by Roma Agrawal
Supporting a book using compression (above left) and tension (above right).
Conversely, if you take a piece of string, tie the book to one end and hold the other, the suspended book – still experiencing the force of gravity – is now pulling on the string. The force of the book flows up into the string, which is said to be in tension. This is the same effect that the weight of your hand has on your arm.
In the first example, the book doesn’t crash down onto the table because the paper tube is strong enough to resist the compression it feels. In the second example, it remains safely suspended because the piece of string is strong enough to resist the tension it feels.
To cause a collapse, use a heavier book. The new force exerted by this book on its support is larger because the weight of the book has increased. The tube is no longer strong enough, so it crushes and the book falls to the table. Similarly, if you try suspending the heavier book, the tension is too big for the string. The string snaps and the book plummets.
The forces in a bridge arise from its own weight, and from the weight of the people and vehicles that travel over it. When working on the Northumbria University Footbridge, I did calculations to find out where the forces were in the structure. As a result, I knew exactly how much compression or tension was at work in each part of it. I used a computer model to test every section of my bridge, then calculated how big the steel needed to be so it didn’t bend excessively, crush or snap.
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The type of force and the way it flows depends on how the structure is assembled. There are two main ways this can be done. The first is known as the load-bearing system and the second as the frame system.
Our early ancestors’ mud huts – which they made by forming mud into thick walls arranged in a circle or square – were built using the first method. The walls of these single-storey dwellings were solid, forming a load-bearing system: the weight of the structure was free to flow as compression throughout the mud walls. This is similar to the book resting on the paper tube, in which all sides of the tube are uniformly in compression. If additional storeys were added to the hut, at some point the compression would become too much for the load-bearing mud walls and they would crumble, just like the heavier book crushes the paper tube.
Two ways to build a home, using load-bearing walls (above left) or a skeleton frame (above right).
When our ancestors had access to trees, they built their homes using the frame system – by tying timber logs together to create a network or skeleton through which the forces are channelled. To protect the inside from the elements, animal skins or woven vegetation were suspended across the logs. Where mud huts had solid walls that bore the forces and protected the residents, the timber home had two distinct systems: the logs that carried the forces plus the ‘walls’ or the animal skins which carried no weight. The way in which forces are channelled is the fundamental difference between load-bearing and frame structures.
Over time, the materials we used to create load-bearing walls and frames for structures became more and more sophisticated. Load-bearing structures were made from brick and stone, which were stronger than mud. In the 1800s, after the Industrial Revolution, iron and steel could be manufactured at a large scale, and we started to use metals for building, rather than just for vessels and weaponry. Concrete was rediscovered (the Romans had known how to manufacture it, but that knowledge was subsequently lost when their empire fell). These moments of evolution changed our structures forever. Since steel and concrete are so much stronger than timber, and well-suited to creating large frames, we could build taller towers and longer bridges. Today, the largest and most complex structures – such as the graceful steel arch of Sydney Harbour Bridge, the triangular geometry of the Hearst Tower in Manhattan, and the iconic ‘Bird’s Nest’ National Stadium built for the 2008 Beijing Olympics – are created using the frame system.
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When I start designing a new building, I study the carefully crafted drawings from the architects which convey their vision of what the construction will look like once it’s finished. Engineers soon develop a kind of X-ray vision, enabling them to see through the building in the picture to the skeleton it would need in order to resist gravity and the other forces that test it. I visualise where the building’s spine will go, where the supporting bones need to be connected, and how big these need to be so the skeleton is stable. With a black marker pen, I sketch over the architects’ drawings, adding bones to the flesh. The thick, black lines I add to the colourful drawings add a certain solidity. Inevitably, there is much discussion – sometimes quite spirited – between me and the architects: we need to compromise to find a solution. Often, I need a column where they have shown an open space; at other times they think I need structure where I don’t – so I can give them more area. We have to understand each other’s perspectives when technical problems arise: we must reach a balance between visual beauty and technical integrity. Eventually, we arrive at a design in which structure and aesthetic vision are (almost) in perfect harmony.
The frames in our structures are made up of a network of columns, beams and braces. Columns are the vertical sections of the skeleton; beams are the horizontal ones, and the pieces at other angles – the braces – are usually called ‘struts’. If you look at a photograph of Sydney Harbour Bridge, for example, you’ll see that it’s formed of pieces of steel at all sorts of angles – a melee of columns, beams and struts. By understanding how columns and beams interact and support one another, how they attract forces and, most importantly, how they break, we can design them so they won’t fail.
The Sydney Harbour Bridge, completed in 1930, built to carry rail, vehicular and pedestrian traffic between the North Shore and the central business district of Sydney, Australia.
