118 Mr. W. A. Scoble on Ductile 



of the continuations of the lines which represent these two 

 limiting states on the stress-strain curves. 



It is probable that Guest's assumption is partly true, 

 because, with the loading adopted by the writer, with which 

 the stresses are unequally distributed, the ratio of the strain 

 to the stress is constant until it increases very rapidly just 

 before the complete breakdown of the specimen. The slight 

 deviation from Hookers law, which is noticed between the 

 elastic limit and the yield-point in a simple tension test, is 

 not observed. 



It therefore appears that for this kind of test the elastic 

 limit and the yield-point practically coincide, and therefore 

 the stresses are now taken, in all these tests, from the point 

 where the strain ceases to be proportional to the stress. 



The Quantities Tabulated, 



The strains have not been tabulated because the maximum 

 strain theory is not supported by engineers in this country. 

 The formulae relating to combined stress which are given in 

 the text-books are based on the maximum stress theory. 

 Recently, however, the shearing stress theory, or the stress 

 difference theory as elasticians prefer to name it, has rapidly 

 gained favour with engineers. It is, therefore, clear that 

 the maximum stress and the maximum shearing stress are 

 most important from a practical standpoint, but the maximum 

 strain hypothesis is indirectly considered later, when the 

 deviations from the shear-stress law are discussed. 



Calculation of the Stresses. 



The maximum tensile stress, p, in the material due to 

 bending is calculated from the formula 



p_M 



in which 



M is the maximum bending moment ; 



I is the moment of inertia of the area of the section about 



its neutral axis, in this case a diameter ; 

 y is the greatest distance of a point in the section from 



the neutral line, and equals half the diameter of the 



section.* 



The maximum shear stress, S, caused by the torque, is 



