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THE use of focal points in the analysis of continuous beams is not new, but the construction given below is quicker and simpler than those in general use; it is applicable to a uniform* continuous beam of any number of equal or unequal spans. The method will first be demonstrated by an example of a three-span beam (Fig. 1.) The
beam is simply supported at A, B and C, and built in horizontally at D.
R.E. Bowles and R.J. Cornish
IT has been generally considered that, as the standard theory does not give the ultimate load at which a reinforced concrete beam fails, it must be discarded. In consequence of this, a number of attempts have been made in recent years to predict the ultimate strength of R.C. beams by different methods, notably by Dr. Glanville (*), Professor Saliger, and C.S. Whitney. The theories advanced by these writers are purely empirical and do not give any idea of the stresses at loads other than the ultimate. This paper is intended to show how the standard theory, which is useful in giving an idea of the stresses at working loads, can alsoobe extended to predict the ultimate loads.
THE USUAL THEORY.-It is usual to estimate the moment of resistance of the lateral pressure of earth against sheet piling and footings by calculation of the passive pressures on each side of the member according to Rankine’s Formula. The full value of passive pressure given by this formula is known to require very considerable movement and only a fraction (n) of it can be allowed.* Fig. 1 shows this method of treatment
of the problem in its simple form applied to a square section pile or pole, where a centre of rotation A is found so as to provide a balance of moments and of horizontal forces. The method suffers from two defects. In the first place it is assumed that the pressure distribution on a tilting surface is the same as it would be on the same surface moving horizontally, whilst in the second place the fraction (n) of Rankine’s value for maximum pressure is a matter of judgment or ignorance.
Arthur A. Fordham