From Cave to Skyscraper
THIRTY THOUSAND YEARS AGO, people roamed from place to place hunting animals for food and looking for wild plants to eat. As they were always moving, they did not build houses. They slept under the stars, got wet under the rain, sweated under the sun, and cooked their meals over open wood fires. Much later on, they began to put up shelters, tents made of animal skins, and tried to protect themselves from the weather. If they were lucky and roamed in mountainous areas, they might find caves where they could cook and sleep. Caves were better places to live in, but tents had the advantage of being easily moved. If the supply of animals or wild plants ran out, men and women could pull up stakes and set up housekeeping where there was more food. They literally "pulled up stakes" because they had found that, without ropes anchored to the ground, their tents could be blown away by the wind. So they fought the force of the wind and stiffened the tent by means of fiber-ropes attached to stakes driven into the ground (Figure 1.1), just as we do today when we go camping.
Of course, for people to be able to live under the tent, a pole made out of a tree branch had to support the top at the center, and the taller the pole, the taller the tent. It would have been comfortable to use poles tall enough to allow men to stand up under the tent, but it was not easy to do this.
If the pole were tall and thin it might bend and collapse under a high wind pressure or when the ropes were pulled too hard (Figure 1.2). If the pole were thick, it would not collapse but would be heavy and hard to carry. The tent people had to be satisfied with thin, short sticks that were both light and stiff, so they could not stand up straight under their tents.
To make sure the wind would not pull out the stakes they also set heavy stones on the skin all around the bottom of the tent. The tent wouldn't blow away unless the wind could lift the weight of the stones and then pull out the stakes. The heavier the stones, the stronger the wind had to be to move them.
A few more thousands of years went by, and about ten thousand years ago people slowly began to learn a new way of getting food. Instead of eating wild plants, like rice that grew by itself in certain spots, they learned to plant vegetables, wheat, barley, millet and rye, to water them, to tend them, and to grow enough to feed their families without ever moving camp. At the same time they learned to catch wild animals and to feed and keep them in captivity. They domesticated dogs, asses, oxen, horses, and turkeys and thus provided meat as well as vegetables and grain for themselves and their families without having to be on the move all the time. Humankind had discovered agriculture.
When early men and women had to break camp often and carry tents on their backs, they could not have very comfortable homes. But once they had found ways of staying in one place, they started to think of building shelters that were larger, stronger, and more comfortable than tents. As they learned to farm, they slowly became builders and their houses became larger and taller.
Each family had its own permanent home. In cold climates it was usually made out of logs or stones set one on top of the other. In moderate climates it was built of mud mixed with straw, a material called adobe, while in hot climates it was made out of wood poles and thatched roofs (Figure 1.3). When many families lived near one another, their houses made up a village. In order to meet together and discuss common problems, the village people built large buildings that served both as their town halls and their churches (Figure 1.4). To get from one house to another, they maintained well-kept paths, and, eventually, to go from village to village, they built roads. Since the roads often crossed deep rivers or rivers that flooded in the spring, bridges of tree trunks supported by wood poles had to be built (Figure 1.5). When the roads had to cross ravines in the mountains, suspension bridges with cables of vegetable-fiber rope and walking decks of wooden planks had to be strung across (Figure 1.6). Gradually people learned how to use the materials they found in nature, such as stone, wood, and vegetable fibers.
Some of these structures, like the pyramids of Egypt, which were built over four thousand years ago to house the bodies of the Pharaohs when they died, were as high as 482 feet and used millions of heavy stone blocks. Others, like the cliff dwellings of the Indians of Arizona and New Mexico, built around 1,000 A.D., had as many as four floors. These houses were built on the rims of cliffs to make it difficult for the enemy to attack them once the ladders used to climb into them had been pulled up.
Now, thousands of years later, we still build houses; and although we do it often with man-made materials, like steel or bricks or concrete, we use the same skills our ancestors did to fight the same natural forces and to make sure that our buildings will not fall down.
We have learned to build high, but safely. There is a building in Chicago that is the tallest in the world. It is called the Sears Tower and is 1,454 feet tall. It has 110 floors, and yet it is perfectly safe (Figure 1.7). Modern men and women have also learned to build meeting halls, as their ancestors did, but they are so large that as many as 80,000 people can sit under the roof of one of them and watch a baseball or a football game (Figure 1.8). Their suspension bridges are made out of steel and can cross rivers over 5,000 feet wide, but they are built on the same construction principles used in the fiber-rope bridges made by their ancestors (Figure 1.9).
