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Jonathan Ochshorn

First published in *On Architecture, the City and Technology* (Stoneham, MA: Butterworth Publishers, 1991), selected articles from the 1990 ACSA Technology Conference, Los Angeles, CA, February 15-18, 1990 (© 1991 ACSA). Images appear only in this online version.

**INTRODUCTION**

Architects are required to know something about the technological systems in their buildings, yet the specialized knowledge needed to actually design those systems is usually left to others. Proposals to "integrate" design education with the study of technology seem to be concerned mainly with organizational strategies (e.g., bringing technology "consultants" into the design studio; or suggesting various forms of team teaching) rather than addressing the basic question of content: what do architects need to know about technology?

Accreditation criteria are not much help, being difficult to implement on the one hand (students should be able to design structural elements from foundations to roofs, and analyze structural systems including rigid frames) yet, on the other hand, being ambiguous enough to include most current approaches to the teaching of technology (students should be able to design "elementary" environmental control systems and "simple" building elements).

Using the teaching of structures as an example, I propose to examine the conflicting requirements of competence (implying a simplification of both numerical methods and scope of material covered); versus literacy (implying a broadened understanding of not only the technical issues actually encountered in architectural/engineering practice, but also the social, economic, historic and intellectual context in which these technical issues are framed) in an attempt to reconcile the content of these courses with the diverse needs of the practicing professional.

**WHY TEACH STRUCTURES?**

At the outset, there are three broad explanations I have encountered for why structures should be taught to architects: first, so that architects can solve structural problems; second, so that they can talk more or less intelligently to their engineering consultants; and finally, so that architectural design, informed by a sound grasp of structural theory, becomes more rational and therefore, perhaps, more beautiful. Let us examine each of these arguments in turn.

*SOLVING STRUCTURAL PROBLEMS.* The first rationale for teaching structures is that architects need to know how to actually solve structural problems — determine the distribution of stresses, compute beam and column sizes, etc. — but only for a relatively simple class of buildings. In other words architects, especially in small practices, might find it necessary or convenient to design and even prepare construction documents for small buildings without utilizing the services of an engineering consultant. The case is never made, however, that architectural education in structures should therefore duplicate the more thorough training given to engineering students.

Yet even if architects are taught to design structures for relatively simple buildings, that does not necessarily imply that they need to understand the mathematical underpinning of the results they obtain. Because of the widespread availability and use of tables, charts and "pre-engineered" items of all sorts, many structural elements can be sized without recourse to any computations (or structural theory, for that matter).

Additionally, even where mathematical formulas are introduced in the classroom, they are not always derived or explained — see, for example, Harry Parker's presentation of column formulas for steel structures.^{1} Thus, the goal of solving structural problems cannot by itself determine the content and methodology of structures courses.

*COMMUNICATING WITH CONSULTANTS.* The second rationale for teaching structures is that, given the extent to which the engineering profession has taken over the task of actually designing structures for buildings, architects must at least be able to discuss structural design issues with these engineers. For one thing, the architect is more often than not the leader of the design team; it would be difficult to exercise this leadership role, involving the coordination of all the design and engineering specialties, without possessing some knowledge about each area. Equally important, it would not be possible to successfully collaborate with engineers on large scale projects.

Specifically, architects would need to know, at a minimum, the essential vocabulary of structures: "moment," "shear," "deflection" and so on. Beyond the minimum vocabulary, insight into the behavior of structures would also be necessary unless, as R.E. Shaeffer warns, architects are willing to risk losing control over some basic design decisions.^{2}

*DESIGNING RATIONAL /BEAUTIFUL BUILDINGS.* The third rationale for teaching structures is that architects need a basic qualitative understanding of structural theory in order to design rational buildings. "Only then," according to Nervi, "will a structure be born healthy, vital and, possibly beautiful."^{3} While this view can easily degenerate into such sterile debates as, for example, whether the "extra" mullions in Sullivan's Guaranty Building are structurally ambiguous and therefore aesthetically (or morally) wrong, there is certainly some merit to the basic argument.

