ANALYSIS OF STRESS IN BEAMS 



51 



SHEAR 



at a distance x from the 

 left support is 



_ P(l -c)x 

 lX I 



provided x < c, and 



K (I x}= Pc ( l ~ x ) 

 I 



if x > c. If x = c, each 

 of these moments becomes 



Pc(l-c) 



I 



and consequently the bend- 

 ing moment and shear dia- 

 grams are as shown in - 



.56. 



(C) Beam bearing sev- 

 eral separate loads. 



In this case the bending moment diagram is obtained by construct- 

 ing the diagrams for each load separately and then adding their 



ordinates, as indicated in 

 Fig. 37. 



(D) Beam bearing a con- 

 tinuous uniform load. 



Let the load per unit 

 of length be denoted by 

 w. Then the total load on 

 the beam is wl, and the 

 reactions are 



wl 



Hence at a distance x from 

 the left support the bend- 

 ing moment M x is 



FIG. 87 



