416 THE STRENGTH 



If the beam be long, and much bent, the 

 leverage is not the length of G/, but Gf x 

 cosine of deflection. Calling Gfzz I, and this 

 cosine = c, gives 



W/c = ~^ Tp + P)* whence 



^=k(P+P') (7). 



which is another expression for the strength. 



Cor. 1. If j9 = y, or the distances of the 

 centers of percussion be the same on each side 

 of the neutral line, 



ale 



This case occurs principally when the sections 

 are the same on each side of the neutral line. 



Cor. 2. If the beam be rectangular as a 

 joist, and the material iron, while the elasticity 

 remains perfect, the neutral line will be in the 

 middle; calling then the breadth h, and the 



depth d, we have g - ~ --^, i' = T=T> 

 5 = --• > ^ — 1 nearly, the deflection being 



small, .*. from Cor. 1, 





Cor. 3. Comparing equations f3) and (7), it 

 will appear that PF — p, and Vfz=p'' 