This book will show you how tents and houses and stadiums and bridges are built and how you can build some lovely small models of these structures by using nothing but paper, strings, ice-cream sticks or tongue depressors, glue, and pins.CHAPTER 2
Building a Tent
THE PURPOSE OF THE TENT is to protect us from the weather: to shade us from the sun, to prevent the rain or the snow from wetting us, and to stop the wind from blowing on us. The old tents were made of animal skins; modern tents are made of plastic fabric. To make our tent work we must keep the fabric up and spread out. But the fabric is so thin that it cannot stand on its own. We keep it up by using a stick or pole at the center of the tent. However, the pole cannot stand up by itself either, unless we push it deep into the ground, and if the ground is hard this may be difficult or impossible. So to keep the pole up we attach three or four ropes to its top and we anchor the ropes into the ground after pulling them taut. We can anchor the ropes either by tying their ends to stakes pushed into the ground in a circle some distance from the center pole, or by setting heavy stones on the ends of the ropes (Figure 2.1). Then we can stretch the fabric over the ropes, pin it to the ropes, and we get a working tent.
Notice that the pole and the ropes and stakes have only one purpose: to keep the fabric up. They are the structure of the tent.
The purpose of a tent structure, like that of a building structure, is to make sure that the tent or the building will stand up. The purpose of the tent fabric, on the other hand, is to protect us: it makes the tent function. In a building, the thin outside walls and the roof protect us; they make the building function, but they must be kept up by vertical columns and horizontal beams of steel, concrete, or wood, which form the building frame or structure.
The outside walls and the roof of a building are often called its skin and the columns and beams its skeleton, since, as with the human body, the skin provides protection and the skeleton makes it stand up.
To build a model of a small tent you will need:
a drinking straw for a center pole
4 thumbtacks or drawing pins
a square slab of wood or Styrofoam. (A Styrofoam slab 2 feet by 2 feet by 1-inch thick is most useful as a base to build models of structures. It can be bought for a few cents in a lumber yard or a hardware store, since slabs of Styrofoam are used for home insulation.)
2 pieces of string or thread, about 2 feet long or 3 times as long as the straw, for ropes
Cut four notches in one end of the straw about the same distance apart. Put the middle point of each piece of string into two opposite notches and anchor the ends of the strings to the square piece of wood or Styrofoam with the thumbtacks (Figure 2.2).
To finish the tent model you must stretch a skin over the strings. The skin can be a handkerchief stapled to the strings, or four triangles of paper glued or stapled to the strings (Figure 2.3). In one of the paper triangles a door flap can be cut and folded back.
The straw, once attached to the strings that are tacked down, stands up because to make it fall you would have to pull out the thumbtacks. We say that the straw is stayed by the strings, just as the pole in a real tent is stayed by the ropes and the stakes or stones. You will notice now that the pull on the strings pushes down on the straw. If you use a Styrofoam base, the straw actually makes a slight dent in the base.
In structures, if you pull on a rope or a string, we say that you have put the rope or the string in tension or tensed it. If you push down on the pole or the straw from the top we say that the pole or straw is compressed or in compression.
To find out how it "feels" to be in tension, grab the knob of a closed door and pull on it: your arm is in tension. If you want to "feel" compression, push with your arm stretched against the door knob: your arm is in compression (Figure 2.4). These two structural words, tension and compression, are most important. All structures, in a one-family house or a skyscraper, in an arch or a suspension bridge, in a large dome or a small flat roof, are always either in tension or in compression. Structures can only pull or push. If you understand how tension and compression work, you understand why structures stand up.
How do we recognize tension and compression? We cannot always put our arm where the structure is and "feel" these forces, but it is still quite easy to recognize them. Take a thin rubber band and pull it with your hands. You are putting the rubber band in tension and the band becomes longer (Figure 2.5a). You now know that whenever a part of a structure becomes longer it is in tension. Take a rubber sponge and push on it: the sponge becomes shorter in the direction in which you push. Whenever a part of a structure becomes shorter, it is in compression (Figure 2.5b).
