, for a roof where nobody goes, the funicular is ideal.  For more information, click here.

Struts and Ties

A strut is always in compression, while a tie is always in tension. Ties pull whatever is fixed at each end, while struts push. In trussed structures, there may be some parts, especially cross-bracing and wind-bracing, in which the forces may change polarity as a result of moving live loads or changes in the direction of the wind, and they cannot be labelled as struts or ties without a knowledge of the current loads. Why have we drawn the strut thicker than the tie? The reason is that there is not an exact symmetry between the parts. If you pull a tie which is slightly curved, it will tend to straighten: if you push a strut, it may tend to become more curved. A tie is therefore intrinsically stable, even if it is a thin cable: the strut is not, unless it is made sufficiently stiff.

A strut that is too slender for the applied forces may buckle. A great deal of the mass in some bridges is present, not to withstand the applied forces, but to prevent buckling. Large struts are often built as trusses, so that a very large truss may include members that are themselves smaller trusses, in order to improve the balance between stiffness and lightness.  The members of the sub-trusses could be trusses too, and so on, but the cost of fabrication and assembly generally make further sub-division uneconomic. Nature's economics are not the same as ours, and the interior of bone, especially in flighted birds, for example, can display an amazing complexity of structure, achieving strength with lightness.  Perhaps one day we will be able to use nature's methods to grow highly efficient parts for structures.  Imagine an organism that could grow to a specified shape, branching exactly where we want, a thousand times quicker than a tree.

In principle, many ties could be made using cables, but stiffness can be as important as tensile strength, and most ties are bars rather than wires. Some long ties are even trussed for rigidity, as in the Forth railway bridge, which has tubular struts and trussed ties. The use of tubes greatly reduces the tendency to buckle, but any given area of a tube is a curved plate, and plates can buckle. What matters is the curvature, the thickness, and the unbraced area. So inside the tubes of bridges like the Forth rail bridge and the Royal Albert bridge at Saltash there are flanges, some of which run along the tube, while others run around it. The purpose is to create a structure in which each unsupported area is stiff enough in its own right. Such stiffeners are often found in the hollow stems of plants.

Struts and ties may be found in many different orientations, and they are usually straight, because the applied loads are much greater than their weights. The pictures below show some examples.

ForthCentral.jpg (212874 bytes)   BeamG.jpg (45611 bytes)   A34BeamZM.jpg (197732 bytes)

Because ties and struts have weight, they tend, however slightly, to sag. That is, they experience bending moments. In theory they should be slightly curved, so that the thrust passes exactly along their neutral axes, though because the live loads can vary, the curvature can only be an approximation to the correct amount. You could in fact regard a pure arch as a pure strut, and a suspended cable as a pure tie. The word "pure" here means free of bending moment, which implies that the member follows a curve called a funicular. Not the funicular, but a funicular, because the funicular isn't a standard curve like a parabola or a circle: its shape depends on the weight distribution of the structure.  

If you load an arch at a point, the funicular moves upwards around that point, but the arch moves downwards around the point.  If you load a suspension structure, the funicular moves downwards, and so does the structure. That is what we mean by saying that the arch is instrinsically unstable, while the suspension is intrinsically stable, even if it is a very wobbly one. Stable in this sense means having a tendency to return to the original shape after being deflected. Real arches, of course, are stable, even under load, because they are made stiff enough (steel) to resist the bending moments, or thick enough (masonry) to contain the funicular.

In practice, the weights of most struts and ties are very much less than the forces along them, and so they can safely be straight, but if you look along a cable of a cable-stayed bridge, you will find that it is slightly curved. Also, Christian Menn built some concrete arches with slightly curved segments. Because cables are not rigid, those of some large cable-stayed bridges are connected by subsidiary cables to reduce oscillations, while the hangers of large suspension bridges may carry small dampers for the same reason.

Medieval cathedral builders knew that weight distribution is important, which is why they sometimes put spires on their flying buttresses, to increase the weight at strategic points. 

The next picture, showing a span of the Royal Albert bridge, like those of the Forth railway bridge, shows dramatically the difference in thickness of a strut (the tubular arch) and a tie (the suspension chain). You can find more about this in the pages about beams and tubes.

Finally, being very pedantic, we could say that you cannot buy a strut or a tie, only something destined to be one of these, because both terms are defined by the forces experienced by the parts, which do not take their final values until the structure is complete. It is entirely possible that the forces in an incomplete structure can be very different from those when complete, so much so, in fact, that temporary supports called falsework may be needed. Incomplete bridges, notably box-girders, have collapsed partly because of insufficient understanding of the forces during construction.

