Background Knowledge
Foundations of Engineering-history of the discovery and defining of basic forces
Here, right here, in the eye, here forms, here colors, right here the character of every part and every thing of
the universe, are concentrated to a single point. How marvelous that point is! . . . In this small space, the
universe can be completely reproduced and rearranged in its entire vastness!
-Leonardo da Vinci 1
Leonardo da Vinci, (1452-1519), was a genius engineer, scientist, and artist that was initially educated by frequently being sent out doors by his uncle to observe and sketch the natural world around him. In his notebooks he notes that engineers began thinking about what works and why in his lifetime. The scientists you will read about below began seeing the world in a new way and in turn lead to our ability to build ever more complex structures. Documenting the entire history of structures and what influences affected the evolution of thought that needed to take place to get where we are with our understanding and knowledge about structures today would take a book. The following is a brief overview of the history of the study of structures.
Until the 1600s knowledge of building was largely based on intuition, common sense, and experience passed on through craftsmen. Certainly much of this is true today especially in building your average home, and certainly foremen and project managers without engineering degrees become knowledgeable about loads and their necessary components through experience. Engineering on some level however is necessary for many structures and is based on an understanding of forces like compression, tension, stress, strain, and a whole bunch of terms that we may not understand in their engineering context. An understanding of engineering begins with understanding when and how some great thinkers started considering and putting names to these forces, and how they became responsible for developing and organizing our patterns of thinking about materials. Things we take for granted, like why we don't fall through or into the Earth, are actually scientific questions. How we can get a bridge to stand up, to span a mile or more, are engineering problems solved by the science we have for the behavior of materials. In the case of the first question, scientists have constructed models of Earth based on how we see it behave in events like earthquakes for instance. In the case of the second question, scientist have defined terms to explain forces and have studied their interactions, and have developed materials to behave for a set of conditions or parameters. The study of forces and how a material will behave is known as material science, or more specifically, the study of elasticity. Structural engineers and material scientists are the ones doing such studies.
The Beginning
The term engineer comes from the Latin word, ingeniator, meaning one with ingenium; the ingenious one.
Some sources credit Galileo's (1564-1642) unfortunate run-in with the church and his subsequent house arrest life sentence, (he supported Copernicus' theory that the Earth actually circumscribed the sun, and not vice versa), with his turn to studying what could today be called material science, however it appears that Galileo had already turned to other scientific interests and studies before this. (The first version is certainly possible though and certainly interesting to mention to students as far as giving them historical context for the climate in which Galileo lived.) What ever the case may be, there is evidence from the notebooks and letters left behind that towards the end of his life, while under house arrest, Galileo was allowed to study tension and correspond with his peers, in this case, a priest named Marin Mersenne (1588-1648) who was working in France and studying the strength of wires. . Later there will be another priest in France by the name of Edme Mariottee (1620-1684) who worked on the strength of metal rods both in tension and bending. What Galileo figured out during this time was: a rod pulled in tension has a strength proportional to its cross sectional area, or in other words, the larger the diameter of wire, the greater the wire's capacity. What this also tells us is that in the western world, we have evidence that material science was born around the early part of the 1600 and it started with looking at how wires behaved in tension.
Tension, compression, elasticity, plasticity, and strength
What is tension you may ask? Tension is when something stretches. Think about a long balance beam supported at each end. When you get to the center it deflects, (it is said to be 'in deflection'), it bows under the load of your weight. Picture what this balance beam looks like—it is an inverted arch and the material just under your foot is in compression because the material had to move closer together in some way -likely the bonds on the molecular level have moved closer together. Meanwhile, in the bottom part of this bow, or inverted arch, the wood had to stretch—this wood is in what we call tension. The molecules may be pulling to keep their shape. If when you get off the beam, the wood returns exactly to its original shape we can say that it is elastic. If it becomes permanently bowed in any measurement, it has reached its plastic state, and if it broke, it reached its breaking stress, also known as its ultimate strength.
