The text presented here is not precisely as published by OUP, but modifications are minor. Illustrations are another matter. Where images used in the original book were not my copyright, I have in most cases been able to substitute links to coloured images on the web.

When this text was submitted as part of a PhD thesis in 1996, the Notes were greatly extended. Most readers may prefer to ignore them. They have been collected at the end of each chapter, with internal links leading to them and back to the text. They are a mixture of: simple page references; additional examples or quotations to justify generalisations; and some afterthoughts.

Introduction.

The final phase of the design process is evaluation. This includes checking individual alternatives to ensure that they are safe and feasible, and the comparison of feasible alternatives in order to choose the 'best' one. As we have seen this will often intrude into the early phases of problem definition and postulation of alternative solutions. Designers often make value judgements subconsciously and, in adhering to prevailing attitudes, unconsciously eliminate possible solutions. However, we shall concentrate in this section on the various ways in which we consciously determine whether a solution is satisfactory and what we mean when we say that one out of several alternatives is 'best'.

We have seen that, in the overall process of politics and planning, a great many subjective value judgements must be made. We have already looked at the attempts of some cost-benefit analysts to include these factors in their investigations (Chapter 4). When it is necessary to compare the aesthetic value of alternatives and the extent to which they fulfil psychological functions such as providing privacy or evoking religious feelings in the observer, notwithstanding the theories of aesthetics and psychological response which are available, the decision-maker is on shaky ground.

As the politician, the businessman and the architect make more and more subjective judgements, so the scope of the problem is narrowed, the solution becomes more circumscribed, and the need for subjective decisions decreases. The resulting problem presented to the engineer, and its solution by him, can, for the sake of argument, be considered in isolation as the 'technological sub-problem', as long as proposed sub- solutions do not throw up new questions requiring subjective or quantitative appraisal from the non-engineers. (In building design the concept of an isolated technological sub-cycle is almost as idealized as that of separate phases in the design process.) Even this technological portion must involve some decisions which leave room for debate. They include the assessment of loads and the choice of safety factors, the estimation of money costs, and the evaluation of factors such as ease of construction and fabrication.

Once these decisions have been made, we come at last to the definition of the mathematical model. After this stage it is possible to apply rigorous analysis and to base decisions on some reasonably quantifiable factors.

Many engineering students accord this final stage an undue amount of respect on account of its alleged intellectual superiority over those that have gone before. It is valued for the intellectual discipline it involves, the clarity of its logic, and the way in which it appears to remove responsibility from the person involved and rest it upon immutable natural laws. Unfortunately these characteristics have been bought at the expense of a great many bold definitions of concepts, and simplifications of theory, and approximations required by variability of data. A feeling of security within this world of computation is thus achieved only by donning a pair of blinkers and refusing to recognize the enormous number of subjective decisions which have gone before. The computations are in fact merely the tip of the iceberg.

Some take the view that aesthetics, economics and functional suitability become irrelevant if the structure falls down, so that technological considerations must be the most important of all. However, it can be argued that if the structure is ugly, does not perform its intended function and is uneconomic, it might be best if it did fall down!

The relationship between the technological sub-cycle and the larger cycle is therefore one of interdependence and little is to be gained from the common practice of disparaging the contributions of other disciplines and professions by comparing them unfavourably to the alleged rigour of structural analysis.

The importance of imagination and general knowledge in evaluation.

The phase of Evaluation is usually treated as a purely rational process of analysis, even in psychological accounts of the creative or problem-solving process. Few authors place sufficient emphasis on the importance of imagination at this stage. In order to criticize a proposed solution the designer must envisage how it will perform in future service. He must imagine what could go wrong and in what way, and how seriously this might affect the functioning of the project. Trying to foresee shortcomings which have not been revealed by the previous experience of the designer requires a degree of imagination which must be closely related to creativity. The more innovative the design, the more creativity will be required in its criticism.

Collins, in his interesting comparison of architectural judgement with legal judgement points out that many legal scholars consider imagination and creativity to be of great importance in the judicial process (1971, p.33). Jones is another who has emphasized the necessity for accurate and imaginative prediction of future performance and underlines the need that this raises for accurate models, be they physical, mathematical or purely conceptual (1981).

The more extensive the designer's knowledge, at both the general and theoretical levels, the more likely are his predictive models to be accurate and comprehensive. (One of the most common mistakes of students in design is to become so mesmorized by the detailed stress calculations that they forget about fundamental criteria, such as overall stability.) There is thus a direct connection, through the evaluation stage, between knowledge and successful purposeful creativity. This is the main service provided by traditional textbooks and by journals.

