) 
<2 ea ae eee eee 
. 
a he eee 
_ system of loads, the 
_ ing foreeand bending 
moment diagrams, 
_ the original bending 
DEFLECTION OF BEAMS 117 
which measures the slope of the bent cantilever at P, will in Fig. 157 
represent the shearing force 
on the cantilever at P, that == 
is, the curve of slope in Fig. H , 
156 is the shearing force —L 
curve in Fig. 157. 
Again, at any section P 
of the cantilever (Fig. 157) 
ll 
the bending moment is pro- i je = --36 --- —»/P 
portional to the area of the : 3 
figure PHKB multiplied by iF 
#, the horizontal distance of : | 
G, the centre of gravity of S.F.D. iy 
PHKB from P, and therefore 
the ordinate P,Q of the 
curve A,P\B, in Fig. 156, 
which measures the deflec- 
tion of the bent cantilever 
at P, will in Fig. 157 repre- 
sent the bending moment on on sltee 
the cantilever at P, that is, the curve of deflection in Fig. 156 is the 
bending moment curve in Fig. 157. 
Hence having constructed the bending moment diagram for any 
curve of slope and 
the deflection curve 
may be constructed | 
by the rules for con- 
structing the shear- 
moment diagram be- 
ing considered as a 
load diagram. 
Consider next the 
case of a beam ABS 
(Fig. 158) supported 
at the ends, and 
under any given sys- 
tem of loads. Let 
AHKS be the bend- 
ing moment diagram G : 
for the given system Fra. 158 
of loads, and let ed bas 
A,P,B,S, be the curve in which the beam bends, B, being the lowest 
point in that curve. 
Let a, a,, and a, be the areas of the figures PHKB, AHP, and 
AHKB respectively. us G,, and G, are the centres of gravity of these 
respectively, and the horizontal distances of the points G,, G,, 
and G, from A are #,, @, and %, respectively. AP=«, and AB=/. 