Robert Hooke
"If I have seen further it is by standing on the shoulders of giants." Isaac Newton in a letter to Robert Hooke, 5 February, 1676. 2
Chronologically, Robert Hooke is the next important figure in the development of material science, a.k.a the science of elasticity. He lived from 1635-1702 and is now considered one of the greatest scientists of his age. He was a true Renaissance man. Besides being an architect, coining the term cell, building Gregorian telescopes, and studying everything from physics, geology, biology, astronomy, and naval technology, he developed and invented an amazing array of devices and correct theories. Hooke realized that every kind of solid changes its shape by stretching and contracting itself when a force is applied to it. He defined tension by explaining that solids push back -that is, if a force is applied he explained that there is an equal and opposite push back. What is important to realize is that the deflection is not always apparent. Compare the deflection for example of sitting on a stone bench as compared to a sofa cushion. One should understand that they both deflect but that one may only be seen deflecting on a molecular level, a way that is not apparent. Molecules have chemical bonds. In solids they are generally strong and stiff. Buildings become shorter when we climb them to upper stories. Cement pillars bulge under a heavy load. The study of forces and deflections is known as elasticity. Elasticity is the property whereby one may load and then unload a structure without any lasting effect on that structure's shape. The object springs back to its shape exactly, (and exactly means more than what one can often perceive with the naked eye). When a substance, or structure if you will, does not completely recover and becomes distorted, this is referred to as plasticity, or the material's plastic state. The object has been permanently deformed.
What might be ridiculously obvious today is that Hooke "discovered" that the deflection of a material is in proportion to its load. This discovery was made about 1800 years after the oldest Roman bridge was built. Double the load and you will double the deflection. This was the state of affairs back in 1676. Hooke published his findings in a paper in 1679 and the principle stated above has been known ever since as "Hooke's law". A limitation of Hooke's law is that it does not consider size, geometrical shape, and the material of which it is composed as factors in the deflection of a structure. Compare for example a thin spring and a metal plate. Which deflects more? Consider shape and size. Now compare a spring of rubber vs. one of steel.
Of interesting note is that no one really made great progress on Hooke's law, at least of any note, for nearly 200 years. Rather sad, but true. Our scientists of yesteryear were much the same as people in all walks today, some egotistical and self-serving competitors. Hooke and Newton had many arguments and disagreements during their time. Newton, a great scientist in his own right, outlived Hooke, criticized him, and invoked a general disregard for this area of science.
For historical context
Shakespeare and Galileo were born in1564, the year Michelangelo died, and the year after Nicolaus Copernicus died. Copernicus had already stated that the Sun was the center of the universe and clarified that Earth revolves around the Sun. Hooke was born in 1635 and Newton 7 years later in 1642-the year Galileo died. Alas, Shakespeare died in 1616. By the time Newton and Hooke were born New York had been founded by the Dutch, Virginia by the English, Santa Fe New Mexico by the Spanish, Quebec by the French, and Harvard had been founded in 1636. Yale opens during their lifetimes in 1701. Worthy of note is that non-western societies had helio-centric theories prior to Copernicus but that Copernicus added the movement of the planets around the sun in elliptical orbits and published his findings in a scientific paper. Another interesting note is that calculus, a math that builds on algebra, trigonometry, and analytic geometry, has roots dating back to 1800 BC in Egypt. During the 17 th century Newton and Gottfried Wilhelm Leibniz brought calculus to a point that solidified it and they are credited with its invention. Several others are also credited with calculus' advancement, including a Japanese mathematician by the name of Seki Kowa. Calculus however appears to have evolved over time in much the same way as geometry for example. Calculus is the math used in engineering today though Algebra can be used to describe concepts.
Stress, Strain, and Progress in the Eighteenth and Nineteenth Century
Materials that one constructs structures from have a molecular structure bonded by its atoms and/or molecules. Depending on whether we are talking about an elemental material like copper for instance, cement which is an mixture, or steel which is an amalgam, a material has it's own set of physical properties and behaviors; all materials have a unique set of molecular properties. These factors affect how a material/structure will react to a load, that is, a force or weight. Compare something tall and narrow to something short and squat, each having the same amount of material. Which is more stable? Obvious, to a builder perhaps, but this concept was not something universally considered in materials and thus not mathematically accounted for until the nineteenth century. To summarize, the behavior of a material is not simply dependent on its composition, but on the geometric form it acquires as well.
The big names in moving material science forward in this period are Euler (1707-1783), Thomas Young (1773-1829) and Augustin Cauchy (1789-1857). Euler looked at cantilevers and their deflections, Young formulated the 'specific modulus' which calculated how much a column may compress depending on a load, and later in 1926 will have Young"s Modulus named after him- an important formula used today in engineering, and Cauchy created a formula to describe the breaking load of a material as well as defining two important concepts- stress and strain.
