To Engineer Is Human Page 5
The British Institution’s definition of structural engineering crowds into the same box the ideas of economy and elegance, for responsible engineering wastes neither physical nor mental resources. Economic constraints are often imposed by the demands of the marketplace, but the requirement for elegance is often self-imposed by the best in the profession in much the same way that artists and scientists alike see elegance in the sparest canvases and the most compact theories—or in the axiom of minimalist aesthetics and design, “less is more.”
Finally, the definition concludes with the idea of safety, an objective that is ultimately more important than either the economic or aesthetic ones, for the loss of a single life due to structural collapse can turn the most economically promising structure into the most costly and can make the most beautiful one ugly. The structural engineers’ definition comes to an end with the idea that structures are safe if they can “resist the forces to which they may be subjected,” but it is symbolic of the virtually endless list of forces to which a structure might in fact be subjected that there is no period at the end of what seems otherwise to be a complete sentence.
The idea of resisting forces is a simple one, but putting it into practice can be rather tricky. On the one hand, the resistance of materials that form the building blocks of the engineer is not ever precisely known, for there is always the danger of the weak link in an otherwise sound chain. On the other hand, predicting the forces to which a structure may be subjected at any time in the future can be as difficult and as unsure as predicting the weather that may be responsible for some of those forces. Hence structural engineering must often deal in probabilities and combinations of probabilities. A safe structure will be one whose weakest link is never overloaded by the greatest force to which the structure is subjected. In order to make such ideas precise enough to be able to order the right amount of steel or concrete for a structure, the engineer must be prepared to posit causes and anticipate as much as possible what forces besides gravity will be acting on his proposed structure, which is like a little man-made solar system created to be set among other man-made systems within the given universe.
The object of a science may be said to be to construct theories about the behavior of whatever it is that the science studies. Observation and experience, inspiration and serendipity, genius and just good guesses—by their presence and absence, in pinches and dashes—all can provide the recipe for a scientific theory. As with all recipes, in which the cook is always the invisible ingredient, the individuality of the scientist provides the inexpressible human flavor. This aspect of science, the concoction of theories, has no universal method. But once a theory has evolved, perhaps from a half-baked idea to a precise and unambiguous statement of the scientist’s entry in the great universal cook-off, the scientific method may be used to judge the success or failure of a given theory or the relative merits of competing theories. Theories entered in the scientific cooking contest are known as hypotheses, and the process of judging is known as the testing of hypotheses.
A scientific hypothesis is tested by comparing its conclusions with the reality of the world as it is. Yet, no matter how many examples of agreement one may collect, they do not prove the truth of the hypothesis, for it may be argued that one has not tested it in the single case where the theory may fail to agree with reality. On the other hand, just one instance of disagreement between the hypothesis and reality is sufficient to make the hypothesis incontrovertibly false. That honeybees always build their hives with hexagonal cells is a hypothesis that has accumulated so much verification that it is hardly called a hypothesis anymore. It is assumed to be a fact. But let some young apiarist discover his bees making octagonal cells, and not only would the hypothesis that bees always use the hexagon be forever smashed, but there would also be quite a bit of excitement among the world of honeybee experts. That the sun rises each morning may also be considered a hypothesis, and our experience that indeed this happens day in and day out serves to confirm—but not prove—the hypothesis. Yet all it would take would be a single “morning” without a sunrise to make the contention that the sun rises every morning categorically false. While it may be beyond our comprehension that this could ever be the case, it nevertheless remains true that our belief that the sun will rise tomorrow is basically a matter of faith rather than of rigorously established fact.
Just as winning the blue ribbon at the county fair is no guarantee that a cake will be everybody’s favorite at next year’s fair, so the present success of a theory, even one so mundane as the diurnal appearance of the sun, is no assurance of its continued success. Hence, Newton seemed to have had the last word on theories of planetary motion for over two centuries, in spite of some intractable phenomena, until Einstein proposed his own more general theory. While it may be the conventional wisdom that Einstein had finally got the workings of the universe right, the history of science strongly suggests that this is presumptuous and highly unlikely. What may someday supersede Einstein’s hypothesis is any genius’ good guess. In the meantime, not only the theory of relativity but also Newton’s laws, with all their known limitations, serve us rather well in navigating through space and in constructing bridges and dams on earth. It is one of the marvels of the practice of engineering and of science that one can accomplish so much with so few and such admittedly approximate theories as Newtonian mechanics.
Engineering design shares certain characteristics with the positing of scientific theories, but instead of hypothesizing about the behavior of a given universe, whether of atoms, honeybees, or planets, engineers hypothesize about assemblages of concrete and steel that they arrange into a world of their own making. Thus each new building or bridge may be considered to be a hypothesis in its own right. In particular, one hypothesis of a structural engineer might be that so and so bridge across such and such river under these and those conditions of traffic and maintenance will stand for so many years without collapsing. Now if such a bridge were built and were to carry traffic year after year without trouble, the hypothesis would be confirmed time and time again—but it will never be proven until the so many years under the original plan had elapsed. But should the bridge collapse suddenly under no extraordinary conditions before those so many years were up, there would be no doubt in anyone’s mind that the original hypothesis was incontrovertibly wrong.
