104 MECHANICS 



VERTICAL SHEAR 



In any beam, as for instance the one shown in Fig. 9, there 

 are forces either loads or reactions acting both upwards 

 and downwards. In this figure, the left-hand reaction RI 



FIG. 9 



acts upwards and tends to push the end of the beam up. 

 On account of the strength of the beam, however, the end 

 remains stationary. If the beam were suddenly cut on the 

 line ab, the left-hand portion of the beam would move up 

 in relation to the right-hand portion. This action of the 

 forces on a beam in tending to make the surfaces at any 

 imaginary section slide past each other, from its similarity 

 to a shearing action, is called shear. 



Consider now the beam shown in Fig. 10. Since the loads 

 are symmetrically applied, each reaction is equal to 40 Ib. or 

 one-half the total load on the beam. Considering therefore, 



i 4 



a a s 



I 



FIG. 10 



any transverse section of the beam between RI and the point 

 of application of the load n, it is evident that the part of the 

 beam at the left of this transverse section is subjected to an 

 upward thrust of 40 Ib., while the part at the right is sub- 

 jected to an equal downward thrust. The result is a shear- 



