1 8 BROOM ALL : 



were it not for another modification, to be mentioned later, 

 which must be considered. This point will be taken up at the 

 appropriate time. 



Let us now consider another phase of the subject of flex- 

 ural stresses, that is, the question of the existence of stresses 

 in the plane of the cross section. As already noted, the 

 upper portion of the beam being subjected to compression, 

 expands, while the lower portion contracts under the tension. 

 The result is, that the cross section of a rectangular beam, for 

 instance, tends to take a trapezoidal form, as indicated in 

 Figure 3. 



FIGUR E 3 



The position of the neutral axis (passing through the centre 

 of gravity of the section) is raised, producing a change in 

 the amount of the longitudinal stresses. The value of the 

 distance to the " remotest fibre," and the value of the mom- 

 ent of inertia of the cross section are both altered by the 

 shifting of the neutral axis, so that there must exist a differ- 

 ence between the true longitudinal components of stress and 

 those calculated on statical principles. This change of value 

 of the stresses is an effect to be superposed upon the stresses 

 of Figure 2, already modified in amount and direction by the 

 existence of stress due to lateral deformation. The calcula- 

 tion of the actual stresses in the absence of exact information 

 as to the change in form of cross section, is impossible. 