The process of engineering design may be considered a succession of hypotheses that such and such an arrangement of parts will perform a desired function without fail. As each hypothetical arrangement of parts is sketched either literally or figuratively on the calculation pad or computer screen, the candidate structure must be checked by analysis. The analysis consists of a series of questions about the behavior of the parts under the imagined conditions of use after construction. These questions may be easily answered for designs that are not particularly innovative, but a computer may be required to perform all the calculations needed to analyze a bold new design. If any of the parts fails the test of analysis, then the design itself may be said to be a failure. A design can be altered by strengthening the weak link and then analyzing the new design. The process continues until the designer can imagine no possible way in which the structure can fail under the anticipated use. Of course, if the designer makes an error in calculation or overlooks some possibility of failure or does not program the computer to ask the right question, then the hypothesis will erroneously be thought to have been verified when in fact it should have been disproved. Absolute certainty about the fail-proofness of a design can never be attained, for we can never be certain that we have been exhaustive in asking questions about its future.
The fundamental feature of all engineering hypotheses is that they state, implicitly if not explicitly, that a designed structure will not fail if it is used as intended. Engineering failures may then be viewed as disproved hypotheses. Thus, the failure of the Hyatt Regency elevated walkways disproved the hypothesis that those skywalks could support the number of people on the
m at the time of the collapse; the failure of the Tacoma Narrows Bridge disproved the hypothesis that the suspension span could carry morning traffic in a forty-two-mile-per-hour crosswind; and the failure of the Teton Dam disproved the hypothesis that it could hold back river water for irrigation. On the other hand, the past success of an engineering structure confirms the hypothesis of its function only to the same extent that the historical rising of the sun each morning has reassured us of a predictable future. The structural soundness of the Brooklyn Bridge only proves to us that it has stood for over one hundred years; that it will be standing tomorrow is a matter of probability, albeit high probability, rather than one of certainty.
Such realizations need be no more disturbing than those associated with the probabilities of disease. Indeed, if we find ourselves having led healthy lives for so many years, we all know deep in our hearts that that is no guarantee that we will not be hospitalized, or worse, tomorrow. We have seen members of our families and friends struck suddenly with cancer or back trouble or a heart attack or the bite of an insect. Or we have known someone in his or her prime struck down by a car or taken as the victim of an airplane crash or a freak accident or even a structural failure. If we were immobilized by the fear of such a fate, we might have to be institutionalized, for we would cease to be able to function in the world as it is. Lightning strikes, and some time it might strike us. We must accept this as a cost of the pleasures of life, and we have no choice. We risk remote dangers every day for the benefit of the pleasures of the day.
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One of the most elementary and most common of structural forms is what engineers call a beam. The essence of the idea of a beam is that it spans some space and resists bending or deflection by forces acting transverse to its long dimension. Some familiar examples will make this somewhat abstract definition concrete. Houses have floor beams, and if we examine them in an unfinished basement we see that they generally reach from wall to wall, sometimes supported by intermediate columns when the walls are especially far apart. The beams support their own weight and the weight of the floor above along with that of the furniture and people that rest and move about on it, which tends to cause the beams to dip, usually imperceptibly, toward the ground. Since ordinary houses have ordinary dimensions, a modern house builder thinks very little about the size or strength of floor beams, for he just builds each new house pretty much as he has built all his previous successful houses.
But what might we have to consider if we were stranded on a desert island with only the lumber for a house and not the plans or experience of a builder? First we might notice as we move the lumber about that a long two-by-ten bends rather easily in one direction but not in the other. The phenomenon is exaggerated in a yardstick that, being smaller and weaker than the piece of lumber, responds more easily to the action of our hands. Thus if we experiment with the yardstick we notice that when it is flat it can easily be depressed, and we can easily imagine that the stick will sag ever so slightly in the middle if we support it on our fingers at the one- and thirty-five-inch marks. An engineer would say, “The simply supported beam is uniformly loaded by only its own weight.” While we would not construct our house out of such pliant yardsticks, we can imagine that our two-by-tens will sag in a similar fashion, especially when more than their own weight rests upon them, and should we build our floor on the beams’ flat sides, we should expect not only a noticeable sag but also an unsettling springiness as we walked about the living room. On the other hand, if we were to support the yardstick near its ends with its advertisement vertical, as if on a billboard, we would notice no appreciable sag. An engineer would say, “The beam is much more resistant to bending under its own and other weight in this orientation,” and we can generalize this experience and experiment to say that floor beams should be installed so that they present their deep and not their flat sides to the weight of the floor.
