AECHES AND AKCHED RIBS 



185 



dW C(M Pjg) , 



= I ZJ ; Zds = 0, 



or 



whence 



- 



If J is constant throughout the rib, this reduces to 







* 



The pole distance P A found from this formula is the third condition 

 necessary for the complete determination of the equilibrium polygon. 



152. Second method of calculating the pole distance. The value 

 of the pole distance P h of the force diagram can also be calculated by 

 assuming that the bending of the rib produces no change in the span. 

 To apply this condition, the change in length which the span would 

 naturally undergo is 

 calculated and equated 

 to zero. 



Consider a small 

 portion ds of the rib. 

 If, for the moment, 

 the rest of the rib is 

 regarded as rigid, the 



bending of this portion would make the end B revolve about D as 

 a center to a position at C (Fig. 134). Let dfi denote the angle 

 between DB and DC, a the angle between DB and a vertical through 

 D, z the ordinate DF, and CE, or A/, the change in length of the 

 span. Then 



BC = DB d{$, DB cos a = z, and A/ = CB cos a. 



FIG. 134 



Hence 



= DB ' dfi cos a = zdft. 



