To explain the objectives of structural design and the uncertainties which affect it; to outline how different priorities might influence the design, and to describe different approaches to quantifying the design process.
The fundamental objectives of structural design are discussed. The uncertainties associated with designing structures in terms of loading and material properties are considered. The development of structural design methods for strength and resistance is reviewed briefly and the importance of achieving structural stability is explained. Other design considerations such as deflections, vibration, force resistance and fatigue are discussed. Matters of construction and maintenance are included. The importance of considering these aspects and others, such as accommodating services and cladding costs, in developing an efficient design is emphasised. The responsibilities of the designer and the need for effective communication are considered.
The precise objectives of structural design vary from one project to another. In all cases, the avoidance of collapse is an important - if not the most important - requirement and an adequate factor of safety must be provided. In this context, the structure must be designed in order to fulfil both strength and stability requirements. These concepts are illustrated in Figure 1 in which a long thin rod is subject to tension (Figure 1a) and compression (Figure 1b). In the case of tension, the load resistance of the rod is governed by strength, that is the ability of the material to carry load without rupturing. The rod can only carry this load in compression if it remains stable, i.e. it does not deform significantly in a direction perpendicular to the line of action of the applied load. The stiffness of the structure is yet another important characteristic, concerned with resistance to deformation rather than collapse. This is particulary important in the case of beams whose deflection under a particular load is related to their stiffness (Figure 1c). Large deformations are not necessarily associated with collapse, and some brittle materials, such as glass, may rupture with little prior deformation. Other considerations may also need to be included in the design process. They include: quantifiable behaviour such as deformation, fatigue, fire resistance and dynamic behaviour; considerations such as corrosion and service accommodation which may influence both detail and overall concept, but in a more qualitative way; and appearance, which is largely a subjective judgement. In addition considerations of economy are likely to be a significant influence on the great majority of structural designs. In this context questions of speed and ease of construction, maintenance and running costs, as well as basic building costs, are all relevant. The relative importance of each of these aspects will vary depending on circumstances.
The approach to structural design is dealt with before which describes how the designer might begin to accommodate so many different requirements, many of which will exert conflicting pressures. In this lecture the focus is on how a satisfactory structural design can be achieved through a rational analysis of various aspects of the structure's performance. It is worth emphasising that the process of structural design can be considered as two groups of highly interrelated stages. The first group is concerned with defining the overall structural form - the type of structure, e.g. rigid frame or load bearing walls, the arrangement of structural elements (typically in terms of a structural grid), and the type of structural elements and material to be used, e.g. steel beams, columns and composite floor slabs. A high degree of creativity is required. The synthesis of a solution is developed on the basis of a broad understanding of a wide range of topics. The topics include structural and material behaviour, as well as a feel for the detailed implications of design decisions made at this stage - for instance recognising how deep a beam may need to be for a particular purpose. Formalised procedures are of little use at this stage. A satisfactory solution depends more on the creative ability of the designer.
The later stages are concerned with the more detailed sizing of structural components and the connections between them. By now the problem has become clearly defined and the process can become more formalised. In the case of steelwork the process generally involves selecting an appropriate standard section size, although in some circumstances the designer may wish to use a non-standard cross-section which, for execution, would then need to be made up, typically by welding plates or standard sections together into plate girders or trusses.
Design regulations are largely concerned with this stage of detailed element design. Their intention is to help ensure that buildings are designed and constructed to be safe and fit for purpose. Such design legislation can vary considerably in approach. It may be based simply on performance specification, giving the designer great flexibility as to how a satisfactory solution is achieved. An early example of this is the building laws published by King Hummarabi of Babylon in about 2200BC. They are preserved as a cuneiform inscription on a clay tablet and include such provisions as 'If a builder builds a house for a man and does not make its construction firm and if the house which he has built collapses and causes the death of the owner of the house, then that builder shall be put to death. If it causes the death of the son of the owner of the house, then a son of the builder shall be put to death. If it causes the death of a slave of the owner of the house, then the builder shall give the owner a slave of equal value'. The danger, and at the same time the attraction, of such an approach is that it depends heavily on the ability of the designer. Formal constraints, based on current wisdom, are not included and the engineer has the freedom to justify the design in any way.
