Bridge Watching

Bridge Watching

Edmund W. Jupp intellect

Bridge Watching

Edmund W. Jupp

intellectTM Bristol, UK Portland OR, USA

First Published in Paperback in UK in 2002 by Intellect Books, PO Box 862, Bristol BS99 1DE, UK First Published in USA in 2000 by Intellect Books, ISBS, 5804 N.E. Hassalo St, Portland, Oregon 97213-3644, USA Copyright © 2000 Intellect Ltd All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without written permission.

Consulting Editor: Masoud Yazdani Production and Cover Design: Peter Singh Production Assistant Vishal Panjwani

A catalogue record for this book is available from the British Library ISBN 1-84150-804-7

Printed and bound in Great Britain by Cromwell Press, Wiltshire

Contents Preface Some Basics Forces and Elasticity Stifness and Strength Kinds of Bridges Beam Bridges Arch Bridges Suspension Bridges Pontoon Bridges Bending Ties Struts Beam Bridges Arch Bridges Suspension Bridges Pontoon Bridges Materials Appendix Glossary Diagrams Photos

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iv 1 7 13 20 20 23 25 27 30 40 47 30 64 74 85 93 100 112 122 146

Preface Wherever we go we seem to meet bridges. Mostly we tend to use them almost without noticing them, except when we see a particularly striking example like the suspension bridge over the river Tamar in Devon. Yet there is much that is worth seeing in even the humblest specimen if we know where to look and, perhaps, how to look. So the aim of this book is to help you to enjoy looking at bridges, by explaining in simple language some features of their design and construction. Although the technical aspects will be treated gently, and the mathematical content will be such as not to frighten the non-mathematician, maybe the serious student, too, will find something of interest here. It is particularly difficult to steer a course between being unduly and patronisingly detailed on the one hand and skipping too lightly over complex matters on the other. If I have erred in leaning too much one way here and there, if you find some of this rather repetitive, I do hope you will bear in mind that bridge-watchers come in all sizes and great variety. There is no attempt to cover everything about bridges, just enough to make a bridge a more interesting object for you, or your camera, or your paint-box. I do hope it will help you to enjoy bridges, wherever you see them. They are such nice comfortable things to watch, especially when you know something about them. As either a hobby or an intellectual pursuit bridge-watching has much to commend it, for people of all ages and persuasions. You don't have to pay a subscription. You can enjoy it on your own or in company, and weather is relatively unimportant. It doesn't need any special clothing or equipment. (If you like, you can use field glasses or cameras, and note-books; but they aren't essential). You need no training, no practice, no coaching. From all angles, bridge-watching is an attractive pastime, all over the world. Go out and enjoy these fascinating structures. You may find them addictive, in the nicest possible way. I do hope so. E.W.

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Some Basics This is not a text-book, nor a highly technical treatise on bridges, though we shall try to cover the essentials, a minimum of what a bridge-watcher should know. Since bridgewatchers are to be found among people of all ages we aim to steer a delicate course to satisfy everyone from schoolboys to pensioners. We cannot deal with everything, though some aspects will be mentioned more than once where it seems appropriate. In the pursuit of simplification, it may be that we shall treat some aspects rather sketchily, but not so as to introduce serious inaccuracy. For the reader who would like to go more deeply into the subject there are many excellent books dealing with more advanced work. Many bridges were designed in the days when the Imperial system of units was almost universal; but British engineers used other systems when they built for some places overseas. So they were in general quite happy to work in any system. Many modern bridges are designed using the metric system. We shall try to avoid using designations of units for forces, weights, lengths and so on, in order to minimise confusion. The word "bridge" can refer to a card game, false teeth, part of a violin, a rest for a snooker cue, a part of your nose, the middle bit of a pair of spectacles, and a good many other things, too. We shall be thinking only about the structures that carry people, goods and vehicles over roads, canals, rivers, railways, or valleys. People who understand something about bridges like to go about and look at them. Bridge-watchers sometimes make notes about the various bridges they see; they list them, photograph them, draw them and paint them. They get interested in the details, and the more they know about them the more they find of interest in every bridge they see. Some basic knowledge is essential to get full enjoyment, so in this first chapter we shall look at some of those fundamentals. Every time a bridge is needed there is much grave chin-stroking. It costs a lot of money to build, and everyone wants to be sure about many things before picking the best plan. Once built, a bridge is there for a long time, and an unfortunate error of judgement is on view for all to see. Much depends upon where the bridge is to be built, how much load it will have to carry, and so on. Will it cross a river, and have to stand up to rushing water and perhaps flooding? Will it be wide enough for the traffic? Are there approach roads to be built? Will it be high enough for ships to pass below? Will people like the look of it? Most important of all, will it be safe under all conditions? There have been some terrifying failures in the past; and even today there are occasions when things can go wrong. So it sometimes takes a long time to come to a decision.

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Bridge Watching A very large bridge is so expensive that there has to be a whole series of meetings, for people to talk about it. It can go something like this. Various committees have to meet and argue the good and bad points of the different ways in which the bridge might be built, and where. When everyone agrees, a decision is made, and then they get someone to draw up a "specification", which describes what is needed. This specification is published, so that people who wish to build the bridge can say how they would do it, what it would cost, and so on. Engineers are trained to solve problems, and their ethical training is towards providing their clients with the most economical solution. Designers of bridges are specialists in that field. They have built many bridges, solved many problems, and have wide experience. So when they have read the specification some preliminary ideas are sketched and discussed and then, drawing upon their experience they set about the calculations, designing and drawing the bridge. Several firms may prepare designs, and they all offer their solutions to the client. These tenders are then carefully considered (more committees!) and eventually one is selected. The firm which has been awarded the contract then allocates the work to contractors who do the actual construction, under the supervision of the designers, sometimes the contractors themselves. The contractors appoint sub-contractors to do the work; and then there is the ordering of the materials, a complicated task in itself. It doesn't always happen like this, but this gives the general idea. The delivery dates have to be so arranged that everything arrives on the site at the right time as far as possible. Quantities are very important, as the lack of cement, say, at some stage of the work may hold up the whole undertaking, and so add to the cost, for delay is expensive. So it sometimes takes what might seem a long time, after the design is completed, before things get going. The design itself is the starting point for a long series of events. Although the first thing is to make sure that the bridge will be strong enough allowing for all expected cases of loading, the engineers think about the looks of the structure, too. Luckily, there are some things that look good anyway, when they are properly designed. A bridge is one of those things. A bridge design that didn't use material properly would look skinny and wobbly, or fat and clumsy. It would grate on your eyeballs; but a well-designed bridge is a lovely thing, a pleasure to see. Most of them are indeed beautiful. Occasionally you may see one which makes some people shudder. Perhaps they'll make you wince, too; but it 2

Bridge Watching won't be often. An ugly bridge, rare though it is, is an obtrusive blotch on the environment, and perhaps sufficient local protest might persuade the authorities to do something about it. There are some interesting primitive ones, well worth more than a passing glance, in far countries, where there aren't many modern industrial facilities. They are fewer nowadays, but you can find pictures of flimsy-looking but strong foot-bridges in old books about explorers. To a keen eye they tell a story of clever use of the materials to hand, and are charming. When you understand bridges they will give you much pleasure all your life. You find them wherever there is a need to cross a track or road or water. They carry people, wheelbarrows, trains, camels, cars, pack-horses, or even liquids in pipes or channels. Although some look pretty much the same as others there are many differences if you know where to look. Bridges differ in type, material, age, decorative features, and so on. They are always interesting to a bridge-watcher, because they stand still, and you can see them from underneath, from the sides, and on top. You can study their methods of construction, and see how they look in different lights, and weather conditions. Once you get into the swing of bridge-watching you will never pass a bridge without examining it. A bridge in bright sunshine looks very different from when it is under snow, or in pouring rain; and you can learn a lot about how it deals with heavy rain or storm water, both on and under it. If it gets very hot and very cold at the site you can often see how the designer has allowed for changes in dimensions due to this. Lighting, too, is important. Lighting systems are costly, and we all want best value for money. You will see many solutions to this problem. Mostly it is pretty well standardised these days, as the factories turn out lamps and posts in large numbers to keep costs low; but now and then you might be lucky enough to spot some original lighting schemes. The Victorians had some wonderful ideas. They built strongly and boldly, so that it would cost more than the councils can afford today to replace, with skinny modern stalks, those lovely monuments to the age of cast iron. I doubt if you will come across many oil lamps now, but the soft glow of gas lamps can still be seen here and there. They are less efficient than some of the garish modern lighting and it is doubtful if they will last much longer, but they did have a charm of their own. Perhaps the best thing of all about bridges is that however long you look bridgewatching is free. There aren't many things like that about nowadays. 3

Bridge Watching The earliest bridges weren't built by man, but by nature. A tree would fall across a stream, and then people and animals would scramble across. Occasionally, too, some long trailing creeper might be blown across a gap and become tangled in plants on the other side; and there you would have a primitive suspension bridge. At times a small crack in a rock would allow a trickle of water to squeeze through. In time, this would carve itself a tunnel through rock; and the arch so made would become a stone bridge over the stream. So it was that from these kinds of beginnings came the fascinating structures of today, linking places with footpaths, roads, railways, and so on. Perhaps the strangest form of bridge is that used by some ants. They make a crossing for themselves by clinging to one another in a chain, letting the other ants walk over them. Over the centuries bridge construction has changed. Wages are higher now, and materials are dearer, too. So bridge builders need to be much more careful about how much wood, steel or stone is used, and how many men and machines are to be involved. Handling materials in the old days was a relatively quiet non-polluting matter of horses and carts, but now the Diesel engine has taken over, solving some problems and creating others. We know much more about the best way to use men and materials now, so we can choose carefully to get a really good-looking structure. There are a few not-so-lovely bridges about, but for the most part they are very comely. Luckily, badly-designed bridges tend to fall down in time. Starting with the specification, engineers need to put in a lot of mathematical work. This at one time was a branch called "statics", dealing with stationary things; but bridge parts do move; they sway in the wind, they give and vibrate. So statics alone won't solve all the problems. Nowadays the bridge designer's mathematical "tool-kit" is new software for the computer. Fortunately, bridge-watchers don't need to understand all the advanced mathematical processes that go into the making of a bridge. We can just enjoy the results. Still, as we stare at the shapes and the separate parts it is interesting to realise how much juggling with numbers and equations lies behind it all. Before electronic computers were invented most of the work was done with slide rules, ingenious little calculating devices that you could hold in your hand. For some very accurate work you might have to use a big one that looked like a rolling-pin. It doesn't seem very long ago, but no-one uses them now.

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Bridge Watching With the modern computer it is possible to speed up the mathematical side of the work, and produce pictures of the finished bridge to show what it will look like, long before the first orders are issued for any material. When you see a bridge nowadays you are perhaps looking at a structure that has been seen on a computer screen before the first bit of earth was dug out for the foundations. We shall try to avoid technical jargon in these chapters, but we may have to use a little here and there; and in any case a little knowledge of some technical expressions is valuable for the bridge-watcher, helping to bring to life some important features of the art and science of this noble contribution to a nation's assets. Some words have different meanings when used as technical terms, so we must make clear these differences. It is important to understand the engineer's special use of some words, and in particular the words stress and strain. In everyday use they mean pretty much the same thing. To an engineer, however, they are quite separate in meaning. When a force is applied to a piece of material we say it produces a stress, or discomfort, and the stress is the cause of a strain, or distortion. So force, stress and strain are linked in this way. These words, then, require our attention in this first chapter, to "clear the air". Most other terms that we shall meet will be explained when we come to them. A force produces a large stress if it is applied over a small area, but only a small stress when it is spread over a large area. This is why it is easier to bang a pointed nail into a piece of wood than it is to make a blunt nail go in. A pointed nail concentrates the force to produce a greater stress at the point of application. In the same way, a blunt knife doesn't cut easily, because the force on the knife is taken by a large area of the material, and thus the stress is less. Mathematically, stress is the force divided by the area, and we shall say more about this in a later chapter. Strain is a measure of distortion. It tells us how much the material is deformed by a stress. If a piece of wire is pulled by a force which stretches it so that its length increases by, say, a tenth, then we say that the strain is one tenth. If the length doubles the strain is one. Materials used in bridges don't deform to that extent, of course. So the strains with which we deal are comparatively tiny. When we speak of a strain of, say, 0.001 we mean that the material has changed by one thousandth of its original dimension. At the end of this book is a glossary for reference should you come across a word which you don't understand. In this glossary the explanations of some words have been 5

Bridge Watching expanded so as to amplify what has been said about them earlier. There are also one or two words not previously mentioned in these pages. It is hoped that this will help in general understanding of the subject.

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Forces and Elasticity We shall start with the simplest of all bridges, just a board or plank resting on a couple of supports. This is the sort of bridge you might throw across a ditch if you were in a hurry, and had a suitable lump of wood handy. If you would like to experiment you can make a bridge like this by laying a board across a couple of bricks in the garden. Although this is indeed the simplest of bridges, yet from it you might learn several things about bridges in general. The plank should be wide enough for you to stand on it, and preferably strong enough to support your weight. Further, it should be so positioned that you won't meet serious objections from the gardener. If you have no facilities at all, you can use your imagination to do what follows; but it is worth a try to actually carry out the instructions. What you have is called a simply supported beam bridge, or just a beam. You can see beams like this, as well as more complicated ones, in all sorts of places. We shall go into more detail about these later on, but first we must understand a few basic points. In some ways the beam bridge is the least complicated of them all, and a good place to start. So we shall set down more exactly what we mean by a beam. Structures make use of several kinds of parts or components, and the principal ones are struts , ties and beams. Struts and ties take forces straight down their lengths, but beams carry "transverse" loads, that is forces across the member. So a beam is a member that carries loads across itself, and the effect of the load is to make it bend. Struts and ties don't bend, only beams. So you can think of a beam as any component that bends when the load comes on. Notice that bending is not the same thing as buckling. If it buckles under load it is a column or strut, and we shall deal with that in the chapter on struts. Looking now at the simple bridge we considered in the garden, when you stand on it your weight acts across the board. Also, the end supports act across it, upwards. You can see at once that the board bends, and it is therefore a beam, subject to those three external forces, the two at the abutments, upwards, and your weight, downwards. While you are looking at this you could alter the span by moving the supports closer together or further apart, noticing the difference this makes to the amount of bending, or deflection. You can try placing your weight in different positions along the board, too, noticing how the amount of bending alters at various points along the beam. In a way this is all very obvious perhaps, but it is important to understand these basic points, as we shall have to refer to them later. 7

Bridge Watching When a beam bends, a curve is introduced into its profile, and the material has to change shape; the way it does this is so interesting that we shall have to leave the details till we know more about materials. For now, we shall just sketch an outline about what happens when we make a piece of material change its shape. This in itself is such an absorbing study that some people spend nearly all their lives getting to know more and more about it. You will probably find it intriguing to know a little, so that your bridge-watching can be more fun. Firstly then, all materials are elastic. That is, they change shape under load, like rubber, and spring back when the load is removed. Some are more elastic than others, of course. A steel spring is obviously elastic, and so is a car tyre. On the other hand you may find it hard to see how stuff like brickwork, air, and oil could behave like this. Well, they do, though the change of shape is sometimes so tiny that you cannot see it. When you look at a bridge you may not be able to pick out any of the changes taking place in the parts, unless you have special instruments. Yet every time something crosses the bridge, or when the wind blows, or when the sun shines, all the parts change a little; and as the load trundles off the bridge, or the wind stops, or night falls everything springs back to its former shape. So although we usually consider a bridge as a static affair, it is really always on the move. You may well feel that this takes some swallowing, but it truly does happen; and when you know more about materials you will see that all bridges must move like this. The other important thing about elasticity is that it is limited. Every material is elastic up to a certain point, but if it is stressed beyond that it stops behaving elastically, and becomes "plastic". That is, it is no longer springy but stodgy. So when the stress is removed, it won't go back into shape, but stays as it is. Butter is something like that, which is just as well or we should never get it to spread on our toast. Well, we don't reckon to build bridges out of butter; and we don't want bridges that won't keep their shape. So we keep the loads well within specified limits. Put another way, we so design our bridges that the material is never loaded beyond the limit at which the materials lose their elasticity. In this way we make sure that the members are resilient, always springing back into shape as soon as the load comes off, ready to change again when the next load is applied. When you look at a great structure like the Forth railway bridge it may be hard to imagine every one of those pieces of steel giving way as the train rolls across, and then coming back into shape afterwards; but it is true and can be proved easily with the right kind of instruments. 8

Bridge Watching Engineers measure very small displacements with things called "strain gauges". There are several kinds, and what they do is to magnify the tiny movements and indicate the amount. Many of them are electrical, for these are simple and cheap to make. An electric strain gauge consists of a tiny length of wire which is stuck to the loaded member and connected to an electrical supply and a meter. Tiny changes in shape cause changes in the resistance of the wire, which show up very well on the meter. They can be used to produce diagrams showing how a member stretches or shortens while a load crosses the bridge. Mechanical ones, too, are used, and here is a simple kind that you can make for practically nothing. Get a knitting needle from a lady friend or relative, and with a little knob of glue stick a length of thin wire across the head as a pointer. Then lay the needle on a table with the wire hanging over the edge. Next lay a ruler across the needle at right angles, so that when you push the ruler it makes the needle roll along the table. You will see that when you move the ruler only a short distance the needle turns, and the end of the wire swings through a considerable distance, much more than the movement of the ruler. This simple strain gauge can be used to measure tiny displacements, and demonstrates the principle of all strain gauges, that of magnifying the actual movement. There are many ideas for magnifying movements. Here is one that you might like to try, to measure how much your simple beam bridge sags under a load. Set up a little horizontal spindle carrying a pulley. Wrap a thread round the spindle, with its upper end attached to the underside of the beam, and a small weight on the bottom to keep it taut. Now fix a piece of thread round the pulley, with a small weight on its lower end so that it hangs down straight. This is rather a fiddly business, and if you can't manage it it doesn't matter very much. Follow it in imagination. Suppose the pulley diameter is, say, 25 times the diameter of the spindle. This would give you a magnification of 25. So a barely visible movement of the bridge of only a smitchin would show on the pulley thread as an easily seen distance. Probably, if you stand on your simple beam bridge near the middle it may give quite noticeably, and you won't need a strain gauge to tell you that it has bent. If it is stiff enough it won't bend too much, and will spring back when you step off it; and if it is strong enough it won't break. So what makes it stiff enough and what makes it strong enough? Here we come to the basis of bridge design, and it will give me great pleasure to show you something of the absorbing world of forces. 9

Bridge Watching For simplicity we shall talk about mechanical forces; but there are many other kinds, financial, spiritual, political, electrical, and gravitational for example, and we might refer to these later. They all obey the same natural laws and in particular have one quality in common, which is that they occur in pairs, one exactly equal and opposite to the other. You may find it helpful to think of a force as something that tends to produce change, opposed by another force opposing the change. Whatever we do in life a knowledge of forces and the way they behave is always helpful. We meet forces of all kinds every day; and whatever kind they are, you never meet one on its own. If you think you have, you have missed one somewhere. For example, when you stand on your little bridge, your weight is a force, pushing downwards, tending to alter the shape of the beam. Inside the beam the material deforms elastically just the right amount to produce an upward force of the same amount, opposing the tendency to change. These two tendencies are always in precise balance when everything is still. The art of the engineer is the solution of problems. That is the whole purpose of his training and education. Problems never dismay an engineer. They are what makes life interesting; and his knowledge of forces is one of the most important of his tools for tackling problems. Given a problem, the engineer studies it and then provides several solutions, from which he makes a choice. With bridges the principal problems involve different types of force. When you understand something about forces, then, you can go out and find your bridgewatching a more rewarding occupation. We start by saying again that materials under load change their shape elastically at first, and then, if overloaded, plastically. In all the bridges still standing you will see that the forces never overload the materials, so the only forces you will meet are elastic ones. They are the ones that the bridge can manage, without permanent change of shape that is. If you should see a collapsed bridge you will be able to notice the plastic changes in the distorted shapes of the members, bent and sometimes twisted, and unable to spring back into their original form. Before we can understand how the forces act in the members of a bridge we must remind you again, because it is so very important, that every force is opposed by an exactly equal one.

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Bridge Watching If we call one direction plus and the other minus, then when the forces are added together they come to zero. This is always true, whatever direction we choose, in any group of forces. So I shall now give you a little equation, written in a kind of shorthand, to help you to remember it. You could almost regard it as an equation of life, for it is true of every kind of force system, political, biological, or any other, wherever there is a tendency to change. This is the equation: Â= 0 It may not be much to look at, but it is powerful and important, so let us see what it means. The first letter, Â, is the Greek letter S which we use to mean "the sum of". The next is just a symbol to represent a force in some particular direction, say upwards. So in words instead of symbols the meaning of this cunning little equation is this: Wherever we have a number of forces acting on a body, if we take any direction we like, and add up all the forces and bits of forces acting along that direction the total will always be nothing. Although not expressed like this, it was Isaac Newton, that talented Cambridge mathematician, who provided us with this knowledge. It is perhaps the most important equation you will ever learn. It will solve all kinds of problems for you, once you know how to use it properly. Later, I'll give you another, similar; but once you really understand this first one the other will be easy to remember. The way we use this for bridges is to look at some part of the structure and then pick a suitable direction. If all the forces along that direction are added up we should get zero. If it doesn't come to zero then there must be some other force there that we have left out. In this way we can find the size and direction of an unknown force. To show what this means, let us think again of that simple beam in the garden. Your weight is a vertical force, so we can pick the vertical direction as the one to use. Your weight cannot be the only one on the beam as it isn't zero on its own. The only other possible forces must come from the two bricks. If we call upwards plus and downwards minus, we use our equation like this : Â= 0 11

Bridge Watching meaning "all the vertical forces add up to nothing". So we have : (Plus forces from bricks)+(Minus force of your weight)=0 that is : brick forces - weight = 0 or : brick forces = weight This tells us that the bricks, between them, push upwards with the same force that the load pushes downwards. You may feel that this is pretty obvious anyway. Well, so it is; but it does demonstrate an important principle. Whatever kind of bridge we have, the supports must push up just as much as the load pushes down. These reactions of the supports are the result of elastic compression of the abutments, the places where the ends of the beam rest. As the load comes onto the beam the supports give way more and more and their springiness resists the load increasingly till they share the full load. The next time you see a beam bridge, look at the ends, or abutments, and you will see the parts that have to give, to provide the upthrust. The movement is so small that you won't be able to see it when a lorry or train crosses; but at least you will know that it is there. Later we shall deal with some other kinds of bridge, and we shall see that whatever the kind of bridge the upward parts of the forces at the abutments are always exactly equal to the downward load. Summarising, this chapter has been concerned with three facts: 1. 2. 3.

Materials in bridges behave somewhat like rubber lightly loaded. A force cannot exist on its own. At any point all forces in a chosen direction balance out to nothing.

In the remaining chapters we hope to be building on these facts.

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Stiffness and Strength In the first chapters we mentioned elasticity and forces , and saw how a bridge is not perfectly rigid, but gives way under load, springing back to its proper shape when the load comes off. Also, we met that valuable equation that showed how the supports had to push up with exactly the same total force as the load pushed down. You may wonder how the bricks under your simple plank could push upwards. So think of what we said about elasticity in the first chapter. When you stand on the board the bricks are squeezed by the load so that, like a spring, they push back against the plank. If you squeeze a spring in your hand you can feel how it pushes back against you. All springs and springy material behave in the same way. Although it all happens quickly you can slow it down in your mind. Imagine the load coming on very slowly, and the bricks just beginning to feel the pressure. They squeeze down a little so that their elasticity gives them some upward resistance. When a little more load is felt they squeeze down just that little bit more. All the time, as the load increases so do the elastic forces in the bricks, until, when the full load is in position the bricks and the load are satisfied and still. By then the material of the bricks is compressed just like any other spring. This assumes that the load comes on gradually; but sometimes a bridge is loaded suddenly. For example, a fast train might suddenly rush on to a bridge. When this happens the elastic give is twice as much and the whole structure bounces up and down for a while. You can see how this happens if, instead of slowly stepping on to your beam you jump onto it (if you jump hard enough, you can break it !). The frequency of vibration depends upon the final amount of deflection , i.e. the deformation when it has come to rest with the load on. There is a very simple equation for this, which you can test for yourself. I shall tell you about this later. When you jump off your little beam bridge the bricks don't have to push up any more, so they spring back to their ordinary thickness. These elastic movements are very tiny of course, and even an ant sitting on one of the bricks wouldn't notice it, (unless he were squashed between the brick and the plank!). The abutments of all bridges are like giant springs, though they may not look like them. You can't always see the actual abutments, as they may be buried; but in many cases they are obvious. When you see a beam bridge across a road, say, look at one end: there you will see it resting on something. This is an abutment, and this is what gives when the load comes on. If a train of heavily-loaded wagons rushes across a steel bridge, it makes the whole thing vibrate, and the supports may bounce. It is possible sometimes to put some light dust on the abutments and see it jump about a little when such a train crosses. 13

Bridge Watching If a load were to make the bridge bounce at what is called its "natural frequency" it could have some unfortunate results; but this can be avoided by proper design for the expected loads. The subject of vibration in general is one calling for some formidable mathematics; but some aspects turn out to be surprisingly simple. The natural frequency depends only upon the initial deflection and doesn't involve a difficult equation. Engineers find it handy to tell which forces they mean by using letters. For example, instead of writing "your weight" each time we could just use the letter "W". If we call the abutments A and B then the supporting forces there, the reactions, could be referred to as "RA" and "RB". We can now write down things like: RA + RB - W = 0 and everyone will know what we mean. (I do hope this is not too simple for you; but someone might be reading this who hasn't done much algebra lately). Now we can think about stiffness and strength, not at all the same thing. Strength is simple enough I suppose. If the bridge is not strong enough it will collapse. So one of the things about a good bridge is that it should be strong enough for the loads it has to bear; but stiffness is equally vital. What's the good of a railway bridge that is strong enough but sags down when a train rolls onto it ? The loco and all the carriages would run away downhill to the middle and wouldn't be able to climb up to get to the other side. So strength alone is not enough. It has to be stiff too, stiff enough to alter its shape by only tiny amounts under load. Absolute rigidity is neither attainable nor desirable. There is always some movement. As long as the material everywhere in the bridge remains elastic it will not collapse. However, if too heavy a load comes along or should there be flood, subsidence or accident, some overloaded part may become plastic, and deform. Then it will not return to shape when the load is removed. The bridge will have failed. Engineers design the various members of a bridge so that none of them will ever become plastic under the expected loading. The bridge is then strong enough. Then they must make sure that no load will produce unacceptable distortions, i.e., they make certain the bridge is stiff enough. At some later date the bridge may have to take heavier loads, perhaps through changes in the expected traffic. Then steps have to be taken by adding material here and there, or by propping it at some point. If your board in the garden has to carry not only you but a friend it might deflect too much, and you could make it stronger and stiffer by putting another brick under the 14

Bridge Watching middle part. This would turn your simple beam into a propped beam, or continuous beam , that is, one that continues as one piece over the supports. Another thing you could do would be to reduce the span, by bringing the supporting bricks closer together. This shorter bridge could carry more load without bending too much or breaking. Again, you could add another plank, on top of the first one, so increasing its strength and stiffness. If you nailed them together it would be even stronger. A deeper beam is a stiffer beam, as you can see by pleating a sheet of paper, thus giving it more depth. Turning the plank on edge, if you could manage to balance on it, would make it much deeper and therefore stiffer. So there are many ways of stiffening and strengthening a bridge. There isn't enough space to tell you about all of them, but the more you look at bridges the more you will see how engineers tackle the problems. It isn't only the upward and downward forces that concern us, but other forces due to wind, and earth movement for example. By being aware of this, you will be able to spot how the engineer has dealt with the sideways stiffness in some of the bridges you meet. By good design we can make a good strong bridge, stiff enough for the job, without using wasteful amounts of material. This is the art of sound engineering. (An engineer has been defined as somebody who can produce an article for ten pounds that any fool can produce for a thousand, or words to that effect). Steel, wood and concrete are expensive materials, and the less we use the cheaper the bridge. Because they cost so much, those who need a bridge usually invite several firms to "tender", saying how much they would want to build it. Then the firm that can do the work for the least money gets the job. Well it isn't quite as simple as that, but that is the general idea. Your plank bridge is a beam which bends under load and recovers its shape when you jump off. It is obviously strong enough. Is it stiff enough? That depends upon several things. If you were using your plank to cross a ditch full of water it wouldn't matter much if it sagged a bit in the middle, so long as it didn't dip into the water and give you wet feet. You could say it was sufficiently strong and stiff; but if, although it didn't break, you got your feet wet it would be strong but not stiff. If it broke and dumped you into the ditch it would clearly lack strength, and its stiffness would be of no interest. The span of a beam is the distance between the supporting forces. Your beam in the garden is not fixed at the ends so we say that it is "simply supported". When you stand on it you may notice that the ends tend to tilt up.

