In February 1965 a revision of CP 114 (1957) The structural use of reinforced concrete in buildings was published as Amendment No.1 (PD 5463), bringing CP 114 up to date with the then new CP 116 (1965) The structural use of precast concrete. These two codes provided for the strength of members to be assessed by the then commonly employed elastic or modular ratio theory. The elastic theory is concerned with the equilibrium at working stresses of the forces and moments due to actual loads, the working stresses being the ultimate stresses reduced by a factor of safety. Concrete structures had been designed using elastic theory from 1932 (First edition of Reynolds' Reinforced Concrete Designer's Handbook) until 1972 when CP 110 (1972) The structural use of concrete was published. Whereas CP 114 was withdrawn, its steel
counterpart BS 449 (1968) remains as an approved method for the elastic design of steel structures. The four decades commencing in 1932, included most of the replacement of buildings demolished during the London blitz. Although no figures are available, it is likely, that in 2005, more structures in Britain have been designed using elastic methods of design rather than limit state design. Limit state design was not in general use until the late seventies. From the late seventies to the mid nineties, the construction industry was the victim of economic experimentation. Thus, until the introduction of limit state design, tried and tested elastic methods of design were used.
Following the introduction of CP 110 Part 1 November 1972, the first limit state British Standard, a few firms received contracts from central government to carry out so called calibration tests to compare calculations produced in accordance with CP 114, with those produced in accordance with CP 110. As computers were unavailable, comparisons between the codes were made for typically half a dozen beam or column designs. Experience in this research, is that half a dozen comparisons between modern and classical methods are inadequate, at least hundreds and preferably thousands of comparisons are needed in order that meaningful conclusions may be drawn. Increasing the number of sets of data to be generated and run, throws up structural anomalies due to the interplay between the rules such as: material strengths, section shape and sizes, exposure condition, concrete cover, fire rating, flange depth, neutral axis depth, percentage of compression and tension steel required, minimum steel percentage allowable, steel added to control deflection...
An inspection of the parameter tables for proforma calculations sc385.pro & sc075.pro given in tables 10.5 & 10.6 respectively, give an idea of just how complicated modern codes of practice have become, with a high dependency of parameters among themselves. A full listing of both proforma calculations will be found in appendix C.
Comparison of the parameter tables for sc385.pro for stainless steel and sc075.pro for reinforced concrete, reveals that calculations for steelwork have a higher interdependency of parameters than for reinforced concrete, 35 dependencies for sc385.pro cf. 23 dependencies for sc075.pro.
Over the past two decades, code writers have increasingly devised expressions and formulae for the ultimate limit state, rather than the serviceability limit states. As an example, clause 3.4.6 in BS 8110, tells us that deflections will be OK if the basic span/effective depth ratios given in table 3.9 are used. In the same chapter, formulae are given for the section design of rectangular and flanged beams at the ultimate limit state, the implication is that chapter 3 of BS 8110 covers both the serviceability & ultimate limit states. Kong & Evans (1987) write "Lateley the serviceability of concrete structures has become a much more important design consideration than in the past, mainly because more efficient design procedures have enabled engineers to satisfy the ultimate limit state requirements with lighter but more highly stressed structural members. For example, during the past few decades, successive British codes have allowed the maximum service stress in the reinforcement to be approximately doubled
and service loading is sufficiently low for the results of an elastic analysis to be relevant."
Before the introduction of the limit state code CP 110 (1972), reinforced concrete design was based on elastic principles in accordance with CP 114, which resulted in structures which had a factor of safety of typically 2.5. Designs in accordance with BS 8110-1:1997 have a factor of safety of typically 1.5. Typically is the best we can do to describe the factor of safety. Rigour is not possible e.g. site operatives in concrete gangs, pat the top of their head meaning toppings i.e. they want more water in the mix.
Changing the water/cement ratio from 0.4 to 0.6 reduces the seven day mean compressive strength of concrete from 33 N/mm² to 18 N/mm² i.e. almost halving the concrete strength, DSIR (1950). Shear reinforcement provided in accordance with CP 114 ignored the strength of the concrete, on the assumption that at least half of the concrete was cracked. The authors of BS 8110-1:1997 took a different view and assumed that cracked concrete has a strength and in consequence the amount of shear reinforcement provided can be less than half of that required by CP 114.
A practical structural concrete cannot exceed the strength of the aggregate used in making it, thus the use of aggregate made from recycled crushed concrete should be avoided for structural concrete. Age on loading has a major significance on deflection.
BS 8110-2:1985, figure 7.1 shows the effects of relative humidity, age of loading and section thickness upon the creep factor. Concrete made with sandstone aggregate has a very much larger creep than that made with granite aggregate, Orchard (1958). Kong &
Evans (1987), in figure 2.5-4 give shrinkages of specimen mixes. Illston (1994) in figure 15.28 gives a relationship between the modulus of elasticity of the aggregate and the relative creep. For a relative creep factor of 1 for basalt, sandstone has a creep factor of 4. Thus choice of aggregate is of major significance for concrete beams and slabs.
The writer recalls a library he designed in the seventies, for which monitored deflections of the waffle floor spanning 12 m were three times those predicted based on C&CA published data from tests using Thames gravel aggregates and not the sandstone aggregate actually used in the library. It follows that some structures designed to BS 8110-1 alone, are likely to fail some of the serviceability requirements hidden away in BS 8110:2.
