50 



STRENGTH OF MATERIALS 



section. Then the moment 

 at mn is li.x ( = x \ and 



the shear is l t = V For 



a section on th.e right of 

 the center the bending 

 moment is R t (l x) an<l 

 the shear is 7? r Conse- 

 quently, the bending mo- 

 ment varies as the ordi n a i s 

 of a triangle, being 

 at either support, and at- 

 taining a maximum valur 

 Pi 



FIG. 35 



-- at the center, \vliilr 

 4 



of 



the shear is 



A to B, and also constant, but of opposite sign. fnm /' to C. 



The diagrams in Fig. 35 represent these va rial inns in bending 

 moment and shear along the beam under the assumed loading. Con- 

 sequently, if the ordinates vertically beneath B are laid nil' t<> scale 

 to represent the bending moment and shear at this point, the bending 

 moment and shear at any 

 other point D of the beam j/> 



are found at once from the 

 diagram by drawing the 

 ordinates EF and HK verti- 

 cally beneath D. 



(B) Beam bearing a single 

 concentrated load P at a dis- 

 tance c from one support. 



The reactions in this case 



are 



and 



P(l ~ c} 



I 



PC 



Hence the bending moment 



Fio. 36 



