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Proceedings of the Royal Society of Edinburgh. [Sess. 
expected, therefore, to differ in their behaviour. A round steel bar, broken 
by torsion, shears along a surface which approximates to a plane at 5° to the 
axis of the bar — that is, at 50° to the direction of principal tension, corre- 
sponding with the direction of sliding in simple tension. Under similar 
conditions, a bar of cast iron breaks along a helicoidal surface inclined at 
45° to the axis of the bar — that is, perpendicular to the direction of 
principal tension, agreeing also with the result of the pure tension test. In 
torsion the principal tension and the principal compression are numerically 
equal, but in cases where the principal stresses have different values the 
form of fracture of a brittle body will depend upon the sign of the principal 
stress which is the immediate cause of breaking. If the principal tension 
is greater than a certain fraction of the principal compression, the broken 
surface will be normal to this tension ; if the tension bear a less ratio to 
the compression, the broken surface will be inclined to the direction of 
principal compression at the angle f3 (less than 45°), found from the crush- 
ing test. 
But the manner in which fracture occurs is also of importance. Thus, 
in a bar of cast iron broken by bending, although the stress upon the trans- 
verse section which is most severely loaded may vary from a pure com- 
pression to a pure tension, with all intermediate ratios between tension and 
compression, fracture usually occurs along such a transverse section — that 
is, in a direction normal both to the principal tension and to the principal 
compression. Observation shows that the metal begins to separate on 
the tension side of the bar, and as the crack progresses the stress suffers 
a redistribution, so that the direction of tension at the extremity of the 
crack remains approximately constant and normal to the original direction 
of the crack. 
Under combined bending and torsion, therefore, the fracture of cast iron 
may be expected to take place in a direction normal to the principal tension. 
In Goodman’s experiments * the fractures had a helicoidal form, and the 
helix due to the intersection of the broken surface with the exterior of 
each bar was found to be, within narrow limits, perpendicular to the 
calculated direction of the principal tension. With regard to the deter- 
mination of the breaking stress, the objections to the use of solid bars in 
experiments of this kind have been pointed out already, and Goodman’s 
figures for this stress are not of great value — a point which he recognises. 
Since the writers mentioned above are all concerned with what is 
usually called the “equivalent bending moment” for a shaft submitted to 
simultaneous bending and torsion, it may not be out of place to give the 
* Mechanics Applied to Engineering, Longmans, 4th ed., 1904, 492. 