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Bridge Watching If we fix the ends, to prevent them tilting, for example by getting a couple of fat friends to stand on the board exactly over the bricks, keeping that part level, the middle won't sag so much. The beam will be stiffer. This idea of "building in" the ends of a beam is often used to make a beam stiffer without using more material. You may wonder why we don't always make beams like this, fixing them at the ends. In some cases the abutments aren't suitable, and sometimes we have to let the ends tilt to allow for other movements. Sometimes it may even be more expensive to fix the ends than to stiffen the beam by other means. Loading a simple beam , you will recall, causes it to bend; and unloading it lets it straighten out again. Look again at that uncomplicated arrangement, your plank supported on bricks. (Really it is much more complicated than you might think; but more of that later). Now imagine yourself standing on it, right in the middle. Since there are only vertical forces on the beam we can write our wonderful equation, and apply it to the vertical direction. Â=0 and as you know this means that the sum of all the forces, taking upwards as plus, equals nothing. We could, if we wished, take the downward direction as plus, and write our equation as ÂØ = 0 It amounts to the same thing. So there is the plank, with your weight pushing it down in the middle, and the bricks at the ends each pushing upwards with half your weight, making the total zero. If you now move along the beam towards one end, the plus force at that abutment will get bigger; and to keep the total equal to nothing the plus force at the other end will get smaller. When you see a train crossing a railway bridge, the upward forces at the abutment which it has just left are decreasing, and the far abutment is pushing up harder. Every time a load crosses a bridge, whatever size or shape it may be, there is always this gradual change in the forces at the abutments during the crossing. Well not every kind of bridge, for there is one rather special exception -- pontoon bridges. We'll look at these later. They depend upon buoyancy, or flotation, and effectively consist of a number of short beam bridges. 16

Bridge Watching At most railway stations there is a little footbridge, and when you walk up the steps on one side, to start crossing, the supporting column under you gives way elastically, to take your weight. As you walk across, that column eases off its loading and the farther column begins to bear your weight until, when you are half-way across, each column takes half your weight. When you reach the far side, all your weight is taken on that farther column, which is squeezed accordingly. On a road bridge, every vehicle that crosses makes the abutments change their reactions in this way. So under a constant stream of traffic the loads in the supports are rapidly changing all the time. If you were to draw a graph of the load on one of the abutments over some period of time it would be a very jagged curve indeed. After a time, the abutments might get tired of these changes, and if the loads were very high the materials might fail from what is known as "fatigue". You can get an idea of this by bending a piece of wire to and fro at some point. If you bend it only a little it will stand up to a large number of bendings; but if you bend it severely it cannot endure so many. It seems to get tired and loses its elasticity. Eventually it may break from this "fatigue". So when we design a bridge we have to remember that it has to put up with millions of changes of stress during its working life, and we must design accordingly, keeping the stresses well within limits set by the particular type of material we use. Materials are tested for resistance to fatigue by subjecting a sample to millions of stress reversals over a range of severity, noting how many reversals it can withstand at different amounts of stress. Below a certain value most materials can withstand a virtually unlimited number of reversals. You will remember that every bridge must be (a) strong, so that it doesn't break, and (b) stiff so that it doesn't bend into a funny shape. To see what makes your plank strong and stiff, we shall take an imaginary look inside. When the plank bends, the upper surface is squashed and the lower face is pulled out. To exaggerate this, stick a couple of long pins in the upper face, some distance apart, and tie a piece of cotton fairly tightly between their tops. When you stand on the beam you will see the thread sag, showing the compression of the upper surface. If you wish you could stick a couple of pins in the underside, and tie some thread between those. Under load the beam would cause that thread to stretch, and might even break it , showing that the lower surface is under tension. So the stress changes from compression at the top to pulling or tension at the bottom.

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Bridge Watching Near the midway point between top and bottom there is a layer where there is neither compression nor tension. If you think of the plank as made up from long fibres then those in the middle aren't doing anything; they are not loaded and thus not deformed. This is an important piece of knowledge, so it is worth repeating, a little differently. In a simple beam there is a layer about halfway down carrying no stress. The layers below this are in tension, i.e. being pulled, and the ones above it are in compression, i.e. being pushed. This is why, if we want to make a hole in a beam, we do it halfway up, where the material isn't under stress. You might see a floor joist, (which is a beam), sometime, through which electric cables or pipes have to pass. You should find that they are poked through holes drilled through the middle, i.e. halfway down. Sometimes you may see a wooden beam with the lower corners removed, or chamfered. It looks very good, but really it takes off material where it is most wanted, so the chamfers ought not to be too severe. Now stretch your imagination a little, and think of yourself shrinking in size till you can get inside the beam, and look at a cross-section. When someone stands on the beam you could see the fibres below the middle all pulling as they are stretched by the loading, the ones at the very bottom pulling the hardest. Further up the section the fibres are less and less under tension, till at the middle they do nothing. Above the middle you see each layer more and more compressed till at the upper surface they take the highest compressive stress. Most of the wood then, doesn't carry much stress, and some of it, the wood in the middle, isn't stressed at all. It might just as well not be there. It would be less wasteful of material if all the layers did their fair share of the loadbearing. Put another way, we could use the same amount of timber to make the plank stiffer and stronger. We could cut out the middle part, the "neutral layer" and put that material on the top and bottom where it could do more good. So when you are looking at some beams you may well find the upper and lower faces wider than the middle. Indeed, you will probably see some steel beams or girders that are very thin in the middle, so that the section looks like a capital letter "I". These are called rolled steel beams because they are formed from soft hot metal blocks being squeezed between pairs of rollers to form the I-section. A hollow square section has the same advantage. 18

Bridge Watching Another way of saving steel is to cut the web, the piece between the flanges, in a zigzag, and then pull the flanges apart, lining up the points of the cut steel and welding them together there. You may come across this kind of thing on a construction site, before the beams are hidden by the cladding. It is a clever way of giving a steel section much more strength and rigidity without increasing the amount of material. When you see a built-up beam or girder, that is a beam made up from separate parts you will be able to notice how the upper and lower parts are wide compared with the more slender members which connect the top to the bottom. Now you know why. An interesting example is Brunel's bridge across the Tamar , in Devon/Cornwall. If you look at it or a picture of it you can see that the upper part of each span is a fat tube, and the lower part a wide thin structure , whilst the two are connected by a comparatively light section. Some modern bridges are made from pre-cast hollow concrete sections. You might get a chance to see that here again the top and bottom are wide and the middle part thin, because it is the top and bottom that carry most of the load. It should be appreciated, of course, that a beam may be required to withstand other loading , so that it is not subjected to pure bending alone. So not all the beams you see may conform with what has been written above. Where this is so you may find it interesting to seek the reason. Summing up this third chapter then, we have tried to cover three points, which should lay the foundations for a sound understanding of the work of a bridge designer: 1. Stiffness, as well as strength, is important. 2. The vertical forces at the abutments alter as the load crosses, and millions of changes in the forces can lead to fatigue failure unless the stresses are low. 3. The material in a beam should be concentrated mainly along the upper and lower surfaces if tension and compression due to bending only are being considered.

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Kinds of bridges Before we go further into some of the technical features of bridges we might look at some of the many types of these attractive structures , so that you can identify them on your travels. We shall deal with the different kinds in more detail in later chapters, so now we shall skip over them lightly to get a general idea. Although some of them may seem very complicated at first sight they can be broadly divided into four principal types: • • • •

Beam Arch Suspension Pontoon

Another way of sorting them is by the kind of material used to build them; but this is not so easy, because they can be built of almost anything, except stuff like thick treacle. The earliest ones were of stone slabs or timber, and there are some modern timber ones too. Then came iron, followed by steel, concrete, reinforced concrete, pre-stressed concrete, and so on. You can find bridges made from all of these. You might even find one made from icing sugar, on a wedding cake. There are rope bridges, made from grass rope or nylon, and pontoon bridges made from canvas and straw. Then again, lumps of stone are put down in shallow streams as stepping stones, and in one way these could be thought of as forming a type of bridge. So sorting out bridges by the material in them is not so simple, and we shall find it convenient to divide our bridges into the four groups mentioned above. This will cover pretty well all the bridges we shall meet. There is a variety of features to look for when you go out bridge-watching. By now you will be able to spot the different types, and tell which is which just by looking at them. That is effectively the first step to becoming a real bridge-watcher.

(a) Beam bridges In its simplest form the beam bridge is pretty well anything fairly stiff set across a gap of some kind. That board on the bricks in the garden is of course a beam bridge, and so is a tree trunk thrown across a stream. However, there are some that are much more complicated than that. Larger beam bridges consist of great steel girders or massive concrete structures. There are some in timber, too, small and large, ingeniously put together, sturdy and good to see. Generally speaking a beam bridge is straight, flat and clean-cut in appearance; but 20

Bridge Watching there is great variety not only in the materials used but in the shape needed to cope with particular types of load and the places where they are built. Some bridges, instead of going straight across a road or river at right angles have to go over at some other angle. These are called skew bridges , and are good to see. Again, some are not level, but connect abutments at different heights. Very large differences in height occur only when people, cattle and sheep use the bridge. The steepness of the roadway would be too much for wheeled traffic. Some are short, of only one span, and others are many-spanned, leaping from pier to pier across wide rivers or great stretches of shallow water. Some are curved when viewed from above. Many are modified in ways that make it hard to recognise them as beams at first. When built in concrete they are apt to discolour rapidly, and their fine simple lines can be marred by dirty grey streaks running down the sides, and blotches of mucky colour. This doesn't detract from their strength or stiffness, but it certainly reduces their charm as things of beauty. This is a pity, as the beam bridge in concrete can be elegant, with its graceful simple lines. If a drip channel is cast in the underside of the concrete near the edge, the nuisance can be much reduced. Perhaps it would be a good idea if motorway bridges were adopted by the people who live near them. Then they could paint them in pleasing colours, and put names on them, maybe the name of the place itself in bold attractive lettering. This would add interest to travel on the motorways, and help navigation, too. Just imagine, as you cruise along, seeing a lovely lime-green bridge with something like "Moon Bridge, Belham" tastefully picked out in maroon. Well, perhaps that is asking too much. Still, it would help to protect the concrete face. On the other hand, motorway bridges are not all the beam kind, nor suitable for carrying lettering; and it could cost a lot. Still, one day perhaps, it might happen, and bridge-watchers among others will rejoice. Beams or girders made from steel need protection against rust. Steel is made from iron, and iron is dug out of the earth in the form of an ore called oxide, which is iron and oxygen combined. To get the iron out of the oxide we have to get rid of the oxygen. Once that is done the iron is melted and mixed with carbon and other elements to form steel. If the steel is kept absolutely dry it stays bright and shiny; but if there is moisture about then the iron tries to get back its oxygen so that it can be iron oxide again. That is how we get that red rusty appearance; and the iron oxide is nothing like as strong as steel. 21

Bridge Watching Rusting has two undesirable effects. It reduces the area of the steel, and it swells; so it can produce cracks in concrete. To keep moisture and acids from the steel we need to paint a coating of some substance over exposed parts. Coatings don't last for ever, so they have to be renewed from time to time. This is expensive, not only for the coating itself, but for the wages of all the men employed. When people decide whether to have a steel or concrete bridge they have to take into account the cost of all this. The problem is not peculiar to steel, for timber too needs treatment, though concrete normally doesn't call for much attention. On the other hand concrete can be tricky stuff. It looks so easy, just mixing together sand, cement and some little stones; but it is really not simple at all, and concrete made carelessly can lead to calamity. When we design in concrete we have to use calculations which assume it is properly made, all materials precisely measured and mixed, with the exact quantities of water added, and the mix carefully placed, vibrated and cured. If the contractor does not see that this is done conscientiously it can lead to trouble, and even disaster. More than one bridge has had to be completely rebuilt because of concrete trouble. Some beam bridges are made from steel plates, riveted or welded together to form large I-sections. Railway companies used to be very fond of these, and you can spot them at most railway stations, and along the line here and there. Many of the early riveted stuctures are beginning to look quite venerable now, and they do seem to have a beauty of their own. They were popular for footbridges , as lots of them could be made from one design, assembled in the railway workshops, and transported on flat wagons to the site. Railway routes come in only a few different widths, depending upon the number of lines, and hundreds of footbridges are needed for the passengers. The railway workshops could turn out more or less standard beam bridges and supporting columns with steps, and the whole network of railways could be supplied with handy footbridges. Where timber is plentiful and cheap you can see some lovely wooden affairs, especially abroad. In some country estates, too, if they had a good carpenter on the staff, they put some pretty little wooden bridges across the streams in the grounds. A couple of heavy baulks would be thrown across and some planks laid on these for the walkway. Then all that was needed was some simple handrailing to complete a useful and decorative addition to the scenery.

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Bridge Watching In some cases the timber wasn't trimmed, so that the bark remained on the members. You may often come across this simple type of beam bridge, and you will find them in paintings too, for artists are fond of them. A pleasing variety of the simple beam is the trestle bridge, where the span consists of several short beams resting on a row of trestles which spring from the bed of a gorge. The flow of water past the obstructions can scour the river bed and lead to loosening of the trestles, and the design must take due account of this peril. People who have a good eye for such things can sit on a rock a little way downstream and study the way in which the various parts are put together, with much satisfaction. Wood is a very attractive material when properly used. If you should find yourself at Middlesbrough in Yorkshire you should go to see the curious bridge called a "transporter bridge", which is a high-level beam bridge with a travelling suspended load. You don't see many of these, so it is worth a good look. Some people like this bridge so much that they rate it one of the best attractions of the place. You would think that the townspeople would have been so proud of such a magnificent treasure that they would have painted it in cheerful colours and made a fuss of it. Perhaps they will one day. Before leaving the beam we should mention the cantilever , which is a beam with only one end, like a diving board. On its own, a cantilever which was fixed to the bank at one end and just waved the other end about in the air wouldn't be very useful of course. So you will sometimes see cantilevers in pairs, meeting in the middle, to carry a continuous road. This is a good point at which to mention swing bridges, for they often use a cantilever. The "fixed" end is mounted on a pivot , and the "free" end rests on an abutment on the other side when the bridge is closed. There aren't many of these about, and you'll probably have to look for where a road crosses a canal, to find one. If you should be lucky enough to be at the head of the queue of cars when the bridge opens you get a good view of the action as the road swings aside to let the water-borne traffic pass. Some cantilever bridges swing upwards, like Tower Bridge in London. There is such a lot to tell you about beam bridges that it is worth a separate chapter for them. So for now we shall pass on to look at arches.

(b) Arch bridges As you know, beams are members that bend, and within the beam we meet both tension and compression. There are some materials though that aren't strong in tension, and others that don't like compression very much. Rock and brick take compression 23

Bridge Watching happily, but not tension. When that kind of material is used in a bridge, the beam is not at all suitable, and the answer is to use arches. It is easy to spot an arch bridge as it rises in the middle, sometimes to a great height. Some beam bridges seem to rise in the middle, too; but they are usually flat underneath, and don't usually rise as much as arches. At different points along the span different depths of beam are often needed, and you will see why this is so when we look at bending in more detail. If the extra depth is given by making the lower surface bend downwards then it is clearly not an arch; but if the upper surface is curved it may look arch-like, and you could be misled. From some points of view arch bridges are the most attractive of all. Some of the smaller ones in brickwork built over railways are truly charming, especially when they are old, with that lovely deep rose-colouring of old brick with perhaps a touch of lichen here and there. Over water, masonry arches are seen at their best, notably when the water is calm. If the shape of the intrados, (the inner curved part), is semi-elliptical the reflection in the surface of the water turns the whole picture into a beautiful oval shape. Concrete arches, too, can provide some elegant scenery, for the material is suitable for moulding into pleasing shapes. Since the arch uses material principally in compression, it could be built in "mass concrete", that is without any steel rods inside; but there is usually some reinforcement , differently placed, and you wouldn't be able to tell from the outside. Timber arches are rare in Britain, but there are some fine ones in Canada and other places where there is plenty of timber to hand; and very imposing they look too. The timber is not bent to form the curves of the arch, but generally laid in overlapping lengths whose angle gradually changes. From a distance this looks like a smooth continuous curve. Metal arches are to be found here and there; and at Ironbridge in Shropshire you can see one made in iron. This one is not only of an intriguing pattern but of special interest because of its origins. If you visit the area you will learn something about the early ironfounders. The bridge is a pretty structure and many people like to just stand and look at it from the river bank, and take photographs, though you can buy postcards of it locally. There seems to be a modern trend towards building flat beam bridges mostly; but you will see many arches on your travels, and will no doubt come to like them very much.

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Bridge Watching Whilst beams rest on supports that push straight upwards, arches tend to spread, and the abutments have to push inwards as well as upwards. So when you look at the ends of arch bridges you will find they differ from those for beams. If a beam bridge is long, and made of steel, it will get longer in hot weather and shorter when it is cold. The supports may have to make allowance for this, perhaps by putting rollers or special pads under the ends of the beam ; but arches can accommodate these temperature changes by hinges. You will probably be able to spot these, at the ends or the crown. You can sometimes see arch bridges that carry a roadway in the form of a beam that runs through the middle of the arch, so that some of the arch is above and some below the roadway itself. These look very attractive. The need for this arises when the approach roads are lower than the height of arch required to carry the load. The height of arch is pretty well determined by what load can be put upon the abutments. The higher the rise the smaller are the horizontal abutment loads.

(c) Suspension bridges What lovely things they are, and readily recognised. The cables or chains droop in natural pleasing curves, and the only thing that can spoil their looks might be an unfeeling design of the pylons that carry the cables. If they are ugly they can ruin the appearance, as they show up from all angles. The pylons are the tall towers that stick up above the roadway. At the top the cables may be either fixed to the pylons themselves or to a kind of trolley that can move a little along the top so that there is no sideways force on the pylon. The roadway is hung from the cables by supporting wires or members at many points along the whole length. Viewed from a distance it all looks delicate and gossamer-like. One feature of the suspension bridge which has given trouble in the past is the effect of wind on the roadway. One famous bridge started swinging in a strong wind some years ago and broke up completely. This was the bridge at Tacoma Narrows, in the northwest of the United Sates. Trouble can arise because the roadway, in section, is a relatively thin affair, flexible like the wing of an aeroplane. As the wind is funnelled past the bridge, between the banks, it is speeded up, and the roadway tends to lift, and fall back again, twisting as it is buffeted by the eddies cast off behind the suction alternately above and below; and as the wind speed is different for different parts of the roadway some parts lift and sag when others are moving the other way. 25

Bridge Watching This results in some twisting, which the road cannot endure, and failure occurs. The classic failure of the Tacoma Narrows bridge is especially interesting because an amateur photographer happened to be there at the right time and took a film of the break-up. This film has been shown many times and I expect you will get a chance to see it one of these days. You will find it a stunning record, well worth the attention of a bridge-watcher. Planning a suspension bridge and building it can be to some extent a fairly straightforward matter in some ways and we have plenty of experience now, gathered over the past fifty years or so. We shall look at these more closely later. Although there are some truly tremendous suspension bridges to be seen you will like some of the smaller ones, too. The cables or chains make bold curves against the sky as they sweep up to the tops of the pylons and plunge down again to the anchorage points on the shore. When you walk across a small suspension foot-bridge you can often make it sway a bit, by swinging your weight this way and that and thus see just how the principle applies. It is probably better to do this when the only other people on the walkway are your friends, or you may get some black looks. There is a good suspension bridge at Clifton, near Bristol. It was designed by that great engineer Brunel. The chains are not ordinary strings of oval links but jointed flat steel strips, an excellent solution to the problem and an example of sound simple design. The bridge spans a gorge, and it is good to see from the roadway itself, or the approach roads, or from down below. It was built a long time ago, and still stands as a beautiful feature of the gorge. Many artists and photographers have made records of it. Suspension cables generally are in the shape of a parabola or catenary. As you will be meeting these curves quite often we shall have more to say about them when we look at suspension bridges in more detail. When the cables of great suspension bridges are being made, special machines are used which operate on the site. If you should ever get a chance of seeing one in action, or perhaps see a film or video tape you will be impressed by the way the machines go to work, building up the layers of strands that form the cable. You might also wonder how the men working up there manage not to fall off. The cables run down to the anchorage points, and these are well worth a close look if you can get near them. They are often easily accessible. The nearer they are to the pylons the more massive they have to be, and they have to sustain an enormous pull from the cables. 26

Bridge Watching In some cases the cables that run ashore support some of the roadway, and are curved; but where the pylons are built a little way in from the edge they slope more or less straight down from the tops of the pylons. The suspended roadway itself doesn't have to be rigid, and indeed it flexes as loads cross, but it isn't likely that you will notice this on a large structure. If you do, you would be well advised to get off it, at once...

(d) Pontoon bridges These are in a different class altogether, for there is usually very little clearance under them. Effectively, they are just strings of little boats tied together, reaching across a stretch of water. You will certainly have no difficulty in recognising these, though you may not find one easily. A pontoon bridge is usually a temporary affair which is removed when no longer needed. An advantage of pontoon bridges is that, generally speaking, they can be carried fairly easily to wherever they may be wanted, and for that matter can often be built from odd materials to hand at the crossing. Military people used to find this very useful, though it doesn't affect them so much nowadays, for there are other types that can be readily transported, such as the Bailey bridge. Yet here again, Bailey bridges are sometimes supported on pontoons. In earlier times, when armies had only horses and mules to carry their equipment they couldn't cope with large heavy items; but now steel bridge parts can be loaded into aircraft or onto ships and tanks and re-assembled wherever they are wanted. War is a nasty business, and sometimes armies have to destroy bridges, however beautiful, ancient or useful they are. They are easily destroyed. So soldiers need to know how to replace them quickly with temporary affairs. Because of this much thinking has gone into the provision of bridge schemes to meet this need. A pontoon bridge is a good way of making a crossing over water in difficult places where aircraft cannot land, and where there are no good roads. In such places the need is usually for a light bridge that will carry people and perhaps light equipment. It doesn't normally have to support heavy gear, for things like that couldn't reach the site in any case. Generally speaking, then, pontoons don't need to be very large, or able to take great loads. As the support depends upon the buoyancy of each pontoon, each must be big enough not to sink completely when the load comes on. Also they must be tied to the banks so that they don't go dashing off downstream in the swirling waters. Construction of a small pontoon bridge usually starts with either making a pontoon on the bank, or preparing one already made and brought to the site. This is then paddled across the water, taking a line to the other side, to be fixed to the bank. In some cases it 27

Bridge Watching may be possible to throw a line across, with a grapnel, or even to use a bow to shoot a line from one bank to the other. With a line across the water-course it is sometimes possible to work a pontoon over by attaching a couple of bow lines to a travelling sheave on the fixed line. By adjustment of the bow lines the pontoon can then be skewed relative to the stream, and away it goes. We shall refer to this in the chapter on pontoon bridges. The first line may be used to haul across a stouter line, to which the other pontoons are fixed, and lined up so that they all point upstream. Then further lines are taken to upstream and downstream points on the banks to hold the line of pontoons in position. The walkway is laid across the floating bases and fixed ready for people to walk over. The bridge is usually fairly wide, and normally handrails are not fitted. Also, the walkway tends to heave up and down as people cross, so users do need to be a little careful. The reason for this is shown in our equation : S=0 In order for the upward buoyancy forces to be exactly equal to the downward force of the load the pontoon has to sink into the water just enough to provide the extra flotation force. So as the load reaches each floating part of the bridge it has to sink to gain the necessary buoyancy, and recover when the load has passed. This causes much bobbing up and down, making some crossings quite entertaining. A pontoon bridge which was well-known to service men who fought in Iraq, or Mesopotamia as it was then known, will be referred to in a later chapter. The bridge was still there in the late 'thirties, giving good service, carrying people animals and vehicles safely if slowly across the Euphrates. During the last war, military needs for crossing rivers and canals were met by a remarkable development of the portable sections of the Bailey bridge, instead of pontoons. This enabled the forces to take much heavier loads across, armoured vehicles that would have presented problems to a pontoon bridge. Often though Bailey bridges rest on pontoons for wide crossing, instead of being self-supporting. It is doubtful if you will get many opportunities to see pontoon bridges. On the other hand you might be able to build a small one yourself. There isn't much to it really if it is for just you and your friends, and you don't mind getting your feet wet whilst you experiment. Try it across a narrow stream, preferably a shallow one, using say a couple of pontoons made of whatever material you can find laying around.

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Bridge Watching Just remember that a pontoon must have enough buoyancy to float, with your weight on it, and must be stable, so that when your weight comes on it it doesn't turn over and dump you in the water. Old crates, tree trunks, empty oil drums, plastic bags filled with grass, anything that will float will do. If your efforts should tip you into the water you will have learned something important. When we come to look at pontoon bridges in more detail we shall say more about buoyancy and stability.

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Bending Whenever a force is applied to a body, either living (people, animals, plants) or inanimate (steel, concrete, wood etc.,) that body experiences a stress . We can think of three kinds of stress: • • •

Tensile or pulling. Compressive or squeezing. Shearing or sliding.

Tensile stress is what happens when you pull or stretch a piece of material. Parts of bridges which feel tensile stress are called " ties " and they tie together other parts. For example, the ropes of a swing tie the seat to the branch of a tree or a framework, and are in tension as the stress in them is tensile stress. So is the stress in your belt, (especially when you have eaten too much). Again, the cables of a suspension bridge are clearly in tension, like the rigging of a yacht. Compressive stress is due to the squeezing action of a load. When you stand up your legs are in compression . There is compressive stress in struts , columns , piers supporting roadways, and the air inside the tyres of a car or cycle. Since we shall be saying much more about struts in a separate chapter we can leave it at that for the time being. If you push down on part of a beam you tend to slide that part downwards against the parts on either side. That is how you get shear stress , and in this case it is called "vertical shear" because the line of sliding is vertical. You would also have shear if you pushed the top half of the beam to the right and the bottom half to the left. This would be "horizontal shear" since the line of sliding between the two parts would be horizontal. This happens in all beams, as we shall show later. Taking these three kinds of stress we can say, generally speaking, that ties take tension, struts bear compression, and shear occurs in beams. This is not strictly true, as you will see, but it gives a good general idea of how different kinds of members handle different kinds of stress. When we look closely at what happens inside a beam we find all three kinds of stress, tension compression and shear all acting at once, and this makes the beam a particularly interesting component. We have already said something about tension and compression, and bending too. Bending may seem pretty obvious, but it isn't as simple as it seems, and we shall have to dig into it a bit more. Bending, or flexure, is happening all around us all the time, and is very important. So with the introductory paragraphs above, here is a whole chapter on some of the interesting things about bending.