The other extreme is a highly prescriptive set of design rules providing 'recipes' for satisfactory solutions. Since these can incorporate the results of previous experience gained over many years, supplemented by more recent research work they might appear to be more secure. However, such an approach cannot be applied to the conceptual stages of design and there are many cases where actual circumstances faced by the designer differ somewhat from those envisaged in the rules. There is also a psychological danger that such design rules assume an 'absolute' validity and a blind faith in the results of using the rules may be adopted.
Clearly there is a role for both the above approaches. Perhaps the best approach would be achieved by specifying satisfactory performance criteria to minimise the possibility of collapse or any other type of 'failure'. Engineers should then be given the freedom to achieve the criteria in a variety of ways, but also be provided with the benefit of available data to be used if appropriate. Perhaps the most important aspect is the attitude of the engineer which should be based on simple 'common sense' and include a healthy element of scepticism of the design rules themselves.
2. UNCERTAINTIES IN STRUCTURAL DESIGN
Simply quantifying the design process, using sophisticated analytical techniques and employing powerful computers does not eliminate the uncertainties associated with structural design, although it may reduce some of them.
These uncertainties include the following:
• constitutive laws of the material.
• structural modelling.
• structural imperfections.
Loading is discussed in more detail in before. Although it is possible to quantify loads on a structure, it is important to recognise that in most cases these represent little more than an estimate of the likely maximum load intensity to which a structure will be exposed. Some loads, such as the self weight of the structure, may appear to be more easily defined than others, such as wind loads or gravity waves on offshore structures. However, there is a significant degree of uncertainty associated with all loads and this should always be recognised.
Constitutive laws are typically based on the results of tests carried out on small specimens. For convenience, the mathematical representation of the behaviour, for instance in the form of a stress-strain curve, is considered in a simplified form for the purpose of structural design. In the case of steel the normal representation is linear elastic behaviour up to the yield point with plastic behaviour at higher strains (Figure 2). Although this representation provides a reasonable measure of the performance of the material, it is clearly not absolutely precise. Furthermore, any material will show a natural variability - two different samples taken from the same batch will typically fail at different stresses when tested. Compared with other materials, steel is remarkably consistent in this respect, but nevertheless variations exist and represent a further source of uncertainty.
Methods of analysing structural behaviour have advanced significantly in recent years, particularly as a result of developments in computing. Despite this, structural analysis is always based on some idealisation of the real behaviour. In some cases, such as isolated beams supported on simple bearings, the idealisation may be quite accurate. In other circumstances, however, the difference between the model and the real structure may be quite significant. One example of this is the truss which is typically assumed to have pinned joints, although the joints may in fact be quite rigid and some members may be continuous. The assumption that loadings are applied only at joint positions may be unrealistic. Whilst these simplifications may be adequate in modelling overall performance the implications, at least with regard to secondary effects, must be recognised.
Yet another source of uncertainty results from structural imperfections which are of two types: geometrical, i.e. out of straightness or lack of fit, and mechanical, i.e. residual stresses due to fabrication procedures or inhomogenities in the material properties. It is not possible to manufacture steel sections to absolute dimensions - wear on machinery and inevitable variations in the manufacturing process will lead to small variations which must be recognised. In the same way, although steel construction is carried out to much tighter tolerances than for most other structural materials, some variations (for instance in the alignment of individual members) will occur (Figure 3).
In adopting a quantified approach to structural design, all these uncertainties must be recognised, and taken into account. They are allowed for by the following means:
• specifying load levels which, based on previous experience, represent the worst conditions which might relate to a particular structural type.