On the other hand, it is important not to overstate the case. For once a structural system has become commonplace, it can be successfully integrated into an architectural design without much consideration for structural theory or behavior, at least on the part of the architect. Consider, for example, the steel skeleton frame, to which so much attention was given in the first half of this century as a determinant and generator of architectural form. In many cases, the architect's qualitative understanding of structural theory with respect to this type has been largely reduced to the deployment of columns along grid lines.

Another argument for a qualitative treatment of structures is that it is a "prerequisite to quantitative analysis."^{4} In other words, students' interest in the mathematical formulation of structural relationships can be stimulated by the introduction of the same material on a more intuitive basis. Yet, paradoxically, it is also held that this qualitative, intuitive feel for structural behavior can only be obtained by first struggling with the more rigorous analytic approach. Giuseppe de Campoli writes: "It would be easy for the teacher… to reduce instruction in structural design to a discussion of the behavior of a few simplified models. But with such an approach, it is very difficult, if not impossible, for teachers and students alike to obtain a true and general understanding of structural behavior, let alone intuitive building creativity."^{5}

A qualitative grasp of structural behavior can sometimes emerge through the use of formulas in which the relationships among various parameters are expressed mathematically. For example, the bending stress formula, f_{b}=Mc/I, reveals in a remarkably concise way that bending stress will be reduced precisely to the extent that the cross section's moment of inertia is increased. But are we justified, therefore, in simply presenting formulas, or should architects be required to actually understand their derivation. And if so, do these derivations need to be more or less rigorous; should they be relegated to textbook appendixes; or can they be simplified, for example, by examining only special cases of a general condition, as in the derivation of the bending stress formula without calculus by considering only rectangular cross sections.^{6}

The use of physical models or computer graphics provides another means of encouraging a qualitative understanding of structural behavior. If, as Salvadori suggests, "purely structural messages originate in our intuitive understanding of structural behavior, which stems both from our daily experience with structural actions and from our perception of structural forms in nature,"^{7} then it would certainly be useful to harness this latent knowledge. Physical models or interactive computer graphics offer the possibility of extending this intuitive response, ordinarily limited by the kinds of structural behavior that can presumably be grasped through our daily experiences, to a broader class of more complex structural types.^{8}

**LITERACY VS. COMPETENCE**

We are still left with the task of translating these various rationale for the teaching of structures into specific curricular guidelines. Leon Trilling makes a distinction between literacy and competence which is relevant to this discussion. He says: "We are literate in a discipline when we understand its presuppositions, its research techniques and some of its more important results. We are competent in it when we are able to use it for our own purposes."^{9} But what exactly are our purposes?

Given the "division of labor" within the profession of architecture (and therefore within the schools) in which practitioners with various levels and types of technical competence find useful employment, it is improbable that a single unified purpose will emerge, or that a single strategy for teaching structures to architects will be found or should be sought. What is important is not that a particular selection of structural topics and methods be canonized, but rather that course objectives be articulated within each school, and course content be made to correspond to those objectives in a more systematic way.

**Principal Stresses.** As an example in which objectives tend to become somewhat obscure, consider the typical treatment of combined stresses in architectural structures courses. Most structures textbooks written specifically for architects discuss combined stresses, but they do this from surprisingly diverse perspectives. In the case of combined bending and shear stress, for example, several texts omit the topic altogether.^{10} Where it is discussed, the stated objectives — that is, the reasons given as to why an understanding of the topic might be important — vary strikingly from book to book.

According to de Campoli, for example, referring to concrete and steel beams, the topic is included because of the "importance of diagonal stresses as triggers of the failure of the structural materials..."^{11} Salvadori and Levy, on the other hand, emphasize its importance in terms of visualizing stress concentrations: "The isostatics [lines of principal stress or stress trajectories] allow the visualization of the stress pattern in complicated situations."^{12} Finally, according to Shaeffer, the "combinations [of internal stresses] must be considered... in the more form-resistant structures which use thin shell or membrane action to carry loads. Compression in one direction, tension in another, and shear can all act at the same point and interact to cause a unique failure."^{13}

In all of the examples cited, considerable effort is expended to derive the rather complicated relationships between principal stresses, on the one hand, and the conventional bending, axial and shear stresses with which we are more familiar. Additionally, the graphical representation of this relationship invented by Otto Mohr is usually presented. Yet in none of the examples is a numerical method suggested that would actually allow one to solve the types of problems for which the topic was presumably introduced in the first place. Thus the insight into, and manipulation of, states of stress encouraged by the use of this topic tends to become rather petrified and obscure; the complexity of the whole procedure seems out of proportion to its actual application in the design or analysis of the types of simple structural elements to which architects are primarily exposed.

