THE I BEAM. 53 



I Beam wherein the forces maj- take whatever directions may 

 be necessary for equilibrium. The built-up I Beam or Plate 

 Girder, wherein the stresses are limited in direction by the 

 various artificial planes of shear due to the arrangement of 

 the plates, will be left for future treatment. 



A loaded I Beam has its upper flange in compression 

 and lower flange in tension, the horizontal direct stress 

 decreasing in value and the horizontal and vertical shear 

 increasing in value as the neutral axis is approached. 

 Ordinarily the straight line law of variation of stress is 

 assumed to apply, but on account of the small vertical 

 thickness of the flanges the horizontal force rnay be con- 

 sidered as uniform throughout the flange cross section. Xow 

 we know that the horizontal force in the flanges gets less and 

 less towards the ends of the beam and that in the flanges 

 something akin to the horizontal shear in beams of rectangu- 

 lar cross section must operate in order to connect up the 

 forces in the edges of one flange with the forces in the edges 

 of the other through the intermedium of the central portions 

 of the flanges and of the web. Horizontal shear in the ordi- 

 nary sense of the Common Theory would increase slowly 

 from the outer to the inner surface of the flange and then 

 would suddenly and largely increase in value as the width 

 suddenly decreased to that of the web. But this is not the 

 true state of afi"airs and the Common Theory does not explain 

 what is really happening and how it is, for instance, that the 

 stress at the outside edge of the flange gets tied in with the 

 stresses in other parts of the beam so as to make it act as a 

 whole. In order that all the elements in the flange shall work 

 together, some sort of shear must act between them. Assum- 

 ing uniform stress throughout the flange, and knowing as we 

 do that external equilibrium requires that these forces decrease 

 towards the ends, there must evidently exist a horizontal 

 shear, with shearing planes vertically disposed, between the 

 elements of the flanges. This shear transforms the excess of 

 horizontal forces acting on " blocks ' of the flanges outside 