• specifying a sampling procedure, a test plan and limits on material properties.
• specifying limits or tolerances for both manufacture and execution.
• using appropriate methods of analysis, whilst recognising the difference between real and idealised behaviour.
These measures do not eliminate the uncertainties but simply help to control them within defined bounds.
3. DESIGNING TO AVOID COLLAPSE
3.1 Historical Background
Structural design is not something which is new. Ever since man started building - dwellings, places of worship, bridges - some design philosophy has been followed, albeit often unconsciously. For many centuries the basis of design was simply to copy previous "designs". Where "new developments" or modifications were introduced, trial and error techniques were all that was available. As a result many structures were built, or partially built only to collapse or perform inadequately. Yet these failures did have a positive value in that they contributed to the fund of knowledge about what is workable and what is not.
This unscientific approach persisted for many centuries. Indeed it still forms part of the design approach adopted today. Rules of thumb and empirical design recommendations are frequently used, and these are largely based on previous experience. Nor is structural engineering today totally free of failures, despite the apparent sophistication of design methods and the power of computers. The dramatic box girder bridge collapses in the early 1970s were a grim reminder of what can happen if new developments are too far ahead of existing experience.
The emergence of new materials, notably cast and wrought iron, required a new approach and the development of more scientific methods. The new approach included testing, both of samples of the material and proof testing of structural components and assemblies. New concepts too were sometimes justified in this way, for instance in the case of the Forth Rail Bridge.
The first moves to rationalise structural design in a quantitative way came at the beginning of the 19th century with the development of elastic analysis. This type of analysis allowed engineers to determine the effect (on individual structural components) of forces applied to a complete structure.
Testing of materials provided information concerning strength and, in the case of iron and steel, other characteristics such as the elastic limit. Of course there were often great variations in the values measured, as indeed there are even today with some materials. In order to ensure a safe design, a lower bound on the test results - a value below which experimental data did not fall - was normally adopted as the 'strength'. Recognising some of the uncertainties associated with design methods based on calculation, stresses under maximum working load conditions were limited to a value equal to the elastic limit divided by a factor of safety. This factor of safety was specified in an apparently arbitrary fashion with values of 4 or 5 being quite typical.
This approach provided the basis of almost all structural design calculations until quite recently, and for some applications is still used today. As understanding of material behaviour has increased and safety factors have become more rationalised, so design strengths have changed. Changes in construction practice, and the development of new, higher strength materials, have necessitated detailed changes in design rules, particularly with regard to buckling behaviour. However the basic approach remained unchanged until quite recently when certain limitations in classical allowable-stress design became apparent. The limitations can be summarised as follows:
i. there is no recognition of the different levels of uncertainty associated with different types of load.
ii. different types of structure may have significantly different factors of safety in terms of collapse, and these differences do not appear in any quantifiable form.
iii. there is no recognition of the ductility and post-yield reserve of strength characteristic of structural steelwork.
The last of these limitations was overcome by the work of Baker  and his colleagues in the 1930s when plastic design was developed. This method was based upon ensuring a global factor of safety against collapse, allowing localised 'failure' with a redistribution of bending stresses. A comparison of elastic and plastic design is given by Beal .
In recognition of the disadvantages of the allowable stress design method, an alternative approach, known as limit state design has been adopted. Limit state design procedures have now become well established for most structural types and materials. The approach recognises the inevitable variability and uncertainty in quantifying structural performance, including the uncertainties of material characteristics and loading levels. Ideally, each uncertainty is typically treated in a similar manner using statistical techniques to identify typical or characteristic values and the degree of variation to be expected from this norm . It is then possible to derive partial safety factors, one for each aspect of design uncertainty, which are consistent. Thus different load types, for instance, have different factors applied to them. The structure is then examined for a variety of limit states. In that case the structure is designed to fail under factored loading conditions, giving a clearer picture of the margins of safety than was previously the case with allowable stress design.
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