RABridge1849Sm.jpg (228902 bytes)

Attachments

Connecting struts, ties and other components is a matter of great importance, because the joints must not produce stress concentrations that cannot be sustained, remembering that we must consider not only static forces, but varying, or even alternating ones, raising the possibility of fatigue. This is especially important for struts, because any error in assembly that diverts the forces, even slightly, from the intended position, is likely to increase the risk of buckling. This is particularly important in compression members made of plates. In the case of ties, the attachments, as we see here, can be much bigger than the member itself.

HangerTop.jpg (40112 bytes)How many parts can you see in the picture, including bolts, nuts and washers? The picture shows a small section of cable of the Severn suspension bridge, with the attachments of two hangers and two handrail supports. The diameter of the main cable is about 20 inches or 51 cm, while that of the hangers is about 2 inches or 5 cm.  The tension in each main cable is 11400 tons. If we compare this with the weight of each cable, 2600 tons, we see that the ratio is not very large, and that is why the cable curves noticeably between the hangers.

There is much more to attachments than simply fixing things together. Consider a truss. If all the joints are pinned, that is, they behave as hinges, all bending moments fall to zero at the joints: the bending of one member has no effect on any other members, except for the second order effect of its length changing as a result of bending. Rigid truss joints, however, may transmit bending forces well. In practice, few trusses are made with a single pin at each joint: a multiplicity of bolts or rivets is more common.  Welding is common too, and creates a very neat appearance, especially with tubular members. If two parts are butted together with ill-matching surfaces, local pressures can be very high. Many segmental concrete bridges are made by match casting, that is, the face of each segment is used as a part of the mould for the next segment.

What happens if we attach more parts than we need, in order to "make something stronger"? That does not always achieve the objective: if a structure is already rigid and we add a new part that does not quite fit, we may cause high stresses in forcing it into position. Even if it fits, we may end up not knowing how the stresses are shared - the structure has become indeterminate. Cable stayed bridges are highly indeterminate, unless the deck is hinged at each cable attachment. Cable stayed bridges are provided with means of adjusting the tension to the required values. Since adjusting one cable may affect neighbouring ones, the process may be iterative.

See also attachments.

Cables

A cable is a tie that is flexible, and it is usually long relative to its thickness, though it may be divided into segments by the attachment of other parts. A main cable is very often so heavy that it is curved. The cables of cable-stayed bridges may look straight, but they are always slightly curved by their weight.

Long suspension cables are often built up on site from numerous thin strands, which are then bound and sealed. Long cables may require dampers or subsidiary cables to reduce oscillations. Some examples of cables are shown below.

WyeCS2.jpg (40240 bytes)   Sabrina3.jpg (61135 bytes)   SSC6.jpg (55445 bytes)   Severn2X.jpg (63967 bytes)

Beams

Beams are usually neither struts nor ties: their action is to rest on two or more supports, providing enough stiffness to retain their shape. All beams experience compression and tension simultaneously. In a European house, a beam is usually a baulk of wood with rectangular cross section, though concrete is sometimes used. Small wooden footbridges often use simple beams, sometimes given depth by laminating numerous sections together.

But we see from the diagram that the tension and compression are concentrated at the top and bottom respectively. The I-beam uses the material very effectively in this respect, and the vertical web takes the shear stresses, which are not shown in the diagram, which also doesn't show the concentrated stresses at the supports. Very large beams may be constructed as trusses or box girders, again, to achieve lightness and make maximal use of the material.

See also beams.

Summary So Far

An ideal strut, an ideal tie, an ideal arch, and an ideal cable experience no bending moment: the first two because their weight would be negligible compared with the longitudinal forces, and the last two because their shape conforms to the forces, including the weight - they follow a funicular. These four parts need not have any significant thickness in order to deal with the imposed forces, but the arch and the strut differ from the cable and the tie in having extra thickness that has nothing to do with strength, and everything to do with the prevention of buckling.

The beam differs from those four parts in that its depth is crucial to its function. It can of course be reduced to a system of struts and ties, for lightness, by using truss construction. Large beams can also be plate girders, box girders and tubular girders.