More formal ways of avoiding inadequate evaluation include the use of check-lists (e.g. Section 6, Jones 1981) and checks by independent designers as in the German 'Prüfingenieur' system. This latter procedure is now common throughout the world in the design of important bridges and multi-storey buildings. Familiarity with reports of failures is another highly important means of avoiding similar catastrophes in other structures, and an introduction to the literature of failure should be a part of every student's education.

Decision-making in subjective areas.

The literature on this final stage of the design process falls into two broad categories. The first contains self-conscious 'Decision-Theory' and includes approaches based on business management techniques mathematics (Linear programming, Reliability Theory, etc.) and psychology. The second includes the codes and standard texts on 'Design of Structures' which explain the traditional rationale. This is mainly confined to the technological sub-cycle, and is rarely identified specifically as 'Decision-Making'.

Since the second category is outside the scope of this book, we shall refer only to the first, beginning with a brief look at what tends to happen in the absence of self-conscious 'Decision-Making'.

Having eliminated all unworkable proposals, the designer is left with a number of feasible alternative solutions. Some of these may be eliminated quite simply. For example, there may be two which have similar advantages but differing capital cost, and the more expensive can be rejected immediately. Others may be ruled out because they far exceed the client's budget allocation. In choosing amongst the remainder, two major difficulties arise.

The first is that no common scale exists upon which the various advantages and disadvantages of each proposal may be totalled to permit comparison with others. Is it preferable to choose a costly proposal which very nearly satisfies the desired function or a cheaper one which is less satisfactory? Is it better to adopt a solution that is functional but ugly or one that is less efficient but beautiful, if they both cost the same amount of money? Can aesthetic merit and utility be awarded numerical values and added on the same scale to afford a comparison?

The most common yardstick proposed even for this task is money, but this raises the problem of deciding the monetary value of intangible factors, such as appearance, comfort and convenience. As we have seen, some cost-benefit analysts assume that such assessments can be made. The market value of a house which commands a scenic view may be several thousand dollars more than that of an identical one without a view. This can be said to fix the value at that point of time of that particular scene in terms of the local community's assessment of its benefit.

In most cases, however, comparisons of this nature are not available and most decisions are made without the aid of such an analysis. What happens is that the person or group making the decision has its own, often subconscious, ideas of the relative values of the factors involved. These are necessarily more nebulous than market values, and in the eyes of goal-centred engineers appear to contrast strangely with the rigorous nature of the associated engineering computations. The more intelligent value judgements are based on wide experience backed up by a comprehensive and critical reading of the literature in a particular field.

Matters of functional and aesthetic sufficiency are discussed in textbooks and journals normally to be found in the architecture section of the library. Unfortunately, this literature is far from complete. Books are available on the functioning of common buildings such as offices, schools, restaurants, hospitals and laboratories, but they rarely assess actual examples in a critical manner. Even less is written about industrial buildings. The recently established disciplines of 'Performance Research' and 'Performance Design' are welcome moves to place judgements in this area on a more sound footing. [Note 1.]

Actual failures in aesthetics and function are not well documented because assessment of the former is highly subjective and functional shortcomings do not force themselves on the public and professional consciousness in the same way as catastrophic structural failures. In fact, the term 'failure' is rarely applied in these most important senses outside the field of Performance Research.

The network of interrelated value judgments employed in decision-making by the new graduate must thus depend more on cultural conditioning than on rational appraisal, until such time as it can be supplemented by personal evaluation based on experience and continued debate. An important factor at work here is the process known as 'professionalization' whereby students working towards membership of a particular profession are persuaded to adopt the traditional perspectives of that body. We have already seen the difficulties that this causes in relations between engineers and architects.

We have also seen how some engineers attempt to avoid this conflict by simply striving to fulfil the architect's demands. However, this approach overlooks the engineer's responsibility to those who finance the project, and to society at large. In any case the cyclic nature of the design process, the impossibility of presenting a complete brief to the engineer and the problems of acquainting the client with the full range of possibilities, ensure that in practice, all engineers must normally employ their own value judgements, consciously or unconsciously, in responding to the demands of client units.