Although columns have been used to resist gravity for millennia; the Greeks and Romans turned them into an art form. Much of the beauty and the solidity of the Parthenon in Athens comes from its outer row of fluted Doric marble columns. The remains of the Forum in Rome are dominated by monumental columns that support the fragile remnants of temples, or which simply strike upwards, stunted, towards the sky. Of course, the columns fulfilled a very important practical function – holding up structures – but this didn’t stop ancient engineers from decorating them with carvings inspired by Nature and mythology. The Corinthian column, with its capital decorated by intricately curled leaves, was supposedly invented by the Greek sculptor Callimachus after he noticed an acanthus plant growing through and around a basket left upon the grave of a maiden of Corinth. There are dozens of examples of it dotted around the Forum, and it has remained a classic of civic architecture for centuries, grandly gracing the façade of the United States Supreme Court Building for example and, more humbly, the entrance to the Victorian block of flats where I live.
Two of the ways in which a column can fail, through crushing (above left) and bowing (above right).
Columns generally work by countering compression. One way they can fail is when they are squashed so much that the material they are made of simply gives up and crushes or crumbles – this is what happens to the paper tube when the heavier book is placed on top. The other way columns can fail is by bowing. Take a plastic ruler, stand it vertically on a table and then press down on it with the palm of your hand: you’ll see it begin to bow. The more you push down, the further the ruler will bow – until finally it snaps.
There is a delicate balance to be struck when designing a column. You want it to be thin so that it doesn’t take up too much space, but if it’s too slender the load it carries can cause it to bow. At the same time, you want to use a material that’s strong enough to prevent crushing. The columns used in ancient structures tended to be stocky, chunky things most often made from stone, and were unlikely to fail by bowing. By contrast, our modern steel or concrete columns tend to be far more slender, making them mostly susceptible to bowing.
Flexing a ruler shows how a slender structure bends along its weake
r axis (top), whereas a column, whether it’s made from concrete or steel, is shaped to resist bending in both axes (bottom).
A ruler is wide in one direction and flat in the other: as you’ll have seen as you pressed down, it bows about its much weaker axis. To stop this effect, modern steel columns are usually made in an H shape, and concrete columns in squares or rectangles so that both axes are comparably stiff – so the columns can resist larger loads.
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Beams work differently. They form the skeleton of the floors. When we stand on a beam, it flexes slightly, channelling our weight across to the columns that support it. The columns in turn compress and transmit our weight to the ground. If you stand on the centre of a beam, half of your weight, and half the weight of the beam is transmitted to each end. The column then transmits that load downward. We don't want beams to bend too much when we stand on them, partly because it feels uncomfortable when the floor is moving below our feet – but also because they can fail. We need to make beams appropriately stiff; using depth, geometry or specific materials to strengthen them.
A beam flexes when it bears any weight, with the top of the beam being squashed and the bottom of the beam being pulled.
To resist this flexing, beams are made in specific shapes.
When a beam bends under a load, the load flows unevenly through it. The top portion of the beam is squashed, while the bottom portion is pulled: the top of the beam is in compression and the bottom is in tension. Try bending a carrot in your hands: as you curve it into a U-shape, the bottom eventually splits. This happens when the tension force in the bottom of the carrot is too big for the carrot to resist. If you repeat this with carrots of different diameters, you’ll find that thinner carrots bend more easily. A carrot with a bigger diameter needs more force to bend it the same amount. Similarly, the deeper the beam, the stiffer it is, so the less it distorts under load.
Using clever geometry is another way to make a beam stiff. The highest compression force a beam experiences is right at the top, and the highest tension is right at the bottom. So the more material you put in the top or bottom of a beam, the more force it can take. By combining these two principles – depth and geometry – we arrive at the best shape for a beam: an I (i.e. in cross-section it resembles that letter), because the greatest amount of material is at the top and bottom, where the greatest forces flow. Most steel beams are I-shaped. (They are subtly different from H-shaped columns because they are deeper than they are wide, whereas H-shaped columns are closer to squares.) Concrete beams can also be made like this, but it is easier to pour concrete into a rectangular shape, so for reasons of cost and practicality most concrete beams are simple rectangles.
Large bridges like the Quebec Bridge are just too long to use a ‘normal’ I-shaped beam. To span the distance, such a beam would have to be so deep and heavy that it would be impossible to lift into place. Instead, we use another type of structure that harnesses the stability of triangles: the truss.
A square is an inherently weaker shape than a triangle.
Most trusses are made up of smaller triangular shapes, although occasionally some do use squares.
Take four sticks and tape the corners together to make a square. Then push it sideways: the square becomes a diamond and collapses. Triangles, on the other hand, do not deform and collapse in the same way. A truss is a network of triangles made up of beams, columns and struts, which cleverly channels forces through its members. And in creating a truss we use smaller and lighter pieces with gaps in the middle, so we use less material than we would for an equivalent I-beam.
Trusses are easier to build because smaller pieces of steel can be transported to the construction site and then joined together. Most large bridges have trusses somewhere. Take a look at the Golden Gate Bridge, for example: a pattern in the metal runs along the sides at road level for the length of the bridge. It looks like the letter N followed by a reversed N, one after another – a careful arrangement of triangles forming a truss.