Arches and struts, too, can be made in truss form, but the cross members there are different from those of beams: they are there to resist buckling, whereas in beams they actually contribute to the load path. This statement is a little too simple in cases where a trussed arch like Sydney Harbour bridge has no hinge at the crown. In those bridges both the top and the bottom chord take the thrust at the crown, while at the abutment, only the bottom chord is active. The sharing between top and bottom chord in such bridges might vary with temperature. Therefore it is plain that the cross members must be distributing some of the load. The Garabit viaduct resolves this by bringing both chords to the same hinge. Even so, the members must be dimensioned in such a way that the chords share the load according to the design. Some form of jacking and packing is often used to ensure the correct force distribution. This is a non-trivial operation, since the dimensions of all the parts are affected by temperature changes, and final closure in extreme weather can cause problems.

These five parts, arch, beam, cable, strut and tie, have in common the fact that they are connected at their ends to something else. To constrain an object completely in two dimensions, two connections are needed: in three dimensions, three connections are needed. The type of connection depends on the requirements of the situation. The minimal connection is determined by kinematics. Anything more than the minimal connection causes over-constraint. A cantilever differs from these five parts in that it is free at one end: all its connections are at the other end. It is essentially a bracket. Some cantilevers in big bridges are connected back-to-back with another cantilever, forming a giant lever.

Towers

ForthTowerAS.jpg (447325 bytes)SSCTowerABE.jpg (126299 bytes)To hold a suspension cable high enough to provide clearance underneath, towers are required. A tower is a form of vertical strut, but it differs from a normal strut in that the force in it may vary significantly from top to bottom because of self-weight. Buckling is again a major concern, and, especially during construction, flexing under wind load is another potential problem. The second and third pictures show the towers of a cable-stayed bridge and a cantilever bridge respectively. The towers of the Forth railway bridge, like those of the Severn suspension bridge, are hollow steel structures with stiffening flanges inside. The Severn cable-stayed bridge uses the increasingly common concrete towers. Note that some cable-stayed bridges, and a very few suspension bridges, have towers that are not vertical. There is a suspension footbridge near Bodmin which has towers that lean outwards.

Piers

ForthPiersA.jpg (68930 bytes)ForthApproachS.jpg (146320 bytes)Piers are vertical structures which hold up everything else. After a disaster, they are sometimes the only survivors. They are often founded under water or deep underground, so that we never see the complete structure. A great many bridges would look very strange if we could see them without the water in which they sit. Piers are not always the most obviously attractive or interesting parts of a bridge, yet their construction can present the most difficult problems and the greatest dangers in bridge building. Deep water requires caissons: the greater the depth, the higher the pressure. Until caisson sickness ("the bends") was understood, there were many deaths and injuries. The nature of the ground is crucial. The building of the Brooklyn bridge was made much more difficult by the presence of huge boulders in the ground under the East river. They could not be lifted out entire, and where they lay under the cutting edge of the caisson, the problem was even worse. Explosives, tried with great trepidation at first, proved to be the solution.

The piers shown above support spans of the Forth Rail bridge, and are very sturdy. Some bridges, however, have supports that are slender, and even tapered to pin joints or ball and socket joints. How can this be? If the bridge is a continuous beam, and it is not too long, its rigidity can be sufficient to prevent movement along its length, because it is attached to the abutments at each end. The bearings at the top and bottom of the piers can be rollers. They can also be made rigid enough to prevent lateral movements, in which case the piers could end in ball and socket joints. In practice these types of connections are not often the most economic. The shape of piers is particularly important when powerful water currents can occur, and large anti-scouring platforms may be provided.

Here are more pictures of piers.

HayOnWyeA.jpg (227466 bytes) WyeNewBridge1334A.jpg (126515 bytes) ChepstowBoth288.jpg (157088 bytes) BredwardineBSm.jpg (133228 bytes) RABridgePier1849.jpg (196240 bytes) RALandSpans35.jpg (339499 bytes)

Are piers, then, simply a means of holding up a bridge? No, not at all. Although many bridges do comprise a beam or two resting on some piers, the supports of a span can play a much more subtle role. An obvious improvement for a bridge of one beam and two piers, is to connect the three parts rigidly to form a bent or frame. No mathematics is needed to see that the sag of the beam will be reduced, or maintained at the same value with less material. We can go further - we can add gussets at the joins, or spread the piers smoothly into the beams. Maillart's mushroom heads teach us that.

The next pictures show a few examples.

 Asymm2.jpg (30817 bytes) AsymmBeam.jpg (30243 bytes) Asymm3.jpg (21561 bytes)

3PinGlos6Y.jpg (38222 bytes)What about this?  It also shows a rigid connection.

