Influence Lines for Beams Continuous Over Three Spans. Discussion on Paper by Mr. R.J. Cornish and M

SIR,-It is rather late in the day to draw your attention to the article on "Structural Engineering in South Africa" which appeared in the Royal Charter issue of the journal last January, but I have waited until I could send the enclosed photographs.

In a previous paper attention was devoted to the general behaviour of plain and reinforced concrete beams particularly in regard to the deflection of beams and the stress distribution along the shear and tension reinforcement. The influence of shear reinforcement on the deflection of reinforced concrete beams and on the stress in the tension reinforcement, in that portion of beams subjected to shearing forces, was also illustrated and discussed. The diagrams given show that in a beam not sufficiently reinforced in shear both the central deflection and the tensile steel stress, in that portion of beams subjected to shearing forces, may be considerably greater than that calculated excluding the assistance afforded by the concrete in tension. That is, in a beam having diagonal cracks the tension reinforcement tends to act as a tie rod such that the stress along it becomes more uniform and the general behaviour of the beam approaches that of a 2-hinged tied arch. The possibility of this phenomenon taking place has already been pointed out by Dr. Oscar Faber, O.B.E., M.Inst.C.E., M.I T.Struct.E.2 In the same paper, as well as in Engineer3, the author also referred to the strain distribution along vertical sections of reinforced concrete beams, the latter being reinforced in tension only. The results obtained showed that the increase under sustained loads of the tensile steel stress, due to the formation of vertical cracks and the plastic properties of the concrete, seldom amounts to more than about 15 per cent. and that the actual position of the neutral axis under working loads is always between the two positions calculated when (a) including and (b) excluding the assistance afforded by the concrete in tension. R.H. Evans

THE following article is intended to act as a summary of the main principles on which strain energy theorems are based. It is of an elementary nature, but may serve as an introduction to more advanced considerations. R.J. Cornish