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Design curves and formulae are presented for the calculation of deflections in reinforced concrete flexural members. These are based on the procedure given in appendix A of CP110 for direct calculation of curvatures and deflections due to short-term and long-term effects. Using the design curves as the basis, an estimate of the errors introduced by the simplifying assumptions presently used in deflection calculation is obtained, and the area of validity of these assumptions is defined. The need for a more realistic assessment of deflections and the use of the design curves are illustrated by an optimum design example. The advantage of the design formulae and the associated curves in deflection calculations is illustrated by considering a doubly reinforced member.
Whilst I am a firm believer in the economy obtained by the intelligent use of grade 50 steel, the submission by Mr. Needham that the present cost differential is an extra £3.50 per tonne compared with grade 43 steel is somewhat misleading. This figure is applicable only when comparing the cost of grade 43A steel with that of grade 50A steel, and is thus limited only to certain rolled sections. Significant economy by the use of grade 50 steel with rolled steel sections is doubtful, especially where deflection is the criterion. When using structural hollow sections in lattice construction, where the maximum economy in weight is possible, it is necessary to compare the cost differential between grade 43C and grade 40C. This is, I am given to understand, as much as 50 per tonne depending on the sections used.
Professor A. L. L. Baker (F): At one time it appeared that we might use a limited tensile strain normal to uniaxial load of cube strength x Poisson's ratio / E
as the general criterion for ultimate strengths for all practical purposes. Indeed, if we assume that the ratio of stress over strain at the ultimate limit state is 2 x l0 to the power 6, and that the Poisson's ratio is 1 over 4.5, we can derive, for a multiaxial strained cube, an equation that fits the mean values shown in Fig A1 in the paper. It also fits the higher ranges, if E is reduced in all the terms of the basic strain equation to agree with low values indicated by the curves in Fig A4 and provided that secondary strains do not at some point reverse.