ANALYSIS OF STRESS IN BEAMS 



53. 



Analytically, if x denotes the distance of any section from the left 

 support, the equations of the three portions A'H, HJK, and KD 1 of 

 the moment diagram are 



trr n ff\ y* 



for 



<x<d -'> 



for 

 for 



77 < 



A 



2' 



Problem 60. Construct the bending moment and shear diagrams for a cantilever* 

 bearing a single concentrated load P at the end. 



Problem 61. Construct the bending moment and shear diagrams for a simple 

 beam bearing two equal concen- 

 trated loads at equal distances |A 

 from the cent* r. 



53. Relation between j 

 shear and bending moment. 

 < ler a beam bearing sev- 

 eral concentrated loads P v F]( 4Q 

 P v eta, at distances d r d v 



eta, from the left support. Take any section mn at a distance x 

 from the left support, and consider the portion of the beam on the 

 left of this section. Then if Q denotes the total shear on this section, 



-*,-/. 



" 

 Also, the bending moment at mn is 



" -A 



where the summations include all the loads between A and the 

 section mn. 



A cantilever is a Iwam which is framed into a wall or other support at one end and 

 projects outward from this support. 



