a historical perspective on empirical and rational design · 1 wcce-ecce-tcce joint conference 2...

1

WCCE-ECCE-TCCE Joint Conference 2Seismic Protec on of Cultural HeritageOctober 31-November 1, 2011, Antalya, Turkey

A HISTORICAL PERSPECTIVE ON EMPIRICAL AND RATIONAL DESIGN

Thomas E. Boothby*

INTRODUCTIONc.1600, from L. empiricus “a physician guided by experience,” from Gk. empeirikos “experienced,” from empeiria “experience,” from empeiros “skilled,” from en “in” (see en- (2)) + peira “trial, experiment,” from PIE *per- “to try, risk.” Originally a school of ancient physicians who based their prac ce on experience rather than theory. Earlier as a noun (1540s) in reference to the sect, and earliest (1520s) in a sense “quack doctor” which was in frequent use 16c.-19c.

(www.etymonline.com)

In this paper, I will outline a viewpoint that incorporates two principal ideas: the fi rst is the central place that empirical design has held in the design of structures since an quity and through the present me. Perhaps this may not be diffi cult to believe for structural design up to the Enlightenment. However, I am convinced that empirical design holds a posi on of great importance in nineteenth century design and in contemporary design. In my inves ga ons of empirical design, I will follow Webster’s Dic onary of American English and defi ne empirical as ‘relying on experience or observa on alone o en without due regard for system and theory.’ On the other hand, I want to show that a concep on of scien fi c design has also been applied to the produc on of buildings since an quity. By scien fi c design, I mean the applica on of some ordered view of the ac on of nature, based on observa on and theorizing, to the produc on of buildings.

In inves ga ng the terms ‘empirical design’ and ‘scien fi c design’ and what they mean to the engineering community, I hope to show that engineering in a modern sense: the applica on of an intellectual understanding of the universe to the produc on of worthy architecture-has been applied con nuously to the design of structures since ancient mes. On the other hand, I want to convince you not only that empiricism is a praiseworthy design method, but also that the 21st century engineering profession

* Professor of Architectural Engineering, The Pennsylvania State University, USA, e-mail: [email protected]

2

A Historical Perspec ve on Empirical and Ra onal Design

unconsciously embraces empirical design, at least in part, because we couldn’t build anything without it.

Thomas Kuhn (1962), in his discussion of the history of science and scien fi c inves ga on invites us to reconsider what we consider to be legi mate scien fi c inves ga on

The more carefully they [informed historians of science] study, say, Aristotelian dynamics, phlogis c chemistry, or caloric thermodynamics, the more certain they feel that those once current views of nature were, as a whole, neither less scien fi c nor more the product of human idiosyncrasy than those current today. If these out-of-date beliefs are to be called myths, then myths can be produced by the same sorts of methods and held for the same sorts of reasons that now lead to scien fi c knowledge. If, on the other hand, they are to be called science, then science has included bodies of belief quite incompa ble with the ones we hold today.

Kuhn argues in general that discarded scien fi c beliefs are no less true than the current understanding of phenomena in nature, but that they embraced a framework for explaining events which eventually became less tenable, and that was discarded for a new ‘paradigm’ or framework for the explana on of natural phenomena.

In the same vein, I would ask us to reconsider some of the ways of analyzing and explaining structures. The descrip ons of medieval architects of the way that a structure works are not evidence of ignorance or supers on. Rather, the success that these men enjoyed in building monumental stone structures should speak for itself.

An example might be found in an anonymous medieval architect’s descrip on of the construc on of support for the bells in a twel h century bell tower.

ca. 1117 ‘Under the beams that hold up the bells, I placed an addi onal perpendicular beam at the top of the walls, fastened on both sides; and beneath this beam, suppor ng it, I placed a very strong wood column, and loca ng the base of the column on another beam, lying perpendicular to the lower beams from one side of the tower to the other. This was done in such a way that the weight of the bells and the wood suppor ng them, previously borne by 6 beams is now supported equally by 15 beams.’ (Mortet 1911)

Perhaps we wouldn’t agree with this architect’s coun ng the collector beams and the columns and the joists equally, and there is certainly no ra onal analysis contained in this descrip on, but the principle stands: he has doubled the amount of support available to the bells.

THE ANCIENT WORLDIn the ancient world, there is a clear and sharp division between scien sts and mechanics, that is, people who think as opposed to people who do. This is presented, among others, by Aristotle, who dis nguishes mathema cs and physics, in brief,

3

Thomas E. Boothby

scien a, from ars fac va, such as building or medicine. The builder, prac cing ars aedifi ca va, the art of building, and the home that he is building are frequently recurring examples of Aristotle, and are an important manifesta on of the realiza on of poten al into ac on. He does express an interest in these arts, in the sense of regarding them as important, but concentrates his eff ort on the discovery of the ra onal make-up of the Universe.

