58 BROOM ALL : 



acteristics of the lines for web and flanges for the whole 

 length of the beam. The upper sketch represents the upper 

 flange viewed from above, the middle sketch shows the eleva- 

 tion of the beam, and the lower sketch shows the lower 

 flange viewed from below. 



The value of the internal stresses can be calculated by the 

 ordinary internal stress formulas. A little consideration of 

 Figure 6 will show which way the forces vary along the lines 

 of maximum stress. In the web, the tension is a maximum 

 below and a minimum above, the compression is a maximum 

 above and a minimum below, while the shear is a maximum 

 at the neutral axis and a minimum above and below. In the 

 flanges, generally speaking, all the stresses increase as the 

 lines approach the web. 



The nature of the stresses at the junction of web and 

 flange, as the plane of the horizontal shear changes from hor- 

 izontal to vertical, is very problematical. The combination 

 of two pairs of right angled shears respectively in vertical 

 and horizontal planes together with direct stress, makes the 

 complexity such that it is impossible to generalize as regards 

 the stresses in this region. 



The lines of maximum stress, as so far sketched out, are 

 lines determined from statical considerations only. In the 

 actual I Beam, however, deformation takes place, and from 

 what we know of the deformation of the rectangular beam, it 

 is easy to predict what will occur. 



As the I Beam deflects, the upper flange and upper part of 

 the web shorten, expanding laterally in all directions. A 

 reverse result follows in the lower portion of the beam. A 

 tension, therefore, exists in all directions at right angles to 

 the axis of the beam in its upper portion. Similarly, in the 

 lower portion, a compressive force acts in all directions at 

 right angles to the axis. This lateral change of dimensions 

 shifts the centre of gravity of the cross section upward and 

 alters the leverage and amount of the horizontal stresses. 



In the web the lines of stress and the values of the 