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Bridge Watching First, although you don't meet bending in every type of bridge, you can see that you are bound to get it in a beam bridge; and in a suspension bridge the roadway bends, for it is just hung from cables. You may have seen some beams or girders which are deeper in the middle than at the ends, and this was mentioned in the last chapter. Also, you will recall that forces were said to lead to change, altering the shape of things and sometimes altering their attitudes as well. We looked at the changes of shape, and used our equation to tell us something about the vertical reactions or forces at the supports. Now think about the way in which forces tend to change attitudes, that is how they tend to rotate things or turn them round. A force cannot do much to alter the attitude of anything unless it has some leverage. Try to open a door by pushing on the hinge instead of the handle. However hard you push on the hinge it makes no difference; yet when you push on the handle the door swings readily if it has been unlatched. The turning effect depends upon the size of the force. The bigger the force the more is the turning effect. It also depends upon the leverage of the force. The bigger the leverage the bigger its effect. So the turning or bending effect depends upon (a) the force and (b) the leverage. If we multiply together the force and its leverage, then that is the size of the turning effect, sometimes called the torque or turning moment . So a force of 10, and leverage 5 has a turning or bending effect of 50. Now we can bring in the other useful equation. The first one was: S=0 and you will remember that this says that if we add up all the forces acting on something in any one direction it will always amount to zero. The other one is pretty much the same; and just as you cannot have a force on its own, neither can you have a turning effect on its own. So the second little equation says that if you add up all the turning effects acting round any axis, calling one direction plus and the other minus, the total is zero. This is written down in the same way as in the first equation:

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Bridge Watching The axis or hinge can be a real one or an imaginary one, and the axis chosen can be indicated by a letter inside the curl. Just as with the first equation we met, if we don't get zero when we have added all the turning moments then there must be another one that we haven't included in our calculations. This equation looks simple but it is really very powerful; and once you get the hang of it you can do all kinds of things with it. With the two equations used together bridges, among other things, can be designed. There is often a lot of argument about units, and every now and again up pops some enthusiast who wants to change things. You never know when another change might take place, so by avoiding all mention of units we can lessen the risk of confusion. In what follows then, in order to make it easier to understand, we shall continue to write about forces and bending effects without using any particular units of measurement. So when I write of a force of, say, 5 it could be 5 Newtons, 5 pounds, or 5 anythings; and a distance of 7 could mean 7 metres, 7 inches, 7 fathoms or any other unit you like, so long as you stick to one system. Whatever you do, don't mix your systems of units, or you will head for trouble. With this in mind, let us first see how we can use our equation to find the forces at the abutments of a simple bridge. We take a span AC of 12, with a load of 9 at B, distant 4 from A. Now let us think of the turning effects of all the forces acting on the bridge. First imagining a hinge at A, we can say that the force at A has no turning effect there since it has no leverage about A. The load of 9 has a leverage of 4, and so a turning effect of 9 x 4 = 36, tending to turn the beam clockwise. Lastly, the force at C, which we can call FC, has a leverage of 12, and hence a turning effect of 12 x FC, this time anticlockwise, or minus. So we have:

(0 x FA) + (9 x 4) + (-12 x FC) = 0 36 - (12 x FC) = 0 36 = 12 x FC FC = 3

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Bridge Watching If you have an inborn fear of mathematics I do hope that didn't hurt too much. The point is that now we know the force at C is 3; and we can use the other equation to find the one at A: S=0 FA - 9 + 3 = 0 FA = 9 - 3 FA = 6 Our two little equations have found for us the values of the reactions at the abutments. Now consider the section of the beam at B, distant 4 from that left-hand force at A, and imagine that we have a hinge here. The force FA of 6 has a leverage of 4, so its turning effect is 6 x 4 which is 24. It is this turning or bending effect which is squashing the top layers and stretching the bottom ones, so producing a bend. We say that this bending effect is of some moment there, or in other words that there is at that point a bending moment of 24. From our equation:

we know that there must be some other bending or turning effect there, exactly equal but minus, to make the total zero. So the beam itself, inside, must be trying to turn the section the other way, with an effect of -24. What happens as the load comes on is that the material gives way elastically like rubber, more and more till it pushes the top and pulls the bottom just the right amount to exactly balance the applied effect, and so make it all of no moment, i.e. all come to nothing. If you look at another section, say distant 2 from the force at A, you will see that, in the same way, the bending effect there is 6 x 2 = 12. So at that section the internal parts of the beam have to supply an equal but opposing bending effect of 12. At various points along the beam the bending effect of the force varies, so the beam has to produce opposite turning effects at these different sections. The further we go along from the force the more leverage it has, and so the more the beam has to resist. This is what is meant by the "bending moment " at any particular section of the beam. 33

Bridge Watching When discussing forces earlier we used letters and I hope you liked the idea. To save space we shall use letters again, using "M" for the bending effect or moment. As you know, the word "moment" means "importance", and when engineers use "moment" they usually mean the importance or size of the bending effect at some point. Now think of a simple beam of length 6, with a load of 24 in the middle. I expect you can work out that the upward reaction at each end is 12. (If not you had better look back over the previous chapters, or badger a friend for some help). If you start at one end the bending moment there, which we call M, is 12 x 0 which is nothing. This means that there is no tendency to bend at the end of the beam. Along the beam a distance 1 from the end the force has a leverage of 1, so the value of M there is 12 x 1 = 12. At a distance 2 from the end M is 12 x 2 = 24, and so on. In the middle you can see that M comes to 36. From all this you see that as we move out along the beam the bending moment M gradually goes up from nothing to 36 at the middle, with the increase in leverage of the force at the end. From this you will appreciate that the beam is more and more curved as we move out from the abutment. When we go past the middle to a section say, 5 from the end A, the load itself has some leverage, equal to 1, in the opposite sense, tending to turn the beam the other way. Let us call the internal effort of the beam Mi. Then, using our little equation, we have :

MI + (12 x 5) +(-24 x 2) = 0 MI + 60 -48 = 0 MI = -12 Thus, the internal resisting moment is 12; and the minus sign shows us that its direction is opposite to that of the one due to RA. If we call the distance from the left-hand abutment d, we can draw up a list of distances from the left-hand abutment (d) with the corresponding bending moments (M) at those points, like this:

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Bridge Watching

I hope you will work these out for yourself. It is a useful exercise which should help you to see, as you go along, how simple it is, done this way. You might like to work it out again, starting from the right-hand end this time, using the right-hand reaction . With luck you will get the same results. A better way to show these values of M at different points, d, from one end is by a little picture, or graph, as we saw earlier. We draw a line to indicate the beam , and then, from each point where we know the bending effect we go up that amount. The top ends of those little lines can then be joined because we know the bending moment alters gradually as we go along the beam. This graph shows clearly how the bending moment starts as nothing at one end, rises gradually to its biggest in the middle, and then falls to nothing at the other end. I do hope you can see how useful this is. Where the bending effect is most the beam is bent most, and at the ends it is straight. Where the tendency to bend is greatest the engineer has to provide the most resistance to bending. For this simple case with just one load in the middle, the diagram of the bending moment is a triangle, and you might think that we could make a beam to suit this, strongest in the middle and tapering to nothing at the ends. Well, we couldn't have one tapering to nothing of course. There would have to be some material at the ends to rest on the supports. Still, as far as bending is concerned it could certainly be thinner there, not so deep. However, there are other effects besides bending to be considered, as we shall see, and they will modify our ideas. What we have just examined is a very simple case and, as you might expect, most bridges are much more complicated, with several different loads at many points; and some of the loads may be moving, too. Still, for every bridge, once you know the loads you can draw a bending moment diagram; and that is something you have to know before you can decide how strong to make the various parts of the structure . If you would like to see how you get on with the diagram of bending moment for a beam you could draw the graph for a beam ABC of length 20, where B is distant 8 from 35

Bridge Watching A. There is a load of 10 at B, and C is of course the other end. You don't need to be accurate in your sketch. Just a rough outline will do; but you must get your sums right. If you are careful, and if you have understood the earlier paragraphs you should get a triangle with a base ABC of 20 and a height of 48 above B. The bending effect of a central load is usually greatest towards the middle, as we saw earlier, and this is why beam bridges are so often swollen towards the centre. The upper part may swell upwards, or the lower face curve downwards. Sometimes both faces are curved so that the girder looks like some fat fish. When a bridge carries a large number of loads at the same time the bending effects of the separate loads are added together to find the total effect. A very large number of equal loads, or one big load spread evenly across the span, is an interesting case. The diagram is a smooth curve that turns out to be a "parabola". What an amazing curve it is, this parabola. We come across it in all kinds of places, as well as in bridges. If you squirt some water out of a garden hose the jet will follow a parabola. When you chuck a cricket ball at the wicket keeper (or anybody else) it traces out a parabola. The reflectors in searchlights are parabolic, too. In suspension bridges we meet this same beautiful curve, but more of that later. For many of the larger bridges, with long spans, the weight of the bridge itself is much more than the traffic it is to carry; so in many cases the load can be considered as pretty well spread evenly across the span. It is practically what engineers generally refer to as a "uniformly distributed load ", or simply a "u.d.l." The diagram for the bending effect is then a parabola. So far, I hope you see that for any bridge we can draw the diagram for M and read off from it, for any point in the bridge, the bending effect due to the loading . I have sketched out a few moment diagrams to show the sort of shape we get for different loadings . As you see, not all of them are highest in the middle. When we know how much bending effect there is at any particular point we can design that section so as to be stiff enough and strong enough to handle that amount of bending. In an earlier chapter we saw how, in a solid beam , the stress is not the same all the way across the section. I think we had better look at that a little more closely now. You will remember that because the higher stresses are near the upper and lower surfaces much material can be saved if the section is wider there, like an I-section. If you think of the top flange, the stress there is nearly the same over the whole area, so that the flange itself is like a lump of push, so to speak. As the load comes on, the flange 36

Bridge Watching is squeezed, and pushes back with a force that gets bigger as the bending effect increases. In the same way, the lower flange pulls. So the two flanges give us two forces. Now imagine a hinge half way up the section, so that the force in the upper flange has some leverage about that hinge. The force from the lower flange has some leverage about the hinge, too. So we have a couple of (force x leverage) turning effects, both tending to turn the section in the same direction . From our second equation :

we know that this couple exactly balances the bending moment due to the loading. If the flanges are further apart these forces have more leverage, taking the middle as our imaginary hinge. So if we put the flanges further apart they have more leverage and don't have to pull and push so much. They can be smaller, as the force they exert is (stress x area), and the maximum stress is fixed for the material. This word "couple" that we have used is a technical term for a pair of equal, opposite and parallel forces, and we shall meet it often. Bending and turning effects are always handled by couples. Those big steel girders continuous beam that are used in beam bridges have upper and lower members to supply the couple to deal with the bending moment M. As we saw, M is zero at the supports, and varies as we cross the span. So we can, if we wish, use the same section along the whole of the upper and lower members, just spacing them further apart where the bending moment is greater and setting them closer where the moment is less. This can be a convenient way of dealing with the variation in bending effects. Another way is by adding extra plates at places where the bending moment requires it. You can often see these extra plates on riveted plate girders. In some concrete beams, too, one or more of the flanges may be curved in side view, thus varying the depth and so the leverage of the flange forces , so that the couple matches the bending moment at every point. Looking at those diagrams of bending moment, you see that although the biggest moment occurs at the middle of the span for a simple beam centrally loaded or carrying a u.d. load, this is not so for all beams. If the ends of the beam are fixed horizontally, by building them into rock for example, the fixings apply bending effects at these points, so that the moments are no longer zero there. 37

Bridge Watching Let us look at this from another point of view. Suppose you have a bending moment diagram for a beam , and at some point along the span you see from the diagram that the moment there is say, 80. Now suppose that you have two steel plates to use for the flanges, each of which can take a force of 160. The value of a couple is the distance between the forces multiplied by one of them. So if your steel plates are spaced apart by a distance of 1, then they will supply a couple worth 160 x 1 = 160. That is more than you need. Spacing them apart a distance of 1/2 produces a couple worth 160 x 1/2 = 80, which is just right. If you spaced them too closely, say 1/10, the couple would be 160 x 1/10 = 16, and the bridge would be distinctly unhappy! So you place the plates with a distance of 1/2 between them. In this way you have the cheapest way of using the plates to give the girder enough strength to deal with the bending effect at that point. At other points, where the value of M is different, you arrange the distance apart accordingly, or use flanges of different sizes. I do hope that all this doesn't sound too complicated, and you don't have to read it through a dozen times, scratching your head more and more each time. In some cases the calculations do get a little more tangled; but the general idea is just the same, whatever the beam. There are handbooks and computer programs which show bending moment diagrams for most of the common cases. That's just as well if you seek a quick result, without the simple mathematics; but most engineers are quite good at the subject. They enjoy seeing the equations wriggle their way towards a solution, especially when it comes out right. They are accustomed to doing much of it in their heads. Also, people who deal with bridges all the time soon get a feel for them, and can make a pretty shrewd guess at what is wanted for many of the conditions met in design work. An experienced bridge engineer will sketch a bending moment diagram and tell you what section is needed here and there before you have had time to load the program into the computer. This makes a profound impression on the less experienced, and tends to cut them down to size .... Given a specification for a fairly common sort of bridge you might hear a grey-haired engineer murmur something like " Span so-and-so, load so-and-so. We should manage that with such-and-such a girder. Just take a look in the third drawer down on the right." Then it's only a matter of checking the details. All good prestigious stuff, this.

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Bridge Watching When you see the next steel girder bridge try to imagine what the bending moment diagram would look like. Think of where the biggest bending moment will be and then try to see what the girder looks like there. Are the flanges thicker at that point, or further apart? If not, you can ask yourself why this might be so. For an overhanging beam , a cantilever , the biggest bending effect is at the fixed end , which is the point most distant from the loads. So when you look at a cantilever you are most likely to notice how deep it is at the fixed end, tapering off to very little at the "free" end. A good natural example of this is a branch of a tree, which is always cantilevered out from the trunk, thinning out towards the outer end. Again, a striking example is the lovely Forth Bridge, much photographed and painted. I seem to have written rather a lot about bending ; but that is because there is so much bending in bridges. There ought not to be much bending in arch bridges; and in suspension bridges there is only the roadway that bends; but diagrams of bending moment are important for beam bridges, and it is useful to know how to sketch them. Drawing these diagrams, either roughly to get an idea of what is needed, or with great precision for graphical calculations, used to be a pleasant occupation for young assistant engineers. It kept them out of mischief and gave them some idea of what was involved in bridge design. Nowadays there is less work on the drawing board and more computer-aided-design (CAD), which makes some of the old greybeards shake their balding heads indulgently. Looking back over this chapter we have looked at the cause of bending, how beams resist this, how to show it on a diagram, and why some bridges are not the same in section all the way across the span. It must be pointed out, though, that bending isn't the only factor. Shearing resistance, too, may modify the section. More of that later. Before going on to the next chapter you may like to think about wire ropes, as used on sailing boats for shrouds to hold up the mast. You will find them supporting telegraph poles, too and on some bridges. Although they are not beams, they are not always of the same section throughout. The ends, where they are pinned, are fitted with bottle screws or other fittings that are thicker than the cable. There is a very good reason for this, and perhaps you can see why. It doesn't matter if you can't, as we shall mention it again later.

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Ties When we were thinking about beams and bending there was some mention of tension and compression . As you know, we meet both of these in beams, as well as shear ; but some parts of bridges are designed to deal principally with only one kind of load. Those components that have to take compression are called struts , and those that take tension are called ties . A word of caution here, though. Tension, compression and shear all turn up here and there, for they are related and to some extent interdependent, as we shall see. Although we shall be treating ties at first as though they carried tension alone, this is not strictly true, and we shall give more attention to this later. Struts and ties take forces which act along them, parallel with the axis; but whereas struts under load shorten and get fatter, ties get longer and thinner when stressed. Although ties are fairly easy to understand they are worth a chapter to themselves because of certain interesting features that may not be obvious to you at first. You can't always pick out ties in a bridge straight away by just looking, though often they are conspicuous, and there are some pointers. For example, any long thin member is bound to be a tie. A cable is clearly a tie, and couldn't possibly be a strut as it can take a pull only and never even a small push. In a beam, as you know, the stress is greatest at the top and bottom surfaces, and there is no stress in the middle; there is tension and compression, and shear too, present in a complex kind of way. That is why beams are different from struts and ties, and behave differently. However, when a tie is under load the tension across any section, except right at the ends, is pretty evenly spread. If it were made up of twenty strands, then each strand would carry about one twentieth of the load. A tie may be a flat strip, a tube, or a rod, of almost any cross-sectional shape, or even a cable, wire rope or a chain. As the name suggests, a tie does its job by tying together two points in a structure and so preventing them from moving apart. Cables are made from wires twisted together so that the strands help each other. It is like the thinking behind cotton thread or any spun yarn made up into rope and so on. Any weaknesses in individual strands are unlikely to occur at the same place, but spread along the length at random points. So where there might be a weak point in a particular strand the others will help to take the load off it. The twisting means that under load the strands tend to straighten out. In so doing they grip one another to make the unity more effective. Straightening out a helically wound wire exerts a powerful inward force . If you examine a rope or cable you will find that the "lay" of the strands differs for each layer. If the outer layer is twisted in one direction the next layer is twisted the opposite way. If 40

Bridge Watching this were not so the inward force produced by the twisting would force the layers to penetrate each other, thus reducing the strength of the cable. This is not true of chains, though. They should never be twisted, even short-link ones. This is why swivel links are fitted where twisting might otherwise take place, on mooring chains for example. Not all ties are cables or chains, though. Most are lengths of steel plate, rod or tube. Rolled sections of steel or aluminium, and lengths of timber, are also used. We saw that I-sections and hollow sections are well suited for use as beams because of the way in which the material is arranged in a cross- section. They are in common use. When we come to talk about struts we shall find that for them, too, the shape of the section is very important . For ties, though, it doesn't matter so much. A tie can be round in section, square, flat, or any other shape. It can be a length of tube, a cable, a piece of wire, even a length of pre-stretched rope. A tie of almost any crosssection will do if it ties the two points together. When we look at the ends, though, some care is needed. It is through the ends that the load is carried to the tie, and you can't do that unless you grip it, put some holes in it, or stick it to something . In a bridge or girder, the end of a tie could be pulled by gripping it firmly, and rods in reinforced concrete are sometimes held in this way, though you may find it difficult to see them, as they are inside the concrete. If, on the other hand, you are able to watch a bridge under construction, you may get a chance of seeing some of these anchorages before they disappear in the construction. In reinforced concrete, where the steel rods are pre-stressed, you might see the ends of the rods held by great nuts. Where very large bridges are being constructed the forces in pre-stressed reinforcement are enormous, and the special machines used to apply the pre-stressing forces are most impressive. They may use hydraulic rams to apply the forces, as this is a convenient method of doing so; but mechanical methods could be used. In steel frames or trusses we have a choice of several methods of fixing the ends. If the tie is a rod, which is fairly common, we can, for example, have screw threads at the ends, which fit into nuts or threaded rings. This used to be a favourite method for the bracing under seaside piers. In a way, these piers are a kind of bridge, with many supports. When next you visit the coast where there is a pier you may see some of those ties as a kind of black spider's web beneath the decking. You may see this method used at some of the older railway stations, too. It is a simple method where you have a lot of ties coming together at a point, or node. 41

Bridge Watching A steel ring is placed at the node, with radial holes in it. The ends of the ties are then poked through these holes and nuts are screwed onto their ends. The nuts can be finely adjusted to just the right amount of tension . Sometimes a simple node is formed by pinning the ends . When the ends of a tie are threaded like this the rods are often thicker at the ends so that the threads stick out from the rod rather than being cut into it. Cutting the screw thread into a rod removes so much of the material that the rod can be considerably weakened there. If a cable is used as a tie the ends are often "swaged", or provided with a screwed or pierced barrel to which a bottle screw can be attached. This is thicker than the cable, of course, as it has to carry the full load. Sometimes, if the upper end of a cable isn't easily accessible, a weakness can be deliberately introduced at the attachment so that in the event of failure the point of failure can be easily reached, and the defect put right. Where several members are put together to make a girder or frame the ones along the top are usually compression members, with ties along the bottom. There are vertical and sloping members in between, forming the web of the girder, and some of these are ties , some struts , as we shall see when we deal with framed structures . The ties are nearly always flat steel strips, especially in "trellis" type girders, where the ties cross over one another. They are connected by gusset plates ; but sometimes lengths of tube or angle are used. At one time thousands of rivets were used to hold the whole thing together, and there are still plenty of bridges where you can see this, especially at railway stations, (always favourite haunts for bridge-watchers naturally.) When old steel bridges are pulled down the material can sometimes be used elsewhere. Pieces of angle or strip can be used up like this if the lengths are suitable. It depends upon whether it is cheaper to recover and adapt the old pieces or to buy new. The old pieces must be at least strong enough; and if they are easily come by it doesn't matter much if they are somewhat over-strong. That is why you may sometimes see members looking a mite too strong for the loads they have to sustain. It is now time to look inside the tie and see how the load is handled. We shall consider a simple length of square rod, carrying a load, along its axis. So that we have some figures with which to juggle, let us suppose that the section is a square of side 2, and the load is, say, 24. Then without, I trust, straining your mathematical knowledge we find the area of the section to be 2 x 2 = 4; so the tensile stress is 24/4 = 6. On each unit square of the section therefore we have a direct force of 6. When the load comes on, the tie stretches by an amount depending on the stress and the elasticity of the material. 42

Bridge Watching (The direct elastic property of a material is defined by the nominal stress that would be needed to double the length of the tie if it remained elastic all the way). The measure, or modulus of elasticity can be used to tell us how much a tie will stretch under load. This is important, of course, for if a tie stretched too much it might introduce unacceptable distortion of the frame. Further, gross stretching might take the material beyond the elastic limit into the plastic range. Then the tie would be weakened and never return to its proper length. Near the middle of its length the stress is pretty even across the section. So we have an area of 4, with a stress of 6 over all of it. You might wonder why a straightforward stress like this should lead to the tie getting thinner. Understanding this will help you to appreciate the complexity of what is at first glance very simple. A tensile stress induces a compressive stress at right angles, as well as a shear stress at 45°. For the present we shall leave that without further explanation; but we shall return to it when we look more closely at the behaviour of materials generally. So this tensile stress in the tie is accompanied by a compressive stress at right angles, that is across the section. It is this that causes the "necking" of a tie, the narrowing of the cross-section. It is unlikely that you will see such necking in a bridge, unless it has failed, for ties are so designed that the stress within them is always much less than that needed to cause plasticity. Should you see a bridge that has collapsed, though, you may be able to identify some ties that have given way, and then you might spot some necking. You can produce this effect quite easily with a length of rubber. Pulling the ends produces a noticeable narrowing of the cross-section near the middle. In the case of rubber the necking can occur without the material losing its elasticity , but this is not so in steel, where the modulus , or stress for doubling the length, is so much higher. What we have said so far assumes that the load acts right through the centre of the cross-section; but this isn't always the case. The load may be, and often is, offset from the centre. For example, if the tie is a piece of angle-section, and the end is pinned through one of the legs of the angle, then the pull is offset quite considerably, and this complicates the stress pattern. You may be able to see this more easily if we refer back to our second miracle equation. For simplicity, think of the square-sectioned tie again, of sides 2, with the load offset from the centre a distance 1.5, say. We saw earlier that the load produces a uniform stress of 6, right across the section. Now though, our load of 24 is producing also a turning effect on the section, about the centre-line, of 24 x 1.5 = 36. 43

Bridge Watching From our equation:

there must be another turning effect equal and opposite to this, which is supplied by the stress distribution inside the tie . So towards the face nearer the offset load the stress is increased; and towards the other face it decreases. The stress on the section is, therefore, no longer evenly distributed. It falls from a high stress on one edge to a smaller one, on the other face. In cases where the offset is large, as here, the stress on one face can fall to zero, or even a negative amount, i.e. a compression . Thus a tie can fail if either the load or the offset should be excessive. The point to bear in mind is that even though the load may be nominally satisfactory, the offset may introduce dangerously high stresses. When you see a tie where the load is obviously offset you will no doubt conclude that the force in that member is a comparatively small one. To some extent what we have said applies to struts too, and we shall look at those in the next chapter. As has been said earlier, materials vary in their physical properties, in the way they handle different sorts of stress. The three kinds of stress we consider are tension compression and shear . Some materials are very weak in shear, some in tension, and so on. So when we load a piece of material in such a way as to produce some complex pattern of stress the way it behaves will depend upon the relative amount of each type and which kind of stress it most dislikes. If, for example, the shear component of stress at a point is greater than the shear strength of a particular substance, then it will fail in shear; but if at that point the compressive stress exceeds the compressive strength of the material we have a compression failure. It may help you to understand this if you think of a tie of some material being pulled till it breaks. You might even be able to see a member that has been broken during demolition somewhere. (Demolition sites can be fruitful sources of interest for bridgewatchers.) It won't break clean across, square with the axis. There will be a jagged break. This is simply because the material has failed, not through a uniform tensile stress across the section, but because of stresses at angles to the axis other than 90°.

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Bridge Watching In general, a metal rod carrying a tensile load along its axis will, as the load increases, start to neck, thus reducing the cross-sectional area. Because stress is given by load divided by area, this reduction in area results in a corresponding increase in stress. By this time the rod will have passed the limit of its elasticity , and be yielding plastically. Due to the different properties of materials, and the way they react to different kinds of stress, the appearance of the fracture when a tie parts is to some extent typical for any particular material. An experienced metallurgist can recognise identifying features of fractures and derive much useful information from them. It should be appreciated, too, that materials do not always remain the same as when they were made. Changes can take place in the structure caused by what has happened to it during its life. When we design a tie to carry a load of say, 50 safely, we must allow for such changes as are liable to take place. One thing that can happen has been mentioned earlier - the onset of fatigue. The danger from fatigue arises when a material is subjected to a large number of fluctuations or reversals of stress, tension to compression and back again perhaps, several million times. You may think that it would take a very long time to get through a million fluctuations; but this is not so if they happen quickly, at a high frequency. After all, at a frequency of 50 a second you reach a million in a few hours. So a tie that is part of a bridge for many years suffers many millions of stress changes in its life-time. The stiffer a member is, the higher will be the frequency of its vibrations. A tie can vibrate along its axis or by bending , and both of these can produce a fatigue failure. Such failures are rare because care is taken to reduce the loads on such members to a safe value. Below a certain stress the effect of a large number of variations is negligible. The designer uses what is known as a "safety factor". That is, he multiplies the expected loading by a factor which will ensure safety. Then the amount of material in the tie is enough to keep the stresses low when the member is working. Safety factors vary according to conditions, but are usually of the order of three or four, only occasionally being much more than this. So broadly speaking you can reckon on a tie being able to take several times the normal load before it would feel unhappy. Another possible condition that could lead to failure is the effect of wind or water flowing past the tie, and we shall look at this a little more closely in a later chapter. For now it will be enough to say that when a rod is exposed to a wind, the air flow meets the rod, divides into two parts, and flows round it. When the air gets to the other side it forms a series of little whirls, first round one direction and then the other. These little whirls push the rod first one way and then the 45

Bridge Watching opposite way, so the rod starts to oscillate across the flow. You can test this for yourself, by drawing a vertical stick through some water. You will feel it wobbling from side to side. A tie-rod that feels a flow of air or water past it will therefore start to wobble. The frequency of the wobble depends upon the speed of the flow, the diameter of the rod, and the properties of the fluid. All ties have what is called a "natural" frequency of oscillation, like a guitar string. If the vibrations due to the flow were to coincide with this natural frequency then they would build up, and the tie might swing so violently as to cause a fracture. Generally, this wobble can be disregarded, as the frequencies are a long way apart; but a careful engineer might have to give some heed to the possibilities in certain cases. With bridges you can never be too careful. In this treatment of ties we have looked at some of the points which affect their design; and we shall have more to say about them when we discuss materials and frames. Before leaving ties, though, it might be worth recalling how unsuitable concrete and brickwork are for tension . So the ties you see will almost always be steel rods or strips. If you think you see a concrete tie it is probably a steel one buried in concrete. Reinforcement is always needed wherever tension occurs in concrete members.

