220 MR ANGUS R. FULTON ON 



But 



w 



aT - a( - C) = W. . •. «(T + C) = W ; and a = ^-^ 

 .'. when the ultimate stresses are T and C we have 



W(L + x) = tk^{y t + y c ) + Wx- ^L |(T + C). 



Eliminating balancing moments, this equation becomes 



CA T + C { ' J ' +y < ) = tA f% (Vt + //f) = WL + IT 

 This means that what was the resisting moment of the section before this 

 alteration of the neutral axis has, by reason of the rearrangement, become equal to 

 the original external bending moment plus the moment of the weight about half 

 the displacement of the neutral axis. > 



Since x is usually small, — - may be considered to be negligible, and therefore 



for all practical purposes the relationship between the external moment and the 

 resisting moment of the section just at the point of rupture may be taken as the 

 same as when there was no resultant, that is : 



WL = tA^- c (y i + y c ) = cA T ^(y t + y c ) .... (III.) 



*«T- ™i-,* + (HI.A) 



Hvt + Vc) c 



n WL T + C mT v 



corC = — — =— ..... . (lll.B) 



MVt + Vc) T 

 Now, if T = C=/, as is approximately the case for W.I. and mild steel, then 



/=T = C = ^ L -._?— (3) 



Experiments. 



The results of experiments undertaken by the author with hooks made from 

 various materials show that the values obtained for "/," as calculated from formula 

 (3) when the ultimate stress-point is reached, agree more or less accurately with the 

 direct stress values. The first tests were carried out on galvanised wrought-iron 

 hooks used for suspending ship's boats. The hooks were of circular section, and had 

 ends long enough to enable ordinary tension test pieces to be cut off. 



Afterwards a series of tests were made on hooks specially manufactured from 

 round bars of various materials. In addition to the length necessary for the pre- 

 paration of the hook, two other lengths were cut off each bar, one being tested in 

 direct tension cold, and the other was first annealed before being so tested. In this 

 way a direct comparison was made between the stress induced in the hook by 

 bending and the ultimate tensile stress as found after heating. 



A hook was also made from a bar of rectangular section, and also another prepared 

 with an approximately rectangular section by flattening the sides of a round bar. 



