4 Limit State Design

condition. It is thus possible to build up an overall, or‘global’, factor of safety from these individual factors.

The global factor of safety may be divided into two groups:

Group 1 The factor of safety to be applied to the materialsand to the workmanship used in the construc-tion of the structure.

Group 2 The factor of safety to be applied to the loads in the overall structure and the consequences offailure.

Group 1

The factor of safety for materials and workmanship will bebased on the probability of the material failing to reach its expected strength. In reinforced concrete, for example,there are two basic components. One is steel, which is man-ufactured in a factory with a high degree of control over itsproduction, and the probability of an inferior piece of steelis moderately low. However concrete is made from naturalmaterials which are mixed together on site, or at a batchingplant, where the degree of control is relatively reduced. Inaddition, the placing of the concrete will affect its overallstrength and, since this is done by unskilled or semi-skilledlabour, the degree of control is further reduced.

The materials used in basic structural masonry are: (a) thestructural units which are manufactured from natural claysor concrete or stone, and (b) mortar which is made up ofcement, sand, water and a plasticiser – usually lime. Thequality control of the structural units could be likened tothat of steel, with controlled sampling of the product fromthe production line. It is also possible to check the strengthof a randomly selected unit, or group of units, by means ofload tests which will give a reasonable indication of thestrength of the units actually used. This is an advantageover concrete in that the method of testing concrete is tomanufacture a cube which may not be cured in the samemanner as the actual concrete used on site. Masonry unitsare, therefore, products over which there is reasonable con-trol and some limit to the probability of failure.

Mortar presents a different problem. Although it is manu-factured from similar materials to concrete, on many sitesthere is less control over the mixing of the ingredients,which is generally done in smaller batches than concrete,and there is only limited control over the placing of mortar.Therefore, there is a greater probability of failure. Howeveron larger sites, where the contractor is able to establish a goodsite organisation, and material testing does not become dis-proportionately expensive, it is possible to exercise a higherdegree of control over the production of masonry. Thus it is

At the design stage of a structure, it is not possible to pre-dict accurately the loadings which will act on the structureduring its planned life. Nor is it possible to define preciselythe behaviour of a structure under these loadings, or to predict with certainty the strength of the materials whichcombine to form the structure. It is necessary, therefore, forthe engineer to introduce factors of safety to be used for anygiven load and material. It is necessary to first define themeaning of the word ‘satisfactory’ when related to the useof the structure.

Obviously, one criterion for the design of the building is that it should not fall down, but there are other condi-tions which need to be examined. The structure should be readily useable by the occupants, as well as visuallyacceptable in the long term as well as the short. It shouldnot excessively deflect or crack, and should be sufficientlydurable to maintain its initial condition. There are other cri-teria which may be applicable to certain structures includ-ing, for example, resistance to fire, explosion, impact andvibration.

In the past, there have been two basic methods of applyinga factor of safety to the design of structures. Both methodshave involved the introduction of a single factor to cover allthe uncertainties mentioned above, in order to ensure thestability and safety of the structure. The first method, andthe one commonly used in the past, is permissible stressdesign. This involves determining the ultimate stresses forthe materials involved, and dividing these by a factor ofsafety to arrive at a permissible or working stress. The sec-ond is the load-factor method which involves multiplyingthe working loads by a factor of safety and using the ulti-mate stress of the materials.

Both these techniques have their faults. The former is basedon elastic stresses, and is not strictly applicable to plastic or semi-plastic materials such as masonry. The latter isapplied to loads and does not take into account variationsin materials. Both have the disadvantage of applying onefactor of safety to cover all conditions of materials, loading,workmanship, and use of structure, thus preventing adjust-ments where one item is, perhaps, of a higher or lower standard than normal.

Limit state design is an attempt to consider each item moreclosely so as to enable a more accurate factor of safety to beapplied in the design, and depends upon the case beingconsidered. This is achieved by breaking down the overallfactor of safety used in the design into its various com-ponents, and then placing a specific factor – known as a‘partial factor of safety’ – on that component for a given

Limit State Design 17

advantageous to vary this partial factor of safety on thedesign of brickwork from site to site. It becomes necessary,therefore, to assess at an early stage the degree of qualitycontrol to be expected on site, and thus the partial factor tobe used.

Group 2

The second group of factors is applied to the loadings to be used in the design of the structure. These factors areintroduced to take account of inaccuracies in the assumeddesign loading, errors in the design of the structure, con-structional tolerances and the consequences of failure. The dead weight of the structure may be determined rea-sonably accurately, but the superimposed loading is muchmore difficult. It is also not possible to predict accuratelythe probability of overloading of the superimposed load,and it is therefore necessary to use a higher factor of safetyfor superimposed loading than dead loading.

It is also advantageous to adjust the factors of safety for dif-ferent combinations of loadings. It is unlikely, for example,that overloading of the dead, superimposed and windloads would all occur simultaneously, and thus the factorsare adjusted for various combinations of loading.

The assumptions and theories used in the design of thestructure will not precisely fit the way in which the build-ing acts. Similarly, inaccuracies during the construction ofthe structure will vary the actual conditions from thoseassumed in the design. The consequences of failure of thestructure vary considerably, depending upon the type, use and location of the building. For example, the effects offailure of a shopping centre or a grandstand are quite dif-ferent from those of site temporary works such as shutter-ing to a concrete beam.

It is thus possible to build up an overall factor of safety fromthose in Group 1, which are applied to the materials, andthose from Group 2, which are applied to the loading usedin the design of the structure. However, it is also necessaryto vary safety factors depending upon the condition beinginvestigated and designed. When checking the ultimatefailure of a structure, it is obviously necessary to use ahigher factor of safety than when checking the deflection ofa beam. Thus the partial factors of safety must be adjustedaccording to the limit state being considered. The followingexamples should illustrate the point. Consider the follow-ing two cases: in each case the partial factors of safety areindicative and not taken from any specific British StandardCode of Practice.

Example 1

A skip of loose bricks is to be hoisted over a busy shoppingstreet. The skip weighs 1 kN and can carry approximately 5 kN of bricks, and is to be suspended from a steel rope ofultimate tensile stress 260 N/mm2. Since the rope is of mildsteel, and to be used in town, it may be assumed that high-quality steel is available and the partial factor of safety inthis material may be taken as 1.15. (Reinforced concretedesign to BS 8110 has a factor of safety for steel reinforce-ment bars of 1.05.)

The skip is to be filled with loose bricks and could easily be overloaded and, as it passes over a busy shopping street, the consequences of failure could be serious. Thepartial factor of safety on the loading should therefore be taken as 1.4 of its dead load, which is not likely to beincreased, and 1.8 on the live load which is liable toincrease. Thus:

Design loading = (1 × 1.4) + (5 × 1.8)= 10.4 kN

Design steel stress = = 226 N/mm2

Area of rope = = 46.0 mm2

Example 2

This is a similar problem to Example 1, but with the bricksin pre-packed units of actual weight 5 kN and passing overa non-navigable river. High quality steel is not available. Soan increased material factor of safety of 1.5 should be used.

The bricks are in pre-packed units of known weight andoverloading is less probable. In addition, the consequencesof failure are not serious, merely the loss of the bricks. Thepartial factor of safety on the loading should be taken as 1.3on the dead load and 1.5 on the live load. Thus:

Design loading = (1 × 1.3) + (5 × 1.5)= 8.8 kN

Design steel stress = = 173 N/mm2

Area of rope = = 51 mm2

The factors used in masonry are explained further inChapters 5 and 6.

8.8 × 103

173

2601.5

10.4 × 103

226

2601.15