STRESS AND STRAIN. 



BY C. M. BROOM ALL. 



It is hoped that the following notes may be of interest as 

 treating of certain phases of stress and strain not commonly 

 dealt with in text books. For example, in the case of a body 

 subjected to direct tension or compression, we are accustomed 

 to consider the applied stress as distributed over the cross 

 section, neglecting any lateral stresses that may be brought 

 into existence by lateral deformation. Again, in the same 

 case, we speak broadly of certain 45° maximum shears, with 

 small heed to the effect of "internal friction" in altering 

 this angular value when rupture occurs. As a further 

 example, in considering the case of a beam under flexure, the 

 stresses are seldom thought of as being other than those given 

 by the "Common Theory," namely, bending moment and 

 vertical shear, and perhaps horizontal shear. We are familiar 

 with stresses in the vertical-longitudinal plane and appreciate 

 lines of maximum stress which result from the combination 

 of direct stress and vertical and horizontal shear. But the 

 fact that stresses exist in the vertical-transverse plane, that 

 is, in the cross section of the beam, does not come often to 

 mind. These considerations suggest an interesting line of 

 thought and it is to them that attention will be directed in 

 what follows. In order to properly appreciate the subject, 

 however, it will be necessary to begin with certain funda- 

 mentals and lead up logically to the question in hand. 



Consider the case of a prismatic body subjected to direct 

 tension. If such body were absolutely inelastic, so that it 

 suffered no deformation, the total stress would be distributed 

 over its cross section as a uniform unit stress. But no body 

 is perfectly rigid, and deformation, lengthening, results, 

 accompanied by lateral contraction in all directions at right 

 angles to the axis of stress. The ratio of the unit lateral 

 strain to unit longitudinal strain, is known as Poisson's Ratio 

 and has been determined experimentally for many materials. 



