Basic Rules for Structures

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Introduction

The laws or rules referred to in this section are applicable to all objects and all structures that we are likely to see around us. In other words, they are consistent with classical physics, which is more or less the physics that was developed up to the end of the 19th century. The advent of quantum mechanics and relativity does not invalidate the use of classical mechanics as a very close approximation to reality in the regime of low speeds and large sizes. And classical mechanics is by no means exhausted: calculating the behaviour of complicated systems such as Saturn's rings is still a challenge.

Structures don't fall down because someone did not follow the the laws of physics:  no matter how you try, you cannot make anything that does not follow the laws of physics. Even while it is breaking, falling, or lying on the ground, your creation is following the laws. What actually goes wrong is not a divergence from any laws, but an attempt to get behaviour from materials and structures that is not compatible with the forces generated. So phrases like "conquering nature" are wide of the mark, in that we in fact have no choice but to work within the laws of nature.  

What is true is that people have faced, and in most cases overcome, enormous difficulties when building structures of all kinds. Injury, illness, psychological damage and death can result from tackling a great problem, though technology has reduced some of the physical hazards. Although we don't fight natural laws, we do have to combat their manifestations in the form of fire, flood, rockfall, pressure, temperature and so on. Great courage has often been needed to invent, design, promote and build large structures.  

Not all obstacles are natural - opposition may be met from people who are too conservative, too bold, or too ignorant, and from people who are protecting an interest, expressing rivalry or envy, and so on.  

"It can't be done." is a sentence that many engineers have heard. Sometimes it is a death sentence for a project. Nevertheless, the statement is sometimes correct at the time it is uttered.

Forces

What is a force? It is easier to say what a force does than to say what it is. A single force acting on an object will change its shape and change its velocity. The only lone force we can experience on earth is weight: all other forces are accompanied by weight. If we drop an object we see that the velocity is changed, but we do not see a change of shape. That is because weight is not a single force such as we mentioned above: every single atom in an object is pulled by its own weight, and the whole object retains its shape when accelerating freely under gravity.

The last statement shows how difficult it is to make a true statement, for although it is almost correct, it needs qualification. The shape of an object is only constant in a uniform field. Real fields are non-uniform, because of the inverse-square law, and this affects the orientation of an orbiting object. The forces on a large do distort it, measurably. In the earth, the changes in shape are, mainly in the sea and the atmosphere, are called tides.

If we take a spacecraft far away from any stars and planets, and then fire its rocket engine, the spacecraft will be very slightly compressed along the axis of the rocket engine. The compression will be greatest near the engine, falling to nothing at the far end. Similarly, if a spaceman pushes or pulls a floating object, it will indeed minutely change shape as well as changing its velocity. Another example is the deformation and acceleration of a golf ball by a heavy club, which is shown below, though the shapes are not realistic.

Note that the distortion of the ball is unavoidable, and indeed essential, as we shall see later. The club head is distorted too, but very much less, because it is more rigid.

Action and Reaction

Why is the club head distorted? It is distorted because the ball exerts a force on the club which has the same magnitude as the force of the club on the ball. This is always true. Forces always occur in pairs. This is easier to show if we separate the two objects as shown below.

At the impact, the club is slightly distorted and makes a slight negative acceleration.

Stress and Strain

Why are the distortions necessary? They are necessary because an object in its normal state does not exert a force on anything else. This sentence illustrates the difficulty of framing even one correct sentence. We should have written that a completely isolated object does not exert a force on anything else. Most real objects on earth push on the ground because of gravity, and are equally pushed by the ground. Objects also push on the air, and are pushed equally by it, as a result of air pressure. 

In order to create a push or a pull, the atoms of the object must crowd closer or separate very slightly, compared with their separations when the object is isolated. When the object reaches equilibrium, every atom must experience equal and opposite forces, so if you push the surface, the surface atoms will move until the next layer pushes back enough to balance them. The same process happens with the next layer, which is in turn pushed by its next layer, and so it goes; the entire object is very slightly compressed. We say that the object is stressed (There are forces inside it.) and strained (Its shape is changed.).

The process just described seems to act instantly, but it doesn't. Normally we handle only quite small objects, but if we could work with very long parts we would find that pushing and pulling forces are transmitted at the speed of sound in the material. In steel, for example, the speed of sound is about 6000 m/s, much faster than the speed of sound in air, which is about 330 m/s at 0 celsius. Shear waves in steel travel at about 3200 m/s. In reality, it is rare for a force to be applied to a surface quickly enough for the transmission time through the material to be a consideration. Nevertheless, the infrequency of a phenomenon is of no help in a case when it actually happens: we must never become complacent.