3PinGlos1.jpg (79053 bytes)3PinM6.jpg (20340 bytes)But when we look at the whole bridge, we see that it is a three-pin arch, like the second bridge shown here. Therefore the legs at each end are not strictly piers. On the other hand, the first bridge is so far from the funicular that it is straining the term "arch" to the limit. Bridges can be found with almost all possible slopes in their supports, from pure beam to pure arch.

Column2734Sm.JPG (202427 bytes)Column2734VVSm.JPG (95666 bytes)We don't usually think of solid stone piers as flexible, but no material is perfectly rigid. These pictures show one of the four piers of Salisbury cathedral that support the tower and the spire. The weight on each pier is not exactly known, but is probably over 1500 tonnes. The upper stages of the tower, and the spire above them, reaching about 404 feet above the ground, were afterthoughts. The extra weight has caused the piers to bend, and subsidiary strainer arches were added in the 14th century to prevent further movement. Note that the material of struts and piers rarely fails by crushing, as the thickness has to be sufficient to prevent buckling and bending.

WharfeStepsSESEB.jpg (120648 bytes)Would you believe in a bridge made entirely of piers? Surely not. Yet it is very likely that such things, along with rope bridges and tree trunks, might have been among the earliest ways of bridging rivers. The picture at left shows an example. It could have been placed in the page about moving bridges, since it may have one moving span (or more), formed by the legs of anyone (or any people) crossing it. If you stand on two piers with your legs locked straight, you are approximately a three-pinned arch, but if you bend your legs, the extra hinges have to be stabilized by the action of muscles, acting as prestressing tendons. 

This line of steps looks pretty simple, but the number of steps that are out of line suggests the difficulty of building in a river, with a bed that is liable to move, and fast flowing water, often turbulent, threatening the piers at all times. A structure is a sort of record of the problems its builders had to solve. If you walk across this river, the Wharfe at Bolton Abbey, you will find that the river is up to two metres deep, and that the stones are actually pillars. Upstream at the Strid, the same river looks almost narrow enough to jump, but the narrowness is compensated by a great depth of water, swirling in great cavities below, in which a body has sometimes whirled around for weeks, after someone has yielded to the temptation to jump across.

A summary of some parts

In this website you will find mention of the following ways of connecting two places -

Arch segments, beams, cables, hangers/suspenders, piers, struts, ties. All of these are more or less long and narrow, with a connection at each end. The one major component that is not in the list is the cantilever, which has its connections at the same end. All the listed parts are either in tension or in compression, except beams. In various other parts of the site you can find explanations that show that these seven types of parts are all quite closely related, and that their properties can be regarded as regions in a single continuum of behaviour.

The differences are these -

In compression or tension or both

Subject to buckling or not

Subject to bending or not

Flexible or stiff

Funicular or not

These variables are generally not all or nothing: a cable, for example is flexible if you have a very long piece, but a piece that is only a few metres long and a metre in diameter may feel very stiff indeed.

Decks

We have not mentioned the one part of a bridge that you are certain to notice when crossing, whatever the type of bridge. That part is the deck. This may not seem very interesting, but aside from the necessity of providing a surface of the required smoothness with high resistance to skidding, there is the problem of what holds that surface up. For a box girder bridge or a suspension bridge with an aerodynamic deck, the answer is straightforward, because the top is flat. The same is true of masonry arches, which are built up to receive the roadway.

For truss bridges, however, something more is needed. Many truss bridges have two trusses per span, often widely separated. A four-lane roadway means a wide spacing, unless a third truss is placed on the midline of the bridge. Plate girders pose the same problem. Both types often have lower members with horizontal flanges, on which some transverse beams can be rested. The problem here is that the downward force of the beams is not repeated on the outer sides of the girders, and so the forces are eccentric.

These cross beams may be placed at the joints of the truss, or they may be placed between. The stresses in the lower members will differ in the two cases. The cross beams will have gaps between them, which have to be filled. In older plate girder bridges these gaps were often spanned by numerous little arches. The road or railway was laid upon these. In the case of a railway over a river there is no need for a solid deck, and the railway could be laid on the cross beams. With a road underneath, there is the risk of objects being thrown from the train, or even falling off, and so a solid deck is preferable.

An extreme example of the decking problem is the Forth railway bridge. In the cantilever spans, the railway tracks run along a continuous truss-and-trestle bridge which is supported by the main tubes of the bridge. It is a bridge within a bridge.

