Structural engineering

“The purpose of the book is three-fold. First, I aim to help the general reader appreciate the nature of structure, the role of the structural engineer in man-made structures, and understand better the relationship between architecture and engineering. Second, I provide an overview of how structures work: how they stand up to the various demands made of them. Third, I give students and prospective students in engineering, architecture, and science access to perspectives and qualitative understanding of advanced modern structures — going well beyond the simple statics of most introductory texts. […] Structural engineering is an important part of almost all undergraduate courses in engineering. This book is novel in the use of ‘thought-experiments’ as a straightforward way of explaining some of the important concepts that students often find the most difficult. These include virtual work, strain energy, and maximum and minimum energy principles, all of which are basic to modern computational techniques. The focus is on gaining understanding without the distraction of mathematical detail. The book is therefore particularly relevant for students of civil, mechanical, aeronautical, and aerospace engineering but, of course, it does not cover all of the theoretical detail necessary for completing such courses.”

The above quote is from the book‘s preface. I gave the book 2 stars on goodreads, and I must say that I think David Muir Wood’s book in this series on a similar and closely overlapping topic, civil engineering, was just a significantly better book – if you’re planning on reading only one book on these topics, in my opinion you should pick Wood’s book. I have two main complaints against this book: There’s too much stuff about the aesthetic properties of structures, and the history- and development of the differences between architecture and engineering; and the author seems to think it’s no problem covering quite complicated topics with just analogies and thought experiments, without showing you any of the equations. As for the first point, I don’t really have any interest in aesthetics or architectural history; as for the second, I can handle math reasonably well, but I usually have trouble when people insist on hiding the equations from me and talking only ‘in images’. The absence of equations doesn’t mean the topic coverage is dumbed-down, much; it’s rather the case that the author is trying to cover the sort of material that we usually use mathematics to talk about, because this is the most efficient language to use, using different kinds of language; the problem is that things get lost in the translation. He got rid of the math, but not the complexity. The book does include many illustrations as well, including illustrations of some quite complicated topics and dynamics, but some of the things he talks about in the book are things you can’t illustrate well with images because you ‘run out of dimensions’ before you’ve handled all the relevant aspects/dynamics, an admission he himself makes in the book.

Anyway, the book is not terrible and there’s some interesting stuff in there. I’ve added a few more quotes and some links related to the book’s coverage below.

“All structures span a gap or a space of some kind and their primary role is to transmit the imposed forces safely. A bridge spans an obstruction like a road or a river. The roof truss of a house spans the rooms of the house. The fuselage of a jumbo jet spans between wheels of its undercarriage on the tarmac of an airport terminal and the self-weight, lift and drag forces in flight. The hull of a ship spans between the variable buoyancy forces caused by the waves of the sea. To be fit for purpose every structure has to cope with specific local conditions and perform inside acceptable boundaries of behaviour—which engineers call ‘limit states’. […] Safety is paramount in two ways. First, the risk of a structure totally losing its structural integrity must be very low—for example a building must not collapse or a ship break up. This maximum level of performance is called an ultimate limit state. If a structure should reach that state for whatever reason then the structural engineer tries to ensure that the collapse or break up is not sudden—that there is some degree of warning—but this is not always possible […] Second, structures must be able to do what they were built for—this is called serviceability or performance limit state. So for example a skyscraper building must not sway so much that it causes discomfort to the occupants, even if the risk of total collapse is still very small.”

“At its simplest force is a pull (tension) or a push (compression). […] There are three ways in which materials are strong in different combinations—pulling (tension), pushing (compression), and sliding (shear). Each is very important […] all intact structures have internal forces that balance the external forces acting on them. These external forces come from simple self-weight, people standing, sitting, walking, travelling across them in cars, trucks, and trains, and from the environment such as wind, water, and earthquakes. In that state of equilibrium it turns out that structures are naturally lazy—the energy stored in them is a minimum for that shape or form of structure. Form-finding structures are a special group of buildings that are allowed to find their own shape—subject to certain constraints. There are two classes—in the first, the form-finding process occurs in a model (which may be physical or theoretical) and the structure is scaled up from the model. In the second, the structure is actually built and then allowed to settle into shape. In both cases the structures are self-adjusting in that they move to a position in which the internal forces are in equilibrium and contain minimum energy. […] there is a big problem in using self-adjusting structures in practice. The movements under changing loads can make the structures unfit for purpose. […] Triangles are important in structural engineering because they are the simplest stable form of structure and you see them in all kinds of structures—whether form-finding or not. […] Other forms of pin jointed structure, such as a rectangle, will deform in shear as a mechanism […] unless it has diagonal bracing—making it triangular. […] bending occurs in part of a structure when the forces acting on it tend to make it turn or rotate—but it is constrained or prevented from turning freely by the way it is connected to the rest of the structure or to its foundations. The turning forces may be internal or external.”