There is a catch to recognizing tension and compression simply by the lengthening and shortening part of a structure, and you probably have noticed it already. The amount of lengthening and shortening in a structure is usually so small that it is not possible to see it with the naked eye. When you pulled on the strings of the tent model, the strings became longer, but only by a little bit. When you pushed on the top of the straw pole, the pole was shortened by only a little bit. (This is because the strings are stiffer than the rubber band and the straw is stiffer than the sponge.) Yet you could easily guess that the strings were in tension and the pole was in compression. If you imagine putting your arm where the structure is, most of the time you can guess how it would feel and whether it is in tension or compression.
Here are some examples.
The elevator in an apartment house hangs from steel cables. Imagine your arm as one of the cables and you will "feel" the tension on it caused by the weight of the elevator. The cables are slightly lengthened by its weight. They are in tension.
When you sit on a chair, your weight pushes down on the legs and makes them a little shorter. Imagine you are trying to hold up this weight with your arms and you will "feel" the compression. The pedestal that supports the Statue of Liberty works in the same way as the legs of a chair. The weight of the statue pushes on it and makes it a bit shorter.
A suspension bridge is also supported by steel cables, anchored on the ground, that go over the top of the bridge towers (see Figure 1.9). The cables are in tension, like the strings staying your model of a tent. The bridge towers, like your straw tent pole, are in compression.
Imagine your arm stretched up as the trunk of a Christmas tree. The weight of the branches and of the trunk itself pushes down like your weight pushing down on the legs of a chair. The tree trunk is in compression.
If your arms were the stones of an arch bridge, they would be in compression. The weight of the stones themselves and the loads going over the bridge put the stones in compression.
If you are in any doubt about compression in an arch bridge, stand 2 feet away from a wall and lean on it, with your hands up against the wall and your body bent toward the wall (Figure 2.6). You are now half an arch and you will feel the compression.
If you and one of your friends put your hands on each other's shoulders and move your feet away from each other, you will become a full arch and feel compressed by each other's weight (Figure 2.7). But if your shoes slip on the floor and you begin to slide apart, the arch will collapse. Its ends must be firmly anchored to prevent it from spreading apart.CHAPTER 3
What Is a Beam?
SOME ELEMENTS OF A STRUCTURE develop both tension and compression at the same time. The most important of such elements is a beam. In a building, a beam is the horizontal structural element that connects the top of two columns. By putting together a group of vertical columns and connecting them with horizontal beams, we obtain the frame of a building: it looks like a jungle gym (Figure 3.1).
The beams, which are supported by the columns, support, in turn, the weight of the floors, and the floors support the weight of people and of all the furniture on them.
To find out why a beam develops both tension and compression, put a thin plastic or steel ruler on two books set a few inches apart. Then put a weight on the ruler, like a stone or a small book, or push down on it in the middle with your finger. You will notice that under the action of the weight or of your finger, the center of the ruler beam moves down, and the beam becomes curved. It bends (Figure 3.2). Now get hold of a rectangular sponge, like those used in the kitchen, or a rectangular piece of foam rubber (the longer the better). With a felt-tip marker, draw a set of evenly spaced, vertical lines on one of its narrow sides and bend the ends up with your hands (Figure 3.3). You will notice that the distance between the vertical lines shortens at the top and lengthens at the bottom of the sponge beam. Because tension lengthens and compression shortens, you will realize that in bending the beam up, the lower part of the beam is put in tension and the upper part is put in compression. If, moreover, you draw with the marker a horizontal line halfway between the top and the bottom of the sponge side, you will notice that the distance between the vertical lines remains unchanged along this horizontal line and so does the length of the line. This means that along this horizontal line the beam develops neither tension nor compression. This is why the horizontal midway line is called the neutral axis of the beam. The ruler under your finger's pressure behaved like a bent sponge beam too, but the lengthening and shortening at its bottom and top edges were so tiny you could not see them.
If you hold the sponge with one hand and push down the free end of the sponge with the other hand, you will notice that the vertical lines spread apart at the top edge and gather together at the bottom edge. In such a beam, which we call a cantilever (Figure 3.4) and which is supported at one end only, the upper part of the beam is in tension and the lower part is in compression because the beam curves down, but there is a neutral axis in it just as in a beam that curves up at one or both ends. The balconies of a building are usually supported by cantilever beams (Figure 3.5). However, they do not bend as much as a piece of sponge because they are made of very stiff materials, like steel, concrete, or wood.
In a framed building the beams are bent by the loads on the floors, and the columns are compressed by the beams. The entire frame works together because the loads on the building develop compression in the columns and bending (which is both compression and tension) in the beams.