The speed of transmission may seem very high, and not very important, but in structures of all sizes we need to be aware that waves and oscillations are an ever present possibility which can become destructive.

There are other wave speeds in a structure besides the ones mentioned above. Those speeds just referred to. These are related to large scale bending and torsion. For example, if a bridge with a span of 1000 metres oscillates with a period of 10 seconds, the speed of the waves is 1000 / 10 = 100 metres/second. The oscillations do not look like waves, but they are. They are the result of equal waves travelling in opposite directions.

Multiple Forces

We said earlier that single forces are seldom experienced, and what we normally see is the result of two or more forces. In every structure, every part is acted on by two, and usually more, forces, and one job of the designer is to ensure that all these forces can exist in equilibrium without any part of the structure exceeding its safe limits. As we stated earlier, objects deflect until the internal forces balance the external ones. If a component breaks, or deflects to an unacceptable extent, before the component has been able to balance the external forces, then we need to redesign the component.

Acceleration

Forces produce acceleration. Bridges don't accelerate, do they? Oh yes they do. They don't sit there in motionless meditation: they may be buffeted by winds or pushed by turbulent water, or rammed by floating ice or wood, and of course they are subjected to the varying forces exerted by the live loads, or traffic. These forces cause acceleration and therefore velocity, but the bridge doesn't drift away, firstly because the bridge is fixed to the ground, and secondly because the loads are transient - they don't last. 

What a bridge does do under the action of external forces is to move until the deflection has created forces that balance the applied ones. By the time this happens, the bridge is moving, and its momentum takes it past the equilibrium point. Eventually the motion will reverse, and it will eventually overshoot in the opposite direction. It will, in fact, oscillate. All structures are subject to more or less random vibration, usually so limited as not to threaten the integrity of the system. One means of reducing oscillation is to introduce damping mechanisms which absorb energy from the structure. This was done with London's millennium bridge, after unexpected swaying occurred when many people walked across.

But relatively small varying forces can ultimately destroy a part through the mechanism of fatigue, which is a gradual change in the internal arrangement of atoms, resulting in different structural properties. Luckily, with steel, by keeping the stresses low enough, we can ensure that fatigue never occurs. Not so with aluminium based alloys: with them there is no fatigue limit - we merely trade the stress against the number of cycles to failure.

Rotation

The only bridges that rotate are those that open for navigation. For stationary structures, allthough we already saw that forces can be balanced to create equilibrium, there is more to it than that. Not only must add up to zero, they must also be aligned in such a way as to avoid rotation. To understand this we need the idea of moment. The moment of a force about a point is the product of the size of the force and the distance from the force to the point, as measured in a direction perpendicular to the direction of the force. This product is popularly called leverage.

Basic Rules Formally Stated

If you would like to see the basic rules more formally stated, read on.

Newton's Laws of Motion

1   The motion of an object is unchanged in the absence of force.

2   Force = mass x acceleration.

3  Every force has an equal and opposite reaction.

Conservation Laws

1  Conservation of Energy

2  Conservation of Momentum

3  Conservation of Angular Momentum

Notes

Newton's third law implies that when we look at the boundaries of a structure, the forces do not stop there: they are opposed by forces in the ground. And those forces also have no end. The force field created by a structure in principle spreads throughout the entire earth. In practice, of course, the forces spread out until they become undetectable. One job of the engineer is to make sure that every part of the structure and the foundations and the ground can sustain the forces they are subject too. In poor ground, a deep foundation is needed to take the forces to the point where the ground can take over.

Particularly important in this respect are dams and the reservoirs they create. The huge masses of water make huge changes in the distribution of stresses in the ground, spreading far beyond the visible areas.

The three conservation laws may look arbitrary, but in fact each one corresponds to a symmetry principle.  These principles are as follows.

1  The laws of the universe do not change with time.

2  The laws of the universe do not change with a change of position.

3  The laws of the universe do not change with a rotation.

Physics includes other symmetry principles, but they do not affect structural engineering. One of these other symmetry/invariance principles says that the laws do not change under a time-reversal operation. This still causes much discussion, partly because it does not seem to correspond to our perception of time. The parts of a broken bridge do not re-assemble themselves, no matter how long we wait. The only known manifestations of time asymmetry seems to occur in a single example in elementary particle physics.

Knowing the rules of any discipline, be it engineering, chess or cricket, is not enough. One needs experience, practice, imagination and creativity. People who think of technical people as uncreative are very wide of the mark.

 

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