“Energy is the capacity of a force to do work. If you stretch an elastic band it has an internal tension force resisting your pull. If you let go of one end the band will recoil and could inflict a sharp sting on your other hand. The internal force has energy or the capacity to do work because you stretched it. Before you let go the energy was potential; after you let go the energy became kinetic. Potential energy is the capacity to do work because of the position of something—in this case because you pulled the two ends of the band apart. […] A car at the top of a hill has the potential energy to roll down the hill if the brakes are released. The potential energy in the elastic band and in a structure has a specific name—it is called ‘strain energy’. Kinetic energy is due to movement, so when you let go of the band […] the potential energy is converted into kinetic energy. Kinetic energy depends on mass and velocity—so a truck can develop more kinetic energy than a small car. When a structure is loaded by a force then the structure moves in whatever way it can to ‘get out of the way’. If it can move freely it will do—just as if you push a car with the handbrake off it will roll forward. However, if the handbrake is on the car will not move, and an internal force will be set up between the point at which you are pushing and the wheels as they grip the road.”

“[A] rope hanging freely as a catenary has minimum energy and […] it can only resist one kind of force—tension. Engineers say that it has one degree of freedom. […] In brief, degrees of freedom are the independent directions in which a structure or any part of a structure can move or deform […] Movements along degrees of freedom define the shape and location of any object at a given time. Each part, each piece of a physical structure whatever its size is a physical object embedded in and connected to other objects […] similar objects which I will call its neighbours. Whatever its size each has the potential to move unless something stops it. Where it may move freely […] then no internal resisting force is created. […] where it is prevented from moving in any direction a reaction force is created with consequential internal forces in the structure. For example at a support to a bridge, where the whole bridge is normally stopped from moving vertically, then an external vertical reaction force develops which must be resisted by a set of internal forces that will depend on the form of the bridge. So inside the bridge structure each piece, however small or large, will move—but not freely. The neighbouring objects will get in the way […]. When this happens internal forces are created as the objects bump up against each other and we represent or model those forces along the pathways which are the local degrees of freedom. The structure has to be strong enough to resist these internal forces along these pathways.”

“The next question is ‘How do we find out how big the forces and movements are?’ It turns out that there is a whole class of structures where this is reasonably straightforward and these are the structures covered in elementary textbooks. Engineers call them ‘statically determinate’ […] For these structures we can find the sizes of the forces just by balancing the internal and external forces to establish equilibrium. […] Unfortunately many real structures can’t be fully explained in this way—they are ‘statically indeterminate‘. This is because whilst establishing equilibrium between internal and external forces is necessary it is not sufficient for finding all of the internal forces. […] The four-legged stool is statically indeterminate. You will begin to understand this if you have ever sat at a fourlegged wobbly table […] which has one leg shorter than the other three legs. There can be no force in that leg because there is no reaction from the ground. What is more, the opposite leg will have no internal force either because otherwise there would be a net turning moment about the line joining the other two legs. Thus the table is balanced on two legs—which is why it wobbles back and forth. […] each leg has one degree of freedom but we have only three ways of balancing them in the (x,y,z) directions. In mathematical terms, we have four unknown  variables (the internal forces) but only three equations (balancing equilibrium in three directions). It follows that there isn’t just one set of forces in equilibrium—indeed, there are many such sets.”

“[W]hen a structure is in equilibrium it has minimum strain energy. […] Strictly speaking, minimum strain energy as a criterion for equilibrium is [however] true only in specific circumstances. To understand this we need to look at the constitutive relations between forces and deformations or displacements. Strain energy is stored potential energy and that energy is the capacity to do work. The strain energy in a body is there because work has been done on it—a force moved through a distance. Hence in order to know the energy we must know how much displacement is caused by a given force. This is called a ‘constitutive relation’ and has the form ‘force equals a constitutive factor times a displacement’. The most common of these relationships is called ‘linear elastic’ where the force equals a simple numerical factor—called the stiffness—times the displacement […] The inverse of the stiffness is called flexibility”.

“Aeroplanes take off or ascend because the lift forces due to the forward motion of the plane exceed the weight […] In level flight or cruise the plane is neutrally buoyant and flies at a steady altitude. […] The structure of an aircraft consists of four sets of tubes: the fuselage, the wings, the tail, and the fin. For obvious reasons their weight needs to be as small as possible. […] Modern aircraft structures are semi-monocoque—meaning stressed skin but with a supporting frame. In other words the skin covering, which may be only a few millimetres thick, becomes part of the structure. […] In an overall sense, the lift and drag forces effectively act on the wings through centres of pressure. The wings also carry the weight of engines and fuel. During a typical flight, the positions of these centres of force vary along the wing—for example as fuel is used. The wings are balanced cantilevers fixed to the fuselage. Longer wings (compared to their width) produce greater lift but are also necessarily heavier—so a compromise is required.”