There are of course matters within the traditional scope of structural design about which it is considered to be the engineer's normal duty to make a subjective choice on behalf of his client. The most important is the choice of safety margins. Although this responsibility is in general borne on behalf of the entire profession by the Committees which frame the Codes of Practice, the individual designer often makes significant decisions about the type of hazards to be catered for, and the degree of damage which will be tolerated in extreme cases.

Quite naturally, texts about engineering 'Decision Making' generally avoid this messy business. The question of whose scales of values will prevail is considered to be a matter of politics and is left to authors in the areas of 'Administrative' or 'Behavioural Studies'.

The philosophy of value is a subject in itself dealt with by philosophers and psychologists. Measurement is also seen as a distinct topic particularly with regard to intangibles, such as values and preferences. Both these areas are discussed of necessity in texts on Operations Research and Systems Analysis. [Note 2.]

All these sources propose methods of subjectively assessing relative worths and weights to arrive at a numerical value factor which includes all the merits and demerits of each alternative. Many practical designers would think, however, that in view of the large number of subjective decisions required to arrive at such a figure, only large differences in value would be significant, and these would be fairly predictable without systematic assessment. Once more, the technologist's need to record the reasons for decisions; to introduce a greater feeling of certainty; to minimize personal responsibility; and to justify the decision to colleagues must provide the major driving force for the development of such techniques.

Even when some comparison of merit has been achieved, a second difficulty may complicate the issue. As we saw in an earlier chapter, factors such as future utilization, performance, and problems and costs of construction may be difficult to predict, so that merit and cost can only be assessed within certain limits. Thus it may be impossible to make a definite decision between two or more alternatives.

This problem of uncertainty has received the attention of mathematicians and the resulting techniques are included under the heading of 'Decision Theory', an offspring of Operational Research. The question of safety and reliability has been discussed at length in both philosophical and mathematical terms, and there is currently great interest in the application of the Theory of Probability.

The application of precise mathematical techniques such as statistical analysis, calculus and linear programming, and even those which in practice involve a certain amount of skill and experience such as calculus of variations and non-linear programming again contrast strangely with the subjectivity of the original value judgements on which they must be based. This has led to the development of 'Fuzzy Set Theory' which attempts to cater for the uncertainty surrounding the parameters in decision-making.

Evaluation and decision-making in the technological sub-cycle.

When we come to the computational sub-cycle of structural design for strength and stiffness, we are on more solid ground. Within the constraints set by previous decisions on subjective matters the engineer is able to define the 'best' structural alternative as that which minimizes some quantifiable factor such as the weight of material required, or the estimated total cost.

Gallagher provides a concise review of the various approaches to this highly restricted problem (1973, p.1-3). First is the "Theory of Layout" which is concerned with finding the minimum weight for an undefined configuration of axially loaded linear members of a given material based purely on strength considerations. This approach produces structures of fascinating shape (Fig. 16.1) but it is of little practical value because it fails to take account of the usual constraints on geometric form. Classical approaches also neglect the problem of buckling. However, one major advantage of such structures is their inherent stiffness per unit weight. Some applications have therefore been found in the aerospace industry. The advent of the computer has permitted more realistic approaches which show considerable promise.

Fig. 16.1. Mitchell structures: structures designed to transmit load from specified points of application to supports using a minimum weight of linear elements.

The next approach described by Gallagher is the "simultaneous mode of failure" concept. This assumes that optimality is achieved by ensuring that each member simultaneously reaches the point of failure. Of course, this can normally be true for only one loading case.

The equivalent goal of the practical designer is "fully stressed design". In this case the idea is that each member should reach its "fully stressed" condition under at least one loading condition. The limiting "full stress" is either the limit which provides adequate safety against buckling or that which ensures against material failure, so that the approach does allow for more than one criterion. However, there is no guarantee that a fully stressed design is an optimum in any sense of the word. Furthermore, the approach is limited to the selection of member sizes for a fixed structure geometry in a specified material. Limits on deflections must be considered separately and often require a departure from the "fully stressed" solution.

While 'F.S.D.' provides a practicable approach to the choice of form and member size in everyday design, its relative simplicity results from the a priori specification of sufficient optimality criteria to reduce the problem to a manageable size. [Note 3.]