Mechanical Problems (He 1936), a short work a ributed to Aristotle, is much more prac cal than most of Aristotle’s work in its choice of problems, and o en in the ad hoc character of the explana ons that are advanced for the solu on of these problems. This is certainly one of the sources for an understanding of the Aristotelian dynamics described by Kuhn in the ini al quota on. The book is a series of ques ons rela ng to mechanics followed by explana ons. Some of the ques ons are par cularly relevant to the science of building. For example, Ques on 14, “Why is a piece of wood of equal size more easily broken across the knee, if one holds it at equal distance far away from the knee to break it, than if one holds it by the knee and quite close to it?”, or Ques on 16, which is taken up later in the seventeenth century by Bernardino Baldi. Both are answered in terms of the beam ac ng as a lever, with an external eff ort and internal resistance. Some of the earlier ques ons relate more directly to kinema cs, such as discussions of the composi on of mo on in two diff erent direc ons, or the kinema cs of circular mo on, which, according to Aristotle, consists of ‘natural mo on’ tangen al to the center and ‘forced mo on’ perpendicular to the center.

Following Kuhn, we need to begin by reconsidering Aristotelian dynamics as a ra onal and construc ve world view. The features of this dynamics is the existence of natural and forced mo on: a substance has a natural mo on downwards (earth) or upwards (fi re) depending on its components. It can only be moved in a diff erent direc on by force or ‘violence.’ When the forcing is removed it reverts to natural mo on.

Mo on can be combined, so that mo on can take place in a straight line (for equal parts natural and forced mo on), or in a curve (for varying parts). The principle of the lever holds in small and large machines.

Figure 1 Composi on of Linear Mo on and Analysis of Circular Mo on

4


Much of what we know about theories of building in ancient Rome has been obtained from careful reading of Vitruvius. This book outlines rules of good building, and methods of good building for temples, private dwellings, public buildings, such as basilicae and theaters, and provides common-sense advice on construc on. The rules that Vitruvius presents are commonly cri cized as over-idealized, not used in actual construc on, as nearly as can be read from exis ng buildings, and an a empt to codify a process that is fl uid, empirical, and responsive to actual site condi ons.

This cri cism can be answered by Vitruvius himself. In laying down his rules for the design of theaters, he says the following

Nevertheless it is not in all theaters that the dimensions can answer to all the eff ects proposed. The architect must observe in what propor ons symmetry must be followed, and how it must be adjusted to the nature of the site of the magnitude of the work. For there are details which must be of the same dimensions both in a small, and in a large theater, for their use is the same. (V.vi.7)

Certainly, according to Vitruvius, refi nements have to be made to general rules to accommodate the percep ons of the eye

For the sight follows gracious contours; and unless we fl a er its pleasure, by propor onate altera ons of the modules, an uncouth and ungracious aspect will be presented to the spectators. (III.iii.13)

The propor ons used by Vitruvius, and by Roman architects in general are signifi cant, fi rst as a primary means of crea ng worthy buildings-the term used by Vitruvius is symmetry, while a be er transla on is commensura on-measuring elements of a building in propor on to the whole, and to all of the other parts. The fundamental reason for this use of propor ons is the ability to conceive and lay out en re buildings en rely by propor onal measures, either on the basis of a module, which is carried

Figure 2 Modular Layout of a Greek Temple on the basis of the Column Diameter. All of the details of the temple: intercolumnia on, dimension of the cella, etc. and its eleva on are

determined on the basis of the ini al module of the column diameter.

5

Thomas E. Boothby

into all of the work, or by subdivisions of the overall dimensions of a building. An example might be the prescrip on of a tetrastyle, systyle, prostyle, Ionic temple for a given stylobate. From the width of the stylobate, and the propor on of the columns and intercolumnia ons, it can be determined that 10 column diameters are needed for the width. Using a dividers the width of the stylobate can be divided into ten parts to determine the column diameter, which then becomes the fundamental module for the remainder of the work.

In the process of layout, we have automa cally made at least two important structural decisions. The stability of the columns is assured by the standard propor on of 8 1/2 to 1 column sha height to column diameter at the base. The propor ons of the stones that make up the architrave have also been determined, with a span/depth ra o of 4 determined for the architrave.

The characteris c of all Roman construc on is this dependence on propor on and the applica on of construc on methods. Roman bridges, such as the Pons Fabricius or the Roman bridge at Rimini display consistent span/rise ra os of 2 or slightly less, span/abutment width ra os around 3, and span/ring thickness ra os of approximately ten. Roman barrel vaults, similarly, are semicircular, and have a span/thickness ra o of approximately 10.

Vitruvius, of course, like any architect through the Renaissance, is also a mechanic. There is a substan al book devoted to the theore cal and the prac cal discussion of machines. This part of Vitruvius’ training and experience must be looked on as equally important to and informa ve of his work with buildings. In this book, he quotes the work of Aristotle’s school Mechanical Problems at great length in his discussion of the principles of mo on and the usefulness of the circle, circular mo on, the balance, and the lever.

