Structures: Or why things don’t fall down by J.E. Gordon

• A structure has been defined as ‘any assemblage of materials which is intended to sustain loads’, and the study of structures is one of the traditional branches of science.
• Structures can, and do, break, and this may be important and sometimes dramatic; but, in conventional technology the rigidity and deflections of a structure before it breaks are likely to be more important in practice.
• Structures are made from materials and we shall talk about structures and also about materials; but in fact there is no clear-cut dividing line between a material and a structure.
• In other words, a force cannot just get lost. Always and whatever happens every force must be balanced and react by another equal and opposite force at every point throughout a structure. This is true for any kind of structure, however small and simple or however large and complicated it may be.
• In may structures, such as buildings, the load is carried in compression, that is by pushing.
• Thus if any structural system is to do its job--that is to say, if the load is supported in a satisfactory way so that nothing very much happens--then it must somehow manage to produce a push or a pull which is exactly equal and opposite to the force which is being applied to it.
• Every kind of solid changes its shape--by stretching or contracting itself--when a mechanical force is applied to it.
• All materials and structures deflect, to greatly varying extends, when they are loaded. The science of elasticity is about the interactions between forces and deflections.
• It is this change of shape which enables the solid to do the pushing bac.
• All materials and structures deflect, although to greatly varying extents, when they are loaded.
• It is important to realize that it is perfectly normal for any and every structure to deflect in response to a load.
• The science of elasticity is about the interactions between forces and deflections in materials and structures.
• When any structure deflects under load in the way we have been talking about, the material from which it is made is itself also stretched or contracted, internally, throughout all its parts and in due proportion, down to a very fine scale--as we know nowadays, down to a molecular scale. Thus, when we deform a stick or a steel spring--day by bending it--the atoms and molecules of which the material is made have to move further apart, or else squash together, when the material as a whole is stretched or compressed.
• If we think for one moment, it is obvious that the deflection of a structure is affected both by its size and geometrical shape and also by the sort of material from which it is made.
• Materials vary very greatly in their intrinsic stiffness.
• Other things being equal, a rod which is pulled in tension has a strength which is proportional to its cross-sectional area.
• In other words the ‘stress’ in a solid is rather like the ‘pressure’ in a liquid of a gas. It is a measure of how hard the atoms and molecules which make up the material are being pushed together or pulled apart as a result of external forces.
• Just as stress tell us how hard--that it, with how much force--the atoms at any point in a solid are being pulled apart, so strain tells us how far they are being pulled apart--that is, by what proportion the bonds between the atoms are stretched.
• The strength of a structure is simple the load which will just break the structure. This figure is known as the ‘breaking load’, and it naturally applies only to some individual, specific structure.
• The strength of a material is the stress required to break a piece of the material itself. It will generally be the same for all specimens of any given solid.
• The strong metals are rather stronger, on the whole, than the strong non-metals. However, nearly all metals are considerably denser than most biological materials. This, strength for weight, metals are not too impressive when compared with plants and animals.
• Stress = load / area
• Strain = extension under load / original length
• By the strength of a material we usually mean that stress which is needed to break it.
• Iron and steel usually vary in strength by only a few percent and very, vary rarely by anything like a factor of three or four, let alone seven or eight.
• Geometrical irregularities, such as holes and cracks and sharp corners, which had previously been ignored, may raise the local stress--often only over a very small area--very dramatically indeed. Thus holes and notches may cause the stress in their immediate vicinity to be much higher than the breaking stress of the material, even when the general level of stress in the surrounding neighborhood is low and , from general calculating, the structure might appear to be perfectly safe.
• When we see to ‘strengthen’ something by adding extra material we have to be careful we do not in fact make it weaker.
• Energy can exist in a great variety of different forms--as potential energy, as heat energy, as chemical energy, as electrical energy and so on.
• In our material world, every single happening or event of whatever kind involves a conversion of energy from one into another of its many forms.
• Energy can neither be created nor destroyed, and so the total amount of energy which is present before and after any physical transaction will not be changed.