46

Struts A strut is a member that shortens under load. Like a tie , it takes the load at its ends; but ties and struts are quite different in other ways. Without some knowledge of bridges, you might not be able to spot which are ties and which are struts just by looking, for in many cases they look pretty much the same. After you have learned something about frames it will be easier to pick out a strut by noticing whereabouts it is placed in the structure. You can often estimate roughly what kind of load it might be carrying, too. A strut is a compression member, like a column , or a pillar. Columns are obvious. They stand under bridges and push upwards from underneath. Some of the old ones were in brick, with some very fancy patterns, and others in beautifully patterned iron. Where they stand in flowing water they often have cutwaters built round the base to minimise scouring. These lead the flow smoothly round the base of the column. On land you can usually see the sturdy foundations on which they stand, and in some estuaries at low tide you can walk out to them and examine the cut-waters. Iron or steel columns are usually round, and can look very handsome. The tubby ones are often classical Doric columns, rather plain, but pleasing in their severity. Some of the early designers of railways stations put up Corinthian columns of delicate beauty, and you can still see these monuments to a more leisured age. They are lovely, even though many are covered in grime. How elegant they must have looked in the days when they were first erected, and when cleaners kept everything immaculate. The lofty roofs of the old stations were necessary because the smoke and steam from coal-fired locomotives needed space to rise and get clear. The Corinthian columns are slender, with interesting fancy work at the top, curly leaves that would cost too much in time and labour to make in concrete nowadays. Columns have to be so placed as to interfere as little as possible with the flow of road or water-borne traffic passing below. Where the thicker Doric type of column was used, fewer of them were required; but the lighter Corinthian columns had to be placed more closely together. Conditions at the site sometimes determined what kind of column should be used. Where the ground could not take much stress , it might be necessary to use many columns, or large footings, to spread the load from each column over as wide an area as possible. In the days when cast iron was cheap and plentiful the engineer had at his disposal a material that was easily cast into almost any sort of shape. Our Victorian forefathers did what they could to imitate the old classical styles, and they made a very good job of it. 47

Bridge Watching You won't see modern bridges held up by Corinthian columns, or even the plainer Ionic ones. The columns are plain, sometimes sloping, often rectangular in section, and severe, with only now and again a rare curve. The modern column or strut has to be strictly utilitarian, designed to do it's job without adornment; and its job is to sustain an axial thrust. So go to the older main-line railway stations and enjoy their elegance. Their charm is still there for those who will look for it, and I hope you are one of those people. Along motorways and over rivers, wherever you see columns under bridges and flyovers they will be mostly dull grey slabs, and seldom interesting. In general, the motorist needs only room under the bridge to clear the roof of his car, and generally doesn't mind what holds the bridge up so long as it stays up. Thankfully, though, they're not all bad. Here and there you can see some striking supports, sloping up perhaps and curving gracefully into the main structure. The three-lane highway demands a bridge of large span, and no pillars between the lanes, to interfere with overtaking. Brick and stone columns deserve a mention, though you may not see them used often in modern bridgework. The old bricklayers could do beautiful work, and some of the old bridges are protected against demolition by being "listed". Still, many of them have been irretrievably lost, where railway lines have been destroyed and buildings erected where the lines formerly ran. Looking at well-laid bricks done by a skilled craftsman is a pleasant occupation. Bridges demand a high standard of workmanship, and those old beauties gave the craftsman a chance to display his skills. Some of the old railway lines were carried over deep valleys on bridges held up by some very tall brick columns, and they remain impressive. They are often the subject of paintings and photographs, preferably with a train crossing. The tops of columns can be of special interest, apart from the classical capitals, for where they come up against the main part of the structure you may sometimes see that they aren't fastened there. This is to allow movement between column and beam without strain. You may even see rollers between the roadway and the columns, though modern practice sometimes uses resilient pads with horizontal layers of steel In some long bridges there is often a lot of movement, some due to temperature changes. If the columns were fixed they would be bent sideways when the top of the column was pushed over a bit by movement of the frame or roadway. Something must be said about the way in which the bottom ends of columns are supported, the manner of transmitting the load to the ground. 48

Bridge Watching Soil, rock, sand, clay, all behave differently under stress , and when a load is imposed over a small area it first flattens that area, and then proceeds to squeeze it downwards. You can, if you wish, do some simple experiments to show what happens. Take a stick with a flat end and poke it into the ground at various spots. In sand it will penetrate easily, but in granite you won't be able to poke it in at all. If you try with different types of ground you will soon see how some will support quite a load, and others yield easily. The resistance comes partly from the base and partly from the frictional forces on the sides. If you try with sticks of different diameters it will soon become clear that the area of contact with the ground is important. A small area cannot support much, because the resultant stress is high; but a large area reduces the stress and hence increases the load that it can support. For this reason the base of a column is designed so that the load it imposes on the ground is spread sufficiently to involve a suitable stress. We cannot go far into the subject of soil mechanics here; but basically it is concerned with studying the behaviour of different kinds of soil under stress. In the laboratory, samples of soil are subjected to loads to see what they will stand. The mode of failure is observed, and data accumulated for use in the design process. Then the sizes of the foundations for the columns can be calculated. A bridge-watcher may gather from the size of the footings, where they are visible, what kind of soil there is at the site; but it must be realised that where there is rock the columns may be pushed down to where the rock layer starts. At a bridge construction site, if you get there when the foundations are being prepared for the columns, you can get an idea of the problems involved and the way in which they are resolved. Try to visit a number of different sites if you can, for the ground varies considerably, and hence the footings for the different abutments. Don't forget to seek permission before entering the site. I hope that when you see some real classic columns still standing in places abroad, you will like what you see. The average tourist seems to like to look at ancient buildings with guide book in hand; but perhaps your knowledge of what a column does will help you to see more than others. Many of the ancient buildings are little more than ruins, the columns in many cases broken and fallen. Yet you can see what they did when they were erect, and how they were arranged to carry the heavy loads imposed upon them by the building. 49

Bridge Watching In particular, when you look at an ancient bridge you should see how the supporting columns are arranged so as to take the load directly to the base, and how you are more likely to see delicate Corinthian columns when the spacing is close, but sturdy Doric or Tuscan style when they are more widely spaced. You will see columns supporting arches in some attractive arrangements under ancient bridges and viaducts (which are effectively bridges). The principle for struts in frameworks is basically the same, but here the members are not usually so thick, and are normally of metal or timber. It is here, perhaps that the chief difference between ties and struts should be made clear. A tie can be of almost any length without making very much difference to the design; but the length of a strut is an important factor which affects its behaviour, as we shall see. If we have a very short rod, so that its length is only a fraction of its diameter, it is called a pad or buffer. When the load comes on it simply squashes down till it can take the force. In some cases it doesn't matter much if the elastic limit is exceeded and it deforms plastically, though this ought not to happen in a bridge. When a pad gives way plastically it spreads so that its area increases. Since the load remains the same, and the stress is given by the load divided by the area, this increase in the area reduces the stress. So the pad spreads out until the stress is suitable for the material. When the length is increased a little, the strut will still carry its load comfortably; but when the length reaches a certain value it may suddenly fail, the middle bowing out sideways. You can see this if you push together the two ends of a knitting needle or a thin cane. A short length won't buckle, but a long one will. This buckling is typical of an overloaded strut. A tie never behaves like this. If it bends sideways at all it is because of some side load on it. The compressive load which can be carried by a strut depends not only upon its crosssectional area, then, but upon its length, too; and there is a further point. The shape of the cross-section affects the supporting ability of a strut. If you stand up a piece of paper on one edge, it will probably flop under its own weight. Now roll it into a tube, and put a rubber band round it or some sticky tape, to hold it in position as a cylinder, and you will find it will take a comparatively heavy force to bring about collapse. So the strength of a strut depends upon the way in which the material is arranged around its axis, and we need to look into this. 50

Bridge Watching If we think about a cross-section whose area is, say, 16 this could be a circle with a diameter of about 4.5. If the rod were now to be replaced by a tube of internal diameter 2, and the same cross-sectional area, the outside diameter would be nearly 5. Now let the central hole be say, 3. Then the outer diameter, for the same area, goes up to about 5.5. Each time we increase the central hole we find the material spread farther and farther from the centre, yet still maintaining the same load-bearing area. Putting these results in a little table they look like this:

You can see from the table that as the hole is larger so the wall thickness decreases, for the same area; but the spread of the material away from the centre is increasing more and more rapidly. It is this spread away from the axis that gives the strut its strength to resist buckling. If the hole is made very large the walls of the tube are very thin. Thus, for a hole size of 20, the outside diameter is nearly 21, and wall thickness only about 0.25. A very thin wall is unstable, like the piece of paper standing on edge. So there is a limit to what we can do in making a hollow strut. Without going into the calculations unduly, here is a table to show the relative resistance to buckling of the tubes in our table in terms of an "anti-buckling factor", taking the solid rod as 1:

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Bridge Watching

This implies that if we replace our rod by a tube of equal cross-sectional area, but hollow, with an outside diameter 5, it will carry nearly three and a half times as much load without buckling. So a tube is much better than a solid rod for a strut. Of course, tubes have no disadvantages when used for ties , either. So we often see frames made entirely of tubes. Scaffolding, for example, is made up from lengths of tubing, some as ties and some as struts. Tubular bridges are common, and you should see some of these around on your travels. We now look at another feature of struts to which the designer must pay attention. This is the length. A strut that is short enough to be a pad will not fail by buckling , but if it is too long even a light load will cause it to collapse. You will not meet very long struts in bridges. Occasionally you might see what appears to be a strut of greater length than you would think advisable; but generally you will find that it is braced somewhere near the middle, effectively splitting it into two struts of half the length. Let us now return to our original strut, the rod we discussed earlier, and see what happens as we increase the length. Let us assume that at first we make a strut of length 1, and then see how increasing the length affects its load-carrying capacity.

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Bridge Watching A glance at these figures shows how rapidly the safe load falls off as the length of the strut is increased. At five times the length it can carry only a fraction of the load. This is because the capacity of a column to sustain a load is, as the mathematician says, inversely proportional to the square of the length. (If you don't much care for calculations you need not bother very much with that.) All this brings out the special features of struts, then. To get the best out of the material we are using for a strut we need a section which has most of the material near the outside, and we must not make the strut too long. In what we have just examined, we have considered a round rod. However other sections are used. The hollow square section is made in quantity, and is suitable for all purposes, ties , beams as well as struts. You may see bridges made almost entirely from these hollow square sections. Again, there are other rolled sections , I-sections and angles for example, which might be used on their own or made up into suitable shapes for use as struts. A couple of channels, connected with their flat faces outwards, makes a very good column or strut. So does a hollow square section. Concrete struts are reinforced with the cage of steel nearer the surface than the centre, and you may see some examples of this in old concrete struts or columns that have failed, usually through moisture getting into cracks in the concrete. There was a time when fencing was made from reinforced concrete. It proved to be not a very good idea, and the ugly remains of such fencing is to be found laying around disfiguring derelict areas. The failure did not always occur in the struts. Sometimes horizontal members were loaded transversely and they failed through tension in the wrong places. A fine natural example of a well-designed strut can be found in flowers such as daffodils. Here the stem is a strut, hollow so as to make the best use of the available material, and of just the right length to withstand the load of the flower. If the stem were any longer it would fail. In this case the failure would probably be due to bending of the strut, because of the offset load of the flower head, or transverse wind loading. This brings to our attention another mode of failure of a strut, that of bending. When the load carried by a strut is offset from the axis, it imposes a bending moment on the member. We referred to this briefly earlier, when discussing the tie. The stress , no longer uniformly distributed across the section, increases the stress towards one face, and decreases it towards the other, so that we have a bending effect.

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Bridge Watching In some cases, where the top of the column is restrained, a small amount of eccentricity of loading can be tolerated; but where the upper end is more or less free, an offset load can lead to failure, not as a strut, but as a cantilever beam carrying an unfair load. Perhaps an easy way of looking at this is to consider a strut with a non-axial load as a beam carrying the usual transverse load, with an axial load applied at the ends. Looking at our bridges, then, we are likely to see several members, pads, columns and struts, taking axial compressive loads with the loads on ties and struts applied near the centre of the section. When we look at frames we shall see that the strut is a vital part of any frame; and though it may be a rod, a hollow section, or made up from rolled sections , we shall be able to identify it usually from its position in the frame. Because hollow sections can deal with tensile as well as compressive loads, it may be that some of the members you see act as both, depending upon the load conditions at any particular time. However, as mentioned earlier, if the member is long and slender it is most definitely a tie. There are other clues which we shall discuss in the next chapter. Summarising, we know that increasing the length of a strut dramatically decreases its load-carrying ability, and that the best way to use the material in a strut is to have it towards the outside of the section. Lastly, off-setting the load adds further to the strut's duty.

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Beam bridges In an earlier chapter we outlined the differences between the various types of bridge. The plan in this chapter is to enlarge upon what has already been said about beam bridges. We started with the simplest bridge of all, a board laid across some bricks in the garden. Simple it is, yet there are many similar to that in daily use. Anyone wishing to cross a ditch dry shod might well toss a plank across; and there are plenty of "clapper bridges" around, which are just slabs of stone laid across streams. If the stream is wide and shallow, small piles of stones may be put down first, and then slabs laid so as to connect each pile. Such a bridge is simple, durable and practical. A pack animal can pick its way over, and so can a man. Where the dip is deep, and the crossing short, one big slab may do the job. Some of these bridges have been around for centuries, and are still doing a good job in remote areas. They need no maintenance. Once put down, there they stay, and they don't suffer from woodworm, rot, rust or wear. So from some points of view they are the best example of a beam bridge that you could wish to find. Because the stone slab is a beam it must take some tension along the lower half. Some kinds of stone are weak in tension, so you can't use just any old sort. Material like chalk is weak in tension, so you won't find clapper bridges in chalk areas like Sussex. If you had to put a slab of chalk down for a bridge it would have to be very thick, to keep the stresses down in the lower part; but a thick beam is a heavy beam, so making the slab thick increases the load, which demands a thicker slab, which is heavier, and so on. You are caught in an uncomfortable circle. In places like Dartmoor there is plenty of rock, mainly granite. Granite can take some tension, and if the slab is thick enough it will cope with the tension it gets underneath, for the loads it has to carry. For this reason the clapper bridge was popular in Devon and Cornwall. There aren't many pack animals about nowadays, but people, horses, sheep and cattle can and do use clapper bridges. Another aspect of these bridges, of interest to the bridge-watcher, is that they are often sited in remote places of great beauty and tranquillity. Even with granite you couldn't use a thin sliver of the rock, as the tension underneath would be more than even granite could stand, under its own weight.

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Bridge Watching A clapper bridge doesn't usually span very far between the piers, as the thickness would have to be so large. Even so, some of the massive pieces of rock to be seen are impressive; and they were taken to the site and laid in position without the help of modern machinery. Imagine what it would be like trying to handle a great slab, twice as big as you are, laying it just where it was wanted, without a tractor or a crane. Timber beam bridges are not perhaps quite as common now as they once were. When you do see one, it will probably be a solid baulk or a pair of baulks, not I-section like steel beams. This is because it doesn't save any money to cut away large amounts of material between the top and bottom, to make the section I-shaped. You can't use the wood you save, and the weight isn't usually so important. The timber baulks are usually just laid across the gap, and then cross members laid on them to take the roadway. If it were your own bridge, and you were paying for it, and it was small enough, you might cut away some of the wood, just for decoration; but this would have to be in places where the stress was low, along the middle of the sides. It is possible that you will come across some timbering where a beam is made up from a flat piece top and bottom and a vertical web between them. This requires a lot of work and isn't worth it unless the finished timber is cheap, and the beam has to be a deep one. When people started to make and sell iron and steel the scene changed, and soon there were plenty of beams in first, cast iron, and then wrought iron and steel. Cast iron is strong in compression but weaker in tension. So to keep down the stress in the lower flange the makers of cast iron beams sometimes made them with fatter lower flanges. You may see some of these now and again, but they are few, and I doubt if they are made at all nowadays. Cast iron bridges are always worth a careful study. You are most likely to come across beams in steel or concrete nowadays, and probably more of the latter than the former. We shall look first at the steel beam bridge, of which there are many to be seen. A good steel beam can be assembled from strips of steel fastened together to make up Isections. The older ones were riveted , and later ones welded, which can sometimes give you a clue as to the age of a bridge. Carrying big lengths of steel plate around the roads can be awkward; so sections were normally sent to the site and assembled there. A straightforward flat beam bridge in steel is very attractive if it is well maintained, painted, and not allowed to rust. Some people say that steel beam bridges look "honest". They mean by this that there is no disguise about them, that they are what 56

Bridge Watching they are, without any adornment. This is generally true, though some of the old railway companies used to decorate everything at the stations with profligate flourishes. Out in the country, however, where the passengers didn't see much of the bridges they were plain, simple, just well-made to do their job. To our eyes they look good today. For a heavy load, like a train over a road, say, a steel beam must be sturdy, and hence deep. This is because the bending effects are large, and the flanges must be well apart to resist this bending. The push in the upper flange and the pull in the lower one, together with the forces in the web, provide the resisting moment. If the web is very deep, though, and the flanges themselves are wide they might fail by buckling. The flanges are in effect struts , taking axial loads, and if they are long struts they are of course, vulnerable. This applies equally to the upper half of the web. So look for the stiffeners welded or riveted between the flanges every now and again along the beam. These stiffeners help to support the web and flanges against the tendency to buckle. The bending moment is not usually the same all along the beam, so different parts have to meet different conditions. You will thus see the flanges doubled in thickness or even trebled to meet bending demands. These extra plates are riveted or welded to the main flanges. Where you see them you may well be able to see why they are placed there. You could think about the probable shape of the bending moment diagram for the beam. The number of steel joists laid across the gap depends upon conditions at the site, but two is usually the minimum. The use of several permits the use of smaller sections, and hence a thinner bridge, an advantage in some cases. It can be helpful, too if standard sections can be used, rather than specials or built-up beams. It is possible that you will find most of these steel beam bridges used over short spans. Generally speaking, it seems that more and more bridges are being built in reinforced concrete. This doesn't hurt the steel industry very much, as concrete beam bridges cannot be put up without steel. The steel is inside, to stiffen and strengthen, or reinforce the beam. It does affect the type of output of the rolling mills, as reinforcement is not called for in flat strips as with steel frames, or rolled sections as for joists. Reinforcing steel is in the form of long rods, so presenting greater surface area to the concrete. Its grip on the concrete is often increased by being ridged, too. The small diameter makes it easier to bend, to meet the requirements at site. As we turn to consider concrete beams we can look at this business of reinforcement to learn a little about its placement. At the site you may find much of the bridge prefabricated, and transported there for assembly; but you may find great bundles of steel rods lying about, too. These are cast into the concrete members. 57

Bridge Watching When we use a beam, as has already been mentioned, we need to deal with compressive stress above the centre and tension below. If we use one material, strong in compression above the centre, and another, strong in tension below, each can help the other. Cement and sand, mixed up with some little stones, and water, makes a very good compression material when it has dried out; and steel is strong in tension. So they are well suited to each other in a beam. Inside the beam near the bottom, where the tension occurs we lay the steel rods and then cover them with concrete so that they are protected against corrosion. Adding more concrete, right up to the full depth of the beam, produces a reinforced concrete beam. Although they are very good, we are not compelled to use these two materials. The bridge may be in a place where they are not available, or too costly. In an emergency we use whatever we have around. For example, bamboo is a good strong material, available in lengths suitable for many applications, and capable of taking a high tensile load; and for the compression side we could use blocks of dried mud. We could ensure that the stresses were within the capabilities of the materials by suitable design. Provided you used the right amount you could, in theory, make a beam from squidgy cake and drinking straws; well, not quite perhaps, but I hope you see what I mean. Earlier we mentioned, in passing, the shearing stress that arises in a beam. We should look at this a little more closely now, the better to understand what is happening inside the component. Let us think of a solid piece of material of rectangular cross-section, forming a beam. Suppose that this beam carries a central load of, say, 12, so that each support pushes upwards with a force of 6. Now consider a vertical section a short distance along from the left-hand abutment. For the piece of beam between the left-hand abutment and our chosen section, we have a length of beam, with forces pushing up on one side and down on the other, so balancing one another in accordance with our equation, S=0 The force of 6 at the left-hand abutment will be pushing up on this section, so the righthand face must be pushing down with a force of 6, too. Thus, there is a tendency for the right-hand face to slide down, and the left-hand face to move up, so shearing the 58

Bridge Watching material vertically. This is an elastic shearing movement, provided the material is not overstressed. Now let us consider a tiny cube of the material at this section. The stress on its left hand face will tend to push it up, and that on its right hand face will try to push that side down. This pair or couple of forces tends to rotate the little cube, turning it clockwise. Well, it doesn't turn clockwise, and we know from our second equation that

So there must be another couple trying to turn it the other way. Hence, there must be an equal and opposite couple, which can be provided only by equal stresses on the upper and lower faces. Looking at the front face of our little cube, then, we find an upward force on the lefthand face, a force to the left on the top face, one downwards on the right-hand face, and finally one to the right on the bottom face. Notice that this arises solely from the shearing tendency on the beam. The whole beam is made up of little cubes like this; so throughout the beam, wherever there is vertical shear , there is horizontal shear too. As the load comes on, not only do the parts of the beam tend to shear vertically, but the layers tend to slide over one another horizontally, as well, like the pages of a book. From this arises an interesting feature that needs to be considered next. Think about the square face pointing outwards, with the forces running along the sides, and imagine a diagonal drawn from the bottom left say to the top right of this face. Now think of the triangle formed by the left-hand side, the upper side, and the diagonal. Those forces, upwards on the left-hand face, and leftwards on the upper face, are together trying to push the triangle upwards to the left. In effect, they act together like a force at right-angles to the sloping face, upwards to the left; and taking the direction up to the left as positive, we know that S=0 Therefore the force inside the material on the sloping face exactly balances this. The meaning of this is that wherever we have vertical shear in a beam there is also horizontal shear, and tension at 45°. This is not the end of it, either; for on the other diagonal you can easily prove for yourself that there is compression. Summing up what we have just written, then, shear stress always gives rise to tension and compression at forty-five degrees. Not many people know this. 59

Bridge Watching Now that you know, you will the more readily understand why reinforcing rods in concrete don't always lay straight along the bottom. Stresses due to bending are additional to those due to shear , so the direction of stresses within beams can be complex, and not at all as simple as you might otherwise expect. There may be some more to be said about this when we deal with materials in general. As this isn't very easy to accept, perhaps the little diagram will help. An ordinary stick. Once you understand it you will find more interest poking around a site where they are building or using reinforced concrete beams. Take care, though, lest you find yourself cast in some great dollop of wet concrete. There's a lot of it about on such sites. You can see this, with a stick of blackboard chalk. Without pulling, apply a pure shear by twisting opposite ends. The tension failure occurs at 45°. just as you might see in a concrete beam where tension failure has occurred. This tie-up between the different types of stress goes further. Not only does shear stress produce tension and compression; the reverse is also true. When a piece of material is pulled it undergoes compression and tension, too. So all three types of stress are linked. You will recall that different materials differ in the way they cope with the three types of stress, tension compression and shear. Concrete is weak in tension; the cement which sticks together the little bits of sand is easy to break if we pull it. This is why, if we overload a piece of concrete in compression it will fail, not because of the compressive stress , but due to the accompanying tension, at an angle. This happens with brick, too, and bricks under excessive compression often lose bits out of the face like little pyramids. When we were looking at the bending effect on a beam we saw how we could draw diagrams to show how the bending moment varied along the span. We can do the same for the shearing force. In some ways it is easier, and this is how it is done. Let us take an uncomplicated example of a beam, simply supported at its ends, carrying a central load of, say, 20, so that the upward force at each abutment is 10. Then the left-hand half of the beam is being pushed up with a force of 10, and the shearing force is upwards, all the way along as far as the middle, where the load is acting, downwards. So as far as the middle, we can draw a horizontal line at a height 10 above the beam to represent this. At the centre we meet the downward force of 20, so changing the shear to (10 - 20 = 10), i.e., a negative shearing force of 10; and this is the same all the way to the righthand end of the beam. So our graph of shear force, our shear force diagram, is a line that goes horizontally at a height of 10 above the line, as far as half way, and then 10 below the line for the rest of the span. 60

Bridge Watching From such a shear force diagram we can read off, at any point along the beam, the shear force at that point. In this simple case it is all pretty obvious, and hardly calls for a graph; but in more complicated cases this kind of diagram is most useful. Different kinds of load mean different shapes of shear force diagram, and you may care to try your hand at sketching some. Take a beam of span 10, with a load of 20 at a point distant 4 from the left-hand support. If you draw the diagram for the bending moment as well as the one for shear you will have the two diagrams that are always used for beam bridge design. When we have these diagrams we can see, for any section of the beam, the shearing and bending effects of the loading. We can then design that section to handle the stresses arising from those effects. These chapters are not intended to make you into a designer of bridges, of course; but by understanding these points your bridge watching will improve considerably. The variation of depth or make-up of a girder will make more sense if you see why. If we know the shearing force and the bending effect at a particular section, we can work out how big the stresses are on the section, and their direction. In the days before computers were available this could occupy an engineer for many days, and might restrict the choice of design. Many beams carry loads that are puny compared with the weight of the bridge itself. Some of those narrow iron foot-bridges are so heavy that the odd person like you walking across makes hardly any difference to the stresses. For these, the load is the weight of the bridge; and that is not a single concentrated load like the ones we thought about earlier. It is what we call a distributed load ; and very often it is the same all the way across the span, a "uniformly distributed load", or "u.d.load". When we have a u.d. load we can think of it as being made up from lots and lots of little concentrated loads strung out along the beam. If you draw the shear force diagram for each little bit, and then add them all together, you get a diagram with lots of small steps, very nearly a sloping straight line. In fact, the shear diagram for u.d. loads consists of straight sloping lines. In general, of course, beams are built to carry all sort of different loads, and the diagrams for these can take many different shapes. We can use any scale we like, so the diagrams may be squat or tall. So when you look at such diagrams in books you will find many different shapes for both. People who spend a lot of time with bridges get to know typical cases like old friends, and can sketch the shear and bending moment diagrams quite accurately for different 61

Bridge Watching systems of loading. Because of this they don't need so much time as inexperienced people, and can often quote a lower price. This is one of the reasons for well-established firms being awarded contracts for bridge design. When long stretches of motorway or autobahn are built lots of bridges of similar design are needed, many of them with the same span and loading. After designing a few, therefore, it is easy for some contractors to just pull out a design from a drawer full of them when a new bridge is required. They know pretty well what it will cost, too. This is why there are so many look-alike bridges to be seen up and down the country. For a good variety of beam bridges you need to look around you when in towns and near railway lines , rivers and canals. Out in the country, too, away from the main highways there are some out-of-the-ordinary ones like those that are skew , curved, sloping from one abutment to the other, and so on. There are some that combine the virtues of an arch with those of the beam, some that swing aside to let shipping pass, and others that lift up. We shall look at arches, suspension and pontoon bridges in separate chapters; but some of what has been written in this chapter applies equally to other types, as we shall see. As you go around you are sure to see some propped beams. So perhaps we should say a little about these before leaving this chapter. A propped beam is one that is supported by members between the abutments. These props need not be vertical. Sometimes the best positions for them are at certain points along the beam where, if they were vertical, they would be in the way of the road beneath. So the bottom ends are planted clear of the road and the props themselves slope upwards and inwards. Properly done, this can lend a graceful air to the bridge, especially when the props are faired into the beam. You 25 can find many examples of this treatment along the motorways. Props are struts , taking compressive loads, and the best shape for a strut is round, as we saw earlier. There are many round, or cylindrical ones to be seen; but often, so as to reduce obstruction to traffic, they are narrow one way, and wide in the direction of the traffic. So their cross-section is rectangular. They may be split, too, and indeed there are several varieties to be seen. You should be able to distinguish between (i) a propped beam, i.e. a continuous beam propped here and there, and (ii) a series of short beams carried on a number of supports.

