204 



JOHN C. KOCH 



Horizontal shear in beams 



50. Effect of horizontal shear in beams. The common theory 

 of beams considers only the tension, compression and vertical 

 shearing forces acting in a beam. In addition there exists a 

 horizontal shearing force tending to cause sliding or shearing in 

 horizontal planes parallel to the longitudinal axis of the beam. 



The effect of these shears is seen in considering a cantilever 

 beam loaded at the free end, the weight of the beam itself being 

 neglected. Afsmall amount of bending will take place in ac- 



6 



Fig. 9 Manner of subdividing any plane figure for the purpose of computing 

 the moment of inertia, without the use of calculus formulas. Tabulations are 

 given in table 1, explained in paragraph 4^. 



cordance with the relative stiffness of the beam. Figure 10, a 

 shows such a beam, the dotted lines indicating the bending due 

 to the load P. The amount of the bending is a maximum at 

 the point where the load is suspended, and as the support is 

 approached, the bending diminishes until it reaches a minimum 

 of zero at the support. 



If a beam having the same dimensions as the one just discussed, 

 is considered, but in which horizontal cuts have been made 

 through the beam, separating it into a number of thin strips 

 as in figure 10, 6, it is evident that the amount of bending in 

 such a loaded beam will be much greater. This is because the 