In spite of this, I am not suggesting that this particular topic necessarily should be omitted. For as we have seen, there may be reasons for introducing topics other than just solving structural problems. For example, the ribbed slab used by Nervi in the Gatti Wool Factory in Rome (1951-53) becomes inexplicable without some understanding of principal stresses, as does the pattern of web-shear cracking in a reinforced concrete beam and the rationale for using inclined longitudinal or shear reinforcement. The real issue becomes clearer when we assess the importance of the topic according to the dual criteria of literacy and competence.

From the point of view of structural competence, it would be necessary not only to master the technique, in this case of determining the magnitude and direction of principal stresses resulting from all possible combinations of axial, bending and shear-type stresses, but more importantly to be able to use the technique in a purposeful way. Given the tendency of structural design codes to propound design and analysis methods for typical structural elements in which these principal stresses are not explicitly acknowledged — in other words, where a purposeful application of those techniques is made largely irrelevant by the standardized procedures suggested by design manuals — it is doubtful whether competence, defined in this way, is a reasonable goal in an architectural curriculum.

From the point of view of structural literacy, on the other hand, what becomes crucial is not so much the technique itself, but that connections be made between the derivation or presentation of rather abstract sets of relationships — the formula for the maximum principal stress has no obvious intuitive meaning, except perhaps in the graphic form invented by Mohr — and the whole range of results to which they contribute. In the example just cited, these results might well include all of the issues we mentioned: the failure mechanism of beams; the crowding of isostatic lines at points of stress concentration; the complex combinations of stress in thin shell structures. Where the results are found to be either inconsequential, obscure, or in some way beyond the scope of the architectural curriculum, then the topic itself might well be omitted. Where the results are deemed important, then the derivation or manipulation of mathematical formulas ought to be considered, not as an end in itself, but rather judged by the extent to which it contributes to a deeper appreciation of those results.

**STRUCTURAL DUALITIES**

This conflict between literacy and competence in the teaching of structures to architects could be framed as a series of dualities in which the second term is typically suppressed. In the previous example, the treatment of axial, bending and shear stress as a collection of discrete entities, each with its own method of analysis and its own criteria for design, was contrasted with the more unified notion of an elemental "state of stress" in which the combined action of shear, bending and so on was seen to produce inclined stresses of greater magnitude than those computed separately.

In a similar way, a whole series of such pairs — statics vs. dynamics; member vs. system; strength vs. stiffness; elastic vs. inelastic; even abstraction (load, shear, moment diagrams) vs. reality (actual structure/building behavior) — all can be seen as expressing a certain tension between the desire for competence and the search for structural literacy. This tension comes about because, by essentially circumscribing the areas of inquiry to those topics represented by the first terms and thereby providing a semblance of structural competence, the kind of structural literacy that would be engendered by an appreciation of both terms of the pairs tends to suffer. Consider the following example.

*DETERMINATE VS. INDETERMINATE.* Virtually all structural design and analysis within the architectural curriculum is limited to statically determinate structures, in spite of the fact that most structures designed today are indeterminate.^{14} The rationale for this policy, as articulated by Mario Salvadori, consists of four arguments: "(1) all structures, both statically determinate and indeterminate, obey the laws of statics; (2) statically determinate structures are still widely used; (3) the behavior of statically indeterminate structures may often be excellently approximated by that of simpler statically determinate structures; (4) the behavior of statically determinate structures can be so easily grasped on the basis of purely physical considerations that statics is the best introduction to the behavior of all structures."^{15}

Yet these arguments are really an explanation of why learning about determinate structures might be useful; not an explanation of why indeterminate analysis need not also be taught to architects. Perhaps the explanation is too self-evident to be stated explicitly: while a qualitative understanding of the behavior of all types of structures (including indeterminate ones) is certainly important, the mathematical knowledge prerequisite to an understanding of modern indeterminate analysis techniques cannot reasonably be required of architectural students.