Vitruvius engages in addi onal theorizing about structures, including his statements about the arch and about wooden roofs. In each case, he uses machine analogies. In the arch, according to Vitruvius, ‘each voussoir pushes out the one below, due to the weight of the overlying wall, while columns suppor ng a lintel are ‘wedged up’ into the lintel (VI.viii)

THE MIDDLE AGESBuilding in Central Europe in the period following the Imperial Rome appears to consist largely of increasingly bold experiments in the development of increasingly large scale buildings, and in a enua ng the walls to the greatest extent possible. Of course, the most successful of these experiments resulted in the development of the style of building that we call Gothic. At the outset of these experiments, say in 700-800 C.E., the builders are not expected to be informed by any kind of ra onal understanding of the universe. They are simply the intelligent inves ga on of piling stones on top of each other and careful observa on of the outcome. I do not mean to devalue this eff ort by this statement. The result, in a way, is all building as we know it. The procedure is strictly empirical. Some of the immediate results of this eff ort

6


were the various regional schools of construc on: The Burgundian, the Angevin, the Bourbonnais, and other schools are clearly forms of experimenta on in the quest to increase the height and available light in load-bearing masonry churches.

However, by the Gothic period, say by 1150, appears that there was a further eff ort to apply Aristotelian dynamics to the understanding of how buildings behave. Two possible sources are available for this understanding: the machinery on the building site that the builders have a constant opportunity to observe, and the contact with educated churchmen needed for the construc on of buildings at monasteries and occasionally for the construc on of cathedrals. All of the educated churchmen would have been raised on the teachings of Aristotle and the disputa ons between various contemporary or near-contemporary philosophers on the meaning of the teachings of Aristotle.

The fundamental procedure of the medieval architect in designing and building buildings is the use of systems of propor oning, very much as described by Vitruvius. The modern study of these structures usually incorporates reverse engineering to determine the propor oning scheme used. The prac ce of designing by propor ons is a construc onal necessity, may have aesthe c implica ons, and occasionally religious signifi cance. However, it is also a powerful and widely used structural design tool.

The works of gothic architecture themselves display a consistent use of geometric construc ons to obtain good results. This is o en in the form of developing plans for a given building, but does extend to eleva ons, and to the commensura on of elements in the eleva on, such as the span/ring thickness ra o for the arches under construc on. Examples of these are widespread in the study of Gothic Architecture: I will cite a few.

The plan of Cologne Cathedral is known to have been laid out ‘ad quadratum,’ that is according to a square, while the plan of the Cathedral of Amiens is ‘ad triangulum.’ In both cases, geometry is employed to relate the plan to the eleva on. Piers in Gothic architecture, usually observe a propor on of 7:1 to 9:1 (verify) height to diameter. Arches are laid out by 1/3 point or by 1/5 point, depending on the desired height, and their ring thickness is generally around 1/20 of their span.

Beyond the simple applica on of geometrical ra os, which is usually understood as the way of doing Gothic architecture, we have iden fi ed some intellectual understanding of the way buildings fail, and how they might be made to stand up. Because architects, as Vitruvius was, are s ll mechanics, and because they may have been exposed to the ideas of Aristotle, which pervaded the intellectual life of the Middle Ages, the thinking of these architects is dynamic, and o en machine based.

The construc on of quadratures is especially important in medieval architecture, and can be observed in the notebook of Villard de Honnecourt, Roriczer’s manual on the se ng out of pinnacles, and in wri en records that survive from the construc on of the cathedral of Florence.

The discussions of the construc on of the Cathedral of Florence, as assembled by

7

Thomas E. Boothby

Cesare Guas (1887) include appeals to panels of experts. Par cularly during the period from 1365-1367, the documents relate the appointment of panels of experts to examine the alterna ve design of the sculptors, painters and goldsmiths, and also to inves gate the cracks that appeared at approximately the me of the closing of the second large vault for the nave. The delibera ons on the proposed design by the goldsmiths are largely concerning propor oning, height, number of bays, and shape of windows; although statements in support of this scheme generally include some statement on its solidity. Statements about the repair of the cracks, however, include a signifi cant component of structural knowledge. Included in these statements is the fi nding that the church remains plumb and ‘sopra se,’ (above itself) which in part echoes Aristotle’s thoughts on falling bodies, or the statement at Milan, to be examined later, that ‘what is straight cannot fall.’ The cracks themselves are said to be due to fresh work. There are statements that the e bar for an arch should extend through both support walls (10-13 August 1366). The loca on of the es is chosen to be below the bearing of the arch. This allows the arch to be ed within the bu ressing scheme.

At the same me, the project was undergoing other altera ons not necessarily mo vated by the structure of the building. The history of this aspect of the project is summarized by Marvin Trachtenberg (2001). The basic module of the nave consists of a 24 braccia1 small measure, equal to 1/2 the width of the aisles, and a 72 braccia large measure, equal to the width of the nave. Following the plague years and the halt of construc on, Francesco Talen resumed construc on of the nave, with a projected three bays of 34 braccia in length, for a total length of 102 braccia, a number corresponding neither to the small nor the large measure. Following a series of lively and adversarial discussions in 1366-1367, a new scheme was adopted, in which a fourth bay was added to the nave, with a total length 136 braccia, the easternmost piers were extended to make the overall length of the nave 144 braccia (2x72), and the diameter of the cupola was readjusted to 72 braccia.