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Bridge Watching If we think of the props being removed from a propped beam we can imagine the beam sagging under the load. If we then picture the props being restored, lifting the beam back into position, they will clearly induce bending effects, and shearing forces , too. So the shear and bending moment diagrams for a beam are modified by the presence of props. The effect of the props in reducing bending and shear means that the beam need not be so deep. A propped beam, then has advantages over the simple beam; but there is the cost of the props to be considered, and the preparation of the ground and the beam to take them. Here again is a case where important decisions have to be taken at the design stage. There are other ways of reducing the shear and bending effects in a beam. One method, though not common, consists of building a pylon in the middle, and running ties down from the top of the pylon to points along the beam. Its advantage is that it leaves the underside of the beam clear, but it some people don't find such construction beautiful. If a beam has some short props underneath, clear of the road or railway, and tied to the ends by a tension member, rod or cable, we have what is known as a "trussed beam". The commonest place to see these is under railway carriages, which is where you should peer to see what it looks like. The principle is sound, but rarely seen in road bridges, except temporary ones. In this chapter we have looked at beams in some detail, but whole books might well be written on beams alone. Further, many bridges have beams incorporated in them at various points. So a fairly good understanding of beams is useful to every bridgewatcher.

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Arch Bridges The arch is a lovely shape, and it is doubtful if you will ever see an ugly one. Perhaps it isn't possible to make a miserable-looking arch. There are so many different types, too; and some bridges that are not really arches can look as if they were. The arch is so pleasant on the eyes that some people make artificial ones that don't actually operate like arches at all. You can see them on the outside of buildings, and it is usually fairly easy to spot the false ones. The special thing about an arch is that it uses material in compression. There are many pleasing materials that lack tensile strength, and the arch uses these efficiently. Almost any solid that is strong in compression can be used. Brickwork, for example, can't manage tension but copes very well with compressive stresses. Bricks are just lumps of baked clay, but they have been splendid building material for many centuries. In the hands of a skilled bricklayer bricks can be transformed into structures of great strength and beauty. Even in unskilled hands they can be built into shapes that can carry a load, albeit if not always elegant in appearance. It is worth noting here that bricks have a rough exterior. So if one brick is laid upon another the bumps on the surface prevent the faces from coming close together. Hence the load is transferred over a number of very small areas instead of one big one. This of course, means that there is a very high stress at such points, and the material is crushed, giving way till the bumps are flattened. This can result in cracks and failure. For even distribution of the load, therefore, the bricks are separated by a layer of wet mortar which can flow into the tiny hollows between the bumps and thus provide a flat surface of contact. Mortar has little tensile strength, and is not there to "stick the bricks together", but to keep them apart. The mortar consists of sand with a binding agent called cement. When it has set each brick bears upon a flat surface which transmits the load to its neighbour. Used in this way high structures of brickwork can be erected, to carry very large loads. You will see brick arches carried on tall brick supports in many places, and they delight the eye. Many have been demolished, but it is hoped that we shall retain enough to give pleasure to the bridge-watcher for a long time yet. To make mortar the sand and cement must first be thoroughly mixed. This can be hard work and back-breaking, even with a machine. When the materials are well mixed, with some cement around each grain of sand, a carefully measured amount of water is added, so that the mixture will flow into the little dents in the bricks. The word "flow" 64

Bridge Watching doesn't mean that the mixture should be liquid, but that it can be placed firmly into position. A mortar that is too watery can be dangerously weak. After the water has been added a chemical reaction starts and the mortar sets hard. It takes a little while for this to be complete and it cannot sustain a load straightaway. The sand that is used should be "sharp", meaning that it is free from rounded corners. Under a microscope sand is a fascinating jumble of multi-coloured rocks. The cement gets into the tiny spaces between the particles of sand, and when the water is added it pushes out all the air, so that we get a solid block, without weakening bubbles in it. Mixing mortar looks easy, but this is deceptive, and great care is needed to produce a satisfactory material. It ought not to dry out too rapidly, or it will crack. It shouldn't contain too much cement, either, for this too can lead to cracking. The strength of the mixture, i.e. the ratio of sand to cement is important, and must be adhered to strictly. When mortar is properly made, with a good dollop between each adjacent brick or block, they rest comfortably on one another, and the loads are transmitted through the pattern evenly. You may feel that a lot of time has been spent on this aspect of brickwork; but this is so that when you examine brick arches you may the better appreciate what wonderful work bricklayers can do. Stone is another good material in compression. This is blasted out of the earth in irregular lumps and has to be shaped if it is to be laid in rows or courses; but it can be laid higgledy-piggledy with mortar between the pieces. In work of the highest quality the ashlars or blocks are dressed or smoothed to such a fine finish that each fits exactly upon its neighbour. A perfect fit would require no mortar. Some of the ancient stonemasons were so skilled that they could build in stone with a precision at which we can only marvel nowadays. When we realise how much careful labour is required to chip away at the surfaces of hard stone to get them dead flat and square it is hardly surprising that we don't see much work of that sort nowadays. Softer stone is easier to work, but is not so durable as the denser materials. If you examine some of the old sandstone arches you will see that the weather has eaten away at the stone in places where it is exposed. Sometimes you can scratch away at the red blocks with your fingers and produce a little shower of sand. Such stone requires a protective layer of some kind to reduce the ravages of rain, wind, and abrasion generally. What makes a structure an arch is the middle being higher than the ends. The shape of the intrados, or the inner curve, is a matter of choice, and there are some delightful 65

Bridge Watching curves from which to choose. Once you are aware of the different kinds of shapes you can find much pleasure in identifying the curves in the arches you meet. If you ever find yourself near Iraq you could marvel at a very ancient arch, the Ctesiphon Arch, perhaps the most famous of all. To everyone's shame, it looks disconsolate and neglected now, out in the desert; but it is a magnificent example of what can be done using local materials. Still standing, after many centuries, it soars up like some ethereal parabola, striking in its drab simplicity. We shall now digress a little to talk about conics, the study of the cone. This common geometric solid is a pointed affair with a round base. It is a deceptively simple shape with some remarkable properties. It is relevant to what we shall say later about the curves we meet in arches. If we take a piece of wood shaped like a cone we can cut it across in various ways to find some charming curves. If you do this yourself, use a fine-toothed saw and a cone about the size of your hand. First, make a cut right across, near the top, parallel with the base, so that you slice off a little cone. What is left is called a frustum, but our interest lies in the shape of the cut surface. This, if your cut has been accurate, is a circle, the same shape as the base. Whenever we cut a cone parallel with its base the surface which results is always a circle, a shape common in nature everywhere. The whole circle is rarely used in an arch, but many arches consist of parts of circles. The simplest one is a semi-circle. The Roman arch looks like a semi-circle, resting on a pair of columns usually, and is an attractive feature. This is sometimes called a stilted arch. However, for a large span it is not very practical, for the rise needs to be half the span. This would generally be a wasteful use of material. So although there are many semi-circular arches to be seen over doors and windows you are unlikely to see many bridges of large span using them. On the other hand, where a viaduct is to be high above the earth, as when it crosses a deep valley, we require a high rise-to-span ratio. In some cases you might meet rows of arches like this, one on top of the other, bridging long deep valleys to carry water. They show the bricklayer's art to good effect. In those places where a bridge leaps across a wide water-way or valley in a series of short spans on pillars there are examples in which each little span is carried on a semicircular arch. These are picturesque examples of what the semi-circle can do. Again, you might come across a short bridge over a canal where the span and rise are such as to fit a semicircle very neatly. Using shorter arcs of a circle, however, the choice is wider, for one can choose an arc with whatever ratio of span to rise we wish. Further, we can design the arch with more 66

Bridge Watching than one circular arc, each running smoothly into the next. Look at some of the brick railway arches for examples of these. There are some pretty specimens of these out in the country, over single or double tracks. Turning back to our cone, let us now make another careful saw-cut right across, just below the previous cut face, this time not parallel with the base, but tilted a little, so that we no longer get a circular cut face. This oval shape is called an ellipse, and is another fine shape that can be used in an arch. The word "oval" comes from the Latin word for an egg, which is not symmetrical, so strictly speaking an ellipse is not an oval. In common use elliptical shapes are called oval, but not if we are to be precise when looking at bridges. Depending upon the slope of your cut, relative to the horizontal, the ellipse will be thin or fat. That is, the breadth will be much greater than, or only a little greater than, the length. An ellipse has two diameters, the larger or major diameter, and the smaller, or minor one. A bridge with an elliptical arch is built with the major diameter horizontal, so the height is equal to the semi-minor diameter. Usually, you will find little difficulty in recognising an elliptical arch, though some elliptical curves look very much like arcs of circles. It is an attractive curve, beloved of artists; and when a bridge of this kind crosses still water the reflection helps one to see the full ellipse. For this reason you may come across paintings, old and modern, showing this type of arch. The choice of curve for a bridge is influenced by the loading and the ratio of span to rise. The availability of material, too, may affect decisions about shape. Let us now return to our cone, and make another cut across it, to find another conic curve. This time, we shall cut right down through the cone vertically, from the upper face of the frustum to the base, somewhat off centre, and parallel with the vertical axis. Now we have another fascinating curve, the parabola. It is a remarkable curve, popping up in the most unexpected places; but we shall look at it only in connection with arches in bridges. One aspect of our interest in the parabola is that it is often to be found in bridges that carry a u.d. load. Simplifying our approach somewhat, we shall assume that the bending moment diagram for a u.d. load is parabolic. An arch of this shape, therefore, would fit closely to the bending diagram, and could thus minimise bending on the arch rib. The algebraic equation for a parabola is a very simple one, relating the square of the rise to the distance along the span. The span-rise ratios are readily adjusted by changing the 67

Bridge Watching constants in the equations, so we can build a short tubby parabolic arch or a lofty slender one. For river bridges, where shipping has to pass beneath, a large rise in the middle is required, to provide adequate clearance. If the navigable channel is narrow, it may be possible to build a bridge which arches high over only the channel itself, with approach links of more modest rise. On the other hand, a bridge over a railway has to allow for only enough room for a locomotive to pass. The size of tunnels is such as to accommodate rolling stock, so bridges over the tracks with more rise than that are not required. Over the tracks then, you will see more arches using circular arcs, two- or three-centred arches. These are so called because the curves are formed by arcs drawn from centres that provide smooth joins between curves of differing radii. However, these are not the only bridges met in the railway system. So, quite apart from the signal gantries, there are other kinds of bridge to be seen in association with railways. In the past, when railway companies were establishing themselves, they acquired great stretches of land, and built some enormous stations. Here and there you can see some of the bridging used to provide access between offices and sheds for goods and passengers. Some of this makes ingenious use of materials used elsewhere in the system. We appear to have spent some time on the circular and parabolic curves, as these are often encountered; but there is one more curve that can be derived from our cone. This is the hyperbola, the shape of the cut surface when the cut is made parallel with the sloping side of the cone. When you cut the cone thus, and compare the shape with the parabola, the difference will become apparent. You are unlikely to see a hyperbolic curve used in bridge design, though. There are other kinds of arch , such as the Moorish and Gothic arches , but these are seen chiefly in windows and door openings, and do not concern us here. Arch bridges provide plenty of variety for you to enjoy. All kinds of materials can be used for arches, but I now invite you to consider a masonry bridge, one made of stones. Stone or rock is excellent in compression , so is ideal for use in an arch. When a beam is loaded it sags till the resisting stresses within the beam are balanced. The supports simply push straight upwards so as to equal the load. However, an arch under load tends to not only sag, but to spread, too. So the abutments have to supply 68

Bridge Watching forces pointing inwards horizontally as well as vertically. This means that the supports have sloping reactions. If there is to be no shear between the stone blocks, i.e. if they are not to slide on one another, then this sloping force must be at right angles to the first block. The first block, then must have an inclined face. As we move along the span there are changes in both shear and bending , with the forces between the blocks tilting over more and more till they are pretty well horizontal near the middle. So the faces of the blocks must lean over more and more till they are nearly vertical, and you can see this on an arch. If the arch is the same shape as the diagram for bending moment there will be no bending effect, and the line of thrust between each pair of blocks is at right-angles to the faces. Thus, the line of thrust goes right along the middle of the line of stones. This isn't quite true, but it is near enough for you to get the general idea, and will do for the time being. Looking at a masonry arch bridge you can see the line of blocks underneath, all tilting over more and more as they get nearer and nearer to the crown. At the crown you might see a prominent block called a keystone. It is so important that sometimes it is decorated with some carved motif. Actually, all stones are of equal importance of course, and the removal of any one of them would cause collapse; but the keystone is the last to be fitted, so it seems more important. In some openings where a keystone isn't really required a builder will often put in a purely ornamental one, but not usually in bridges. You can usually spot a fake keystone if you look carefully at the opening, and the arch itself. These false keystones appear commonly in flat "arches" where the gap is spanned by a concealed rolled steel section. Brick arches sometimes achieve the change of slope by uneven placing of mortar, and sometimes by bricks having sloping sides. It is interesting to compare the appearance of the two systems. Many brick arches consist of sevral ???, the joints in adjacent ??? being off-set When building an arch in brick or stone some support is needed until the crown is reached, or the blocks would just drop inwards. So a light wooden framework is first put up, of the exact shape of the intrados, or inner curve of the arch. This is called "centering" or "shuttering". When all the blocks have been laid on this, the last one is the key to holding the whole arch in place. Once the keystone is in place the shuttering can be "struck" or removed. Notice that if the shuttering were taken away at any time before all the blocks were in position the arch would collapse, and failure would occur if any one of the blocks were 69

Bridge Watching removed. So every block is vital to the integrity of the arch ; but as the last one to be put in is the one at the top we tend to make a fuss of it. Some keystones in the old bridges are richly decorated. Even in cast iron arches , the arch ribs sometimes meet in a kind of keystone, a panel with some pattern of flowers or heads. There aren't many about, but they are worth seeking. Building in timber, we can use wooden struts so arranged as to look like a smooth curve from a distance. Some of these look very elegant, and the builders occasionally put a wooden ornamented panel at the crown as a kind of nominal keystone. Concrete can be reinforced so as to take tension ; so concrete arches don't need to avoid the bending stresses. Hence there can be more scope in choosing the curves. Arches are used to support roadways and railways, which are usually straight, and the space between the curve of the arch and the line of the road is filled with material, depending upon what has been used for the arch itself. In some steel arch bridges the space, called the "spandrel", may be braced. These "spandrel braced arches" are an artist's delight, and have a fairy-like appearance in certain lights. Another arrangement that can look very attractive is the one where the arch, rising from the abutments, soars above the roadway, which is carried partly on struts, near the abutments, with the middle length hung from the middle section of the arch. When you see one of these you will understand why it is called a "bowstring" girder. One of the attractions of steel arch bridges is that, from a distance they can have a delicate lace-like look. On the other hand, the brick ones have their own charm, as the colours are warm and mellow, changing with the time of day. Very high brick arches use enormous numbers of bricks. One cannot help thinking of all those bricklayers placing such vast numbers of bricks, and all the people carrying and fetching the scaffolding, sand, cement, and bricks, and all that mortar. Those old brick viaducts were built when labour was cheap, even skilled labour; the cost would be too much today. Modern machinery and equipment could not bring down the cost enough to offset the savings on labour. Concrete arches usually require formwork to delineate and support the part-finished arch, and then machines prepare and place the concrete round the reinforcement. In some cases the arch ribs are pre-formed, and brought to the site as required. If you can, it is worthwhile finding a concrete bridge under construction, and visiting it, preferably during working hours, under supervision. There is much freedom in designing a concrete bridge, and where arches are used they can be drawn with some flow. They can even be designed to take some tension here and there. So concrete arches can look particularly graceful. 70

Bridge Watching The rise of an arch bridge, that is, the height in the middle, depends upon several things, like the clearance needed beneath it, the span, the condition of the ground at the ends, and so on. The higher the rise, the less is the horizontal push needed at the ends, though you can't go high enough to get zero horizontal push! Whatever the rise, the upward thrust at the abutments will be the same. They are the reactions you would get if you put a beam bridge there. It is only the horizontal part of the reactions that changes with the rise. You can think of a beam bridge as an arch with zero rise, and hence zero push horizontally at the abutments. Where the abutments have to be we dig away the soft soil till we get down to something much firmer. Then we measure how much stress that layer will take without yielding too much. From this, and knowing how much load there will be at that abutment, we can calculate how big an area is needed to take that load. The load must then be spread over the area by placing a grillage or a concrete slab on which to build the ends of the bridge. Sometimes we put down piles, which are long stout poles, often driven to refusal, that is, hammered in till they will go no more. Screw piles are not hammered, but screwed into the ground, a much less noisy process. Remembering that the push of the abutments for an arch is not purely vertical, the ends of the arch must rest on something that will not only push upwards but inwards, too. We can build up bricks or concrete to do this, and ensure that they won't slide outwards when the load comes on to them. This can be achieved by a suitable tilt and you can often see this if you look at the abutments of an arch. We can make the bottom of the slabs saw-toothed, or they can be put very deeply into the ground. Sometimes there is some stout rock nearby, into which the anchorages may be fixed. When the temperature changes, the arch distorts, and this can give rise to stresses; but if the arch is made in two parts, with a hinge in the middle, at the crown, the two parts can move relative to one another so easing the arch. Of course, the ends of the arch, too, must be hinged if this is to be effective. That is why we have three-pinned arches. Although the movements are small, they must be allowed for in the design. You should be able to spot a three-pinned arch fairly easily. A similar freedom to alter shape can be achieved by pinning one end, and letting the other end slide, though this can induce tension in the underside of the arch rib. If only the ends of the rib are pinned we have a two-pinned arch. These variants may be seen in steel arches, where the temperature movements may be comparatively large, but you are unlikely to see this in brick or concrete arches. You see then, that whereas a simple slab of concrete at the supports suits a beam bridge, an arch bridge requires something special. If the springings come from some pretty solid river banks the ground itself is banked up above the abutments; it is even possible 71

Bridge Watching to tie the ends together below the roadway, as another solution to the problem of supplying the horizontal parts of the supporting forces. Where the roadway or railway is entirely above a brick arch, the spandrel may be earthfilled, and tamped down so that it is a pretty solid type of structure. This applies especially to those little bridges over streams for sheep and cattle that you see in fields and on the moors. Those that go up rather a lot in the middle are called hump-backed bridges , and are usually built like this. Hump-backed bridges are not as common in villages as they once were, more's the pity. Where you do see them, they are very useful, as they slow down the tearabouts in cars and lorries. That isn't the reason they were built like that, though. As you saw earlier, a high rise means less horizontal end thrust. So when a bridge was wanted over a sloshy-sided stream, where the banks could not take the thrust of a lowrise arch, they just had to go up high. Some of them have been standing for centuries, and look very pretty. Some people would like them brought back in villages to prevent arrogant drivers from being dangerous ones. Oddly enough, the principle is being brought back with the so-called "sleeping policemen", which are humps without a bridge. A simple and elegant way of taking a large pipe across a canal or small waterway is to run it along a simple steel arch spanning the water. The ends of the arch can be sunk into the ground to provide the side thrust, and the space beneath the arch lets barges pass freely. Keep your eyes open for these. Many of them are old, and may not be with us for much longer. When looking at certain bridges you will see curves that make you unsure as to whether or not you are seeing an arch. Sometimes there is a curved piece between upright pillars and a horizontal roadway. Sometimes, too, the curve is so slight that you can see it only when looking from one end. Some of the curved parts are brackets off the columns , to take the beam , and the very slight rise that you may see in bridges which have a fair depth are not true arches, either. From what has been written in this chapter I hope you will see that the variety is pretty well endless, and you will never be able to see every bridge that has been built. You can't even see every arch bridge that there is. However, arches can be seen in other structures , too, and you might notice some arches in buildings that you don't have a chance to see in bridges. For instance, churches often use pointed arches , called Gothic, for doors and windows. Over the years this type of arch has acquired an ecclesiastic association. These are not entirely unknown for bridges, but you are unlikely to see them. The reason is that the Gothic arch , although highly decorative, is not in itself the right shape for dealing with the bending and shear usual in bridges. 72

Bridge Watching The Roman arch is to be found on very old bridges, as you might expect. The flat arch occurs in some houses, over doors and windows, often with a prominent keystone. The Moorish arch is a very odd-looking but not unattractive shape, composed of big arcs of several circles. They really don't seem to fit any shear or bending demands normally encountered. They are fun to see, though, and give a pleasant touch of fantasy to oriental buildings. You can see that the arch is a very old form of construction for bridging a gap, whether it be a river, a road, a canal, or a door or window opening. Also, although modern materials, methods and machines have given us some opportunities to do all kinds of interesting things with arch bridges, the basic ideas are still the same. Well, that is a rather brief look at arches. There is much more that might be written about them, if there were sufficient space; but one of the good things about knowledge is that it has no limits. There is so much of it that, however long you keep dipping into it, you can go on having more and more for as long as you like. There are plenty of books about arches, which I hope will lead you to greater enjoyment of arch-watching.

73

Suspension Bridges The chief feature of a suspension bridge , the thing that first strikes you, is the great curve of the cables or chains, sweeping down from the tops of the pylons. So we start with a look at the beautiful curve of a hanging cable or chain. If you can get hold of a length of light chain or cord, and hold it by the ends you will find that it droops in a sweet curve. This is called a "catenary" curve, and is a fascinating shape when you know something about it. If you move your hands apart or bring them closer together the ratio of the span to the dip changes, but the kind of curve is the same. Even though your hands may be at different levels you will still have a catenary. The word "catenary" comes from the Latin word "catena" meaning a chain; and is the curve taken up by a heavy flexible cable or chain hanging freely by its ends. The ends are usually, but not necessarily, on the same level. The word "heavy" is used, because too light a line may be stiff, and unable to follow the curve exactly. We shall not go very deeply into the special properties of the catenary, though I assure you that they are really quite surprising. There is one special thing about the curve, though, that is important for you to know in order to understand the suspension bridge. Half-way along the chain or cord you will notice that it is horizontal. If you now hang a load on it at the middle you see the shape alter, so that the chain runs up more steeply each side of the load. Since the load is vertical, some of the pull of the cord has to be upwards. Recalling our first equation:

Σ↑= 0 the two pieces of cord, each side of the load, have to supply an upward force equal to the load; but we can also write:

Σ> = 0 Hence the two pieces of cord pull horizontally, also, with equal forces. If you now put a large number of equal loads on the chain, at equal distances apart, the chain slopes upwards from every loading point. As you go along the chain you seem to be going round the outside of a curve made from lots of straight lines. The more loads you have the more little lines you get, and the nearer the outline is to that of a parabola, that wonderful conic curve, which we have encountered already. 74

Bridge Watching If you had a very large number of equal loads hanging at equal distances along the chain it would be like the kind of load that we have when a roadway is hung from the chains or cables of a suspension bridge. It is a uniformly distributed or u.d. load , a load evenly spread along the horizontal. This u.d. load makes the catenary very nearly a parabola. Without in any way wishing to deter the non-mathematical reader, it is of interest here to note that the mathematical equations for the parabola and the catenary are both very simple, though different in appearance. For the parabola, we have: y = ax2 and the catenary one is: y = cosh x The catenary one looks simple enough, but don't let it deceive you. You would need some pretty advanced mathematics to cope with it. However, you will not seriously diminish your enjoyment of bridges by lacking those skills. For the suspension bridge in general the roadway is very nearly a u.d. load, and each cable hangs down in a curve closely approaching that of a parabola. Perhaps that is why the suspension bridge is such a lovely imposing structure. To carry the roadway there are lots of vertical links running down from the cables to the edges of the road. To the artist each of these bridges presents an entrancing picture, in black and white or colour, and I hope you will derive much pleasure from looking at them, especially as you get to know more about them. If a bridge is for vehicles only you won't be able to hang about for long looking at it from the roadway; but if you can find one with a footpath you can dawdle happily, inspecting at your leisure the way in which the links are joined. While you dally thus you can look up at the magnificent sweep of the cables overhead, and the tops of the towering pylons. Another thing you can do is to amble along the river banks, or the road beneath if the bridge spans a highway. Take a pair of field glasses, pick a comfortable spot, and squat down. Then loll back and enjoy the sight of those pylons, cables, links, and joints, each quietly doing its part, helping to carry safely the loads imposed upon the structure. At this point it would be useful to write a little about forces , and in particular the forces in the suspension cables. So we shall look at one of the points on the cable where the weight of the roadway is taken by one of those links. 75

Bridge Watching There are three forces acting here : • • •

The load in the link, pulling downwards The force in one part of the cable, pulling up to the right. The other cable force, pulling up to the left.

