SECTION IV 



STRENGTH OF BEAMS 



32. Nature of bending stress. For a horizontal beam carrying a 

 set of vertical loads the method just explained for drawing the 

 moment and shear diagrams is to combine the forces on one side 

 of any cross section into a single force, arid the moments of these 

 forces about the centroid of the section into a single moment. For 

 equilibrium the stresses in the beam at the given section must 

 therefore also reduce to a 



single force and moment, 

 called the shear and bend- 

 ing moment, respectively, 

 equal in amount and op- 

 posite in direction to the 

 external resultant force 

 and moment. 



By considering a few 

 simple cases the nature 

 of the shearing and bend- 

 ing stresses will be ap- 

 parent. Thus, in Fig. 46, 

 suppose that a small ver- 

 tical slice is cut out of 

 the beam, as shown ; then 



/ 



7 



M 



L 1 



FIG. 46 



there will evidently be a tendency for the top of the cut to close 

 up and for the lower side to spread apart. This might be prevented 

 by placing a small block in the upper edge of the cut and connect- 

 ing the lower edges with a link. Supposing this to be done, there 

 will, in general, still be a tendency for the part on one side of the 

 cut to slide up or down past the part on the other side. To pre- 

 vent this vertical motion, it would be necessary to introduce a 

 vertical support, as shown in the lower diagram of Fig. 46. 



49 