The term stress describes not only the breaking stress, but how hard molecules within a material are being pushed together or pulled apart as the result of a external load. Cauchy defined stress as the load divided by the area. It is a vector because the load has a directional force.
S = P/A
s=stress
P=applied force or load
A=cross sectional area of the material
Strain is another important concept and is defined as how far molecules or atoms are being pulled apart or pushed together, that is, how far bonds within atoms are being stretched or compressed. The formula for Strain = extension of the length/ original length. (This is essentially the same as the percent change formula: difference/ original x 100, just not expressed as a percentage, that is taught in the 8 th grade Pre Algebra curriculum). Note that these formula have become more complex today as a result of refined research on behaviors for particular conditions, (just try goggling Formulas for stress), however these simplified formulas are sufficient for this unit.
Augustin Cauchy (1789-1857) will define the breaking point at which a substance, say a wire for instance, will break. As mentioned above, elasticity is the property where a material under a load deflects and then upon removal of the load, recovers completely. Plasticity is where upon removal of the load, the material remains changed, or deformed din some way. The breaking point is such a load that fractures the material. Cauchy defined the breaking point as the force divided by the area of the fracture. Once the breaking point of a material was known this equation could be rearranged to figure out an unknown variable, such as the maximum load that can be carried for a particular size of material.
Young's Modulus plots strain on the x-axis (abscissa) against stress on the y-axis (ordinate). The resulting line communicates the stiffness of a material; the greater the slope of a line for a given material, the stiffer the material. The formula for Young' Modulas is E=Stress/ Strain. The resulting calculation remains a constant for any given material. It is worthwhile looking at some examples of stress strain diagrams. 3 Today engineers test for and understand the load that a substance can withstand as a result of these diagrams.
Engineering Today
In the 19 th century the French did much work to expand upon these principals. Interestingly enough, as is so often the case with theory, it took time to put these scientific and mathematics discoveries into practice. People went on building as they had done for centuries and likely the builders were largely uninterested in listening to theoreticians. The same attitudes can pervade building today. Artisans who are intelligent and skilled understand how loads affect the materials they work with. A good engineer or architect listens to the craftsperson and vice versa. Ideally there is an open dialogue and mutual respect between builders, engineers, and architects. Not every structure needs to be designed by an architect or engineer today. House builders without formal educations often design their own for example but must comply with building codes. Building departments however can and do occasionally call for engineered drawings for certain elements in a building during a permit process. In today's world though we would not consider foregoing engineering in designing big bridges, big structures, and our roads.
By mid-nineteenth century engineering began working its way into architecture and today we have obviously come a long way. Materials are regularly tested; metals and cements for example are sampled, analyzed, and engineered for maximum strength. Research continues on polymers, ceramics, nano-technology, fiber options, semi-conductors, photovoltaic technology, and the list goes on. Engineering takes into account fracture mechanics and the concept of "creep". Calculus has become a regular tool of engineering, and computer-modeling programs are commonplace. More recently, we have people like Santiago Calatrava applying engineering to bring to life structures that none have thought to create before, pushing our ideas and our structures into new realms, all made possible due to current understandings of forces and principles of structural behavior. In Santiago Calatrava's case, we are fortunate to have an artist, architect, and engineer wrapped into a creative designer of bridges, buildings, and art.
Types of Bridges (Note that the following discussion of bridge types is arranged alphabetically as opposed to the previous chronological organization of the historical section on material science above.)
Arch
The arch is one of the oldest bridge types and was used in ancient civilizations like Mesopotamia, Samaria, Babylonia, and Egypt. Perhaps one of the oldest and most famous uses of an arch from this time period is the Ishtar Gate from 575 BC, a masterpiece and part of the ancient Wall of Babylon, today housed in Berlin. Romans went on to use arch construction, most famously perhaps for their aqueducts which largely still stand today and China has a masterpiece arch bridge known as the Anji Bridge. Arches in bridges may be used in a variety of ways and are based largely on compressive forces but arched spans experience thrust and either abutments are necessary to support this outward force at the base, or a tie is required, or both. In a bridge this tie can be the roadbed itself. Span to rise ratios as well as material use will determine specific needs. Arched bridge designs are generally excellent in addressing spans between 30-800 feet depending on the design and material. There are a variety of ways that arches are incorporated into bridges as one will see with just a bit of investigation. A search for arch bridges will yield numerous examples and one will see arches supporting roadways from above and below the arch support. Round, segmental, pointed, and 3-hinged arches are all common in bridge design and are commonly constructed from steel, iron, concrete (pre-stressed, post-stressed, or reinforced), and stone. The keystone was an important discovery for early arch construction. It is the last stone placed into the top of a stone arch which structurally completes the arch structure.