The weight carried by the link is a proportion of the weight of the roadway and traffic. Knowing this, and the angles of the parts of the chain, we could calculate the values of the forces in the cable. However, there is a neat way of finding the forces without calculation. It is a graphical method, and needs only a little careful drawing. This is how it is done. We draw a line parallel with the force in the link, i.e. upwards vertically, and make the length of this line equal (to some suitable scale) to that force. For example, suppose the force in the link is 5 somethings. We then choose a scale where one of those somethings is represented by some unit of length. If we now make the length of the line 5 units then this line represents the force in the link, and our scale is established. We then draw a couple of lines through the ends of this first line, parallel with the pieces of the cable. This gives us a triangle and some odd bits which we can ignore. If we now measure the sides of this triangle, to the same scale, we have the three forces acting at the point, one in the link and the others in the two parts of the cable. We can do this for every link, and so get a number of different triangles, since the tilt of the cable is different at the various points along the span. You will soon see from this that the cable is carrying a load that varies throughout its length. When we have a sloping force, such as that in a piece of sloping cable, it is really like two forces, one horizontal and one vertical. These are called the "components" of the force. For different parts of the cable, it is the vertical component that varies, since the horizontal component is the same throughout the span. You can perhaps see this by thinking about the cable between two loading points. If it pulls horizontally at one end it must pull the same amount at the other end, and so on along the length of the cable. This is very important, so putting it another way, the horizontal part of the pull is the same all along the cable. Only the vertical component alters, the steeper the slope the bigger the vertical component. So the ends of the suspension cable take the greatest load. Assuming the load-carrying links are equi-spaced, with each carrying the same proportion of the total load, we can emphasise what has just been written. For the points along the span where the load-carrying links meet the cable we can draw the triangles not separately, but on top of one another. Then you can see perhaps more clearly how the cable load changes, whilst the horizontal part stays the same. 76

Bridge Watching You might feel that we could save money by using a cable of varying strength along its length. In practice, though, it isn't worth the cost and complexity of doing that. So you will always find a uniform cable used. Suppose now that, instead of a cable, lengths of steel rod or plate are used. Would it be worthwhile to use pieces of different section across the span, using a heavier section near the pylons and lighter near the bottom of the dip? Not really, and you are unlikely to see this. Let us now look at the pillars or pylons that carry the cables. It is the horizontal pull in the cables which tends to pull over the pylons. At the bottom of the dip, where the two parts of the cable are horizontal, the total pull is the one which is the same throughout. This is the overturning force at the top of the pylons. With such great leverage, the bending moments at the foot of each pylon would be considerable; so if you look carefully with field glasses you may be able to see that the cables are not fixed to the pylons themselves but to carriages that can move, or rollers; thus the horizontal components of the cable forces are not transmitted to the pylons. Cables fixed to pylons could produce tilting moments. The problem with the overturning moments can be met by putting a hinge at the base of the pylon, so that it can turn a little to accommodate the uneven pull. If you look at some of the shorter suspension bridges, with less lofty pylons, you might come across this idea. On most suspension bridges, if you examine the angles of the two parts of the cable, at the top of the pylon, you may appreciate that the forces in the cables produce one vertical force straight down through the centre of each pylon so that it carries a pure compressive load. Thus in this arrangement each pylon is simply a strut. You will also see that although the pylon is thin when viewed from the side, it is thicker across the bridge, being coupled to another to form a deep cantilever to resist side loading from wind. Beyond the pylons, towards the outer ends of the bridge, the cables run down to anchorages , and these parts of the cables don't always carry part of the road. So they are then pretty well straight; but if they do take loading, they too are pulled down into that parabolic curve. How high should the pylons be? There are several points here for consideration. First, high pylons obviously cost more than short ones. They use more material and may take longer to erect. The wind affects them more, so they need sturdy bracing. They are heavier, so they need stouter foundations. Again, maintenance may be more expensive. The higher the pylons, the longer the cables; and cables are very very expensive. 77

Bridge Watching Taking all these points into consideration you may well wonder why we don't use short pylons. The answer is simple. The level of the roadway is fixed, and the lowest part of the cable is really settled by that. Now the shape of the cable depends upon how hard the ends are pulled. You can try this for yourself. A piece of line held by the ends sags in the middle less when pulled tight. So if short pylons were to be used, then the ends of the cable would demand a high tension if the cable were not to sag too much and interfere with the roadway. Here then is the reason for high pylons. The horizontal pull in the cables is pretty well the same throughout its length, and the cost of cable depends upon how strong it has to be. If we use tall pylons we can accept a bigger dip, with a resulting smaller horizontal component of the pull in the cable, and so use lighter material. So there are points for and against high pylons and part of the skill of the bridge designer lies in making decisions about this. If you look at a number of suspension bridges you will see that the proportions are all pretty much the same, with the pylons neither too high nor too short. In fact, they will look right, and in general that is one of the tests of a good design of anything. The forces on the anchorages, too, are affected by pylon height, though it also depends upon the positioning of the anchorages themselves. If we bring the cables down steeply they will tend to lift these fixings; and if they slope down too gradually they will tend to drag them along, or put tension on the rock. Here again, careful work at the design stage can save money. The anchorages themselves have to match the conditions at the site. When you visit a suspension bridge you will see, sometimes, how the ends of the cables are secured to the ground, differently for different sites. It won't always be possible to see the anchorages themselves, of course, as they are often buried. However, at some sites, where they are proud of the bridge, and make it a tourist attraction, there may be drawings and photographs to show you something of what went on during construction. There may be some local bridge-watchers, too, who can tell you what it was like when the bridge was being built. Let us now turn our attention to the tops of the pylons. Here there are three forces to consider, one vertically upwards from the pylon itself, and two sloping downwards from the pulls in the two parts of the cable. If there is a pulley or sliding fitting the horizontal components of the two parts of the cable must be equal, and the vertical components will, with the force from the pylon, add up to zero. In other words, the push up from the pylon must exactly balance the 78

Bridge Watching downwards pull of the cable. The steeper the cable here, the greater the downward pull, so the stronger the pylons must be. The cables have a tremendous job to do, and making them is a tricky specialist task, exciting to watch. Special machines are used which run to and fro along the cables winding on the strands. Unless you can get up close to these cables it is difficult to imagine what mighty things they are. From a distance they may seem so fairy-like, especially on the very long bridges, that you may not realise their giant proportions. As mentioned earlier, some suspension bridges don't use cables, but chains, lengths of steel plate linked together with pins.The vertical links, too, are made similarly. Such bridges are an interesting example of good design, and in many cases you can see the links closely from the roadway. This kind of chain behaves pretty much as the cable, but with no curvature between the suspension points. From some points of view it is much simpler to make this kind of suspension bridge, for shorter spans, anyway. Having settled the nice balance between short pylons with heavy cables, and taller pylons with lighter cables, the engineer can consider the number and size of the supporting links for the roadway. The roadway itself is a suitably-shaped slab which forms a continuous beam , running across a number of supports, the links from the cables. When we looked at beams earlier, we found that a beam carrying a u.d. load had a parabolic bending moment diagram, and that the diagram for a single load was a triangle. If you think of a section of a beam with a u.d. load, and then support the middle, you are really applying an upside-down bending diagram (a triangle) on the u.d. diagram (a parabola), so reducing the height of the whole thing. If you have a simply supported beam therefore, with a prop of some kind in the middle, then whatever the loading the bending effects will be reduced, as clearly shown on the resulting bending moment diagram. In the extreme case, if the loading were a single load in the centre, producing a triangular bending moment diagram, a central prop would have a triagular diagram that could be made to fit that due to the load, and there would be no bending at all along the beam, as the prop could take all the load. Returning now to our suspension bridge, with its u.d. load, the forces of the supporting links are like an inverted load system tending to bend the beam (the roadway) the other way. If there were no links between the roadway and the suspension cables the road would sag right down due to the imposed loading. So the combination of the loading and the forces in the links leads to much smaller bending effects throughout the beam. 79

Bridge Watching The more supporting links the less is the bending effect. When you look at a long suspension bridge you will see lots of links between road and cable; and the roadway looks pretty thin. This is what helps them to look so light and delicate. On a misty morning a long suspension bridge can look as if it is floating in the skies like a gossamer web. The choice of type for a bridge is largely a matter of weighing up exactly what duty it has to perform. Each type has its own particular advantages. Ask yourself where you are most likely to find long suspension bridges, and you will generally find the answer to be where wide stretches of water are to be crossed. Some of the points that come to mind about bridging water are: • • • • • • • •

How much clearance is required under the bridge? How far is it between abutments? How deep is the water? What is the ground like beneath the water? What is the ground like on each shore? How much does each type cost? What is the maximum traffic loading ? What is the weather like, especially the wind?

This list is by no means exhaustive, of course; but when you have given some thought to these questions you may begin to see why some places have suspension bridges, some cantilevers , some arches , and so on. We now turn our attention to an important aspect, that of wind loading. Generally speaking, most suspension bridges are peculiarly vulnerable to loading due to strong winds, because of sites they usually occupy. When a fluid of any kind flows along a channel of varying width it has to go faster where the channel is narrower, as there is less space for it to pass. This is easily seen when you look at the flow in a brook. Flowing placidly though it may, where the banks are wide apart, it goes along at a spanking pace when the waterway narrows or shallows. When air moves across the ground it meets hills and valleys in its path, and the speed changes accordingly. If it flows through a valley, it rushes along much faster where the valley narrows. When selecting the site for a bridge across a river it is natural to choose a place where the crossing is narrowest if possible, so that the bridge will be short, and so less expensive. Hence a suspension bridge is often, though not always, at a spot where a valley is narrowest. Here, even when there is only a mild breeze elsewhere, there is likley to be a strong wind in the ravine or gorge. So a bridge built there may be exposed to powerful side winds. 80

Bridge Watching Further, the bridge creates an obstruction, and as the air passes below the roadway it is still further speeded up, so that the wind is even more rapid. The next point is that the various parts of a construction look at the wind in different ways. If the air meets a round bar, say, like a steel rod, it buffets it and the rod starts to vibrate. This is because as it passes round the rod and reaches the back it turns round behind and meets the puff from the other side. These two currents fight one another and in the tussle first one wins and then the other. They form little eddies of air, one to the right and then one to the left, the next to the right, and so on, a whole series of whirlpools each turning in opposite directions. These aerial whirlpools are the vortices which trail off downwind, leaving the rod shaking from side to side. So the rod starts to oscillate. If the size of the rod and the speed of the wind happen to match one another in a special way, the rod vibrates more and more like a guitar string, and may even break. Every rod has a "natural" frequency of vibration, just as a guitar string produces its own particular note. I expect you know how to make a blade of grass shriek by putting it between the palms of your hands and blowing on the edge. It is the same sort of thing. In ancient times people used to hang up strings in the trees to catch the wind. They called them Aeolian harps, and they must have made a miserable sort of sound; but they "sang" in the wind in the same way that your blade of grass does, and on the same principle that produces vibrations in a bridge member subjected to wind. You may like to see just what this means with an easy experiment. Make a simple pendulum by hanging a chunk of something on the end of a piece of thread or string. The length isn't important, neither is the weight, so long as it dangles down, and will swing to and fro when released. Holding the upper end still, set the weight swinging gently through a small angle. (You can steady the upper end by resting your wrist on the edge of a table). The time to swing from one side to the other is proportional to the square root of the length of the string. So if the string is one metre long it will take just about one second to swing from one side to the other. If it were four metres long it would take two seconds each way, and so on. Set the weight swinging gently through a small angle. The movement will gradually die down, but will swing at the same frequency till it stops. We measure the frequency by the number of full swings, i.e. there and back, per second. Now steady the weight, and move your hand very slowly from side to side through a small distance. The string will remain straight, if you move sufficiently slowly, so that the movement of the weight is the same as that of your hand, with the same frequency and moving through the same distance or amplitude.

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Bridge Watching If you now increase the frequency of your hand movement you should notice a different effect on the weight. When your hand frequency reaches the "natural" frequency for your pendulum you will see the amplitude of the weight increase strikingly. This demonstrates what is sometimes called "sympathetic vibration". As you increase the imposed frequency still further, however, the swing of the pendulum will decrease. At very high frequencies of your hand movement it will almost come to rest, even though your hand is moving rapidly. The point made by this experiment is that in a vibrating system any imposed vibrationary movement may have little effect at high frequencies; and very low frequencies produce equal movements of the system. Once the frequency reaches the natural frequency of the system however, the movements are magnified, and may result in very large displacements. This has an important bearing on the design of suspension bridges, as we shall see. A rod, or any other part of a bridge structure that "sings" can give trouble, since a component subjected to stress reversals can fail through fatigue if the stress is high enough and the number of reversals is large enough. If we know the likely wind speeds we can either ensure that no rod in the wind is the right diameter for that to happen, or we can fit spoilers to stop a dangerous build-up of such vibrations. You may see helical fins on metal chimneys for this purpose. Parts of the roadway, in section, may resemble to some extent the wing of an aeroplane. A wing has air pushed under the lower surface and sucked away from the upper surface, causing the wing to rise. Although the cross-section of a roadway doesn't look much like the wing of an aeroplane, the same kind of thing can happen to a roadway when the wind blows over it if the section is suitable. In a strong puff the road may lift, and then fall again, lift once more, fall back, and so on. After a while it may get into a shaking fit, up and down more and more, till it is fluttering like a ribbon. When the wind-induced vibrations coincide with the natural frequency of the roadway like this the movements build up just as they did with your little pendulum. Soon the roadway bends more than it ought, and may no longer be elastic. Then there is real trouble. This kind of result can arise from buffetting even when the section is far from aerofoil in shape. 82

Bridge Watching At the design stage we can test the possibility of this kind of thing happening by building a small model and testing it in a wind tunnel. Correct in every detail, the model is subjected to an artificial wind that correctly imitates the real wind to scale. We don't have to blow at the same wind speed that the real bridge will meet, since the model is smaller. We have to take into account the "scale effect". This is not the place to discuss scale effects fully; but a few words will give you some idea of what is involved, and there are many good sources of detailed information on the subject. Very much simplified, then, here is the general idea. In model experiments every aspect is made to scale. If the length of the model is 1/10 the span of the real bridge then the lengths of the cables must be 1/10 those of the real cables, the pylons must be 1/10 the height of the real ones, and so on. So the shapes of the model and the those of the real bridge are the same. Now think of a square bit of the bridge, with the wind blowing against it. Since each side of the corresponding square bit on the model is 1/10 of the "real" size, its area is 1/10 x 1/10 = 1/100 of the actual bit. This applies to every area of the model. If the same wind blew on the model and the real bridge, the force on the model would be only 1/100 of that on the actual bridge. Similarly, the volume of any part of the model would be only 1/10 x 1/10 x 1/10 = 1/1,000 that of the full-size part. So if it were made from the same material it would be only 1/1,000 as heavy. Flow velocities over the bridge would depend upon the time scale used, for this too can be chosen to suit the experiments, though it need not concern us here. Putting this together, I hope you see that if, for example, the model bridge were half the span of the real bridge, and used the same materials, all areas would be 1/2 x 1/2 = 1/4 as big, and all weights and volumes would be 1/2 x 1/2 x 1/2 = 1/8 as much. This is an example of the important "square-cube law". Applied to our model it says that the area scale is the square of the length scale, and the volume scale is the cube of the length scale. You can use this for all sorts of things, besides bridges. Because of this square-cube law, the wind used in the model must be carefully controlled. Then we can blow a pretend wind up to typhoon strength and beyond to see how the real bridge would stand up to it. If the model starts to sway dangerously, or bits fall off or get bent, then it is better for it to happen on the model than on the real thing. When the model tests are successful the real bridge can be built with confidence. We can test the action of the river on the banks and the supports with models, using the same ideas. Hydraulic modelling is widely used. With this we can predict movement of the bed of the river. We can examine water movement, too, under various conditions of tide and wind. Some of these hydraulic 83

Bridge Watching models may look a little odd, as the depths have to be exaggerated in some models. If you can get a chance to see some of these you may find them fascinating, especially the tidal ones of estuarial waters swirling around the piers of bridges. These enable a close study of scouring to be made. This has been a long chapter for, as you see, a suspension bridge is by no means as simple a structure as it might at first appear. More and more of these graceful bridges are being built, and afford much pleasure to the serious bridge-watcher. I hope you will enjoy them.

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Pontoon bridges A pontoon bridge consists of a series of floating units connected by a roadway, a kind of jointed beam on floats. In one sense these strings of floating members are not really bridges at all. They do get you across water, but there is often very little space underneath them, as with the other types of bridge discussed earlier; their supports are not landborne but waterborne. There aren't many of them about, but you may come across one occasionally, mostly abroad. This kind of bridge is really a series of little boats in a line, across water, so that people, animals and vehicles can get over dryshod. You may never have seen one, and for that matter you might not spot one in the future. The fighting services used them frequently at one time, but advances in lightweight strong girders have eased the task of providing emergency bridging. Even so, Bailey bridge units are often supported on pontoons. There is one exceptional example of the pontoon bridge, across the river Demerara, in Guyana, South America. There are two points of special interest. Firstly, the bridge is about a mile long, and seondly it has a raised part in the middle to allow the passage of water-borne traffic. The river Demerara is a fast-flowing heavily silted river, and it imposes severe conditions upon the bridge. The bridge can be opened somewhere near the middle for larger vessels to pass. To understand pontoons you need to know something about buoyancy, and the stability of floating bodies. So we start with seeing what makes something weigh less in water. If you pour water into a glass it will collect in the bottom, because the gravitational force will pull it down there. You can pour in more and more, and it all runs down to the bottom, gathering there, with the upper surface flat and horizontal. If you then poke your finger into the water the level rises, as you can see against the side of the glass. All the time that your finger is in there the force of gravity is trying to pull down the water; and it can't go down till you remove your finger. You may not notice it, because it is so small, but your finger is exerting a force on the liquid. You can probably see that the volume of the water pushed up is equal to the volume of finger that is immersed. If you are uncertain about this, fill the glass to the brim, stand it in a saucer, and drop in something whose volume you know, say a short length of round steel rod. Then measure the volume of water that spills over the edge. You will find that the volume of displaced water is always equal to the volume of the solid, or part of solid, that is immersed.

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Bridge Watching This is an important principle. It always applies, whether the object floats or sinks. If it floats, the volume displaced is the volume below the surface. Everything displaces its own immersed volume of water. This is obvious, really, but it is significant. If you are dealing with something that floats, the water is moved upwards, and tries to return to its former level. So it pushes down around the object and so keeps it up. If the thing is heavier than the water it displaces then it sinks, since the force of the water is less than its weight. So everything that is heavier than its own below-surface volume of water sinks, and anything lighter floats. It would be helpful at this stage to do a simple experiment. If you take a block of wood, about the size and shape of a house-brick, there are some tests you can try in the bath, washbasin or sink. First, putting the block in the water, you will notice that it floats with the water-line roughly half-way up the sides, and with the largest face at the top. If you now tip up the block it will return to its original position. If you try to make it float with one of the smallest faces uppermost it will refuse, and again go back to largest face up. If you push it down into the water it won't stay there when released, but pops up again and settles back as before. From this we have the following:• • •

The block is buoyant. The material has a density roughly half that of water. The block is stable when one of the largest faces is uppermost.

Not all buoyant objects behave like this. A floating ball doesn't seem to mind what attitude it adopts. Roll it a little one way and it stays there. It has neutral stability. However, if you stick something onto it, say a blob of putty, then it will float with the putty at the bottom, and will return to that position if disturbed. It no longer has neutral stability. Returning now to the block of wood, if it is held upright, with one of the smallest faces at the top, it will topple when released, since it is unstable in that position; but just as with the ball, it can be made stable in that position by adding a weight to the lowest small face. When floating shapes are prepared for a pontoon bridge these two factors, buoyancy and stability have to be considered. The floats can be of pretty well any shape, but the rectangular block is generally most convenient. If there is a strong current the ends are usually rounded or pointed to reduce the drag; and if they are to be tied closely together they need not be individually stable. In an emergency old oil drums, bundles of straw, or any other buoyant materials ready to hand might be used, and indeed have been used.

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Bridge Watching You will find most pontoon bridges consist of a series of more-or-less rectangular blocks, and we shall look at this kind of float in some detail so that if you see one of these bridges you will be able to understand the construction. We start by considering our little wooden block floating in a stable condition. If we multiply together the width, breadth and depth in the water we get the immersed volume, or the volume of displaced water. This is the volume of water pushed up above the surface by the block, not the volume of the block itself. It is trying to get down, under the force of gravity, and this weight of water is just balanced by the weight of the block, since, considering the vertical forces acting we have

Σ↑= 0 The sum of the (positive) force due to the buoyancy and the (negative) one due to the weight of the block must add up to zero. If you take the block out of the water and then, very slowly, lower it in again, you can feel the weight in your hand lessening as the upthrust from the water increases until, when the block has pushed up a weight of water equal to its own weight you have no force on your hand at all. The upward force goes straight up through the centre of the block, and the weight of the block goes straight down through the same point. The forces are in line with one another, so there is no tendency to turn. If you tilt the block, however, the displaced water has a different shape, with a different centre, so the upthrust goes through a different point, and the two forces are no longer in line with one another. Two equal and opposite forces which are not in line form a turning couple , so the block turns back to its earlier position. It may go past it, and then swing to and fro a little before settling down again in its stable "flat-side up" position. When you try to float the block upright, with the smallest face at the top, any tilt alters the shape of the displaced water, but in such a way that the couple acts the wrong way; instead of turning back the block to where it was, it tilts it over more. That is why it is unstable in the "end up" position. With the block floating comfortably in a stable position, that is with the largest face uppermost, try tilting it by a little downward push on a short edge, then one on a long edge. You will find that one recovery is quicker than the other, since the shape of the water pushed aside is different in the two cases. Pontoons are usually hollow, of steel, treated against corrosion and, unlike our wooden block, carry a load, a load which can vary. So it is worth putting something on the block to look at its stability when loaded.

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Bridge Watching One of four things may happen, depending upon the load and its position. You may find it interesting to try different amounts of weight, put on the block in various positions, to see which of the following occurs. • • • •

Buoyant and stable, the block just settles a little more deeply into the water, with the load sitting quietly on top. Buoyant but unstable, it sinks a little deeper and capsizes. No longer buoyant, but still stable, it sinks to the bottom without changing attitude. Unstable as well as lacking buoyancy, it rolls over and sinks with the weight attached.

Extra weight, then, can upset things for a pontoon, if it is put on top; but if it is put underneath it can help stability. This is because any tilting moves the weight out to one side, so that it has some leverage to bring things back to normal. All of the preceding discussion really boils down to two simple rules for floating bodies :1. 2.

The lighter the pontoon and the bigger its volume the greater its buoyancy. The lower the weight the better the stability.

This isn't the whole story, but it will do for our purposes. With this knowledge we can now think about actual pontoons. Let us suppose we need to cross a small stream, too wide to jump, and we decide that a pontoon bridge would provide the best solution to the problem. The first thing we shall need to know is what materials are available for the job. Then we must decide about the number and size of the pontoons and the fixing arrangements. When we think about the weight to be supported by each pontoon, we have to realise that the load, as it traverses the bridge, will be supported in turn by one or more pontoons. The roadway must be flexible, since the pontoons yield under the loading. How much they yield will depend upon our design. As a pontoon takes a load it sinks by an amount such that the weight of water displaced equals the load; but this weight is the water density times plan area of the pontoon times the amount it sinks under load. Put another way, the extra depth of immersion is the load divided by (the plan area of the pontoon x the density of water). Knowing the load, and the density of water, we choose the plan area of the pontoon to suit the extra depth of immersion we want.

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Bridge Watching A small plan area will result in a very flexible bridge, but a large pontoon will be relatively rigid. The depth of the pontoon must be such that under load there is still some freeboard. This means that the total depth of the pontoon has to be greater than the immersed depth by the amount of freeboard. This determines the space between the underside of the pontoon and the water surface. Usually, the freeboard is not very much, and in conditions of calm water may be just enough to ensure some clearance when supporting the heaviest anticipated load. If the bridge is to cross a fast-flowing stream or river and if the pontoons are open at the top care must be taken to ensure that water does not surge over the upper edges. Pontoons with closed tops, in placid water, can manage with less freeboard, though a margin is normally provided to cope with unusual loading. The roadway helps to tie together the separate pontoons, so individual stability would not appear to be very important; but handling unstable parts of the bridge is likely to present difficulties. In all this we assume that the sides of the pontoon are vertical, which is generally the case, for ease of manufacture. For convenience in transport, however, the sides are sometimes tapered so that the components can be stacked inside one another. The disadvantage of this arrangement is the extra cost of manufacture. The plan of the units can be, and often is, rectangular, but semi-circular ends are sometimes seen. If the bridge crosses a fast-flowing river, blunt ends may impose undue forces on the bridge, and this may call for pointed, or even streamlined shaping of the ends. The force on a large flat face directly into the flow can be considerable, tending to sweep the bridges downstream. When a series of obstructions is placed across a flowing liquid, as we have when a pontoon bridge crosses a river, the flow between the parts has to speed up, because of the reduced area of flow. Due to this faster flow, the level falls, so the level between the pontoons is lower than the level of approaching and receding water. The general effect of this is to cause the units to sink still further. This is not usually very marked, however, except when units are close-set in a rapid stream. Under those conditions due attention has to be paid to the possibilities. The construction of a pontoon bridge offers scope for ingenuity, depending upon the width of the stream, its speed, and accessibility to the site.

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Bridge Watching The usual way with small bridges is to send over a line by someone paddling a pontoon across the stream, or by heaving a line over with a grappling hook attached, to catch in a tree or undergrowth on the other side. This can then be used to take over a stouter line. For longer bridges, lines are usually taken across by boat, and then the pontoons are towed into position, and fixed to the cables. Where the stream is fast flowing the units must be held against the force of the current by attachments to suitable anchorages on the banks. The lengths of these cables determine the angles at which they meet the banks. This will depend to some extent upon the force of the stream. Strong currents require long lines, making small angles with the banks. Finally, the roadway is positioned, and if the pontoons are wide enough handrails are not fitted. The roadway must be flexible, to accommodate the dip of individual pontoons as the load crosses. Generally speaking the pontoon bridge is a temporary affair. Sometimes some part or even the whole of it can be swung aside to allow the passage of water-borne traffic, and then hauled back into position after the boats have passed. The pontoons themselves are often removed after use and taken somewhere else for redeployment. Often they are considerd as expendible. Because of their often temporary nature the pontoons themselves are not necessarily factory made. In an emergency any floating objects can be used. At times of disaster, when normal bridges are down, the pontoon bridge is a useful expedient. We can use bundles of timber, inflated plastic bags, steel drums, or anything buoyant which is available. In a short time, with unskilled labour, an engineer can provide a safe passage across a river, lake or stream, with a pontoon bridge. You may not see many pontoon bridges; but those you do see will generally be interesting, from the ingenuity displayed in their construction. As mentioned in an earlier chapter, there was a pontoon bridge across the river at Baghdad, built by the British Army, which remained a useful and decorative feature of the city for many years afterwards. It was known as the Maude Bridge, after a famous soldier of the time. When the river was in spate, people looked doubtfully at the yellow turbulence rushing past, but it never gave way and never dunked anyone, as far as I know. As we leave our discussion of pontoon bridges, it might interest you to learn that the card game "vingt-et-un" is known as "pontoon" in English, and the French word for a bridge is "pont"; further, bridge is the name of a British and American card game! 90

Bridge Watching Under the heading of pontoon bridges we can think of other kinds of floating bridge, too. There are plenty of these about. You can see them in many an estuary and creek, doing good service economically. Large floating bridges are great flat platforms to carry people and vehicles. They are connected to the shore by massive chains. These chains, which lie on the bed of the water when not in use, are hauled into the forward end of the contrivance and passed out at the other end. The whole thing grinds and clanks its way across the water, kept on course by the chains. Broadly speaking, they are unlovely things to observe, but they do a very good job, and many of these have been in use for a very long time. Provided the chains receive proper attention from time to time they are a most reliable form of water-borne transport, with little to go wrong. They hardly merit the name of "bridge", but they are always so called. It is a convenient arrangement, which allows shipping to pass unhindered. There is no steering, and the construction is simple. It has no bows or stern as it makes its way to and fro across the water, and doesn't require a numerous crew. Altogether, it is hard to imagine a less demanding post than that of captain of a floating bridge.... When you travel on one you will probably notice that the passengers, who probably use it daily, don't even look at the fascinating points of interest of this ungainly craft. However, there is usually something for the curious eye to see. The freeboard is very little, since the floating bridge doesn't operate in stormy waters, but the quiet reaches of estuaries. A low freeboard makes it easy for traffic to roll on and off at each end, too. The ramps at each end of the vessel take quite a hammering each time they meet the shore. You can appreciate this when you travel on this kind of bridge. Each time the crossing is completed the ramps are rubbed against the concrete slip as the whole thing swings and settles. Chain, especially heavy chain, is terribly expensive; and the corrosion is daunting, since they are being hauled out of the water and dunked back in again many times a day, a procedure which encourages corrosion. The conditions are about as bad as one could wish, from that point of view. You may find it worth a little time to look at them and to consider the arduous life they lead. At the other extreme we have the little ferrying devices that you occasionally meet, for foot passengers. These are often ancient replacements for fords or old bridges and ferryboats. Strictly speaking they are not bridges at all in one sense, and are certainly not so if the ferry is a simple boat rowed from shore to shore. 91

Bridge Watching However, the boat is sometimes hitched to a straining wire, and the ferryman hauls it across by pulling on this wire. This is a sort of cross between a pontoon and a ferry. It is much cheaper than a fixed bridge, and in the days of low wages was much more economical to run, too. These arrangements are for the most part being replaced nowadays by light bridges, which are modestly priced and pay for themselves within a few years. If the water has a fast current, a straining wire can be used to take a pontoon or boat across without effort. The principle is basically that of an aerofoil or hydrofoil, that is putting an asymmetric section in a stream. When a pontoon of rectangular plan is hitched to the straining wire by one corner the flow along the two sides will be different, giving rise to a side thrust. The pontoon will then, with luck, travel across the stream. By hitching the line to another corner it can be made to travel back the other way.