A great deal of work has been done on computer programs for iterative progression towards the optimum. Once again it is necessary to make an initial guess as to the structural form that will provide the best starting point for the iterative process. Obviously this should contain as many elements of the final solution as possible. Horne and Morris in discussing Limit Design suggest that the programmer should use the practical engineer's approach by "exploiting the fact that certain criteria are known to be of over-riding importance" (1973, p.267). They suggest that starting the iteration from an initial solution which satisfies the ultimate strength criterion will ensure rapid convergence. In contrast, "initial proportioning based on limiting deflections or on maximum stresses is highly non-linear, making these criteria an unsuitable starting point computationally".

Referring specifically to reinforced concrete design, Bond points out that many decisions, such as the arrangement of sizes so that formwork is re-usable, the adoption of precasting with its resulting problems of connectivity and the adaptation of the design to local site conditions are difficult or impossible to program (1973, p.283). Also, overall dimensions of members are reasonably accurately chosen by experienced designers without computation and are in any case liable to be fixed by architectural considerations. Furthermore, if the designer is to use the program for the practical purpose of searching for the solution of least cost rather than least weight, he must depend on unit costs which are subject to the inaccuracies outlined in a Chapter 4.

Automatic decision-making by computer is therefore at a fairly elementary stage in its development and can serve only as an aid to the technological sub-cycle for the foreseeable future.

Recent years have seen the development of Reliability Theory which recognizes that there is a relationship between the projected life of a structure, the magnitude of the loads to which it is likely to be subjected and the behaviour of the materials of which it is composed. Thus the 'best' structure is considered to be that which has the optimum life for a chosen factor of safety, or the optimum factor of safety for a given life.

Structural engineers (other than those engaged in the aeronautical industry) have not been particularly concerned with such considerations in the past, although bridges and cranes are two obvious categories of structure to which they can be profitably applied. Reliability Analysis is related to Probabilistic Design and is becoming more relevant as attempts at optimization reduce the true factors of safety of complete structures, as highly random but extreme loadings such as earthquakes, tornadoes and ocean waves are taken into consideration, and as structural engineers recognize the real complexity of the definition of 'failure' of a structure in terms of Limit Design.

Thompson and Hunt have sounded a note of warning with regard to optimization by the F.S.D. method without reliability analysis (1974, p.99, 100). If this approach is applied rigorously, the result may be too low a factor of safety against total collapse. A popular illustration of this is Oliver Wendell Holmes' fictional 'one-hoss shay' (a light open carriage) which was so well-proportioned that, precisely at the end of its appointed design life, it totally disintegrated! [Note 4.] Building owners prefer some warning of impending failure and the option of repairing or restoring the structure before it collapses.

In summary, it can be said that while structural engineers have been very concerned about optimization of the goal-centred computational sub-cycle either as practitioners applying traditional methods, or as academics developing mathematical techniques, there has been little of the formal interest in decision-making in the larger cycle that would have led to the application of design methodology, systems analysis and operations research.

Admittedly, these techniques are not panaceas. When the internal politics of an organization take over, and political skill and force of personality count for most, it is little help to have three alternative theories of value. [Note 5.] However, like our theories of mechanics, these concepts are useful tools which enable us to grapple more effectively with the increasingly complex problems that the engineer is now being asked to handle.

Notes.

Note 1. Broadbent (1973), pp. 283 and 284. See also Brill,M. Evaluating buildings on a performance basis, pp.316-9, and Gutman,R. and Westergaard,B. Building evaluation and user satisfaction and design, pp.320-9, in Lang,J.T. et al (eds) (1974). [Return.]

Note 2. Hall (1962) (Chapter 8 on measurement, Chapters 9, 10, and 12 on value), Bross (1953) (Chapter 5 on value, Chapter 12 on measurement) and Churchman et al (on values: pp.122-3 and 130-1, and Chapter 6). Second thoughts on the value of Operations Research are expressed in Ackoff,R.L. The future of operations research is past. Journal of Operations Research, Vol.30 (2) Feb. 1979, pp. 93-104. [Return.]

Note 3. Based on Gallagher (1973). General coverage pp. 19-32. A priori specification, p.33. [Return.]

Note 4. There were two famous Oliver Wendell Holmes's. The father was a doctor and minor poet. The son was a highly-respected lawyer. The poem is reproduced in full in Petroski (1982), pp. 35-9. It is long, but commences with:
"Have you heard of the wonderful one-hoss shay,
That was built in such a logical way,
It ran a hundred years to the day,
And then of a sudden it &" [Return.]

Note 5. This was a reference to the economic, the psychological, and the casuistic theories of value as described in Hall (1962), Chapters 9, 10, and 12. [Return.]

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