433 
1908-9.] Crushing Strength. 
be so short that any bending is negligible. The results apply only to the 
yield point, and not to the breaking stress of a substance. In the case of a 
ductile material, after the yield point is passed, the conditions change 
greatly, and the test-piece does not rupture by shearing. A brittle bar, 
however, does usually break by the sliding of some portion over the 
remainder. A brittle material is often defined as one in which the yield 
point and the breaking stress are coincident. This is hardly correct, since 
most brittle substances suffer some permanent deformation before rupture ; 
but it suggests that the calculations may not be very incorrect when 
FIG. i. 
applied to the breaking strength of brittle materials in compression. This 
point is examined more fully in sections 4 and 5. 
2. End Friction Neglected. 
Let the length of the bar be such that the surface of sliding does not 
cut the extremities, and suppose first that there is no end friction (fig. 1). 
Let g be the compression yield point of the material — that is, the stress 
on a normal cross-section at the moment when sliding commences. Let f3 
be the inclination of the surface of sliding to the axis of the bar, and let /m 
( = tan </>) be the coefficient of internal friction for the material. 
Then, as has been shown already, the shearing stress along a surface of 
sliding is c sin l3 cos /3, and the resistance to sliding along this surface is 
vol. xxix. 28 