1 A Floren ne braccio measures 58-60 cm.

Figure 3 The Construc on of Quadratures.

8


The builders of the Cathedral of Milan surely built empirically. Ackerman, in his discussion of these documents notes as much: for all the gothicizing tendencies of the builders called in from the north, the Milanese builders tend to keep to the program of a large-scale Lombard church. Under the 18th century decorated pseudo-Gothic, pseudo fl ying bu resses of the present cathedral can be seen a typical Lombard bu ress, projec ng above the aisle roof, and angling to the clerestory wall in a solid mass. Their reliance on proven techniques, such as e rods for arches to solve problems of arch thrust, rather than worrying about whether the arch generates thrust is equally typical of an empirical builder. The history of the project through 1409 has been extracted from these documents by James Ackerman (1949). Beginning with the laying of the founda on in 1386, the architects of Milan Cathedral have sought assistance from French and German masters at several mes during the course of construc on. They seemingly rejected most of the advice that was off ered, but the discussions are illumina ng. In the key exper se of 1400, the architects of Milan seem to be defending their posi on in terms that bear on the subject of this paper.

To summarize the events up to 1400,

In 1389, a Frenchman Nicolas de Bonaventure, was appointed to address faults in the design of the founda ons

In 1390-91, a German Annas de Firimbourg is present, and wishes to make the

Figure 4 Bu resses of Milan Cathedral

9

Thomas E. Boothby

nave sec on ad triangulum. A mathema cian from Piacenza, Gabriele Stornaloco, is summoned to help in dealing with the geometrical complexi es introduced by the triangular scheme. His report is given in Frankl and is discussed later in this commentary.

In 1391, Heinrich Parler was appointed to the posi on of ‘maximus inzignerius.’ A council was called in 1392, in which Parler’s scheme for building the nave ad quadratum and other ma ers, such as the size of the piers, and the need to use the chapel walls for bu ressing, were discussed. Parler was dismissed shortly a er this.

In 1399, a group of three French experts were engaged, including the conten ous Jean Mignot, presumably to determine the readiness of the suppor ng structure for vaul ng. Mignot immediately declared that the structure was threatening ruin-a frequently recurring expression in the contemporary documents on medieval construc on--and when nobody would listen to him, appealed to the Duke. The reports of the various exper ses and council mee ngs are almost the only medieval construc on document in which theory is discussed, rather than a par cular project, and are thus among the most cherished and most studied documents from medieval architecture. Mignot’s list of 54 faults or ‘doubts’ is presented on 11 January 1400, along with the responses of the Milanese architects. In a further council on 25 January, Mignot elaborates on his main objec ons: the four towers intended to sustain the burio at the crossing are not built with suffi cient founda on or piers and the bu resses around the chevet are inadequate .

In the earlier mee ng, in defense of their chevet scheme, the Milanese architects make the statement that “pointed arches do not exert a thrust on the bu resses.” Having had some me to think about this, Mignot counters two weeks later.

“...and what is worse, it has been rebu ed that the science of geometry does not have a place in these ma ers, because cra is one thing and theory is another. The said master Jean says that cra without theore cal knowledge is worthless, and that whether vaults are round or pointed, if they don’t have good founda on, they are nothing, and nevertheless when they are pointed, they have the greatest thrust and weight2.”

In the generally accepted interpreta on of this conference, Mignot is the ‘theore cian’ and shames the Milanese by quo ng rules of geometry that pertain to building construc on, of which the Milanese are unaware, and faults them for having only prac cal knowledge, without any scien fi c context in which to place it. The response of the Milanese is widely considered to be scien fi c posturing, rather than introducing signifi cant ideas, is to paraphrase two passages from Aristotle’s Physics.

In the Milan Exper se of 1400, the exact statement that the Milanese architects make regarding thrust of pointed arches is : ‘archi spigu non dant impulzam contrafor bus.’ The term ‘impulse’ appears in The Physics and is elaborated by Thomas Aquinas (Piro a 1953) as, “It is called an impulse, when the mover pushes

2 Ackerman translates this as ‘a very great thrust and weight.’ The present transla on is equally admissible and casts some doubt on Mignot’s knowledge.

10


something moved, but does not detach, the one carrying the other. ” which appears to be an appropriate descrip on of the push of an arch on a bu ress, not en rely removed from Vitruvius’ dynamical descrip on of the mechanics of the arch

“each voussoir pushes out the one below, due to the weight of the overlying wall.”