As a result, a number of approaches have been used, alone or in various combinations, to introduce this subject to architectural students: non-mathematical examinations of indeterminate structures based on intuition, models, etc.; approximate analyses (based on simplifying assumptions about relative stiffness or location of inflection points) that reduce the problems to statically determinate ones; iterative methods, such as moment distribution, in which "exact" solutions are approached using relatively simple mathematics; and finally, the presentation of results without explanation, as occurs, for example, in the "beam diagrams and formulas" of the AISC *Manual of Steel Construction*, or in the analysis of indeterminate structures using computers. In the latter case, results can be obtained without having any knowledge of the matrix algebra underlying the method.

Since the early part of this century, it has been hard to make the case that architects ought to be able to do the engineering design for large or complex buildings, which are often statically indeterminate. At the same time, it is hard to imagine how an architect can design and execute such buildings without some insight into their structural behavior and without some method of evaluating different structural options. Yet even if the architecture student possesses some reasonable means of analyzing indeterminate structures, the following pedagogical dilemma remains: how does one impart a sense of structural literacy when the behavior of complex structures and the choices among structural systems often hinge upon the subtle interaction of many variables, some of which, like the costs of material and labor or the availability of particular technologies, are in a constant state of motion and, strictly speaking, are not even structural parameters. Eduardo Torroja says that the "achievement of the final solution is largely a matter of habit, intuition, imagination, common sense, and personal attitude. Only the accumulation of experience," he continues, "can shorten the necessary labor or trial and error involved in the selection of one among the different possible alternatives."^{16} But given the relatively small amount of time allocated to structures within typical professional programs in architecture, coupled with a general insecurity in the use of mathematical tools, how can the architect accumulate such experience?

**PEDAGOGICAL GOALS**

In fact, there are several reasons why the quest for structural literacy is not hopelessly compromised by the architect's lack of quantitative technical competence. As I have suggested elsewhere, architects are able to obtain particular kinds of knowledge about appropriate structural systems either because they have designed similar projects in the past, or because they have studied similar projects designed by others.^{17} Knowing the typical spans and depths of beams, the approximate sizes of columns, and the usual options for the provision of lateral bracing becomes more or less routine in architectural offices that deal repeatedly with conventional structures. Yet this type of "competence" should not be confused with that of the engineer: an architect's "rule of thumb" methodology implies neither insight into structural behavior nor the facility for quantitative analysis. This is not meant as a criticism. Architects, after all, are in the habit of "controlling the spaces to be used by people," and do not primarily think of form "as the means of controlling the forces of nature."^{18}

And what about unconventional structures — "the emergence each year," according to Nervi, "of new structures of increasing size, such as railway and air terminals, industrial buildings, stadia, large theatres and very tall buildings."^{19} For these types of structures, conventional wisdom and rules of thumb may well be inadequate. A more substantial understanding of structural behavior — a more educated intuition — is required. But designing structures of the sort represented in the works of Nervi, Torroja or Frei Otto cannot be the goal of architectural courses in structures. For one thing, few engineers, let alone architects, possess the combination of mathematical competence and artistic intuition which the design of such structures presuppose. As Felix Candela has said, this type of creative act is the "result of long and painstaking work, the fruit of many years of constant effort and steadfast mental occupation with the problem concerned. This is," he says, "…the only way to get the sort of inspiration that all ambitious young architects so ardently wish for."^{20}

Additionally, this quest to "cover increasingly large spans with ever diminishing quantities of materials,"^{21} that is alleged to have animated the history of building construction, has a far more limited role within the great majority of architectural practices. Architecture is no longer defined primarily by the sorts of temples and churches amply represented in history of architecture texts in which the expression and continual refinement of structure contributed to the sense of architectural accomplishment. While structures of that type continue to be built, the heirs to that tradition have generally separated themselves from the profession of architecture, becoming engineering specialists with enormous skill acquired from years of study and practical experience. Architects, on the other hand, have increasingly come to view technical systems as preexisting products of an "optimized technology," to use Frampton's phrase, that can be assembled and manipulated according to rules embodied in codes, specifications and so forth.