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Materials The subject of materials and their properties is so vast that many people spend the whole of their lives studying only one part of it. So we can do little more than dip into it here and there. However, no dedicated bridge-watcher should be ignorant of some of the more important aspects of materials science. Every substance has its own particular properties. Some are dense, some light; some are fragile and some strong, and so on. As far as we are concerned, some things about them, such as their smell or taste, don't matter when it comes to using them in a bridge; but others, such as how they stand up to stress , and bad weather, are very important. We have a wide choice, for the earth is bountiful, full of good things for building, like stone and clay, and metals. We have things that grow, too, like trees and shrubs. The attractive thing about all this is that they are free. All we have to do is dig up or cut down with due regard to aspects of care for the environment. In the so-called "under-developed" areas people just use what they find in the immediate vicinity, tree trunks, lianas, reeds, whatever is appropriate. In "advanced" communities materials tend to be imported from other places, (not always to the environmental benefit of those areas). Materials are free, then; what costs money is labour; but then, money is a means of exchanging labour. When we do work of some kind somebody (usually) gives us money, which we then pass on to buy somebody else's labour. Our society rates every person's labour at so much an hour, or day, or year. Most people feel the scales are wrong, and that their own special types of labour are worth much more; but the price of everything is set by the one who pays. If one kind of labour is too costly, the purchaser uses another source. For building a bridge in stone, for example, we get the stone free, for the earth belongs to us, and everything that is in it, for the duration of our lives; but we pay for the labour. There are all sorts of people whose labour is used in getting the stone into the bridge. There are those who survey the ground, the men who dig out the rock, the ones who make the tea for the men who dig, the operators of the machines, the truck drivers, the accountants who add up (and subtract!) the figures, the "man in London" who crouches over a telephone to make money out of the undertaking, and so on and so on. Everyone in the remotest way connected with the provision of the bridge labours in his or her way, so we have to buy all that labour. This it is that costs the money, not the materials themselves but the work that goes into transferring the rock from the ground into the structure. 93

Bridge Watching We face the same arrangement for all the other materials, whether it be steel, cement, paper, water, or tea. It is all free, and we pay for the work. In effect, we exchange our labour for somebody else's labour, for that is how we get the money in the first place, by selling our work. What we do may be laying bricks, doing sums, backing horses, or coming into a fortune by signing our names. It is all labour of some sort. You may well think some kinds of labour are easier than others, and you may be right; but the best kind of labour is the kind you happen to like. Broadly speaking we choose what suits us best. If we don't, we may make lots of money, but lose much happiness. Well, all this may seem to be off the subject, and more like a discussion of economics. However, it is relevant; and when there is insufficient money forthcoming for the construction of a bridge it may call for much ingenuity, both financial and technical, to solve the problem. When a bridge saves a long détour, a toll system is sometimes installed, to recover the cost of building and maintaining it; but often the money must be recovered in some other way. In any event, it falls to the engineer to make some critical decisions, choosing whether to build in steel, concrete, timber, or any other material. Although we could use pretty well any material except stuff like pink jelly, in practice we are restricted to a few solids like timber, metal and stone. Most modern bridges are in concrete, and a stretch of road in a developed country may be crossed by hundreds of similar concrete bridges. Timber may be bought in its "raw" state, just bits of trees, or in ready-dressed boards or baulks. Metal is available in strip, drawn sections, or plate, of iron, steel, aluminium alloy etc. The choice is wide. Then there are the hard materials, like quarried stone, or something made up, like brick or concrete. We shall look at these in a general sort of way. Starting with steel, we can think about those properties that are especially significant in bridges, like strength, elasticity , density and resistance to corrosion. Steel starts as iron ore in the ground, and much work has to be done before it can be used as a structural material. After refining it is mixed or alloyed with small quantities of other materials to give it certain desirable properties. So we have a very wide range of steels from which to choose. There is no need to test all the steels ourselves, as it has all been done by somebody else who has specialised in the subject, and has the equipment to carry out the tests. So we buy these lists of properties, which is like buying the labour of the test people. 94

Bridge Watching In the production of steel the factories must keep a very tight control on every process, since the designer of a bridge has to place absolute reliance on the integrity of the supplier. The bridge designer has to allow a "safety factor" to cover unforeseen effects, but figures for the properties of the steel don't require an additional "factor of ignorance". The breakdown of something like a television set is not usually a very drastic matter, but the reliability of a bridge is a matter of life and death. So those who test materials are very careful people. To test a sample of steel for exemple, a specially-shaped piece is made, to fit the testing machine. As mentioned earlier, there are three kinds of stress , tensile, compressive and shear, not entirely separate from one another. The commonest test is the tensile test, which examines how the material behaves when pulled. The tensile testing machine grips each end of the test piece and pulls it until it fails, at the same time noting the load and the extension. Different materials behave in different ways, just as humans or other animals do under stress. Stress is the amount of force taken by unit area. In the form of an equation, we can write: stress = force divided by area If we apply a force of 12 on an area of 2 somethings then the stress is 12/2 = 6. The same force on an area of 3 somethings would produce a stress of only 12/3 = 4. So to make it easy to judge one steel against another we need to know the cross-sectional area used in the tests. From this, knowing the load, we can calculate the stress. In practice, we use a standard test piece for all the specimens, so that the actual stress is easily worked out and compared. Holding one end firmly, the other end is pulled with a gradually increasing load to stretch the specimen. If the load were removed, it would shrink back again to its former length because of its elasticity. As more and more load is applied, it stretches more and more, still behaving like a piece of rubber. The testing machine is often fitted with an automatic device which draws a picture of the behaviour of the specimen, a graph showing the amount of stretch according to the applied load. While the material is elastic the stretch is proportional to the load. Double the load and the extension is doubled, and so on. With the load measured along the vertical line, and the extension measured horizontally our graph is a straight line from the origin, and the slope of this line, the angle it makes with the horizontal, is a measure of the elasticity of the material. This is an important property, and of course is different for various types of steel. 95

Bridge Watching Usually, for the sake of standardisation, we draw a graph of stress against strain. The stress is, as we mentioned above, the load divided by the area. The strain is the elongation divided by the length, showing the stretch per unit length. If we use the small letter "e" for the elongation, and the capital letter "L" for the length, then the ratio e/L is the strain. If the load is represented by the letter "P" and the cross-section area by "A", we have the stress given by P/A. We shall refer to this in the appendix. Returning now to our specimen under test, still being strained elastically, we know that if we continue to stress it the material will cease to be elastic. It will stretch plastically, and on relief of the stress at this point the specimen will not return to its former length. This means that the strain will be permanent. On the graph, this shows up as a deviation of the line. It begins to bend over, showing the strain increasing more quickly, and no longer porportional to the stress. Eventually, the specimen may break, the load falls back to zero, and the line may bend right over and come to an end. Each kind of material has a different shape of stress-strain curve, and people who are in the know can look at the graph for any material and spot what that material is, pretty well. When the steel reaches the limit of what it can take elastically the line bends, and the stress at this point is called the "elastic limit". We can't use a higher stress than that in bridge design. In fact, we had better not go anywhere near as high as that if we want to feel safe. We want to make sure that every part of the bridge will behave elastically under load. If any part were plastic the distortion would be permanent, and a funny shaped bridge would result.... The working stress for every part of the structure is perhaps only half the stress at the elastic limit, or a tenth as much, or whatever we feel safety might demand. Here again the engineer must use his professional judgement and experience to steer a careful course between too high a stress for safety and too low a stress for economy. The breaking stress, i.e., the stress when the steel fractures, may not be the same as the stress at the elastic limit. This is because after reaching the elastic limit the steel goes on stretching like a lump of putty, until it breaks. During this time the metal flows slowly into a different shape. Where it is going to break, it gets thinner.

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Bridge Watching As this is a smaller area of cross-section the stress goes up still more, although the load may be the same, or even less. (You will recall that the stress is given by load/area). I do hope this doesn't sound too complicated. Stretching and breaking a piece of steel is a rather complex affair when you look into it, and I have left out quite a lot in this simplified treatment of it. The points of importance to you are (i) steel stretches elastically up to a certain stress , and (ii) we must work well below that stress if we don't want trouble. Normally, you won't see over-stressed members; but if you look at pictures of bridges destroyed by war or natural disasters you should see typical types of fracture. We shall now take a peek inside the steel while it is being stretched. Its behaviour depends upon the atomic structure , and that is affected by what elements are mixed with the iron, and how the steel has been treated before the stretching. Broadly speaking, it is like this: As the stress is felt, the particles inside the steel move out of position so that their elastic resistance to displacement can supply the opposing forces. As mentioned earlier, this tensile stress produces a shear stress at 45°, and a compressive stress at right angles. So the rod stretches along its axis, shrinks across its axis, and shears at 45° to that axis. While it is elastic it is hard to see this, as the movement is small; but when it breaks you can see that the rod is longer, that the diameter is smaller at the break, and that the broken ends are like a little 45° cone and socket. You may not get a chance to see a steel tie that has failed in tension , and it isn't easy to break a steel rod in tension yourself, but you might come across a failed rod in a scrap yard. Steel ties then, when they are overloaded, pull apart as indicated above; but other materials are different. Some are strong in tension and weak in shear; others may be weak in compression , and so on. When we use materials we need to know their weaknesses and their strengths, so that we can pick the best material for the job. For instance, if we want a tie we would certainly not choose concrete, since its tensile strength is very low. For a column or strut , on the other hand, concrete would be a good choice, and so would brick or stone, all strong in compression. Timber is an especially interesting kind of material, as it has different properties in different directions. Parallel with the grain it is good in tension, but it is weak across the grain, as you can readily see for yourself by trying to break small pieces of wood. It is quite good in compression, though most timbers give quite a bit under heavy compressive stress across the grain.

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Bridge Watching When a solid timber beam is used in a bridge, the wood has to cope with both tension and compression along its length, and shear across the grain. This suits the material very well, and timber beams have been, and still are, used with great satisfaction. Since the tension, compression and shear vary as we go along the beam, the stress resulting from the combination of these is at all sorts of different angles to the axis. Timber copes with this very well. Modern developments with timber are full of promise. New adhesives are producing laminated members of great strength. They can be formed into useful shapes, too. An arch member of laminated timber is strong and attractive. Bridges using such arches have much to offer. You aren't likely to see such bridges across motorways and railways; but inside some modern buildings, where bridges are required for people, a few engineers and architects have been taking advantage of the new opportunities offered by timber developments to produce some striking designs. Indoor bridges are not subjected to the rigours of bad weather, so they don't need the kind of protective coatings which might hide the beauty of the timber. However, timber suffers from one defect not found in metals, stonework or brick. It is edible. Small organisms find it irresistible, and their predations can seriously weaken a structure. Fungi, too, can draw nourishment from timber, and in so doing can reduce its strength. Various kinds of treatment are available to provide protection, of course, just as there are treatments against corrosion of steel, and deterioration of brickwork. For indoor bridges proper treatment can ensure that there will no trouble. This is a convenient stage at which to consider again the actions of two or more forces acting together. Earlier, we saw that at a given point, two forces acting at an angle to one another produced the same effect as a single force there, at some other angle. For example, the effect of equal vertical and horizontal forces is the same as a single force at 45° to the horizontal. Conversely, a single force could be replaced by two or more other forces whose combined effect would be the same. Stresses can be treated in the same way. If we think of a point in some material where there are tensile, compressive and shear stresses, their combined effect can be calculated, and the resultant figure is the effective stress at that point. The knowledge of the stress everywhere in a component can be useful, and there are several methods of assessing these.

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Bridge Watching One cunning device is the transparent plastic model. This is mounted on the laboratory bench, and subjected to loading corresponding to that in the actual structure. With polarised light shining through the model, coloured patterns are produced. These rainbow-like patterns can then be interpreted to show the direction and intensity of the stresses in the system. The use of this photo-elastic scheme has not yet been out-moded by the excellent modern computer programs now available. It is possible to see on the computer screen exactly what happens in a bridge or a bridge member, under proposed loading, and to alter dimensions so as to accommodate the loading without over-stressing at any point. Areas of high stress can occur in members if they are not designed with care. For example, if a tie is made with any sudden change of section, a shoulder for example, or a sharp ridge, such a "stress raiser" will be the cause of a very high stress there. This is why you will see, if you look carefully, that when a tie has a change of section at some point, the corner is rounded off, so that the section changes gradually. There are other forms of stress raiser, such as sharp-edged holes. When a tie breaks it is usually at one of these points. It is not only steel that can fail in this way, either, but when looking at steel bridges you will soon see that sharp changes of section are shunned by the designer. Members other than ties can suffer from sudden section changes, in the same way, and this can be demonstrated clearly on the computer screen. Some programs that are being produced are remarkably ingenious and a boon to the designer. Such methods were not around when earlier bridges were designed, and much waving of slide rules and painstaking pen-and-paper work was needed. The slide rule is now no more than a decorative souvenir on one's desk, but it is worth thinking about how important it once was, and how recent has been its demise, with the invention, and proliferation, of the pocket calculator.

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Appendix Some technical matters In the earlier chapters we had to treat some of the basic technical matters rather lightly. In this appendix the aim is to cover in a little more detail some of those points, to help to extend your enjoyment of bridge-watching. We shall look also at one or two other items that can improve your appreciation of the bridge. Since not all bridge-watchers are avid mathematicians we shall, in this appendix, keep the approach free from complicated calculations. However, readers who are well up in the calculus can refer to some of the excellent publications on statics and structures , where they will find some fascinating reading. We start by taking a closer look at the elastic nature of materials, or what makes the parts of a bridge yield, and then go back into shape as loads go on and come off. Whatever the type of bridge, or kind of materials used, the elastic actions are vital. Our first requirement is a means of assessing how elastic a material is; that is, we want a measure of elasticity. We need to be able to state that the elasticity of this substance is so much, and that of another substance is more, or less. Our measure of elasticity will enable us to compare different materials, and determine their suitability for our purpose. Going back to what was written earlier about stress being the spread of force over an area, using P for the force or load, and A for the area, we can write: f = P/A The letter "f" is used here for the stress because it is often used in text books, and "s" is used for something else. We can use any letters we like to represent these quantities, but we do need to take care not to use the same letter for different things, to avoid confusion. This is a very simple equation, but it is an important one, and in constant use, so it is worth remembering when we look at a bridge. Consider a tie which is taking a stretching force or tension of 80, on an area of 8. Here P = 80, and A = 8. So we can write:

f = P/A 100

Bridge Watching = 80/8 f = 10

If the tie has twice the cross-sectional area and twice the load it would still undergo the same stress, because:

f = P/A = 160/16 f = 10

On the other hand, if we retained the load of 80, but reduced the area to only 4 the stress would rise, since from the equation:

f = P/A = 80/4 f = 20

Thus, the load, the area and the stress are tied in with each other and we can use this equation in another way. Equations can be twisted around, so long as we obey the rules of algebra. Using this idea we can write A = P/f This means that if we know the load P which a component has to carry, and the safe working stress f, we can work out the area A of the section needed in the structure. This is the usual way in which the formula is used. A stressed tie grows longer, and a very long one will stretch quite a lot; but a short one, under the same stress, won't stretch so much. So we want to know by how much each unit length of the tie increases. This is called the strain. If we write L for the overall length of a tie, and e for the total elongation, then the stretch per unit of length is the strain, given by e/L. If we put the same stress on equal lengths of different materials, we can see different amounts of strain. A piece of rubber, for example would show more strain than a 101

Bridge Watching similar piece of steel for the same stress. The ratio of stress to the strain resulting fronm this stress is an indication of how elastic a material is. It is easy to measure the stress and corresponding strain for a material. We put a lump of it into a machine, apply a stress, and measure the resulting strain. Once we know these we have a measure of the elasticity of the material. The ratio stress/ strain is the measure or modulus of the material's elasticity and is usually denoted by E, so E is also the stress which would be needed to produce unit strain. This might be possible. A strain (e/L) of 1 would mean that a tie had stretched an amount (e) equal to its original length L. This might be possible for some materials, but not for those used in bridge construction. Steel would fracture long before this amount of deformation had taken place. So the stress to cause this is a fanciful or theoretical figure for construction materials; but it is a useful way to assess elasticity for any material. The direct modulus of elasticity, E, then, is the theoretical stress that would cause a strain of 1. We use the word "direct" here because, as we shall see later, there are other elastic moduli. For all elastic moduli we have a similar relationship.

E = stress / strain = (P/A)/(e/L) E = PL/eA

Measuring the elasticity of a bridge material by the ratio stress/strain has applications beyond bridge-watching. We can apply it to the resilience of people under stress , the strength of somebody's faith when sorely tried, the behaviour of a crowd, or a population of creatures. Wherever we want to measure how elastic something or somebody is, we can assess it with this relationship. Values of E for many materials are listed, and when we want to know the elasticity for a particular material we simply look up the value, and use it in our calculations. One of the attractions of equations is that when we want to know something we put in the numbers for the things we know, stir it up a bit, and out pops the answer for the thing we didn't know. Suppose, for example that we were designing a tie of length 20, to take a load of 12.

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Bridge Watching Suppose, too, that we didn't want it to stretch more than 0.03. We should look up the elastic modulus in a list. Suppose it was 40,000. Then we would write the equation like this: A= PL/Ee Putting in the figures instead of the letters and stirring it up a bit we get the area like this:

A = (12 x 20)/(40,000 x 0.03) = 240/1200 A = 0.2

So we choose a tie with a cross-sectional area of 0.2. In a similar manner, if we wanted know how much stretch to expect in a tie, knowing everything else about it, we could find the elongation, e, from e = PL/EA Earlier, the other moduli were mentioned. The transverse modulus, the one for shearing, is usually referred to as G, and is the ratio of shearing stress to shearing strain. Similarly, when a piece of material is strained volumetrically, to squeeze or dilate it, we use the bulk modulus , K. So these are the three moduli or measures of elasticity. As you might expect, they are related to one another for any particular substance. Shear strain is measured by the angular deformation under shear, and bulk strain by the fractional change in volume of a cube, when equal stresses are applied to each face. They are treated in a similar way to that shown for the direct modulus. We turn now to some thoughts about forces , which we mentioned earlier. So we shall discuss vectors. Vector quantities are quantities that are defined by direction as well as amount. Quantities which are independent of direction, like area, are called "scalar" quantities. Scalar measurements are wholly defined by the amount only; but five somethings added to five somethings is not necessarily ten somethings. It depends upon the directions of the distances. Five somethings east plus five somethings west brings you back to your starting point, in which case five somethings plus five somethings equals nothing. On the other hand, five somethings west plus five somethings north takes you to a point a little over seven metres away. 103

Bridge Watching Forces are vector quantities, as their direction is important. We can show the effects of adding forces by drawing lines to represent how big the forces are and their directions, just as we can for distances, or any other vector quantities. A force of strength 7 straight upwards can be shown by a vertical line of length 7 to some scale. For a horizontal force of 5 we draw a horizontal line of length 5. We can show the sense of the forces by arrows on the lines. So our vertically upwards force could carry an arrow pointing upwards. Drawing vectors is a surprisingly powerful tool which is widely used, and it is easy, too. If you were in a boat sailing due north at speed 4, and at the same time the current set you sideways at a speed of 3, the boat would move at an angle to the north since both movements would be taking place at once. The effect would be just the same as if you first went due north a distance of 4, and then sideways a distance 3. The total distance would be 5. Think of the forces at the abutments of an arch bridge. There is an upwards force to cope with the loading , and an inwards force to resist the spreading of the arch. If we draw two lines for these forces, one up and one along, joined at one end, the result is the same as one force shown by joining their free ends. It is helpful to letter the lines, and if we call the upward force ab we can put a at the bottom of the line and b at the top to show that the force ab acts upwards. From b we can then draw the horizontal line bc to scale in the right direction, to represent the side thrust. The resultant force is shown by the line ac, to scale, and its direction is in the sense from a to c. We can do this with any number of forces. In a frame, which consists of ties and struts , this method not only helps us to find the forces in the members, but will show which members are ties and which are struts. In many cases an experienced engineer can do this kind of thing mentally. In a straightforward Warren girder, for example, all the members are the same length and form equilateral triangles, so all the angles are known. Sketching the vector triangles in his head, a bridge engineer can come up with the forces in the members to a high degree of accuracy, with no difficulty. Take the node at the left-hand upper joint of a Warren girder, say, where the supporting force is 36. The only other forces there are those in the members, one of which runs up at 60°; and the other is horizontal. So we have one vertically upward force of 36, one horizontal force, and one at 60°, these two either pushing or pulling.

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Bridge Watching There is a clever scheme of notation for forces acting at a point, invented by a man called Bow. He put a capital letter in each space between the members, and named the member by the letters each side of it, going round the node in a clockwise direction. The force itself can then be referred to by the same letters, in lower case. This turns out to be a simple and powerful way of dealing with forces in frames. In the case under discussion above, suppose we put the letter A in the space to the right of the vertical force, B in the space to its left, and C in between the two members. Then with Bow's notation, the vertical force is ab, the force in the horizontal member CA is ca, and that in the sloping mamber BC is bc. Now the triangle abc can be drawn, the line ab vertically, with bc and ca parallel with the members BC and CA. To the same scale, the forces in the members can now be read from the diagram. A good engineer can do this in his head, for he can see by inspection that if the vertical line ab measures 36, then the horizontal line bc, from trigonometry, must be 36/√3, or 12√ 3 which is about 12 x 1.7, or roughly 20.4. The sloping force ca is twice this, about 40.8 (a 60° triangle has sides in the ratio 1, 2, √3, a fact familiar to engineers making mental calculation of forces in a Warren girder simple). If we now consider the member CA, then from the vector diagram we have the force ca running down to the right. So it is pulling at the node ABC and is therefore a tie , since only a tie can exert a pull. Again, from our diagram, either on paper or in one's head, the line bc runs from right to left, so the force in BC is pushing to the left and BC is thus a strut. Note that we go round the node in the same direction whenever we refer to a member. It doesn't really matter whether we choose to go clockwise or anti-clockwise, so long as we always go the same way round every node. This method is a wonderful idea and can be extended to the whole frame. We shall take a simple example to show it being applied to a different kind of frame, a Pratt girder. If we decide to adopt one particular direction for the lettering always, we are unlikely to make serious errors, so we shall use clockwise lettering as above, for our work here. Let us take a four-panel Pratt girder, of height 6 and length 24, simply supported at its lower end nodes, carrying a load of 100 at the second node along the top from the left, that is distant 6 from the left-hand support. A Pratt girder looks like a lot of letter "N's", and in this case each panel is square, having sides of length 6. Let all the sloping members in the two left-hand panels slope upwards to the left, and the others upwards to the right.

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Bridge Watching We now use the relations:

Σ↑= 0 =0 When we work out the supporting forces , these come to 75 at the left hand end and 25 at the right. Let us call the large space to the left of the load A, that to the right B, and the space between the supports C. Now we have the forces ab = 100, bc = 25, and ca = 75. On a vector diagram the letters a b and c will lie on a vertical line. We need to name the spaces inside the frame, and we can do that by putting the letters D, E, F, G, H, J, K and L in the spaces, working from left to right. (We generally avoid using the letter "I" as it can be confusing.) Picking a node where there are not more than two unkown forces, we can draw the vectors for the forces there. Choosing the bottom left hand node, we already have the force ca, and we know that the line ad for the force in the vertical member must be vertical, passing through a. Also, the horizontal force dc in DC must pass through c. The point d, then has to lie on a horizontal through c and a vertical through a. The only place for d must therefore be at c. So c and d coincide. This means that the force dc is zero, perhaps a surprising result. However, it is clear from inspection that it must be zero, for there is no other horizontal force there to balance it. Similarly, we see that the force ad coincides with the force ca. Note that the force ad is downwards at the node ADC, so the member AD is a strut , taking the whole of the supporting force, and the member DC is unloaded. These are important results, which an engineer would know without drawing or calculation. We turn our attention now to the node AED, where again there are only two unknown forces. We note that the force ae in the member AE is horizontal, so we can draw a horizontal line through a on our vector diagram. The member ED slopes up to the left at 45°, so a line is put in, through d, sloping up to the left at 45°. Since e is on this line and the horizontal through a, the point e must be where these two lines meet. This triangle gives us the forces ae and ed. The force AE acts to the left, so the member AE is a strut, pushing at the node AED. The force ed acts down to the right, so it is pulling at the node AED, and the member ED is thus a tie.

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Bridge Watching We can carry on in this way for all the other nodes of the frame, moving each time to a node where not more than two of the forces are unknown. Here the next node would be EFCD, for we know the forces in the members CD and DE. After that, we could move to ABGFE, for the only unknown ones there would be BG and GF. In this way we could determine all the forces in the frame. The results are shown below in the table, where S represents a strut, and T a tie.:

Although it takes a long time to write down all this, in practice it is a rapid method of finding the forces in the members. A practised engineer would probably write down the results quite quickly from inspection, probably on the back of an envelope. You will notice that three of the members, CD, CL, and GH carry no load at all, and might feel that they could be omitted from the structure. However, if you look carefully at, say, GH you will see that at the top there are two struts , BG and BH thrusting together at that point. They are finely set, and the slightest wobble would cause them to pivot round the node and produce collapse. The member GH, though nominally carrying no load, stops that movement. These members that appear to be carrying no load in fact perform the useful duty of preventing collapse from instability. It is clear, though, that they do not need the same strength as, say the member AD. There are some bridges where you may see what appears to be a greater number of members than would seem necessary. This is because in some structures we build in redundant members or forces to reduce the sizes of certain parts.

