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XIX. On the Plastic Bending of Metals. By F. Lloyd 

 Hopwood, B.Sc, A.R.C.Sc, Demonstrator of Physics^ 

 St. Bartholomew's Hospital Medical College, London *. 



IF a uniform straight rod, clamped at one end and not 

 otherwise supported, is allowed to sag from a horizontal 

 position under the influence of its own weight, one of three 

 things will happen : — 



a. It will quickly take up an equilibrium position in which 

 the external forces are balanced by internal elastic 

 forces, or 

 Plastic yielding will occur and the sag will steadily 

 increase with time, the rod coming slowly to rest 

 ultimately in an approximately vertical position, or 

 (If the ratio of the length of the rod to its diameter 



exceeds a certain critical value) 

 The plastic yielding will take place so rapidly that 

 owing to its momentum the rod will bend until its 

 free end passes below the clamp and oscillates about 

 a point below the clamp. (See fig. 1.) 



Fig\ 1. 



b. 



c. 



The complete mathematical theory of Case a is worked out 

 in treatises on Elasticity. 



Cases b and c involving as they do finite flexure and plastic 

 yielding, under what is, in effect, a travelling load, are 



* Conimniiiealed by Prof. A. W. Torter, F.E.^. 



