Design of structural elements

Table 1.1 illustrates some risk factors that are asso
ciated with activities in which people engage. It
 can be seen that some degree of risk is associated
 with air and road travel. However, people normally
 accept that the benefits of mobility outweigh the
 risks. Staying in buildings, however, has always beenTable 1.1 Comparative death risk per 108
 persons exposed
 Mountaineering (international)
 Air travel (international)
 Deep water trawling
 2700
 120
 59
 Basis of design
 critical points, as stress due to loading exceeds the
 strength of the material. In order for the structure
 to be safe the overlapping area must be kept to a
 minimum. The degree of overlap between the two
 curves can be minimized by using one of three dis
tinct design philosophies, namely:
 Car travel
 Coal mining
 Construction sites
 Manufacturing
 Accidents at home
 Fire at home
 Structural failures
 56
 21
 8
 2
 2
 0.1
 0.002
 regarded as fairly safe. The risk of death or injury
 due to structural failure is extremely low, but as we
 spend most of our life in buildings this is perhaps
 just as well.
 As far as the design of structures for safety is
 concerned, it is seen as the process of ensuring
 that stresses due to loading at all critical points in a
 structure have a very low chance of exceeding the
 strength of materials used at these critical points.
 Figure 1.2 illustrates this in statistical terms.
 In design there exist within the structure a number
 of critical points (e.g. beam mid-spans) where the
 design process is concentrated. The normal distribu
tion curve on the left of Fig. 1.2 represents the actual
 maximum material stresses at these critical points
 due to the loading. Because loading varies according
 to occupancy and environmental conditions, and
 because design is an imperfect process, the material
 stresses will vary about a modal value – the peak of
 the curve. Similarly the normal distribution curve
 on the right represents material strengths at these
 critical points, which are also not constant due to
 the variability of manufacturing conditions.
 The overlap between the two curves represents a
 possibility that failure may take place at one of the
 Fig. 1.2 Relationship between stress and strength.
 1. permissible stress design
 2. load factor method
 3. limit state design.
 1.2.1 PERMISSIBLE STRESS DESIGN
 In permissible stress design, sometimes referred to
 as modular ratio or elastic design, the stresses in the
 structure at working loads are not allowed to exceed
 a certain proportion of the yield stress of the con
struction material, i.e. the stress levels are limited
 to the elastic range. By assuming that the stress
strain relationship over this range is linear, it is pos
sible to calculate the actual stresses in the material
 concerned. Such an approach formed the basis of the
 design methods used in CP 114 (the forerunner of
 BS 8110) and BS 449 (the forerunner of BS 5950).
 However, although it modelled real building per
formance under actual conditions, this philosophy
 had two major drawbacks. Firstly, permissible design
 methods sometimes tended to overcomplicate the
 design process and also led to conservative solutions.
 Secondly, as the quality of materials increased and
 the safety margins decreased, the assumption that
 stress and strain are directly proportional became
 unjustifiable for materials such as concrete, making
 it impossible to estimate the true factors of safety.
 1.2.2 LOAD FACTOR DESIGN
 Load factor or plastic design was developed to take
 account of the behaviour of the structure once the
 yield point of the construction material had been
 reached. This approach involved calculating the
 collapse load of the structure. The working load was
 derived by dividing the collapse load by a load factor.
 This approach simplified methods of analysis and
 allowed actual factors of safety to be calculated.
 It was in fact permitted in CP 114 and BS 449
 but was slow in gaining acceptance and was even
tually superseded by the more comprehensive limit
 state approach.
 The reader is referred to Appendix A for an ex
ample illustrating the differences between the per
missible stress and load factor approaches to design.
 1.2.3 LIMIT STATE DESIGN
 Originally formulated in the former Soviet Union
 in the 1930s and developed in Europe in the 1960s,
 5
Philosophy of design
 limit state design can perhaps be seen as a com
promise between the permissible and load factor
 methods. It is in fact a more comprehensive ap
proach which takes into account both methods in
 appropriate ways. Most modern structural codes of
 practice are now based on the limit state approach.
 BS 8110 for concrete, BS 5950 for structural
 steelwork, BS 5400 for bridges and BS 5628 for
 masonry are all limit state codes. The principal
 exceptions are the code of practice for design in
 timber, BS 5268, and the old (but still current)
 structural steelwork code, BS 449, both of which
 are permissible stress codes. It should be noted, how
ever, that the Eurocode for timber (EC5), which is
 expected to replace BS 5268 around 2010, is based
 on limit state principles.
 As limit state philosophy forms the basis of the
 design methods in most modern codes of practice
 for structural design, it is essential that the design
 methodology is fully understood. This then is the
 purpose of the following subsections.
 1.2.3.1 Ultimate and serviceability
 limit states
 The aim of limit state design is to achieve accept
able probabilities that a structure will not become
 unfit for its intended use during its design life, that
 is, the structure will not reach a limit state. There
 are many ways in which a structure could become
 unfit for use, including excessive conditions of bend
ing, shear, compression, deflection and cracking
 (Fig. 1.3). Each of these mechanisms is a limit state
 whose effect on the structure must be individually
 assessed.
