, 
. 
. 
‘ 
9 
COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 179 
The experiments which have been recorded indicate that a plain shaft 
subjected to combined bending and torsion should be designed for an 
equivalent torque, /M?+ T?. The maximum stress theory gives M + 
/ M2 + 'T?. The latter emphasises the importance of the bending moment, 
and bending yield is much more serious than torsion yield. A small 
bending yield would cause a considerable deflection of the shaft, but a 
twist would fully stress more material with a strain of little importance. 
It is not at all clear that the formula which gives the equivalent torque 
to cause yield is the best for the purposes of design. The results of the 
repeated loading tests, at least for the harder steels, lend further support 
to this view. 
The important cases of combined stresses in practice are usually accom- 
panied by a variable stress distribution. We may assume that the shear 
stress theory will allow the load at yield to be calculated, but the engineer 
requires to know the fracture load to estimate the reserve of strength. 
Bridgman 7 7 states he found that he could raise the yielding pressure 
of a thick cylinder under internal pressure tenfold by giving it a set. The 
reserve strength here is not only due to the difference between the yield and 
maximum stresses, but also to the understressed material. A law of 
failure does not help an engineer to calculate to fracture in many such 
cases, and he must depend on experiments made under the conditions of 
each case. 
The above considerations point to the advisability of confining tests 
on ductile steels to the elastic limit or yield point, and of considering the 
importance of tests to fracture in cases of ‘Special Problems’ which 
involve complex stress distributions. 
16. Conclusion. 
Most experimental work has been done on ductile steel, but more tests 
are required under three-dimensional stress, and particularly under com- 
pressive stresses. 
One point appears to have escaped notice. A material might appear 
to have different shearing strengths under different systems of stress, as 
in the case of cast iron in shear and under compression. The shearing 
stress has been shown to be approximately constant at the elastic failure 
of steel under modification of the same general type of stress distribution. 
Are these maximum shearing stresses the same under all conditions of 
loading ? 
They have frequently been compared with the tensile strength, and the 
differences do not seem to be great, but it would be of interest, and neces- 
sary for further refinement, to test exactly the same material under very 
different combinations of principal stresses. 
Few experiments have been made with the materials now classed as 
brittle, and those already made should mostly be repeated. Here we can 
assume that there is a clear field. The same applies to non-elastic ductile 
metals, and to those intermediate between ductile and brittle. 
The methods of experiment will require further consideration. Simple 
tension and compression are the most direct tests available. Longi- 
tudinal tension and internal fluid pressure applied to a thin hollow 
cylinder appear to be the readiest means of securing two tensions. 
Longitudinal compression and external fluid pressure have been used 
N 2 
