56 BROOM ALL : 



In order to find the lines of maximum internal stress pro- 

 duced in the material, the above forces must be resolved for 

 the various kinds of stress and the direction of the maxima 

 determined. The formulas for determining the direction of 

 the lines are : 



Shear : tan 2^ = s / 2V (4) 



Direct Stress : cot 2^ :== — s/ 2v (5) 



where <f> = angle of shearing plane with longitudinal direction, 

 ^ = angle of direct stress with longitudinal direction, 

 s = direct unit stress, tension positive, compression 



negative, 

 V == unit horizontal shear. 



These are the ordinary formulas used to determine lines of 

 maximum stress in beams, and by their use lines more or less 

 similar to those of Figure 5 are obtained. In the case of the 

 web of the I Beam the lines will have the general character- 

 istics of those in the rectangular beam. These lines, how- 

 ever, do not cut the inner surface of the flanges at 0° and 90° 

 for direct stress, and 45° and 135° for shear, as at the upper 

 and lower surface of the rectangular beam, since the horizon- 

 tal shear is not zero at these points. 



To find the direction of the lines of maximum stress in 

 the flanges we can obviously use the same formulas, for we 

 are again dealing with two right angled shears and with 

 direct stress, the only difference being that the forces vary by 

 another law, the shears following a triangular variation and 

 the direct stress the rectangular law. If we plot these lines 

 they will be found to have the characteristics indicated in 

 Figure 5. They will cut the outer edges of the flanges at 0° 

 and 90°, and at 45° and 135° just as at top and bottom of a 

 rectangular beam. They do not, however, cut the sides of 

 the web at these angles, because the direct stress does not 

 reduce to zero at these points. 



In Figure 6 the attempt is made to show the general char- 



