STRENGTH OF PIPES 



39 



Po 



p a 



increasing with the size of pipe. In a riveted pipe the efficiency of the 

 riveted joint must be taken into account in determining this thickness. 

 This may be taken at about 55 per cent, for single and 70 per cent, for 

 double riveting. A minimum thickness of about ^ inch should be 

 adopted to allow for any reduction by corrosion. 



Where the pipes are to be exposed to considerable pressure, and 

 especially when made of cast iron, the distribution of pressure over the 



walls is not so simple, those 

 fibres of the metal nearer the 

 centre being more heavily 

 stressed than those further re- 

 moved. In this case consider 

 the equilibrium of a portion 

 of an elementary ring of metal 

 concentric with the pipe, having 

 inner and outer radii r and r + 

 B r, and subtending an angle B B 



FlG 21. a t * ne centre (Fig. 21). Let 



the radial pressure on the faces 



of this element be p and p + B p, and the circumferential stress in the 

 metal be /. 



Then, for equilibrium of this element we have 



(p+8p) (r + B /) B 6 p r B d +/ B r B = (1) 



.*. r B p + p B r -\-f B r = 



P -? ft)\ 



or i g r = J P- 



Again, if we assume that the plane ends of the pipe remain plane 

 during extension, we get the further condition that 



pf= constant = 2 A. (3) 



Combining this with (2) we have, in the limit : 



or 



(4) 



... = 2 4 r. 



d r 



Integrating this expression we get 



p i 2 = A r 2 + .B 



(5) 



