Shear-stress systems and combined stress

This paper discusses an objection which has been raised to the law of elastic failure under combined stress which was given in a paper read before the Society in 1900 - namely that, instead of the volumetric stress then used, the average volumetric stress should be employed and that only shear stresses should be associated with it. A resolution of a stress system into uniform tension and shearing stress, of a type which is advocated to-day and appears to offer advantages, is first discussed and is shown to be inapplicable as not being a complete representation. It is then pointed out that there are usually an indefinite number of shear-stress systems and only in certain cases are the shears unique. For the precise expression of a law of failure the indefiniteness must be removed, and the simple limitations available for the purpose are discussed and shown to be inapplicable. Finally it is shown that the adoption of the suggested scheme could only be applicable to such materials as have a failure limit in simple compression less than three times that in simple tension. Thus it is incompatible with a law of failure which is to be of general application.