Of the two passages from Aristotle cited by the Milanese, the fi rst is taken from Book 8 of the Physics: ‘local mo on is either a straight line or a circle, or a combina on of the two.’ The subject is the existence of infi nite mo on, and the iden fi ca on of circular mo on with the infi nite. This statement has appeared to Ackerman as a feeble a empt to jus fy the design of the cathedral as containing ‘straight lines’ and ‘circles.’ An alterna ve interpreta on is to understand that the straight line mo on, according to the pseudo-Aristotle, is unmixed natural (downwards) or violent mo on, while circular mo on is a varying combina on of the two. The quarter circle shape of the bu resses themselves bears a resemblance to a medieval no on of an ar llery trajectory, where the violent mo on (lateral thrust) is steadily overcome by natural mo on (gravity). Several surviving drawings of medieval fl ying bu resses show them as quarter circles, consistent with an Aristotelian view of mixed natural and forced mo on. It is possible to believe that even the Milanese architects were informed by some sort of conceptual idea about how their structure behaved founded in part on understanding the func oning of machines, and in part on the basis of Aristotelian dynamics.

RENAISSANCE/ENLIGHTENMENTBrunelleschi, celebrated as the fi rst Renaissance architect, is renowned for his courage in vaul ng the 72 braccia octagon prepared for the crossing of the cathedral of Florence, the measures taken to relieve or redirect the forces from the weight of the dome, and especially for the machines that he invented for the construc on of this dome. Although we o en like to project an aura of science onto such ac vi es, these are primarily the characteris cs of an architect working empirically.

On the other hand, Leon Ba sta Alber , an architectural theorist, as exemplifi ed by his Ten Books on Architecture (Bartoli 1565), is much less a theorist on the subjects of machines and structures. This work contains detailed descrip ons of the func oning of machines, principally cranes. His discussions are very consistent with the descrip ons of such machines in Vitruvius. His view of weights is, not surprisingly, Aristotelian, ‘loads are heavy by nature and obs nately search for the lowest point, and with all their power do not allow themselves to be raised.’ By the art or ingenuity of men, weights can be moved in diff erent direc ons than their nature dictates.

As an example of Alber ’s prac cal and empirical understanding, consider this descrip on of the rigging for a crane.

The pulleys should be neither so wide that the rope slips nor so narrow that they cut the rope. The axles of the pulleys need to be of iron no less thick than one sixth part to of the inner diameter of the pulleys, nor larger than the eighth part

11

Thomas E. Boothby

of the outer. The ropes should be soaked to prevent their burning…

Curiously, one of the key Renaissance documents on architectural and structural theory is another exper se of Milan Cathedral, this me concerning the construc on of the burio, or crossing tower. Deposi ons have been le by three architect/engineers of note, Leonardo, Bramante, and Francesco di Giorgio Mar ni. All three had proposed designs for the tower that had been rejected in favor of Amadeo and Dolcebono’s octagonal design, while Francesco was engaged to assure the stability of the selected design, the other two were con nuing to argue for their design (Bruschi 1978).

Both Leonardo and Bramante argued for a square crossing tower, considering it to be more stable and more in conformity with the original design. Some sketches of Leonardo appear to be a acking the diffi culty of placing an octagonal tower on a square bay, while others seem to show a more complete concep on of a square crossing tower. The resul ng tower, like much of the cathedral, is a curious hybrid, incorpora ng a Renaissance eight-part cupola behind a highly Gothicized facade, much as the cathedral itself has gothic fl ying bu resses (added in the eighteenth century) used as decora on for what are essen ally Lombard bu resses.

Among the other architectural theorists of this period, a late writer, Bernardino Baldi (1621), stands out in importance and in thoroughness. Baldi is a late Renaissance, pre-Newtonian theorist on the subject of structures. His background is both architecture and mathema cs. His trea se on mechanics is presented as an elabora on of Aristotle’s Mechanical Problems; however, in his treatment of Problem 16, for instance, he introduces the behavior of beams, arches, and trusses.

Problem 16: Why is it that, the longer the beam, the weaker they are, and, if li ed, bend more, even for a thin beam two cubits long, or a thick beam one hundred cubits long?

Figure 5 Alber Drawing of a Crane.

12


His discussion is understandable to a modern engineer, and explains in geometric terms why a deeper beam is more eff ec ve in bending than a shallower beam (greater internal lever arm), why a thicker arch is less likely to fail, and how a king-post truss works. His discussions are mechanis c and dynamic: the truss is explained by the shortening of the top chords that would be required for failure. The arch is explained in terms of the displacements necessary to eff ect a failure. The discussion is not numerical, and appears to be intended to give the user an understanding of failure mechanisms and some ideas about how to avoid them.

Figure 7 Interior View of Tiburio: Milan

Cathedral

Figure 6 Exterior View of Tiburio: Milan Cathedral

13

Thomas E. Boothby

NINETEENTH CENTURYThe nineteenth century may well be viewed as the golden age of empirical design. Although scien fi c theories certainly come to be applied regularly to the design of buildings, empirical rules and prac cal thinking are used as a necessary adjunct to such design. Textbooks from the me contain a signifi cant propor on of prac cal instruc on. Baker (1897), in his Trea se on Masonry Construc on alternates prac cal and theore cal considera ons. As an example, in refu ng Rankine’s insistence on the middle third rule, Baker states,

‘A reasonable theory of the arch will not make a structure appear instable which shows every evidence of stability.’

