STRESS LINES IN BEAMS. 85 



US take up the determination of the general character of the 

 stresses and deformations in the Channel Beam, set with web 

 vertical and loaded uniformly. For the present let us assume 

 this loading to be in a narrow line along the web, so as to 

 avoid consideration of the bending of the flange by the 

 direct load. 



In order to balance the external forces and reactions, each 

 element of the body will be aeted upon by certain forces 

 which for convenience we will resolve vertically, transversely 

 and longitudinally. These are the resultants of the various 

 external forces acting upon the body, and necessary to 

 equilibrium. By resolving the forces acting upon the ele- 

 ments in various directions the actual direction and amount 

 of the true internal stresses acting in the material may be 

 found. In the present article we will consider more particu- 

 larly the direction and characteristics of the lines of maxi- 

 mum stress rather than the absolute value of the stresses. 



As the Channel stands on edge subjected to its load, we 

 know it is acted upon by vertical shear and bending moment. 

 Further, we know that if a vertical unit shearing stress exists 

 at any point, an equal and opposite longitudinal unit shear- 

 ing stress must exist also, as required by the principles of 

 statics. This opposing longitudinal unit shear is produced 

 by or results from the decrements in the value of the horizon- 

 tal direct stresses already mentioned. Hence, each element 

 of the body must be acted upon by two equal right-angled 

 shearing unit stress. As a consequence of the bendmg 

 moment we know also that each element must in addition be 

 acted upon by direct stress, tension or compression. 



As far as the web is concerned these are the same forces as 

 are met with in a beam of rectangular cross section. 



In the flanges we meet a rather different array of forces, 

 similar to those already mentioned in connection with the 

 I Beam. A longitudinal shear, with vertically arranged 

 shearing planes must exist in order to transfer the decrements 

 of longitudinal stresses to the web and thence by ordinary 