 Some of the above limit states, e.g. deflection
 and cracking, principally affect the appearance of
 the structure. Others, e.g. bending, shear and com
pression, may lead to partial or complete collapse
 of the structure. Those limit states which can cause
 failure of the structure are termed ultimate limit
 states. The others are categorized as serviceability
 limit states. The ultimate limit states enable the
 designer to calculate the strength of the structure.
 Serviceability limit states model the behaviour of the
 structure at working loads. In addition, there may
 be other limit states which may adversely affect
 the performance of the structure, e.g. durability
 and fire resistance, and which must therefore also
 be considered in design.
 It is a matter of experience to be able to judge
 which limit states should be considered in the
 design of particular structures. Nevertheless, once
 this has been done, it is normal practice to base
 6
 the design on the most critical limit state and then
 check for the remaining limit states. For example,
 for reinforced concrete beams the ultimate limit
 states of bending and shear are used to size the
 beam. The design is then checked for the remain
ing limit states, e.g. deflection and cracking. On
 the other hand, the serviceability limit state of
 deflection is normally critical in the design of con
crete slabs. Again, once the designer has determined
 a suitable depth of slab, he/she must then make
 sure that the design satisfies the limit states of bend
ing, shear and cracking.
 In assessing the effect of a particular limit state
 on the structure, the designer will need to assume
 certain values for the loading on the structure and
 the strength of the materials composing the struc
ture. This requires an understanding of the con
cepts of characteristic and design values which are
 discussed below.
 1.2.3.2 Characteristic and design values
 As stated at the outset, when checking whether a
 particular member is safe, the designer cannot be
 certain about either the strength of the material
 composing the member or, indeed, the load which
 the member must carry. The material strength may
 be less than intended (a) because of its variable
 composition, and (b) because of the variability of
 manufacturing conditions during construction, and
 other effects such as corrosion. Similarly the load
 in the member may be greater than anticipated (a)
 because of the variability of the occupancy or envir
onmental loading, and (b) because of unforeseen
 circumstances which may lead to an increase in the
 general level of loading, errors in the analysis, errors
 during construction, etc.
 In each case, item (a) is allowed for by using a
 characteristic value. The characteristic strength
 is the value below which the strength lies in only a
 small number of cases. Similarly the characteristic
 load is the value above which the load lies in only
 a small percentage of cases. In the case of strength
 the characteristic value is determined from test re
sults using statistical principles, and is normally
 defined as the value below which not more than
 5% of the test results fall. However, at this stage
 there are insufficient data available to apply statist
ical principles to loads. Therefore the characteristic
 loads are normally taken to be the design loads
 from other codes of practice, e.g. BS 648 and BS
 6399.
 The overall effect of items under (b) is allowed
 for using a partial safety factor: γm
 for strength
Basis of design
 Fig. 1.3 Typical modes of failure for beams and columns.
 7
Philosophy of design
 and γf
 for load. The design strength is obtained by
 dividing the characteristic strength by the partial
 Design strength  
safety factor for strength:
 characteristic strength
 m
 =
 γ
 (1.1)
 The design load is obtained by multiplying the
 characteristic load by the partial safety factor for
 load:
 Design load = characteristic load × γf 
(1.2)
 The value of γm
 will depend upon the properties
 of the actual construction material being used.
 Values for γf
 depend on other factors which will be
 discussed more fully in Chapter 2.
 In general, once a preliminary assessment of the
 design loads has been made it is then possible to
 calculate the maximum bending moments, shear
 forces and deflections in the structure (Chapter 2).
 The construction material must be capable of
 withstanding these forces otherwise failure of the
 structure may occur, i.e.
 Design strength ≥ design load
 (1.3)
 Simplified procedures for calculating the moment,
 shear and axial load capacities of structural ele
ments together with acceptable deflection limits
 are described in the appropriate codes of practice.
 Questions
 1. Explain the difference between conceptual
 design and detailed design.
 2. What is a code of practice and what is its
 purpose in structural design?
 3. List the principal sources of uncertainty in
 structural design and discuss how these
 uncertainties are rationally allowed for in
 design.
 These allow the designer to rapidly assess the suit
ability of the proposed design. However, before
 discussing these procedures in detail, Chapter 2
 describes in general terms how the design loads
 acting on the structure are estimated and used to
 size individual elements of the structure.
 1.3 Summary
 This chapter has examined the bases of three
 philosophies of structural design: permissible stress,
 load factor and limit state. The chapter has con
centrated on limit state design since it forms the
 basis of the design methods given in the codes of
 practice for concrete (BS 8110), structural steel
work (BS 5950) and masonry (BS 5628). The aim
 of limit state design is to ensure that a structure
 will not become unfit for its intended use, that is,
 it will not reach a limit state during its design life.
 Two categories of limit states are examined in
 design: ultimate and serviceability. The former is
 concerned with overall stability and determining
 the collapse load of the structure; the latter exam
ines its behaviour under working loads. Structural
 design principally involves ensuring that the loads
 acting on the structure do not exceed its strength
 and the first step in the design process then is to
 estimate the loads acting on the structure.
 4. The characteristic strengths and design
 strengths are related via the partial safety
 factor for materials. The partial safety
 factor for concrete is higher than for steel
 reinforcement. Discuss why this should be so.
 5. Describe in general terms the ways in
 which a beam and column could become unfit for use.