The design of bridges in the nineteenth century is composed of equal parts of empirical knowledge and ra onal design. Although extremely sophis cated methods were applied to the design of masonry arches, such as the applica on of Mery’s method to the design of the Union Arch shown here, the determina on of the confi gura on of these structures con nued to be based on conven onal ra os.

A mul plicity of basic confi gura ons adopted for iron bridges: many of them have commercial signifi cance, due to patents obtained on the design of the bridges. The

Figure 8 Illustra on from Baldi, Problem 16

14


two fundamental trends are eff ec vely the arch and the truss. The arch, of course, follows the applica on of the stone arch, and reproduces this form in cast iron. Early examples include the patented design for iron arches of William Moseley. An addi onal refi nement is presented in the patents of William Douglas for the len cular truss bridge. The truss form was equally slow to develop into the understood assembly of smaller pieces into a single load bearing structure. Early trusses were more experiments in bracing a longer top and bo om chord. Bow´s (1874) methods, which evolved into methods for the analysis of trusses, were originally intended as analysis methods for braced beams. The web members were thought of as bracing for the remainder of the structure, either an arch, as in Moseley´s designs, or a beam as in a queenpost or a Howe truss. The analysis methods were o en similarly ad hoc. Bow´s methods for analyzing braced beams, required the iden fi ca on of the correct class, whether a parallel chord, gabled, curved top chord, etc. and the applica on of formulas for the force in the bracing. Merrill´s (1870) semi-graphical approach stands out as a method of par cular interest as it can be applied simply to very complex trusses. However, the shortcoming of this method, as graphic methods applied to bridge trusses in general, is that a separate analysis must be undertaken for each important load posi on.

In later applica ons, the engineers narrowed these dis nc ons to bridges with parallel chords and bridges with curved chords. Although graphic methods for the analysis of trusses were widely available, later nineteenth century bridge engineers, used almost exclusively analy cal methods. The analy cal methods for parallel chord trusses were based on the idea of ‘indexing,´ which is presented in its perfected state by George Fillmore Swain, both in his 1905 class notes and in his 1927 trea se on structural design. In this method, the loads are added throughout a truss in the form of ver cal components of truss forces: the procedure can be followed quickly for a variety of truss types. For all of the truss types available, the civil engineering profession, through experience, and through calls for standardiza on, eventually se led on the Pra truss and its variants as the principal truss form for highway bridges.

Many of the bridge forms that engineers of this me period were led to were sta cally indeterminate, especially those types of bridges that had mul ple web systems, for instance the double Pra truss (Whipple truss) and the quad Warren truss, as shown in the examples of the Hayden Bridge in Oregon and the Slate Run Bridge in Pennsylvania. The sta cally indeterminate aspect of these bridges was managed through an empirical procedure of dividing the bridge into mul ple systems and analyzing each of the systems separately. What this method loses in accuracy, it gains in expediency, and in terms that were well-understood, but formulated 75 years later, this type of analysis sa sfi es the lower bound theorem of plas city and, for all its empiricism, is scien fi cally valid.

The knowledge developed by bridge engineers, and incorporated into their designs and textbooks went well beyond the applica on of methods for stress analysis in the chords of the trusses. It included careful adapta on of details to various condi ons, and a willingness to allow sta cal indeterminacy in the design of bridges, by permi ng

15

Thomas E. Boothby

frankly approximate analysis, and recognizing that the result was redundancy. The adop on of conven onal bridge forms, and their applica on to nearly all bridge problems of span 200 feet or less amounts to a form of empirical design, that is that the selec on and most aspects of the design of the structure depended on factors such as proven worth of the structural type, constructability, etc. In the end, such bridges were built almost exclusively as through Pra trusses from about 1900-1920.

Figure 9 Bridge by William Moseley (Historic American Engineering Record MA 72-1)

Figure 10 Double Pra Truss. Historic American Engineering Record Documenta on of Hayden Bridge, OR.

16


Masonry structures of various types con nued to be built empirically and eff ec vely. Masonry bridges have been discussed already. Masonry buildings were built by rules that included the thickness of walls based on the number of stories, resul ng, for instance in the empirical design of the Monadnock Building, a 16 story load-bearing masonry building, where an addi onal wythe of brick was added for each fl oor.

