THE I BEAM. 59 



Stresses differ from the statical values in amounts determined 

 ( I ) by the lateral expanding or compressing stress in all 

 directions, and (2) by the change of value of horizontal 

 forces due to change of lever arms. 



The effect of deformation on the flange stresses is as fol- 

 lows : The dilating or compressive force due to deformation 

 may be resolved vertically and horizontally. The vertical 

 component may be neglected as not affecting the horizontal 

 system of lines in the flange in which we are interested. The 

 horizontal lateral component will have the effect of adding 

 one more force to the internal forces acting on a given ele- 

 ment. The internal forces instead of being as indicated in 

 Figures 5 and 6 will have a lateral direct stress in addition to 

 those indicated. The general effect of this horizontal stress 

 will be to modify the maximum stresses in the material and 

 alter the curves somewhat. The general nature of the lines, 

 however, remains the same, so that qualitatively speaking the 

 lines already plotted will represent well enough the character- 

 istics of the lines of maximum internal stress. 



In the foregoing, no attempt at quantitative results has 

 been made. It would not be difficult to obtain definite 

 results, at least approximately true, for given loadings. The 

 ordinary assumption of putting all the shear in the web and 

 most or all the bending moment in the flanges, is probably a 

 safe method of design, although the results are by no means 

 correct. The existence of horizontal shear, with vertical 

 shear planes in the flanges, should not be overlooked, nor 

 should the large horizontal shear in the web at its junction 

 with the flange be neglected. If the web is thick enough for 

 this the flanges will usually be ample, since the maximum 

 horizontal shear with vertical shearing planes in the flange, 

 on either side of the web, will be only one-half the shear in 

 the web itself. The common assumption of average vertical 

 shear over the web, in some cases may give a value of the 

 horizontal shear at junction of web and flange less than its 

 true value. Evidently the junction of web and flange is 