Other solutions may be found for concrete bridges.

But . . . . 

We now know what all our parts are supposed to do. The problem is that things are never that simple. A strut or a tie has weight, and if it isn't vertical there will be some bending effect, though in most cases the weight will be much less than the force that the member is transmitting. More important is the method of application of the force to the ends of the member. If it is applied eccentrically, that is, not along the centre line, there will be bending. Furthermore, if parts are joined rigidly, deflections will be transmitted from one part to another, causing extra stresses which may be complex. Unless parts are connected by freely movable ball and socket joints, transmission of deflection is inevitable. This is not always bad: by suitably connecting beams together, we can create a more favourable distribution of stresses in a long bridge.

We have looked at parts that have one dimension much longer than the other two, as in struts and ties, and we have assumed that bridges are made by connecting many such parts together. In fact, there are components such as gusset plates and other metal plates, and concrete floor sections, which have two large dimensions and one small one. Some parts are even large in all three dimensions.

Then there are possibilities such as casting large segments in concrete, or even whole spans, so that the concept of parts becomes rather meaningless. The calculation of stresses in complicated shapes is not easy, and some kind of semi-automatic process such as finite element analysis is used.

We haven't, either, mentioned composite materials such as reinforced concrete, pre-stressed concrete, and glass reinforced plastic, which are discussed in the pages about materials.

Any part that has more than one large dimension, such as a plate, a tube or a box, is inherently difficult to calculate as compared with a slender strut or tie. The use of such a part therefore demands more thorough investigation. Construction of Stephenson's Britannia bridge was commenced only after exhaustive tests on models and samples, until the behavior of the cellular tube was fully (though empirically) understood. Today, of course, with finite element analysis, one can calculate and even visualize the distribution of stresses in fine detail, with the proviso that in any region of the model one has used a fine enough mesh of nodes.

We only have to look at the bones in a skeleton to see that in a complex object, many of the parts cannot be assigned one of the simple functions in our list. In electronics we see the same sort of thing: we can buy capacitors, inductors and resistors, but we should never forget that each type of component includes doses of the other two, which in the wrong circumstances (for example too high a frequency) can render the part useless. The mechanical equivalents of the three variables are mass, elasticity and friction, which are present in most objects to some extent. In fact, whenever we try to make distinct categories, we will find examples which are sure to cause discussion. A batsman in cricket may make a variety of classical strokes which have names, such as the "leg glance" and the "cover drive", but in a real match he may receive balls which allow or compel strokes which lie in the vague region between two categories. And a great batsman when seeing the ball well can manufacture strokes almost at will, from almost any ball, to the despair of the toiling bowlers.

Such is the complexity of many structures that engineers can even disagree about the way they work. One such is Brunel's Royal Albert bridge at Saltash.

Torsion

M5CurveNov.jpg (91204 bytes)Torsion, or twisting, isn't the name of a part, and it isn't normally designed into bridges. But it can be extremely important, for example when a long bridge is supported by intermediate piers along the centre line. This type of design may be chosen for its effect on appearance, for it avoids the irregularity that perspective imposes on double or multiple rows of piers. The single row may well be cheaper, too. The problems arise when the loads are asymmetrical. A vehicle will load one side of the bridge, causing it to twist. If the bridge is curved, there may be permanent torsional stresses. The bridge must be stiff enough to transmit the load back to the abutments with acceptable deflection. The deflection is never zero, because it is by deflecting that any structure generates the forces that balance the external ones. Similar considerations apply to cable-stayed bridges with one plane of wires.

Foundations and the Earth

Foundations are the structures that connect the main structure with the ground.  Forces do not end at the ends of a bridge. They do not even end at the boundaries of the foundations. In theory, they spread throughout the earth, getting weaker as the distance increases, though at some point they are so weak that they cannot be detected. Foundations must be made wide enough to reduce the stresses to values that the ground beyond can sustain indefinitely. The size and strength of foundations will depend on the quality of the ground. Over bridge and the famous Pisa campanile are examples where the combination of foundations and ground were less than ideal. The foundations may be deep underground, and in some cases under water as well, requiring the use of pneumatic caissons with sharp cutting edges, and pressurised air keep the water out. Eads' Mississippi bridge and the Roeblings' Brooklyn bridge are early examples of the use of caissons.