Beam
Beams are the earliest and still most common form of bridges. A tree that has fallen across a river constitutes a beam bridge. Beams are ideal for spans up to about 70' and then usually prove themselves an inefficient use of material. Trusses then become a more efficient use of material and can span up to 150' to 200' effectively. Often beam construction integrates abutments or pier supports. Beams are structural members which typically have compression in the top fibers and tension in the bottom fibers.
Cantilevers
A cantilevered structural member is one which is like a beam continuous over a support, however it differs by projecting horizontally into space extending beyond its support. There are a variety of cantilever bridge designs. One often sees the use of cantilever design during the construction phase of suspension bridges. Most often, one sees
pre-stressed concrete cantilever bridges that are designed with cantilevers on either side, either connected directly to one another, or to a beam that bridges a gap between the two cantilevered sections. A highly engineered pin system joins this later design and must be designed allow for expansion and contraction at the joints. Cantilever bridges designed to carry heavy loads can be constructed from steel, iron, and concrete. The required structural design for this type of bridge is affected by the distance of the extension and the forces this bridge will be exposed to. One will often see use of arches in the lower section of the cantilever, supported on a pier. Cantilevers cause a reversal of internal compression and tension, depending upon where one looks. Sections between two piers act as a beam and have compression in the top part of the member, and tension below whereas in the cantilevered section, one finds tension in the upper part of the member, and compression below. Trusses are often adapted to this structural type.
Cable Stayed
Cable stayed bridges are the most recent invention in the design of bridges, and perhaps due in part to this freshness strike one as incredibly artistic. Though they date back to the late 1700s, they are not common in history. The most recent incarnations of a cable stayed bridge is the Millau Viaduct in rural France, completed in 2004 and the Alamillo Bridge in Seville Spain, completed in 1992, both strikingly modern and inspired. The design of a cable stayed bridge incorporates a pylon from which cables are attached directly in support of the bridge deck. Cabled stayed bridges are ideal for spans up to a thousand feet and use much less cable than a suspension bridge and they use less material than a cantilevered bridge of similar span. Cable stayed bridges do not require the anchorages needed for suspension bridges and may be chosen when anchorages are a poor choice. One sees compression in the bridge deck supported by the tension in the support cables. Cable stayed bridges are generally categorized as either fan or harp in design, depending on the pattern of placing the cables.
Suspensions
Modern suspension bridges are unmistakably identified by their tall pylons, sweeping arched cables, and wire hangers. Modern suspension bridges incorporate trussed bridge decks, trussed piers, and span ever longer distances. Currently the Akashi Kaikyo Bridge in Japan holds the record for the distance between it's piers at a total length of 6,532 feet, (equal to 1.23 miles, or 1991 meters). Suspension bridges require anchors at both ends to support the forces in the suspended cables from which the road bed hangs. The main forces in a suspension bridge are tension in the cables and compression in the pillars and pylons. Suspension bridges are one of the earliest forms of bridges, having their roots in rope and vine foot bridges across rivers. These early form of suspension bridges still exist in less developed areas throughout the world are worthwhile examples of structural ingenuity.
Truss
Trusses are incorporated into so many bridges that it easy to forget that the truss alone with an attached bridge deck constitutes its own category. Truss bridges frequently take on the appearance of an x-ed in flattened arch and this structural component sits either above or below the deck. Early applications were constructed of cast iron and wood where as most trusses today are built of steel or wood. Trusses rely on the inherent stability of a triangle. When a load is transmitted across the bridge it is supported at differing times by tension or compression in the truss. In a variety of designs, the structure's skeleton is filled in with shapes of a K, or X, or simply a triangle with vertical supports where needed to carry a compression load. The truss bridge is best illustrated through diagramming:
figure 1: 4 truss designs.
Moving Bridges
There are a variety of types of moving bridges that incorporate truss, cantilever, and cable stayed elements in their design, and include draw bridges, swing bridges, vertical lift bridges, and old-fashioned transporter bridges. These are not covered in this unit but may be of interest to the reader.
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