Figure 11 Quad Warren Truss. Slate Run Bridge, Slate Run, PA. (Historic American Engineering Record PA 460-3)

Figure 12 Monadnock Building. Historic American Enginneering Record, Ill, 16 Cig 88-1

17

Thomas E. Boothby

Another empirical builder of note, Rafael Guastavino and his son, proposed in trea ses (Guastavino 1893) that the domes that their company built of layers of le laid fl at in portland cement mortar did not exert thrust on their supports. They argued that, being cohesive in nature and monolithic in character, the inherent resistance to bending of the domes, unlike voussoir arches and domes, meant that they did not generate horizontal thrust. Although Rafael Guastavino the elder did resort to structural engineering arguments in explaining the ac on of his construc ons, he is almost en rely an empirical builder, deciding on the number of layers of le required by his vaults based on size and other considera ons. However, many of the major structures designed and built by the company, such as the massive dome over the crossing of the Cathedral of St. John the Divine in New York were built with iron reinforcing. When Rafael Guastavino, the younger, patented his system of construc on, he showed probable loca ons for metal reinforcement. This behavior is curiously similar to the ac ons taken by the architects of the Cathedral of Milan, who inserted iron es into their completed arches and vaults, including those that they said did not exert thrust on their supports.

Figure 13 Guastavino Patent Drawing showing inser on of iron es.

18


EPILOGUEWe are all raised in a thoroughly ra onal and scien fi c tradi on. Even in grade school, we are immersed in the contribu ons of science to modern culture and modern progress. In such an environment, it becomes diffi cult to separate empirical and prac cal knowledge from the applica on of science. As engineers, this is a necessary exercise: although much of the public may think it possible to predict the exact load at which a structure will fail, we certainly know otherwise and are reduced to talking about probabili es and rejec ng structures based on an unacceptable probability of failure. In fact, our profession goes about its business primarily in an empirical fashion, based on precedent, adop ng designs that are known to work, and applying trial and error and the use of empirical rules. I would like to go over some examples of this, being as li le provoca ve as the subject allows. In order to be clear enough on this, we need to remind ourselves exactly what we are talking about when we speak of empirical design, that is, ‘relying on experience or observa on alone o en without due regard for system and theory.’ For the opposite, scien fi c or ra onal design, I will understand design ‘using a (consistent) theory based in scien fi c inves ga on to complete a structural design.’

Figure 14 Pi sburgh City-County Building: Barrel Vaults of Main Corridor by R. Guastavino and Son. Historic American Building Survey PA-5193-5.

19

Thomas E. Boothby

To speak, for instance, of one way slab design: two-way slab design, with its minimum thicknesses, column strips, middle strips, shear perimeter, etc. is too obviously empirical, I would think of a slab perhaps spanning one meter over 10 equally spaced concrete joists. We would have to think of the slab’s behavior as the same as a very wide beam. It is most likely that we would take the bending moment of the slab as wl2/8, probably using the center-center distance of the supports as the slab span. We would either put in a standard size mesh reinforcement, or design reinforcement to suit the bending moment that we have calculated. The design would be based on the reinforcement being located at mid-depth of the slab. If I review this statement, I would fi nd that I have made at least fi ve oversimplifi ed or incorrect assump ons. Even if I didn’t use a standard mesh, the design of the slab is fundamentally empirical. To check in with Webster’s paradigm, our design of fl oor slabs relies on experience and observa on, in minimum thickness, in span to thickness ra o, and in construc on, the regard for system and theory is par al at best, we ignore actual support condi ons, and we ignore the actual state of the reinforcement. These errors and erroneous assump ons are all jus fi able on the grounds that slabs designed and built this way work This is the primary feature of empirical design, and the reason it is so eff ec ve. It insists on the use of designs that work, and rejects those that haven’t been shown to work.

Others aspect of slab design: the other point about slab design that makes this process frankly empirical is the applica on of appropriate span/depth ra os in the concrete design code. These ra os are applied constantly as the minimum design thickness for this type of structure. The design according to span/depth ra os is a key feature of empirical design methods.

A simple example of the diff erence between empirical and modern methods is provided by the skyline of New York City. Un l 2008, the NYC building code required a simple wind load of 20 lbs/ 2 (0.960 kPa) up to 300 feet (91 m) above grade, 25 lb/ 2 (1.2 kPa) for eleva ons of 300 to 600 feet (182 m) and 30 lb/ 2 (1.4 kPa) at higher

eleva ons. These requirements, in place since 1968, were supplanted in 2008 by the incorpora on of ASCE 7, which requires a series of complex wind load calcula ons in which wind loads vary according to building height, eleva on tributary area, and building fl exibility. Any building constructed prior to 2008 would fail some part of these calcula ons. As a result, the strict applica on of these standards would require some form of strengthening to buildings that have manifestly endured the loads for which they are being strengthened.

