MancJiester Memoirs, Vol. xlvi. (1902), No. \. 3 



Assuming that such a die is supported by a ring MIS' , 

 infinitely near the outer edge of the die, it can be seen 

 that the pull of the tube would produce both bursting and 

 bending effects. The hoop tension at the inner back 

 edge will be due to the bursting pressure of the tube 

 together with the tension due to bending. 



The maximum stress due to these forces is shown 

 in the following pages to be approximately — 



(0 /=-^.,( 4-5 + 15 — - — ^') 



where 7'= total pull on tube in tons, 

 „ ('/= thickness of die, 

 „ r^ = minimum radius of hole, 

 „ ;-! = radius of outer edge of die. 



This stress is a tension per[iendicular to a radial 

 plane, and occurs at that edge of the die where the tube 

 leaves. [It is independent of the slope of the hole under 

 the given assumption.] 



Formula (i) is an approximation, inasmuch as it 

 depends upon the following : — 



id) Assuming that there is no internal traction parallel 

 to the axis of the die, i.e., to the direction of motion of the 

 tube, a solution of the equations of internal equilibrium for 

 an elastic solid can be found without difficulty. 



This assumption with regard to the internal traction is 

 made by Saint- Venant when considering thick circular 

 plates and the flexure of beams. It is probably most 

 questionable at the curved inner face where the tube is in 

 contact with the die, but the inclination here is slight, and 

 its effect should rapidly vanish as the distance outwards 

 increases. 



ip) The solution should satisfy the external conditions. 

 At the outside rim there should be no radial pressure or 