• The bow is one of the most effective ways of storing the energy of human muscles and releasing it to people a missile weapon.
• This quality of being able to store strain energy and deflect elastically under a load without breaking is called ‘resilience’, and it is a very valuable characteristic in a structure. Resilience may be defined as ‘the amount of strain energy which can be stored in a structure without causing permanent damage to it’.
• A reasonable amount of resilience is an essential quality in any structure; otherwise it would be unable to absorb the energy of a blow. Up to a point, the more resilient a structure is the better.
• All elastic substances which are under load contain greater or less amounts of strain energy, and this strain energy is always potentially available for the self-destructive process which we call ‘fracture’.
• Since, when a solid is broken in tension, at least one crack must be made to spread right across the material, so as to divide it into two parts, at least two new surfaces will have to be created which did not exist before fracture. IN order to tear the material apart in this way and produce these new surfaces it is necessary to have broken all the chemical bonds which previously held the two surfaces together.
• The easiest structure to think about are generally those which have to resist only tensile forces--forces which pull rather than push--and, of these, the simplest of all are those which have to resist only a single pull: in other words unidirectional tension , the basic case of a rope or a rod.
• Since the function of a joint is to transmit load from one element of a structure to its neighbour, stress has somehow got to get itself out of one piece of material and then get itself into the adjoining piece; such a process is only too likely to result in severe concentrations of stress and consequent weakness.
• Creep in any material causes the stress to be redistributed in a manner which is often beneficial, since the more highly stressed parts creep the most.
• Out of all the different kinds of structures which might be made, the masonry building is, as we shall see, the only one in which a blind reliance on traditional proportions will not automatically lead to disaster. This is why, historically, masonry buildings were by far the largest and most imposing of the works of man.
• The basic condition for the safety of masonry is that the thrust line should always be kept well inside the surface of a wall or column.
• The structural function of an arch is to support the downard loads which come upon it by turning them into a lateral thrust which runs round the ring of the arch and pushes the voussoirs against each other. The voussoirs, naturally, push in their turn against the abutments or springings of the arch.
• The strength of any structure which is liable to fail because the material breaks cannot be predicted from models or by scaling up from previous experience.
• Buildings do not normally fail by reason of the material breaking in compression.
• The stresses in masonry are so low that we can afford to go on scaling them up almost indefinitely. Unlike most other structures, buildings fail because they become unstable and tip up; and for any size of building this can be predicted from a model.
• The American railways could be built quickly and cheaply because wooden trestle bridges were used very extensively to save the cost of earthworks.
• In practical terms, the purpose of a bridge is to enable heavy objects, such as vehicles, to cross over some kind of gap or chasm. Provided that the weight is supported in a safe manner it usually does not matter very much by what technical means this is done. As is turns out, there is a very considerable variety of structural principles which can be employed.
• A simple masonry arch can quite safely be built with a span of well over 200 feet.
• The cables of a suspension bridge take up the best shape automatically, because a flexible rope has no choice but to comply with the resultant of all the loads which are pulling on it. We can therefore determine the shape of the cables for a suspension bridge either by loading a model of it, or else by means of a fairly simple exercise with a thing called the ‘funicular polygon’ on the drawing board.
• A solid roof over one’s head is one of the prime requirements of a civilized existence, but permanent roofs are heavy and the problem of supporting them is really as old as civilization itself.
• The first problem in constructing a sailing ship is to erect some kind of mast upon which sail can be hoisted. The second, and much more difficult, problem is to keep that mask in place.
• A load which acts at right angles to the length of the beam is supported without putting any longitudinal force upon whatever is supporting the beam. This is essentially what all beams are for.
• A ‘cantilever’ is a beam one end of which can be considered as being ‘built in’ to some rigid support, such as a wall or the ground.
• A simply supported beam is one which rests freely on supports at both ends.
• Every beam must deflect under the load which is applied to it and it will therefore be destroyed unto a curved or bent shape.