If the weight of earth removed for foundations is greater than the weight of the structure supported, the foundations on average cannot settle, because the structure is floating. Nevertheless, a building might still tilt in these conditions, while not sinking overall. This principle of isostasy applies approximately to huge mountain ranges, whose roots go deep below the mean surface level of the earth. If glacier ice melts in large quantities, the rock below will start to rise, and in fact parts of the earth's surface are still moving slowly, and have been moving, since the end of the last ice age.

It is in dam construction that knowledge of the ground is most important, because of the potential for great loss of life. The dam must be integrated into the rock to avoid leakage and uplift; extensive grouting is often required. Just as important is the huge weight of the water in the reservoir, and its effect on the rocks below and around. A terrible catastrophe resulted when water behind the Vajont dam penetrated the ground and enabled a large piece of a mountain slope to slide into the reservoir.

Communication

Communication is of course vital at all stages of a project. Unclear messages, or slow transmission, especially when things begin to go wrong, can contribute to the generation of problems and accidents, in almost any walk of life. Instructions must be unambiguously and correctly stated, transmitted faithfully, understood correctly, and acted upon with sense. In the book "The reason why", the author suggests that failures in communication and management contributed to "The Charge of the Light Brigade". The failure of the first Quebec bridge was inevitable, given the design, but the resulting deaths might have been avoidable with better communication with the distant designer.

Any project requires a well-defined chain of command, with well-defined paths of communication in all relevant directions. The airline QUANTAS has a good safety record; it has been said that one contribution to this is the freedom of communication within the cockpit, irrespective of the relative rank of the individuals within the hierarchy. In earlier times, for anyone to question an order or an action of the captain on a British warship was a capital offence - a sort of anti-QUANTAS principle. 

No means of communication will work without training in all aspects of its use, and that applies to every other aspect of a project. Among the reasons that emerge after catastrophic accidents, poor training and inexperience often rank high.

Safety

Safety1991Sm.jpg (125633 bytes)Our list of real and virtual components, then, could have included safety, symbolised by this picture, which incidentally shows an old building that is cracking up, but held together by its intrinsically sound construction. There is no such thing as perfect safety, though: all we can do is find a balance between cost and speed of construction, and probability of accidents. We could, for example, crawl along the ground to eliminate the possibility of falling over, but it would be extremely expensive in time, knee-pads and gloves, and the number of injuries avoided would be rather small.

Many footpaths in British towns have a white line along them, with diagrams of a pedestrian and a bicycle painted on the ground at certain intervals, as well as posts bearing blue and white signs also showing a walker and a bicycle. On many of these paths one might meet someone every ten or twenty minutes at peak times, and even more infrequently during the remainder of the day. The chances of two people failing to pass in a safe manner are very small, and it is likely that the probability of a serious collision per mile of path per year is negligible. The cost per avoided accident is probably large.

Skill, Knowledge, Discipline and Courage

Nothing can be built without skill and knowledge. If the construction is of a new type, or bigger than anything that has gone before, new knowledge and new skills may be needed. New knowledge may be obtained by theoretical calculation, backed up by practical tests. But calculations can be exceedingly complicated, and in any case are no better than the assumptions that go into them. And no knowledge is of any value if someone insists on going beyond what is known, on the grounds that extrapolations have worked before, and will therefore work again. We can walk on H2O at -12 C, -7 C and -2 C, but we can't do so at + 3 C.

Courage is needed in the face of those who say "It can't be done.", and in the face of grave difficulties which threaten to stall or bankrupt a project. But courage alone is not enough: knowledge is vital. The first Panama canal project failed, not through lack of courage and determination, but because of ignorance about the mosquito which carried yellow fever, and failure to understand the magnitude of the difficulties caused by the geological conditions and the river. And those who say "It can't be done." might just be right.

Money

It is so obvious that you can't build without money that it's hardly worth stating.  What may be less obvious is how to calculate how much should be spent, and how to calculate the return on the money spent. If we make a road that is just adequate now, it wll be too small in twenty years, but if we over-estimate future needs, money will be wasted. The Humber bridge is still relatively little used. In the case of a toll bridge, calculating the return on the investment is a matter of relatively simple arithmetic, but in other cases there may be no way of calculating the benefits. A by-pass around a town may cut twenty minutes from journey times, and greatly ease the noise and pollution in the town, but how do we measure the value of these results? We could, for example, attach a value to the time no longer spent in a car, but there are imponderables like stress and frustration, arriving at work already fatigued by the journey, and so on.

You can find pages about attachments, beams, buckling, indeterminacy, joining, funiculars and foundations in this website.

 

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