40 



RESISTANCE OF MATERIALS 



4. Beam bearing a contin- 

 uous uniform load. 



Let the load per unit of 

 length be denoted by w. 

 Then the total load on the 

 beam is wl, and the reac- 

 tions are 



7? 7? wl 

 - R i = - R ^ : =-2' 



Hence, at a distance x from 

 the left support the bending 

 moment M is 



wl 

 



FIG. 42 



The bending-moment diagram is therefore a parabola. When x = - 



M x = <> which is its 

 8 



maximum value. The 

 bending-moment and 

 shear diagrams are 

 therefore as repre- 

 sented in Fig. 42. 



5. Beam bearing uni- 

 form load over part of 

 the span. 



Let the load ex- 

 tend over a distance 

 c and be of amount 

 w per unit of length. 

 Then the total load is 

 we. The reactions of 

 the supports are the 

 same as though the 

 load were concentrated FIG. 43 