The appreciation of structures that can be attained through both qualitative and quantitative study within the limited framework normally provided by architectural curricula should not be confused with the type of creative act outlined by Candela. Even the most rigorous presentation of structural concepts will not promote real structural competence if the material is not internalized — taken apart and re-synthesized — by each student over a period of many years of careful study. And where sufficient information about the structural systems used in the overwhelming majority of building types can be assimilated by the typical architect without such a lifelong commitment to the pursuit of structural knowledge, it is unrealistic to expect such an effort to be made. What should be expected is a certain degree of structural literacy, in which mathematical relationships are studied and employed, not to engender a false sense of competence, but so that the vocabulary of structures, intrinsic to any definition of literacy, becomes more tangible and intelligible.

**NOTES**

^{1} Parker, Harry *Simplified Design of Structural Steel,* 5th Ed. John Wiley & Sons (New York, NY) 1983, pp.197-198

^{2} Shaeffer, R.E. *Building Structures: Elementary Analysis and Design,* Prentice-Hall (Englewood Cliffs, NJ) 1980, p.4

^{3} Nervi, Pier Luigi, "Foreword" in Salvadori, Mario with Heller, Robert *Structure in Architecture: The Building of Buildings,* Prentice-Hall (Englewood Cliffs, NJ) 1986

^{4} Salvadori, *ibid.,* p.449

^{5} de Campoli, Giuseppe, *Statics of Structural Components,* John Wiley & Sons (New York, NY) 1983, p.vii

^{6} This approach is adopted in Salvadori, Mario, *Statics and Strength of Structures,* Prentice-Hall, Inc. (Englewood Cliffs, NJ) 1971, pp.153-157

^{7} Salvadori, Mario, *Why Buildings Stand Up: The Strength of Architecture,* W.W. Norton & Co. (New York, NY) 1980, pp.292-293

^{8} The construction and use of physical models to illustrate structural concepts is discussed in Cowan, Henry J., *Architectural Structures,* Elsevier (New York, NY) 1976, pp.289-300; for a discussion of interactive computer graphics as well as "interactive-adaptive methods," see Abel, John F., "Interactive Computer Graphics for Applied Mechanics," *Proceedings of the Ninth U.S. National Congress of Applied Mechanics American Society of Mechanical Engineers* (New York, NY) 1982, pp.3-27

^{9} Trilling, Leon, "Technology as Part of a Liberal Education," *Technology and Science: Important Distinctions for Liberal Arts Colleges,* Davidson-Sloan New Liberal Arts Program (Davidson, North Carolina) 1984, p.70

^{10} See, for example, Lauer, Kenneth, *Structural Engineering for Architects,* McGraw-Hill Book Co. (New York, NY) 1981; and Benjamin, B.S., *Structures for Architects,* Van Nostrand Reinhold Co. (New York, NY) 1984

^{11} de Campoli, Giuseppe, *Strength of Structural Materials,* John Wiley & Sons (New York, NY) 1984, p.67

^{12} Salvadori, Mario and Levy, Matthys, *Structural Design in Architecture,* Prentice-Hall, Inc. (Englewood Cliffs, NJ) 1981, p.285

^{13} Shaeffer, *op. cit.,* p.170

^{14} This claim is made in White, Richard N., Gergely, Peter and Sexsmith, Robert G., *Structural Engineering, Vol. 2: Indeterminate Structures,* John Wiley & Sons (New York, NY) 1972, p.5; as well as in Salvadori and Heller, *op. cit.,* p.63

^{15} Salvadori Statics, *op. cit.,* p.4

^{16} Torroja, Eduardo, *Philosophy of Structures,* University of California Press (Berkeley, CA) 1958, p.313

^{17} Ochshorn, Jonathan, "Separating Science from Architecture: Why Technology is Taught Outside the Design Studio," *Proceedings of the 1990 ACSA Annual Meeting* (San Francisco, CA)

^{18} Billington, David P., *The Tower and the Bridge,* Basic Books, Inc. (New York, NY) 1983, p.14

^{19} Nervi, Pier Luigi, *Buildings, Projects, Structures 1953-1963,* Frederick A. Praeger (New York, NY) 1963

^{20} Candela, Felix, "Foreword," in Roland, Conrad, *Frei Otto: Tension Structures,* Praeger Publishers (New York) 1970

^{21} Candela, *ibid.*

Last updated 25 January, 2008 [minor re-formatting]