• Material on the concave or compression face of a bent beam will be shortened or strained in compression. Material on the convex or tension face will be lengthened or strained in tension.
• If tension is about pulling and compression is about pushing, then shear is about sliding. In other words, a shear stress measures the tendency for one part of a solid to slide past the next bit: the sort of thing which happens when you throw a pack of cards on the table or jerk the rug from under someone’s feet.
• As long as they are not subjected to ‘unnatural’ loads, most animals can afford to be weak in torsion.
• Not only our legs, but virtually all bones, are surprisingly weak in torsion.
• When we stress a solid in tension we are, of course, pulling its atoms and molecules further apart. As we do so, the interatomic bonds which hold the material together are stretched, but they can be safely stretched only to a limited extend.
• Beyond about 20 percent tensile strain, all chemical bonds become weaker and will eventually come unstuck.
• The actual fracture nearly always takes place by shearing.
• As we said in the last chapter, both tensile and compressive stresses necessarily give rise to shears at 45 degrees; it is these diagonal shears which generally cause ‘compressive failure’ in short struts.
• All practical brittle solids are full of cracks and scratches and defects of one kind or another. Even if this is not the case when they are first made, such materials very soon become abraded from all sorts of virtually unavoidable causes.
• In general, fastenings like nails and screws do not much weaken timber, always provided that they are in place and fit tightly. Once they are removed, however, the resulting hole has a much more serious effect; and no doubt the same is true of knots in timber.
• The use of tubes is extremely popular both with engineers and with Nature, and tubular struts are very widely used for all sorts of purposes.
• In engineering structures, panels and shells are very often stiffened by means of ribs or stringers which are glued or riveted or welded to the plating, through this is not always the lightest or the cheapest way of doing the job.
• The acceptability of various materials changes with time in curious and interesting ways.
• Advanced devices require advanced materials, and the newer materials, such as high-temperature alloys and carbon fibre plastics, consume more and more energy in their manufacture.
• Every structure must be built so as to be ‘safe’ for what may reasonably be considered an appropriate working life.
• In most types of structure, rot and rust are very active agents of decay.
• However, with modern knowledge and methods of treatment, it should be possible to get a practically indefinite life from almost any kind of wood.
• Most metals corrode in service. Modern mild steel rusts very much worse tan Victorian wrought iron or cast iron, and so rust is, to some extent, a modern problem. Because the cost of labour is high, the cost of the painting and maintenance of steelwork is high. This is one good reason for using reinforced concrete, since steel embedded in concrete does not rust.
• One of the most insidious causes of loss of strength in a structure is ‘fatigue’: that is to say, the cumulative effect of fluctuating loads.
• Almost every structure has a tendency to turn out heavier than its designer intended. This is partly due to over-optimistic estimating in the wights office, but it is also due to a tendency on the part of almost everybody to ‘play safe’ by making each part just that much thicker and heavier than is really necessary.
• In nearly all accidents we need to distinguish two different levels of causation. The first is the immediate technical or mechanical reason for the accident; the second is the underlying human reason. It is quite true that design is not a very precise business, that unexpected things happen, that genuine mistakes are made and so forth; but much more often the ‘real’ reason for an accident is preventable human error.
• Nine out of ten accidents are caused, not by more or less abstruse technical effects, but by old fashioned human sin--often verging on plain wickedness.
• People do not become immune from the classical or theological human weaknesses merely because they are operating in a technical situation, and several of these catastrophes have much of the drama and inevitably of Greek tragedy.
• Engineers have to deal, not only with people and all their quirks and weaknesses, but also with physical facts. One can sometimes argue with people, and it is not difficult to deceive them; but it is of no use to argue with a physical fact. One cannot bully it or bribe it or legislate against it or pretend that the truth is something different or that the thing never happened at all.
• It may be the engineer’s job to point out that the emperor has no clothes on, but however embarrassing this may be, we clearly need more, not less, of this kind of realism.
• It is confidence that causes accidents and worry which prevents them. So go over your sums not once or twice but again and again and again.