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Gravity exerts a predictable pull on objects on the surface of the Earth. An engineer knows what it is, and can design columns, beams and trusses to resist it. But other, equally destructive forces are not so easily reduced to equations. One of these is the wind. Random, fluctuating, unpredictable, wind has challenged engineers throughout history, and it remains a problem all engineers have to solve if their structures are going to remain stable.
When I visited Athens, one of the monuments that I was most excited to see was a large white marble octagonal tower in the Roman Agora, just north of the Acropolis. Built around 50 BC by Andronicus of Cyrrhus, a Macedonian astronomer, the Horologion of Andronikos Kyrrhestes or ‘Tower of the Winds’ was a timepiece with eight sundials, a water clock and a wind vane. Taking a slow walk round the tower I could see that each of its sides had a relief at the top depicting one of eight Wind Gods, winged figures flying forwards with a stern or benign expression, and sometimes an amphora or garland of flowers in their arms. Originally a bronze statue of Triton stood on top of the tower and acted as a weathervane, pointing towards whichever Wind God was blowing.
The tower is a testament to the respect the Romans had for the wind and its potentially destructive force. The Roman master builder Marcus Vitruvius Pollio (born 80 BC), who is sometimes called ‘the first architect’, talks extensively about the importance of considering wind in De Architectura, his hugely influential ten-volume treatise on the design of structures. In Book 1 he tells us about the four main directions: Solanus (east), Auster (south), Favonius (west), Septentrio (north) – and the other four, which act in directions between the primary winds.
To me it seems amazing that Roman engineers already had such a deep understanding of how wind acts differently in different directions. Even though the way engineers calculate this is now much more sophisticated, the basis of our work was carved into the sculptures on that octagonal tower 2,000 years ago.
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Wind acts on structures everywhere on our planet. When I am working on a construction that is less than 100 metres tall, I typically use a wind map. This is essentially a weather map with contours that tells me what the basic wind speed is at a particular location, created using data measured over decades. I take the basic wind speed and combine it with other numbers that define, say, how far the place is from the sea, how high up it is, and the variability of the surrounding terrain (how hilly it is or how many buildings there are). Formulae combine these factors to tell me how much wind a structure will feel in 12 different directions – every 30 degrees around a circle – which is not far off the eight directions enumerated by Vitruvius and featured on the Horologion’s reliefs.
Horologion of Andronikos Kyrrhestes (Tower of Winds) built in the 2nd–1st centuries BC in Athens, Greece.
But when I design a larger structure, such as a skyscraper, the numbers on the wind maps no longer hold. Wind is not linear: it doesn’t change in a predictable way the higher you go into the atmosphere. Trying to extrapolate the data, or using mathematical trickery to adjust the numbers for 100-metre towers to fit 300-metre towers, will only produce unrealistic results. Instead, the structure has to be tested in a wind tunnel.
When I was working on the design of a 40-storey tower near the Regent’s Canal in London, I visited one such facility. The miniaturised world of the wind-tunnel testers is a marvel in itself. In Milton Keynes, modelmakers had created a scaled replica of my building that was 200 times smaller than the real thing would be. Not only that, they had also created tiny versions of all the other structures in the area, and the whole model sat on a turntable. The structures around my building were crucial to the data. If my tower was in the middle of a field, it would be hit directly by the force of the wind, unimpeded by any other object. In the middle of a metropolis, however, the densely textured cityscape with its mix of different structures affects the wind flow and turbulence, so the forces my building feels would differ.
I stood behind the model o
f my building and peered down the ‘tunnel’ – a long, square, smooth-walled passageway – towards the gigantic fan at the other end. It was set at the wind speed the building would feel from that particular direction. Once the cables connected to the apparatus were checked and the operatives ready, the fan was switched on. I braced myself as the blades whirred and a blast of chilly air shot through the miniature city in front of me, and hit me in the face. Inside the model of my building, thousands of sensors detected how much they were being pushed or pulled, and sent the numbers to a computer. The turntable was rotated by 15 degrees and the process repeated until the system had logged data from 24 directions. Over the next few weeks, engineers at the facility organised the data and prepared a report. I entered their numbers in my computer model to test my building. It was imperative that my structure remained stable against all the different effects that the wind could have on it, in every direction.
There are three ways in which wind can adversely affect a structure. First, if the structure above ground is light, wind can make it topple over, like the scattered traffic cones you see after a storm. Second, if the ground is weak, wind can cause the building to move and sink. Think of a sailboat on a windy day. The strength of the wind pushes the boat across the water – which of course is the desired effect if you’re out sailing. But you wouldn’t want your building or bridge to move sideways in the soil as the wind hits it. Now, soil is not as fluid as water, so you wouldn’t see a building floating past you in a storm (if you do see this, take my professional advice and run the other way). But soil can still be squashed and moved around, so engineers need to provide an anchor – foundations – to keep their buildings in place.