The action of a heavy piece of furniture or people on the floor can be examined by holding the yardstick at its ends and pushing with our knee against the middle. We should not only see the much greater bending when our knee pushes against the flat side; we should also notice that the yardstick will tend to twist out of shape if we do not take care to hold it straight when our knee pushes against the sharper side. The engineer calls this kind of distortion an “instability” or “buckling,” and we can feel that the phenomenon appears in the yardstick all of a sudden as we increase the force of our knee. To be sure that our house’s floor beams will not exhibit this tricky action, we might brace them at one or two places along their span to offer resistance to undesirable motion of the beam. Now whether or not we anticipated all these actions in our first attempt at house building on a desert island might depend on whether or not the sagging of the lumber struck us as significant, whether or not we happened to play with a yardstick as we considered the construction task before us, and whether or not we tried to lay down our floor beams in the less convenient way. For if we had no man Friday, it might certainly be easier to lay the beams flat than to attempt to balance a bunch of them in the top-heavy position while we laid a floor over them. That might take the patience and luck of a builder of a house of cards.
Something so common as the construction of a floor may thus be viewed as the statement of a hypothesis, albeit one reached possibly by trial and error and never made quite explicit. When we install our beams in a certain way we say implicitly that they will support the floor without excessive sagging, without snapping out of place, and without breaking. If we did not appreciate the different action of a beam laid flat and a beam balanced deep, if we did not expect a beam to snap out of place when we moved in a big flat boulder for a coffee table, or if we did not expect to exceed a beam’s breaking point when we jumped up and down doing our morning exercises, then we might find our hypothesis disproven in a funnel of rubble in the basement. On the other hand, if our house does stand, that does not necessarily mean that we had, by luck or by design, hit on the optimal way to lay floor beams. We might have laid them flat over a relatively short span and not imagined anything undesirable or unavoidable in the slight sag and bounce we noticed as we walked across the room. Or we might not miss the bracing because we abhorred large coffee tables. Or we might do our exercise out of doors and thus never test the floor’s limits of endurance. Thus we might never test the hypothesis of our floor construction with a critical experiment.
Should another person then be shipwrecked on our island with another load of lumber, we would naturally have our experience in house building to share with him. But his lumber might be of longer lengths or of more slender dimensions, and he might want to build a larger house than ours. Had we had any structural failures, we would have tested certain hypotheses and found them to be wanting. Thus we could tell the neophyte what not to do. However, if our original house were still standing, our neighbor might just copy our design, scaling it up and employing his longer boards in his more ambitious structure. And the house might stand if the boards were not too much longer or too much weaker or if the new resident were not so heavy as we and not so much disposed to furnish his house with boulders as with bamboo tables and chairs. But should he someday decide to redecorate, and should the two of us drop the boulder sofa in the middle of the floor, we might disprove the hypothesis that his house is solid as a rock.
Now a house can fail in ways other than having its floor collapse, and we can imagine that walls and roofs can have their own weaknesses. These can generally be avoided by copying successful designs, but as with our island occupants, deviating from an exact copy can be disastrous. And deviations inevitably occur, through carelessness, greed, and well-intentioned new hypotheses to build bigger houses more quickly and with less lumber. But the builder who is overconfident in his new departures or who does not brace his frame adequately may find it flat on the ground after a midnight storm. And a bad winter can so overload roofs with snow that their collapses become endemic. The winter of 1979 saw so much snow ac
cumulate on barn roofs around Chicago that a number of them that had stood through many a more routine winter collapsed.
If building a house or barn is fraught with such dangers, what must be the task of the engineer charged with building a record-length bridge, which may be thought of as just one great big beam, or a record-high skyscraper, which may be thought of as a tall, tall beam rooted in the ground. In these cases there is nothing to copy, and there may be little relevance to experimenting with the likes of yardsticks or even of twigs. Even should the engineer have had the opportunity to experience similar but less ambitious structures than the one he is called upon to design, there always remains the question as to how validly he can extrapolate his experience and how far he can go beyond the last confirmed hypothesis. It is here that engineering comes to resemble science in another way, for engineers find it necessary to study beams and other elements of construction as if they were the natural stuff of science. Indeed, the discipline of taking the universe of structural elements as one’s field of study is known as engineering science, and it has a long and separate history from that of pure science.
Galileo was working in the spirit of modern engineering scientists when he considered the resistance of solids to fracture in the second day of his Dialogues Concerning Two New Sciences. Among the matters Salviati discusses with Sagredo and Simplicio is the strength of what is known today as a cantilever beam. This is a beam held only at one end while supporting weight or resisting motion all along its free length. Trees and skyscrapers act as cantilever beams when they resist the pressure of the wind tending to bend and topple them. Our outstretched arms, holding biscuits just out of our dog’s reach, are also acting as cantilever beams, as are flagpoles and balconies. Galileo’s cantilever resembles a piece of lumber embedded at one end in a section of a masonry wall and supporting a great boulder from a hook at the beam’s extremity. The seventeenth-century drawing is often reproduced, and its embellishments of vegetation and shadows put to shame many of the bare illustrations in today’s engineering textbooks.