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The Structural Engineer, Vol. 72, No. 2, 18 Jan. 1994

Limit state at 40: new beginning or midlife crisis?

A. N. Beal BSc CEng MlStructE MICE

Thomason Partnership

Introduction

The development of limit state design, based on partial safety factors, began in earnest with the formation of the European Committee for Concrete (CEB) in 1953. As far as many engineers are concerned, the limit state revolution is now all but over: permissible stress design is still in use, but most new Codes worldwide are based on the partial factor approach and it forms the basis of all the new draft structural Eurocodes.

In some senses, however, the revolution has yet to begin. Although the early limit state Codes like CP110 [1] gave no significant advantage in economy over their permissible stress ‘cousins’, it was always intended that this stage would be only a beginning. Once engineers were used to the complexities of the new approach, statistics and probability theory were to be used to transform and refine safety calculations, bringing substantial improvements in structural economy. As Rowe, Cranston & Best put it in 1965 ‘... it is necessary at this stage to introduce conservative factors in the limit state approach to design; these will be reduced in a logical manner as more experimental data are obtained’ [2].

In the mid-1970s, enthusiasts talked [3] of safety factors as low as 1.1 and the Codes that appeared (e.g. BS5628 [4] and BS5400 [5] were even more complicated than CP110. However, despite considerable effort, there has been little real progress towards the original goal and the technical basis of most partial factor Codes remains ‘comparison with existing practice’ in other words, just like CP110, they are intended to give similar results to their permissible stress predecessors.

The reasons for this lack of progress are partly practical (such as lack of adequate research data), but also theoretical, where some fairly serious difficulties have been encountered. At present, limit state Codes lack a coherent theoretical basis and there are a number of problems that require attention.

Statistics and probability theory

In principle, the idea was simple: the uncertainties that affect structural design would be identified and their potential variations quantified statistically, allowing appropriate partial safety factors to be calculated. These would then combine to generate designs with the intended probability of failure. However, the idea has proved unexpectedly difficult to implement in practice.

(1) ‘Characteristic’ loads were originally defined in statistical terms, based on probabilities of exceedence during a stated design life. However, today’s ‘characteristic’ dead load is simply a mean value and ‘characteristic’ imposed floor loads are simply the traditional values based on practical observation and experience. The term ‘characteristic’ no longer seems to serve a useful purpose.

(2) Most superimposed dead loads (partitions, ceilings, floor finishes, roof tiling, etc.) can generally be calculated quite accurately when the structure is new, but they may change completely in the course of its life [6].  How should the ‘characteristic’ values of superimposed dead loads be defined and should they he allocated a high or low value of γf?

(3) Changes in permitted lorry weights and the nature and volume of traffic have combined to make a mockery of the designs of some modern bridges built only 25 or 30 years ago. In these circumstances do statistical ‘120-year design life’ loadings have any real meaning?

(4) Design Codes refer to statistically-defined ‘characteristic’ strengths for steel and concrete but the relevant materials specifications give acceptance rules that bear no real relationship to the ‘characteristic strength’ definition. Statistically-based acceptance rules for concrete were tried in CP114 and CP110 but both were impractical to use and often generated odd and illogical results [7]. The proposals in the latest European draft specification for concrete, ENV206 [8], are similarly flawed.

Partial factors

There are many different systems of partial factors - BS5950 [9] uses one factor, BS8110 [10] uses two, with one incorporated into tabulated stresses, BS5628 uses two explicitly and BS5400 uses three. Indeed, when differences in γ values are taken into account, there are probably as many different systems of factors as there are Codes.

PD6529: 1990 [11] proposes that in future γf values should be determined by the loading Code committee, rather than the main structural design Code committees. Some see this as a way of creating consistency but such a division of responsibility could be dangerous, with neither committee seeing itself as responsible for overall safety. Normal engineering wisdom stresses the importance of single lines of responsibility in safety matters.

There are also some engineering anomalies to be addressed. In buckling calculations, member strength depends on the modulus of elasticity E but, in present Codes, the full γm is not usually applied to E; this leads to the surprising (and surely wrong) conclusion that long, slender columns should have lower safety factors than short, stocky ones. In prestressed concrete, γm is not applied to the prestressing force, so when unbonded tendons are used the safety factor is reduced. On the other hand, BS 5628 applies γf to standard ‘middle third’ overturning calculations, resulting in needlessly conservative results.

Calibration

Although current limit state Codes are supposed to give similar results to past practice, many do not. There has been a general tendency to reduce safety factors, motivated by the need to promote use of the new, more complex Codes. The steel Code BS5950 has introduced the lowest overall safety factors ever permitted by a British building Code (typically only 1.45-1.55 compared with the BS 449 [12] general value of 1.7).

Most limit state Codes allocate lower values of γf to dead loads than to imposed loads. It was argued that the self-weight of the structure can be determined more accurately than imposed loads - hence the lower safety factor. However over time the term ‘dead load’ has come to include other items such as finishes, partitions, suspended services, and ceilings. In today’s Codes the lower γf covers almost any permanent or long-term loading, including items such as earth pressure which are among the least accurately known loads acting on the structure.

On the other hand, the safety factor on wind load is tending to increase: for structures resisting only dead load and wind load, BS8110 and BS5950 allow no increase on basic design stresses for the wind load combination, whereas previously a 25% increase was permitted. The draft Eurocodes take matters even further, classifying wind load as an ‘imposed load’ with γf of 1.5, compared with 1.35 for permanent loads.

This leads to the paradoxical situation where a wall designed to resist a once-in-50 years wind gust requires a safety factor equal to, or greater than, that for one resisting permanent earth pressure.