“When structures move quickly, in particular if they accelerate or decelerate, we have to consider […] the inertia force and the damping force. They occur, for example, as an aeroplane takes off and picks up speed. They occur in bridges and buildings that oscillate in the wind. As these structures move the various bits of the structure remain attached—perhaps vibrating in very complex patterns, but they remain joined together in a state of dynamic equilibrium. An inertia force results from an acceleration or deceleration of an object and is directly proportional to the weight of that object. […] Newton’s 2nd Law tells us that the magnitudes of these [inertial] forces are proportional to the rates of change of momentum. […] Damping arises from friction or ‘looseness’ between components. As a consequence, energy is dissipated into other forms such as heat and sound, and the vibrations get smaller. […] The kinetic energy of a structure in static equilibrium is zero, but as the structure moves its potential energy is converted into kinetic energy. This is because the total energy remains constant by the principle of the conservation of energy (the first law of thermodynamics). The changing forces and displacements along the degree of freedom pathways travel as a wave […]. The amplitude of the wave depends on the nature of the material and the connections between components.”

“For [a] structure to be safe the materials must be strong enough to resist the tension, the compression, and the shear. The strength of materials in tension is reasonably straightforward. We just need to know the limiting forces the material can resist. This is usually specified as a set of stresses. A stress is a force divided by a cross sectional area and represents a localized force over a small area of the material. Typical limiting tensile stresses are called the yield stress […] and the rupture stress—so we just need to know their numerical values from tests. Yield occurs when the material cannot regain its original state, and permanent displacements or strains occur. Rupture is when the material breaks or fractures. […] Limiting average shear stresses and maximum allowable stress are known for various materials. […] Strength in compression is much more difficult […] Modern practice using the finite element method enables us to make theoretical estimates […] but it is still approximate because of the simplifications necessary to do the computer analysis […]. One of the challenges to engineers who rely on finite element analysis is to make sure they understand the implications of the simplifications used.”

“Dynamic loads cause vibrations. One particularly dangerous form of vibration is called resonance […]. All structures have a natural frequency of free vibration. […] Resonance occurs if the frequency of an external vibrating force coincides with the natural frequency of the structure. The consequence is a rapid build up of vibrations that can become seriously damaging. […] Wind is a major source of vibrations. As it flows around a bluff body the air breaks away from the surface and moves in a circular motion like a whirlpool or whirlwind as eddies or vortices. Under certain conditions these vortices may break away on alternate sides, and as they are shed from the body they create pressure differences that cause the body to oscillate. […] a structure is in stable equilibrium when a small perturbation does not result in large displacements. A structure in dynamic equilibrium may oscillate about a stable equilibrium position. […] Flutter is dynamic and a form of wind-excited self-reinforcing oscillation. It occurs, as in the P-delta effect, because of changes in geometry. Forces that are no longer in line because of large displacements tend to modify those displacements of the structure, and these, in turn, modify the forces, and so on. In this process the energy input during a cycle of vibration may be greater than that lost by damping and so the amplitude increases in each cycle until destruction. It is a positive feed-back mechanism that amplifies the initial deformations, causes non-linearity, material plasticity and decreased stiffness, and reduced natural frequency. […] Regular pulsating loads, even very small ones, can cause other problems too through a phenomenon known as fatigue. The word is descriptive—under certain conditions the materials just get tired and crack. A normally ductile material like steel becomes brittle. Fatigue occurs under very small loads repeated many millions of times. All materials in all types of structures have a fatigue limit. […] Fatigue damage occurs deep in the material as microscopic bonds are broken. The problem is particularly acute in the heat affected zones of welded structures.”

“Resilience is the ability of a system to recover quickly from difficult conditions. […] One way of delivering a degree of resilience is to make a structure fail-safe—to mitigate failure if it happens. A household electrical fuse is an everyday example. The fuse does not prevent failure, but it does prevent extreme consequences such as an electrical fire. Damage-tolerance is a similar concept. Damage is any physical harm that reduces the value of something. A damage-tolerant structure is one in which any damage can be accommodated at least for a short time until it can be dealt with. […] human factors in failure are not just a matter of individuals’ slips, lapses, or mistakes but are also the result of organizational and cultural situations which are not easy to identify in advance or even at the time. Indeed, they may only become apparent in hindsight. It follows that another major part of safety is to design a structure so that it can be inspected, repaired, and maintained. Indeed all of the processes of creating a structure, whether conceiving, designing, making, or monitoring performance, have to be designed with sufficient resilience to accommodate unexpected events. In other words, safety is not something a system has (a property), rather it is something a system does (a performance). Providing resilience is a form of control—a way of managing uncertainties and risks.”

Antoni Gaudí. Heinz Isler. Frei Otto.
Eden Project.
Bending moment.
Shear and moment diagram.
Pyramid at Meidum.
Master builder.
John Smeaton.
Puddling (metallurgy).
Cast iron.
Isambard Kingdom Brunel.
Henry Bessemer. Bessemer process.
Institution of Structural Engineers.
Graphic statics (wiki doesn’t have an article on this topic under this name and there isn’t much here, but it looks like google has a lot if you’re interested).
Constitutive equation.
Deformation (mechanics).
Compatibility (mechanics).
Principle of Minimum Complementary Energy.
Direct stiffness method. Finite element method.
Hogging and sagging.
Centre of buoyancy. Metacentre (fluid mechanics). Angle of attack.
Box girder bridge.
D’Alembert’s principle.
S-n diagram.


April 11, 2018 - Posted by | Books, Engineering, Physics

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