Finally, and more to the point of this conference, I think it is worth discussing the general character of earthquake resistant design. For all its scien fi c trappings, including the inves ga ons into the dynamics of mul ple degree of freedom systems, and the current trends for the inves ga on of non-linear dynamics, and for the applica ons of this science to building materials of steel, masonry, reinforced concrete, and mber. It is also a process that certainly admits the characteriza on be characterized as trial and error. The examples I might invoke in support of this idea are Fazlur Khan’s 1968 ar cle on the use of a so story as an energy absorbing device, the Northridge connec on in steel structures designed for duc lity, and any

20


of a number of other perfectly sensible sounding ideas that were simply proven incorrect by the next earthquake. Certainly in the current trend towards ever more prescrip ve code wri ng, one sees a strong element of empiricism: as with the wind loading codes I described above, when the designer is remote from the process of knowing where the loads are coming from, the process becomes empirical: relying on received wisdom. None of these codes ever take account of the competence of historic materials or the competence of historic designers, using their own methods, to design competent structures. I have seen this issue repeatedly in the inves ga on of historic structures, not only for earthquake resistance. In the end, the ques on should be, where do we want earthquake resistant design of historic structures to be placed in the con nuum of ra onal/scien fi c versus empirical design? How much do we want to simply rely on cau ous experimenta on around what is known to work, on proven ra os, such as aspect ra os for diaphragms, or span/thickness ra os for arches, or to what extent do we want to rely on the results of increasingly numerically intensive structural analysis? When we have come to terms with the role and the importance of empirical design in our contemporary work in structural analysis, we can begin to frame an answer to these ques ons.

CONCLUSIONAt its heart, building art remains an art in the sense of ‘knowledge acquired by skill and experience’, as opposed to knowledge discovered by ra onal science. For all that proponents of science in building, from 1300 through the present me have done to alter this situa on, the fundamental strategy in the design of buildings is empirical. This is an important insight for anyone involved in managing buildings designed in the past. The basic building knowledge of a medieval architect is no less because their concep on of science or their concep on of the applica on of science to building diff ers from ours, and the modern-day scien fi cally based designer needs to approach earlier construc on with a sense of respect for the methods by which this structure may have been designed. In our me, and for all our scien fi c approach to building design, we seldom do any be er. Our best buildings result from the same impulses as the best buildings of medieval, Renaissance, or nineteenth century mes: from response to human needs, and from the applica on of proven formulas,

proven construc on methods and cau ous experimenta on. The best building is not scien fi c, but a process of trial and error and reliance on precedent in the form of accepted types, span/depth ra os, building materials, and a collec on of strategies, standard responses, and standard prac ces, occasionally informed by science.

Acknowledgements

I owe much of the thinking that I am presen ng about the applica on of Aristotelian principles to medieval construc on to Steven Walton.

21

Thomas E. Boothby

References

Ackerman, James. “Ars Sine Scien a Nihil Est” Gothic Theory of Architecture at the Cathedral of Milan The Art Bulle n, Vol. 31, No. 2 (Jun., 1949), pp. 84-111

Aristotle, Mechanical Problems, in Minor Works (tr. He ) Loeb Classical Libarary, Cambridge, Harvard University Press, 1936.

Baker, Ira Osborn., A Trea se on Masonry Construc on, 7th edi on, New York, Wiley & Sons 1897.

Baldi, Bernardino. Bernardini Baldi In mechanica Aristotelis problemata exercita ones. Mainz, 1621.

Bartoli, Fioren da Cosimo. L’archite ura da Leonba sta Alber . Venice, 1565. (available at www.books.google.com accessed 26 April 2011).

Bow, Robert H. A Trea se on Bracing with its Applica on to Bridges and Other Structures of Wood or Iron. New York, D. van Nostrand, 1874

Bruschi, Arnoaldo. Scri Rinascimentali d’archite ura. Milano, Il polifi lo, 1978.

Guastavino, Rafael. Lecture wri en for the Congress of Architects : in connec on with the Columbian Exposi on, on cohesive construc on, its past, its present, its future? Chicago, 1893

Guas , Cesare, Santa Maria del Fiore: La costruzione della chiesa e del campanile. Florence, M. Ricci, 1887.

Khan, Fazlur. Shock-absorbing so story concept for mul -story earthquake structures. ACI Journal, 65(5), May, 1968.

Kuhn, T.S. The Structure of Scien fi c Revolu ons. Chicago, University of Chicago Press, 1962.

Merrill, William. Iron Truss Bridges for Railroads. New York, D. van Nostrand, 1870

Mortet, Victor, Recueil de textes rela fs à l’histoire de l’architecture et à la condi on des architectes en France, au moyen âge, Paris, 1911-1929, A. Pickard et fi ls.

Piro a, M. In Octo Libros De Physico Audutu Sive Physicorum Aristotelis. Naples, 1953

Swain, George Fillmore, Notes on the theory of structures. Comprising the stresses in beams, girders, and trusses, bridge designing, graphical sta cs, earth pressure and retaining walls, masonry dams, stone and iron arches, can levers, etc. [mimeograph print], Boston, 1905.

Trachtenberg, Marvin, “Architecture and Music Reunited: A New Reading of Dufay’s ‘Nuper Rosarum Flores’ and the Cathedral of Florence. Renaissance Quarterly, 54(3):740-775, Autumn 2001.

a historical perspective on empirical and rational design · 1 wcce-ecce-tcce joint conference 2...

Documents