Major changes have been made in the treatment of overturning. Until its latest revision, the permissible stress steel Code BS449 specified overturning safety factors of 1.2 for dead load and 1.4 for imposed and wind loads; these factors were accepted as reasonable and used without trouble for many years. However, although BS5950 specifies the same factor for (dead+wind) load, it increases the factor to 1.4 for dead load and to 1.6 for live load but reduces it to 1.2 for (dead+live+wind) load. The concrete Code BS8110 is generally similar but reduces the safety factor for (dead+live+ wind) load to only 1.0.

It is difficult to believe that the changes outlined above are the result of a considered programme of scientific research, yet many of them can clearly not have arisen from calibrations against proven past practice. In engineering terms, they have a distinctly haphazard ‘feel’, which does not inspire confidence.

Problems with numbers

It is clear from experience with limit state Codes that, no matter how plausible and logical an idea may sound in principle, its validity can be assessed only when it is translated into firm, detailed proposals, complete with all the relevant numbers. Some apparently plausible ideas simply do not work in practice, while others work in some situations but create unintended new problems in others.

The most obvious area is in the treatment of overturning stability, briefly referred to earlier. In the 1970s, engineers were frequently reminded that overturning stability was the Achilles heel of permissible stress design and a major aspect of the superiority of limit state Codes such as CP110. What appeared to escape attention was that the CP110 recommendations (which were the same as those in BS8110, outlined previously) gave odd and unsatisfactory answers, requiring safety factors for ordinary dead and live loads which were possibly a little high but a factor for (dead+live+wind) load (1.0) that was indefensibly low. BS 5628 [4] has had even greater problems, which are still not properly resolved: as originally drafted, the required safety factor against overturning for imposed load could be anything between 1.78 and 5.3, depending on the clause referred to.

The reason for these problems is that, while it is easy to devise a system of partial factors that gives sensible answers for simple beam design, or one that works for overturning stability, it is very difficult to devise a system that reliably gives sensible answers for both. To date, as far as the author is aware, no published (or draft) limit state Code available in this country has given a satisfactory treatment of overturning stability; all of them have been clearly inferior to BS449.

A second problem that has proved surprisingly intractable in practice is the apparently simple matter of analysing a continuous beam under dead load. Because dead load can vary in practice, it was proposed that it should be factored up or down, with different values of γf applied as appropriate for worst effect. Unfortunately, this can generate some highly improbable loadings that play havoc with the detailing and economics of balanced and continuous structures [13, 14]. The problem was partially solved in BS5400 by ignoring local dead load variations and in BS8110 by allowing some beams and slabs to be designed for the single load case of ‘all spans loaded’. However, these create new anomalies and the problem still awaits a proper solution.

Conclusions

Many of the originally claimed benefits of limit state design have proved elusive in practice and, instead of an orderly progress towards more rational safety factors, there appears to have been a series of uncoordinated and haphazard changes, some of which give results clearly less rational than their predecessors.

In this situation, the temptation is to seek a new scheme or formula - a ‘cunning plan’ which would allow us to escape the problems of the past and transform design for the better. If there is one lesson to be learnt from the last 20 years, it is the need for caution in assessing the claims made by proponents of a new approach, particularly when it is offered only in ‘in principle’ form, without all the numbers worked out. As experience with existing limit state Codes has shown, the devil is in the detail ...

Where do we go from here? There is a need to harmonise and simplify the existing Codes and, clearly, overturning stability needs to be sorted out urgently; unless someone has a bright idea, the best answer would be simply to treat it separately from normal design, with appropriate safety factors to suit. Also, is the present division of safety margin between loads and materials correct? Current Codes allocate 1.4-1.6 to γf and 1.0-1.15 to γm (steel), yet studies of real failures show that, except in clear cases of misuse, they are almost always caused by inadequate strength rather than the variability of normal loads. This suggests that most of the safety margin should be transferred from loads to the materials side of the equation.

References

1.     CP110 The structural use of concrete: Part 1, London, British Standards Institution, 1972.

2.   Rowe, R. E., Cranston, W. B. and Best, B. C.: ‘New concepts in the design of structural concrete’, The Structural Engineer, 43, No. 12, December 1965, p. 402.

3.     Rose, G., quoted in ‘Where do we draw the limit?’, New Civil Engineer, 29 April 1976.

4.     BS5628 Structural use of masonry: Part 1, London, British Standards Institution, 1978.

5.   BS5400 Steel, concrete and composite bridges: Part 4: Code of practice for design of concrete bridges, London, British Standards Institution, 1978.

6.    Beal, A. N.: ‘Secondary dead load and the limit state approach’, Concrete, September 1981, p. 31.

7.   Beal, A. N.: ‘Concrete cube strengths - what use are statistics?’, Proc. ICE, Part 2, 73, December 1981, p. 1037.

8.   DD ENV206 ‘Concrete - Performance, production, placing and compliance criteria’, London, British Standards Institution, 1992.

9.   BS5950 Structural use of steelwork in building: Part 1: Code of practice for design in simple and continuous construction: hot rolled sections, London, British Standards Institution, 1990.

10.  BS8110 Structural use of concrete: Part 1: Code of practice for design and construction, London, British Standards Institution, 1985.

11.  PD6529 Report on a new approach for design loads for buildings, London, British Standards Institution, 1990.

12. BS449 Specification for the use of structural steel in building: Part 2: London, British Standards Institution, 1969.

13.  Beal, A. N.: ‘What’s wrong with load factor design?’, Proc. ICE, Part 1, 66, November 1979, p. 595.

14.  Beeby, A. W.: ‘Are our Code provisions for slabs safe?’, The Structural Engineer, 59A, No. 11, November 1981.

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