ICE - Institution of Civil Engineers - Virtual Library

The Paper presents a general plastic theory for the solution of statically indeterminate reinforced-concrete frameworks, and also for calculating the ultimate strength in bending of reinforced-concrete and pre-stressed-concrete beams, of both bonded and non-bonded types.

The Author has attempted to avoid the use of complex mathematical methods by assuming that all bending strains have linear distribution. The neutral axis of members subject to bending is located by the ultimate strains at the extremities of the section for non-sustained load, and safe limiting values are determined by tests. The shape of the compression-stress distribution and the position of its centre of gravity are denoted by symbols for which safe limiting values are obtained experimentally.

A plastic theory for the ultimate longitudinal bending strength of cylindrical shells is also presented. The Author indicates the distribution of longitudinal stress which causes maximum transverse bending stress so that, again, simplification is achieved by the use of safe limiting values which may be based on experimental evidence.

Tests to destruction on pre-stressed beams and two cylindrical shells, and the methods employed for measuring strains by dial and electrical gauges, are described and also the procedure for determining, from the tests, safe limiting values of the factors which govern ultimate strength. The experimental work is not yet complete, but some of the results so far obtained are given. Final results will be given in an Addendum to the Paper.

A new method of testing is described, in which a machine referred to as a bending-simulation machine, is used to obtain the fundamental stress-strain data required for calculations within the plastic range.

Experimental investigation of the pressures exerted by waves breaking against a vertical wall has provided further numerical information in support of the theory published in 1939 by Bagnold, who concluded that an air pocket between the wave and the wall played a dominant part in the generation of shock pressures.

Although many precautions were taken to obtain exactly constant waves, which were then allowed to break in calm water, the pressure observations varied greatly; however, by taking a large number of waves it was possible to apply statistical methods of analysis which showed that the pressures were substantially proportional to wave-height. The greatest pressures were exerted on the upper part of the wall and extended chiefly over the upper four-tenths of the wave height. Their duration was very brief, of the order of 0.001 second for the more intense shocks, and, as found by Bagnold, the product of pressure and duration tended to be constant. The impulse contained in the shock was relatively small compared with the ordinary impulse of reflexion of the whole wave, and did not exceed 0.07 of the momentum of the wave; but the pressure-rise was very rapid, and the Paper includes an estimate of the greatest rate of rise of pressure to be expected from sea-waves. The probability of true scaling-up of the model results is also discussed.