88 BROOMALL : 



deflection the upper portion of the beam expands in all direc- 

 tions, while the lower portion contracts. This means that a 

 transverse unit tension in all directions must exist in the 

 upper portion of the beam and a transverse unit compression 

 in the lower portion. These forces may be resolved vertically 

 and horizontally and their effect considered. The vertical 

 components in the web and the horizontal forces in the 

 flanges are those which will act to modify the lines of maxi- 

 mum stress as already found. The actual effect, of course, 

 is small, and if the deformation were known these forces 

 might be added to those of Figure 2 before making the reso- 

 lution. 



Another effect of the expansion and contraction just men- 

 tioned is to raise the centre of gravity of the section and con- 

 sequently the neutral axis. This alters the amount of the 

 horizontal forces, producing another modification in the lines 

 of maximum stresses. These modifications in the stress lines 

 are naturally small, and for all practical purposes may be 

 neglected. 



Let us now consider the Channel used as a beam with web 

 horizontal and flanges vertical, for example, turned upward. 

 The position of the neutral plane will usually be in the lower 

 part of the flanges. The lines of maximum stress in the 

 flanges will be calculated in the usual way, and will have the 

 general characteristics shown in Figure 3. The figure also 

 suggests the forces acting on the elements of the body and the 

 manner in which they vary in value from top to bottom. 



The lines of direct stress cut the upper edges of the flanges 

 at 90° and 0°, and they cross the neutral axis at 45°. They 

 do not, however, intercept the upper surface of the web at 90° 

 and 0°, since the horizontal shear does not fall to zero. The 

 lines as sketched are only meant to indicate the general char- 

 acteristics of the curves. 



The lines of shear in the flanges cut the upper edge 

 of flange at 45°, and the neutral axis at 90° and 0°. 

 They do not cut the upper surface of the web at 45°, because 