Whereas models for the design of structural steelwork components have to be able to recognise serial sizes for the many types of steelwork sections, necessitating the need to invoke procedures from the parameter table, models for the design of reinforced concrete components are more straightforward. Table 10.6 shows the parameter table developed as part of this research for proforma calculation sc075.pro for the design of flanged beams in bending with optional: shear, bar curtailment, lap length and span/effective depth checks. A complete listing for this proforma calculation will be found in appendix C. Proforma calculation sc075.pro was developed by Professor Bill Cranston (C&CA & Paisley University) and checked by Jim Steedman, the author of
The first four parameters have no dependencies, the fifth parameter M dictates the size of the section, using engineers' arithmetic for a beam carrying bending moment M kNm and effective depth d mm and breadth of rib bw=d/2. For 2% reinforcement of characteristic strength fy N/mm², we may write:
M*1E6=d*d/2*0.02*d*fy, rearranging we get d=(M*1E6*2/0.02/fy)^(1/3) which gives a sensible effective depth for the section. Parameter sizes h, b, bw & hf respectively overall depth, breadths of flange and rib and thickness of flange, commence at parameter 17. The overall depth and breadth and thickness of the flange are limited by expressions involving d, the breadth of rib is in turn limited by expressions involving b.
The remaining parameters have straightforward dependency conditions.
Table 10.6 Parameter table for reinforced concrete flanged beam design.
PARAMETER Start End Type Dependency conditions
39 re2 1 3 3 Options for comprn. bars.
40 diacs 16 25 -3 Diameter of comprn. bars.
41 nlegs 4 20 1 >nbars/2 <nbars No. of legs.
42 flag1 1 2 2 Reduce spacing or links option.
43 dialr 8 12 3 Reduced dia. of link legs.
44 flag2 1 2 2 Adopt spacing or redesign optn.
45 sv' 50 3000 0 >d*.2 <d*.9 Chosen link spacing.
46 flag3 1 2 2 Options for incr. No. of legs.
47 ans6 0 0 2 Undertake another shear calc.
48 expos 1 5 5 Exposure condtn mild to severe.
49 mod 1 0 2 Systematic checking regime.
50 fire 0.5 2 4 Chosen fire resistance period.
51 expo 1 1 2 Indoor=1, outdoor=2.
52 aol 3 7 1 Age on loading 1 to 365 days.
53 Es 200E3 200E3 0 Young's modulus for steel.
54 Ec 28E3 28E3 0 Young's modulus for concrete.
BS 8110-1:1997 Clause 2.5.2 states that when linear elastic analysis is used, the relative stiffness of members may be based on:
• the concrete section
• the gross section on the basis of modular ratio
• the transformed section on the basis of modular ratio.
A modular ratio of 15 may be assumed, a consistent approach should be used for all elements of a structure. Thus BS 8110 permits linear elastic methods to be used for both the structural design of concrete frameworks and the design of reinforced concrete sections. This would permit a self-check to be included to compare the reinforcement required for elastically designed sections with that required by classical elastic methods.
NCE, 8 December 2005 reports A £200M shopping complex in Bournemouth is being closed indefinitely due to shear cracking and diagonal spalling at the ends of long span beams. Almost certainly the design complied with many of the clauses in BS 8110 but as the foreword to BS 8110 states in bold text Compliance with a British Standard does not of itself confer immunity from legal obligations. One such legal obligation is that a structure should be suitable for the purpose for which it was built. As mentioned in section 10.4, when limit state design was first introduced, with the exception of shear reinforcement for reinforced concrete beams, the equations were adjusted to give similar answers to designs produced in accordance with elastic theory.
Prior to the introduction of limit state design, shear reinforcement design using stirrups, was based on the simple equation discussed by Pippard & Baker (1957) who derive the formula used in the code of practice i.e.
Stirrup load = S.p/a where S is the shear force at the section being considered, p is the distance between centres of stirrups along the length of the beam, a is the moment arm or lever arm. The strength of concrete was ignored as typically two thirds of the concrete is always in tension and thus cracked. Bray (1960) in figures 15 to 18, and Reynolds (1957) in figure 25 give typical examples for the provision of shear reinforcement prior to the introduction of limit state design. On 18.4.06 the writer and
a simple support. Typically half of the bars were bent up to carry typically 50% of the shear force, the remaining 50% being carried by stirrups, now referred to as links.
Today eight 25 mm tension bars would be curtailed to four at the support and just two 10 mm diameter link arms could be required. As James Steedman says "all of concrete failures are shear failures". For this reason, in the self check, shear reinforcement for the serviceability limit state for shear cracking will be calculated using the basic equation for stirrup load, as given above.
The self check, developed as part of this research, will be found in appendix C at the end of proforma calculation sc075.pro. Following the incorporation of the parameter table into sc075.pro, the model was run for various sets of automatically generated data to test for the presence/absence of bugs in the model. One bug was found:
• the variable diacs was erroneously set to zero causing problems when compression reinforcement was required.
More importantly, the automatic generation and running of up to 996 sets of data, highlighted strange behaviour with the shear check when the distance from the support was given as a low value. This matter is discussed in section 10.9.