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Bridge Watching A very simple example of redundancy is a propped beam. Theoretically a beam doesn't need a prop under it; but if we do fit one the section of the beam can be reduced, which may result in a lower cost for the structure. The girder we have just examined is a "statically determinate" structure, one where the forces can be found from the ordinary simple rules of statics. The calculations for redundancies require more advanced methods, not needed by the bridge-watcher. However, knowing that some bridges may contain redundant members or forces may avoid some puzzled feelings. The computer handles problems of this kind with ease, and design offices have software to deal with bridges of all kinds. The outline above will serve to give you some idea of what a program would do for a simple statically determinate frame. The great advantage for the computer here is that of showing at once the effect of changes in design or loading. Design office time is costly, and when competitive tenders are called for costs are of prime importance. We turn now to a note about arches. When arches were being considered earlier the shape of the bending effect diagram was mentioned. You will perhaps recall that for a u.d. load the bending moment diagram was parabolic. If the arch itself is parabolic it will, so to speak, fit the diagram, and there will be no bending tendency at all in the arch. With the ashlars lying snugly against one another arranged along this curve there is no tendency to tilt. It can be shown that for this to be the case the line of thrust must pass through the middle third of the face of each block. When you look at an arch in brick, stone or concrete blocks you can imagine this thrust line running down through the separate pieces of the arch. The u.d. load is not the only, but perhaps the commonest, form of loading on a bridge, as it is usually the bridge itself which is the main load, heavier than the traffic it carries. We now look at some points concerning reinforced concrete. The bridge-watcher will see reinforcement only during the construction stages, and no opportunity should be neglected to visit the site when a bridge is being erected, even if you have to view proceedings from a distance, with binoculars. Think of a concrete beam , oblong in section, with some rods in it near the bottom face. Suppose it to be simply supported at its ends, so that the upper part of the section is in compression and the lower part in tension. Concrete being weak in tension, we can ignore its contribution to the strength of the lower part of the section. So the concrete below the middle serves only to hold the steel rods in place, and to protect them from corrosion. 108

Bridge Watching The word "middle" doesn't mean exactly half-way up the section, but the place where the stress is zero, the "neutral axis". The stress starts at the bottom face as a maximum, falls to nothing at the neutral layer and rises to another maximum, of the opposite kind, at the top face. In our example beam the steel rods take the tension, below the neutral layer, and the concrete above the neutral layer deals with the compression. The force in the rods is pretty well in one line, with the stress evenly taken across their area; but the stress in the concrete varies from nothing at the neutral layer to a maximum at the top. This unevenly distributed stress in the concrete is equal to a single force at some point below the upper face. This is usually about a sixth of the depth from the top. So for our concrete beam, rectangular in section, the couple that balances the bending effect there is a pair of forces, one from the steel, and one from the concrete, with a leverage roughly two thirds of the overall depth. To avoid complications, all this is a rather inexact explanation; but it should give you an idea of what is happening. Concrete beams are not all rectangular in section, nor are they all solid. You will come across tee-sections, and hollow sections of various shapes, which make the best use of the special qualities of concrete. A bridge may have to carry cables and pipes, perhaps railing, and walls to separate pedestrian traffic from vehicles, maybe maintenance platforms too. If the shape of the section is carefully thought out, the engineer can cater for all of these in designing the section. He can set the wide parts of the section where there is compression , and then accommodate the reinforcing steel in the narrower parts of the section. The area of steel is very much less than that of the concrete, so some deft work with the calculator might yield a useful cost-saving section. When done well the resultant shape can be elegant, and when you see this kind of thing in a bridge you can appreciate the work of the engineer who produced it. There are some interesting methods of putting a bridge across water. Some bridges have been built by floating sections out and then hoisting them into position. Others have been cantilevered out from both banks and joined at their meeting point. There have been cases where the whole span has been built on the bank, and then swung across the river with one end held firm, afterwards being raised to the desired height. A word about soils would perhaps be helpful here, as you will often see sloping ground in the vicinity of bridges. 109

Bridge Watching This may be to help buttress the approaches, or supply bulk where needed. All granular solids, when poured into a heap, tend to adopt a sloping surface at an angle to the horizontal typical of the material, called the "angle of repose". A simple and convincing illustration of this may be seen in a sugar bowl. If the contents are disturbed, and sugar poured on from above, a conical heap is formed making an angle with the horizontal which is easily measured. Repeated trials will always produce the same result. If flour, instead of sugar, is used, then the angle will be different. If this angle of repose for a particular soil is exceeded, the soil will roll down the slope until its particular angle of repose is established. Hence, wherever we have sloping surfaces, we know in advance what angle will be stable. The sloping ground close to bridges never exceeds the angle of repose of the soil used. After the surface has been colonised by grasses and other plant life, it would be possible to add further material to steepen the slope, since the growth would hold the soil in position; but you are unlikely to see this. It might be noted that the angle of repose for wet soil is not the same as that for dry soil. This is easily confirmed by making piles of sand or soil of different condition. Mention was made earlier of the piers built in mid-stream to carry river bridges. They are easily seen, and you can see what a variety there is to enjoy. A bridge pier has a strange and difficult job in life. It has to stand still, with wet feet, holding up a massive structure which shakes a lot under heavy loading ; and when the river is in spate the water roars round it, trying to snatch it out of its bed and hurl it downstream. Before any pier is built the bed of the river must be thoroughly examined. We need to know how much sloshy mud and how much firm rock there is. If the bottom is slime, how far do we have to go down to find something solid? Does this solid material sustain a high bearing stress? We must so design the footing that the pier doesn't sink into the bed when the load comes on. The flotsam that comes downstream may contain trunks of trees, and other heavy material which can damage the pier. There may be shipping or other craft too, which might collide with the pier and cause serious damage. So the base must be protected against such hazards. Depending upon the site of the bridge, there may be cutwaters to reduce the buffeting from the water, or other forms of protection to be put around the base. You will see many different treatments. In some places there may be large tidal variations in the depth of water, and the bases of the piers will be correspondingly high. 110

Bridge Watching The piers themselves are struts or olumns , and may be hollow, of steel , brick or concrete. If they are of timber they are of special interest, as there are few to be seen nowadays. Not all bridges are built over flowing water, of course; but where they are, one of the dangers faced by the piers is the scouring action round the base. Engineers like to satisfy themselves about the proposed shape before construction, and calculations on scouring are difficult and not always reliable. This is where scale model techniques can be so very useful. Experiments can be conducted in a laboratory flume or water tunnel. A model pier squats on a bed of similar material in the channel, while a model flow does its worst. The results can give valuable information about the conditions in the real river. The technical content of this discussion has been pitched low deliberately. For deeper consideration of technical aspects there is a vast literature of books, papers and journals.

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Glossary Note : This is not intended to cover all the words used about bridges. Some words have been included that have not been mentioned earlier, as they are of general interest; and in some cases a fuller explanation or comment is supplied. Arches - Curved members or structures , using material in compression , the centre part rising above the level of the ends. They may be pinned at one end, at both ends, or at both ends and in the centre. The pinning of an arch rib ensures that there is no bending effect at that point, and permits movement to accommodate alterations of dimensions due to temperature changes. The chief feature of an arch bridge, apart from it being a handsome structure, is that at the abutments there are horizontal forces as well as vertical ones, so that the resultant reactions at the abutments are inclined to the vertical. The invention of the arch was a wonderful forward step in structural design. Bailey bridge - This is a structure composed of rectangular panels; each unit can be carried by half-a-dozen men and can be pinned to another panel. In this way, strong bridges can be assembled placing successive runs of panels alongside or above others. Although designed as an emergency structure, some Bailey bridges may still be seen. Military engineers consider the Bailey bridge as essential factor in victory in World War II. Since then, modern versions have been built all over the world. Bascule - A kind of balanced lever. Bascule bridges are usually found over rivers and canals. The roadway hinges about one end, the thick end, so that it may be swung up to permit passage of water-borne craft. There aren't many to be seen, but they are attractive in action. The balance is such that only a small amount of power is required to operate the mechanism. There aren't many large ones to be seen, but they are worth seeking. They are particularly attractive when opening and closing, and you might get an opportunity of seeing the mechanism itself if you approach the authorities. Beam - Any member that carries a transverse load, i.e. one that causes bending , as distinct from bowing, or buckling. A beam bridge consist of one or more beams, simply supported or built in at the ends. A long beam, may be supported from below by props , which may be erect or sloping. When the beam has a "free" end it is called a cantilever. Although superficially simple, the stress pattern within a beam is often complicated, calling for great care in placing reinforcement, when this is used. Deflections in beams can be reduced by increase of either width or depth. Long spans can undergo large bending moments near mid-span, and some beams may have significantly deeper sections there. Near the neutral layer material can be reduced, since the stress there is less. Steel beams may consist of a plate girder with much of the material of the web cut away, if the shear is modest. Bending - The change of shape when a straight or curved member is so loaded as to cause a change in the radius of curvature. The member is not necessarily horizontal, and may be vertical, or at any angle to the vertical. The amount of bending depends 112

Bridge Watching upon the dimensions and material of the member, and the magnitude of the bending moment , i.e. the force and its leverage. Bending, caused by transverse loading , is not to be confused with buckling , caused by axial loading. Bending is peculiar to beams, and the variation in bending effect, or "moment", determines the section at the different points along a beam. Although mostly horizontal, a beam can be at any angle. A telegraph pole is a beam, as it carries transvers loading. BSEA - The abbreviation used for the British Standard Equal Angle section. The steel mills at one time rolled vast quantities of this V-section material, in addition to other sections. The place to spot this is at a railway station. Masses of BSEA were used for foot-bridges. BSUA British Standard Unequal Angle. - The unequal angle refers not to the angle itself, which is 90°, but to the legs of the sections. At the steel rolling mills the billet of hot steel passes and repasses between rollers which shape the section. At one time there were few sections to be had, but there have been many changes. In older steel bridges there are many pieces of BSEA and BSUA. You will see this especially at railway stations and where small steel bridges cross the line. Rectangular hollow sections (RHS) and tubing is now used extensively. Buckling - The bowing of a strut due to the axial force exceeding the designed load. The safe load depends upon the ratio of the length of the member (L) to the radius of gyration (k) of its section. The value of k is a measure of the hollowness of the section, a tube or channel having a larger k than a solid section of the same area. The effective length L can be reduced by intermediate supports attached to the strut. The value of L/k is large for long slender struts and small for short stubby ones. Instability arises from large values of L/k. When the load increases beyond the critical value, the strut suddenly bows, i.e. adopts a curved shape. Built-in - The fixing of the ends of a beam so as to fix the direction there and thus reduce the bending moments along the span. Such beams are often refered to as "fixedend" beams. They are easily distinguished from "simply-supported" beams, which are free to tilt at the ends. Cantilever - A beam that "sticks out", supported at one end only. Cantilever beams may be seen in pairs, with their thick ends joined, sitting on a pier in a river. The feature of a cantilever is the zero bending moment at the "free" end, and maximum at the thick end. A natural example is a tree, fixed at its lower end, the upper end free, carrying the horizontal transverse wind loads. You may often see a cantilever used for a swing bridge, which is pivoted on one bank. Columns - Vertical supports that carry a compressive load. Some of the Victorian columns in iron are bridge-watchers' gems, with fanciful decorations cast in to the shape. They are still to be seen in old bridges. The classic columns in masonry are associated with the Greek and Roman eras. The plainest of these was the Doric, a sturdy column capable of carrying large loads. These could therefore be spaced more widely than the more delicate and decorative styles such as the Corinthian. 113

Bridge Watching You can identify the Corinthian style from the leaves at the top, and this is the kind most often chosen by the old bridge designers working in iron. Wonderful brick columns were used in some of the early railway bridges, those of long span in Cornwall being particularly impressive. The modern concrete column tends to be plain and severe in treatment. The principal requirement of a column is that it shall neither crush nor buckle under load. Further reference to this is made under "Struts". Compression - The squeezing of material by external forces. Compression is always present somewhere in every bridge. When this kind of stress is present, tension and shear also occur. Columns and footings carry compressive loads. In beams the upper part of the member is under compression. Piers carry compressive loads over their cross-sections. In girders the struts are in compression. Most materials are strong in compression, but a strut may fail by buckling , the member curving out of its original alignment. Demolition sites often provide examples of compression failure, though you should seek permission and tread warily, at such sites. Continuous beam - When a beam runs across several supports it is said to be "continuous". Such a beam can be of smaller dimensions than one supported at the ends only since the effective span is less. If the beam is discontinuous, there is no bending effect at the supports, and the ends are free to move. Each part, therefore, is not helped by its neighbours. In choosing whether to make a beam continuous or not the designer takes several factors into account. For example, savings on beam section have to be balanced against the costs of the supports. A very long continuous beam may involve large changes in overall length with variations in temperature. Contraflexure - When part of a beam is bent one way and part the other way, the place where the curvature changes from one to the other is called a point of contraflexure. It is like the middle part of the letter "S". At this point the bending moment falls to zero. A good idea of what this is like can be seen by laying a thin lath across a support, so that both ends drop downwards, and then lifting one end till it bends the other way, i.e. one part is curved upwards. When a continuous beam passes over a support it is concave downwards, whereas between supports it is concave upwards. Points of contraflexure occur where the concavity changes from upwards to downwards. Since there is no bending effect at points of contraflexure, pins could be fitted there without loss of strength. Couple - A pair of equal, parallel and opposite forces which are not in the same straight line. A couple provides a pure torque or turning effect. The value of the couple is given by the joint turning effects of the forces about the mid-point between them, which is the same as the product of their distance apart and one of the forces. Sometimes it can be convenient to introduce the idea of a couple to an arrangement of forces to make clearer what is happening. As a simple example, consider the following: Suppose a force P acts down on the end of a cantilever of length L. Apply equal and opposite vertical forces P1 upwards and P2 downwards at the support. (On their own these would have no effect.) 114

Bridge Watching Then P and P1 together form a couple (P x L) tending to turn the beam , and the remaining force P2 tends to push the beam downwards. Thus, the load P has both rotating and translating effects on the beam. Deflection - Sometimes spelled "deflection", the amount of distortion of a member, for example the amount of sag of a beam at a point. Radial deflection is usually measured in radians. If you can handle diffrential calculus, when the deflection at points along a beam is a continuous function of distance across the span, successive differentiation yields interesting and useful information about slope and loading. Conversely, successive integration can yield values for deflection. Distributed load - The kind of load which is spread along part, or the whole length, of a member. If it is spread evenly it is referred to as a uniformly distributed or u.d. load, and is the commonest load on a bridge, due to its own weight. Wind loading is usually treated as a u.d. load. This is in comparison with "point loads", where loads are concentrated at points on the bridge, e.g. at the nodes of framed structures. Elasticity - That property of a material that returns it to its former shape after distortion. It is quantified by the stress that would be needed to cause a distortion equal to the original dimension. For most materials this is a theoretical figure, as fracture would occur at well below that stress. All materials behave elastically for a limited stress range; plastic distorsion occurs when this is exceeded. The measure of elasticity, the elastic modulus , for the materials used in a bridge, is of importance in design calculations. Tables of values of the elastic moduli are available for materials commonly used. Usually, the letters E, G and K represent direct, transverse and bulk moduli respectively. Expansion joint - Due to changes in temperature, and settling, there is need sometimes for members to move relative to one another, to avoid undue strains. An expansion joint allows for such movement. There are many varieties, some being simple overlapping breaks in a member. They are easily recognised. Extruded sections - Lengths of material with particular cross-sectional shape produced by squeezing metal or plastic through hardened dies of the shape sought. Very high pressures are involved in this process. See rolled sections. Complicated sections which cannot be produced by rolling are amenable to this process. It is largely used for aluminium sections. Fixed end - When the end of a beam is free to turn it is referred to as "simply supported"; but if it is restrained so that it cannot rotate the beam is said to have a "fixed end" or a " built-in end". At the abutments of a simply-supported beam the bending moment is zero, but restraining moments are present at the ends of a fixed-end beam. The fixing of the ends reduces the deflection that would otherwise occur, as is readily seen from diagrams of bending moment. 115

Bridge Watching Force - That which tends to cause change. It is not possible for a force to occur singly. Every force is opposed by an equal and opposite force, e.g., gravitational, inertia, friction. Gravity is really an inertia force, given by the product of the mass and the gravitational acceleration. It is referred to as the "weight" of an object. Elastic forces are important in bridge design, as every part of the bridge moves elastically to provide forces opposing those produced by the loading. Bridges are static affairs, so inertia forces are not normally of prime interest. Dynamic loading, however, may involve consideration of such forces, as does vibration. When the forces are known together with the area over which they act, the stresses and strains in the material can be considered. If limiting values of stress and strain are known , then for given forces, the areas can be determined. Gothic arch - An attractive pointed arch. Although popular in churches, the Gothic arch is rarely seen in modern bridges. You will have to look among the old bridges; but there are plenty still to be seen, for old bridges last a long time. The gothic arch was once much favoured for window and door openings in brick or stone walls, especially in ecclesiastic structures. Gusset plate - A piece of flat material to which members meeting at a node are attached. Look for them on wooden girder bridges and steel frames. On the older railway bridges you can see them, with the round heads of rivets showing how they are fixed to the members. As rivetting gave way to welding you can see gusset plates with fillet welds at nodes of steel frames, on later structures. Influence line - A line drawn to show how some quantity varies as unit load crosses a bridge. For example, the influence line for say the left-hand reaction of a beam would be a triangle, of unit height at the left-hand end, decreasing to zero at the right-hand end. This would show that as unit load crossed the span the left-hand reaction would fall away to nothing when the load reached the right-hand abutment. Again, suppose we drew the influence line for the force in a particular member. Then if a train of loads crossed, the sum of the heights of the influence line under each load would give the total force in that member for the chosen position of the train. With a suitable computer program the train could be moved about to find the maximum load in that member. This can be especially useful for the case of two trains crossing at the same time in opposite directions, a tedious calculation otherwise. Influence lines can be drawn for shear at a particular point, bending moments, and so on. Keystone - The stone which completes an arch. It is at the top in the middle, usually given some prominence because of its importance. When a stone or brick arch is being 116

Bridge Watching built a wooden framework is first set up, on which the blocks are laid, starting at the abutments. When the top is reached and the keystone fitted the framework may be removed. Were the keystone to be removed an arch would collapse. Hence its importance. However, not all keystones are what they seem. Sometimes a purely decorative stone is fitted to an arch that owes its support to some other form of construction. The keystone, real or decorative, is a stone wider at the top than at the bottom and is easily recognised. Many arches have false keystones, which are purely decorative, sometimes in metal. They add pleasing touch to the crown of an arch. Loading - A system of forces applied to a structure. Many of these occur so often that in some design offices they can be standardised. Rolling loads such as railway trains are particular examples. The word is applied to the forces in individual members, too. A member is said to be "loaded" when a force is exerted on it. A structure is loaded when it bears the forces imposed on it by its own weight and/or external forces such as travelling loads, wind and thermal effects. Modulus - A measure. In the study of materials the chief measures of elasticity for example are the direct, transverse and bulk moduli. Commonly, when reference is made to an elastic modulus, or modulus of elasticity, it means the direct modulus, sometimes called "young's modulus". Moment - Importance. For example, the importance of a force in producing bending at some point is called the "bending moment", or even just the "moment". In structural work, when reference is made to the moment of a force it is taken to mean the bending effect of that force. Moorish arch - A very pretty arch much favoured east of Suez. Although possessing no particular structural virtue it is pleasing to the onlooker. The bridgewatcher is unlikely to see such arches other than in oriental buildings, to bridge over door and window openings. Sometimes the façade of a moorosh arch may be superimposed upon a semicircular arch. Moving load - A load which travels across a bridge, e.g., a train of wagons or vehicles, as distinct from a "dead" load such as the weight of the structure itself. Some times we speak of "live" loads in the same way. It may be noted that when a fast train suddenly comes onto a bridge the stresses are instantaneously twice what they would be were the train to be slowly loaded onto it. Influence lines offer a ready mean of assessing the effects of moving loads. Post-stressing - Pulling on the reinforcing rods in a concrete beam after the concrete has set.

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Bridge Watching This puts a higher stress in the rods and a compressive stress in the concrete to avoid tension in the concrete when the bridge is loaded. You are not likely to be able to tell by just looking whether or not this technique has been used, but you might see the forces being applied during construction. Usually the arrangements for applying post-tensioning are not visible once the span has been completed. Pratt truss - A truss made from panels, in which the members form the letter "N". This is a popular truss, and there are plenty about, in both timber and steel. At the nodes, the members may be pinned to permit free movement to accomodate thermal stress and deformation due to loads generally. The upper horizontal members are usually struts, and the lower ones ties, and may be of different section. Pre-stressing - Pulling on the reinforcement in a concrete beam before the concrete has been placed. The rods are thus under stress even before the load comes onto the bridge. As for post-stressed work, there is usually no visible indication in the finished bridge. The pre-stressing process means that when the member is complete and the prestressing forces removed, the rods return towards their former length, improving compressive loading on concrete otherwise in tension. This reduces the tendency to the formation of cracks on the tension face. Prop - An extra support under a beam to reduce the bending moment and deflection at that point. On motorways they are often splayed to clear the carriageway. They come in great variety, and you may find some interest in deciding why a particular style was chosen in each case. If you imagine a prop removed you will probably see that under load the roadway would sag at that point. The prop reduces the deflection that might otherwise occur here. Reaction - The response to an action, or applied force , i.e. the reactive, opposing or balancing force. Sometimes pairs of forces are referred to as the action and reaction. Every force invokes an opposing force, without which it cannot exist. So a reaction is the natural accompaniment to any force, whether it be physical, mental, demographic, spiritual, or any other kind. "Action" and "reaction" are words which must occur in pairs, since neither can exist without the other. Reinforcement - Material which strengthens another material. It usually refers to the steel rods or mesh inside concrete structures. Other substances can be used, however, such as nylon, bamboo and glass. Members weak in tension can be reinforced with materials of high tensile strength. Although the reinforcement is usually buried within the concrete or rather material, you may see it made up before pouring. The rods are sometimes formed with helical or other excrescences to give them a grip on the concrete. Rolled section - Ingots of metal can be shaped, usually while hot, by passing the material between shaped rollers to produce strips, channel sections, angles and so on, standard shapes useful in construction work. The properties of such rolled sections are 118

Bridge Watching listed in tables available to designers, greatly facilitating the choice of shapes for particular jobs. See extruded sections. Tables of rolled sections are readily available, and you may find it instructive to examine such tables, to see the choice available to the structural engineer. Shear - The sliding of one layer of a material relative to another layer. Shear stress is an important factor in the strength of beams , where the shear force diagram is used to show the variation of shear along the span. Where shear stress exists it induces tensile and compressive stresses at an angle to that of the shear stress. Shear loading may therefore lead to failure in tension and compression if the material is weak in respect of such stresses. Skew bridge - A bridge that crosses a gap at an angle other than 90°. Skew bridges in brick are very attractive, giving scope for the art of the bricklayer. Although expensive, there are savings on the construction of approach roads and bends otherwise required. Where a roadway approaches a crossing at an acute angle the bends required to accomodate a crossing at right-angles would necessitate much extra roadway. Stanchion - An upright prop or supporting member, often a rolled section , or built up from rolled sections. The word is used loosely for steel columns or tubular pillars. Strain - A measure of change of shape. It is expressed as a fraction or ratio of the change to the original dimension. Thus, a tie of length 200 which is stretched a distance of 4 suffers a strain of 4/200 or.02. If within the elastic limit it is an elastic strain, the sort normally encountered in bridges. If the elastic limit is exceeded plastic strain is encountered, which is irrecoverable. When, for a given material, stress is plotted against corresponding strain the resulting stress/strain curve is straight at first, but bends over when the elastic limit is reached. Stress - The amount of force taken on unit area. So a force of 300 on an area of 5 imposes a stress of 60, if uniformly applied. In many members the stress is nonuniform. For example, in a beam the stress on a vertical section varies from maxima at the upper and lower faces to nothing at the neutral layer. In bridge design, the materials available have been tested, and their behaviour under stress is known. The limiting stresses under steady and varying loads are known and recorded. Where materials are subjected to fluctuating stress they may fail due to fatigue, at stress values well below that sustainable in steady conditions. Structure - An assembly of components to fulfil particular requirements. Materials are just materials before they are put together in the desired way to form a structure. The word is used also when referring to the assembly of the atoms and the molecules inside a material, and indeed any arrangement of discrete parts. Bridges are structures of great variety, though all serve the same purpose, providing access over some obstacle. Modern motorways require hundreds of bridges of more-or-less standard design; but elsewhere there is entrancing diversity.

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Bridge Watching Strut - A member that shortens under load. Struts must be designed to resist compression and buckling. You may sometimes see a strut composed of several slender members held wider apart in the middle than at the ends by a spacer, where lightness is important. Perhaps the most prominent struts of all are the pylons on suspension bridges which are really huge struts, resisting the heavy vertical loads imposed by the suspension cables. In framed structures the identification of struts by the bridgewatcher requires some thought. Tension - The pulling of a member or part of a member, resulting in an increase of length. All ties are in tension, as well as one side of beams. Tensile stress results in tensile strain. Tensile stress is accompanied by compressive stress at right-angles, and shear stress at 45°. Three-hinged arch - An arch with hinges at the abutments and one in the middle. This type of arch allows movement of the parts to accommodate changes due to temperature and settlement. You may have to look widely to see one, but they are easily recognised. They may be called "3-pinned" arches, but you may not be able to see the three "pins". Tie - A member designed to stretch under load. To a certain extent the cross-section shape is unimportant, unlike the strut, where the section affects the carrying capacity of the member. The end connections aim to ensure even distribution across the section for as much of the length as possible. Ties need not always be rigid members. A flexible connector such as cable or chain may be used as a tie. Truss - A number of components joined by their ends to form a framework to span a gap. Trusses may be of timber or metal. The Warren truss is a popular frame in which all members are of the same length, making a series of equilateral triangles. The Pratt, or N-girder is another commomly encountered type, easily recognised. Two-hinged arch - An arch that is hinged at the abutments only. Its shape alters with changes of temperature, inducing bending effects in the arch rib. In those conditions it is a redundant structure , no longer statically determinate. There is no bending effect at the abutments. For this kind of structure to be statically determinate one end would need to be free to move horizontally. Universal beam - A rolled steel section, generally called a "UB". Tables of these sections are available from steel stockists. For this type of section, the designer needs only to pick out the one that suits the conditions. Changes taking place from time to time may mean that the sections used in some older bridges may no longer be available, quite apart from dimensional changes occasioned by metrication. Universal column - A rolled section , generally called a "UC". Like the UB the properties of such sections have been listed for easy reference. There is some advantage in the simplification arising from the use of standard sections like this. 120

Bridge Watching Vibration - An oscillatory motion, when an object changes position and repeats this identical motion continuously with decreasing, constant or increasing amplitude (displacement each side of the mean position). Voussoir - A tapering stone or brick. They are to be seen in arches , and are attractive in themselves. Warren truss - A truss that consists of a top and bottom member with other members filling the space between with struts and ties forming "W"'s, so that every member is of the same length, and all the angles are 60°. See the entry under Truss.

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Bridge Watching

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Bridge Watching

143

Bridge Watching

144

Bridge Watching

145

Photos Note: These are samples of the bridges mentioned in the text.

Arch

Arched Piers

Beam 146

Bridge Watching

Brick

Brick Arch

Brunets 147

Bridge Watching

Columns

Concrete Bridge

148

Bridge Watching

Continuous Beam

Good plain functional design of a continuous beam bridge

Foot Bridge 149

Bridge Watching

Forth Railway Bridge

Approach section of bridge. Unusual places of girders on piers

Lattice Girder Bridge 150

Bridge Watching

Lattice Girder

Modern Concrete Arch

Old Iron Bridge

151

Bridge Watching

Piers

Riveted Street Bridge

Rumbling bridge traversing deep gorge

152

Bridge Watching

Rumbling, Scotland. Lower crossing is original bridge

Stone bridge, narrowed at crown, over Ceres burn

Stone Bridge over Ceres burn

153

Bridge Watching

Simple beam bridge (planks on girders) one burn at Ceres, Scotland

Simple Bridge

Sloping

154

Bridge Watching

Supported Beam

Suspension Bridges

The Normandy Bridge 155

Bridge Watching

Swing Bridge

Tay Bridge

156

Bridge Watching

A foot bridge well loaded

Y Prop

157

Bridge Watching Edmund W. Jupp The aim of the "Watching" series is to draw attention to some of the very interesting items around us, things that perhaps we don't notice as much as we might. The first was "Bridge Watching", and when this was put "on the Net" it produced, to the surprise of the author, such a pleasant flood of e-mail that another was written, called "Water Watching". This, too, was kindly received. So it was tempting to continue with the theme. Wherever we go we seem to meet bridges. Mostly we tend to use them almost without noticing them, except when we see a particularly striking example like the suspension bridge over the river Tamar in Devon. There is no attempt to cover everything about bridges, just enough to make a bridge a more interesting object for you, or your camera, or your paint-box. I do hope it will help you to enjoy bridges, wherever you see them. They are such nice comfortable things to watch, especially when you know something about them. As either a hobby or an intellectual pursuit bridge-watching has much to commend it, for people of all ages and persuasions. You don't have to pay a subscription. You can enjoy it on your own or in company, and weather is relatively unimportant. It doesn't need any special clothing or equipment. (If you like, you can use field glasses or cameras, and note-books; but they aren't essential). You need no training, no practice, no coaching. From all angles, bridge-watching is an attractive pastime, all over the world. Go out and enjoy these fascinating structures. You may find them addictive, in the nicest possible way.

Author Edmund W. Jupp (BSc (Eng), FIMech E) was born during the First World War in Sussex, England and received his early education at Brighton. After service in the 1939–45 war he worked in engineering and education, and travelled widely. He was appointed Principal of the Technical Institute in Guyana.

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