Mr Wimperis, Some Experiments upon Beams, etc. 191 



Some Experiments upon Beams under endlong compression. 

 By H. E. Wimperis, B.A., Gonville and Caius College. 



[Received 2 April 1901.] 



1. To know at what particular load a beam will break 

 requires a knowledge of several important and many obscure 

 points. Among the more important points are the elasticity of 

 the metal (supposing the beam to be of metal), the method of 

 applying the load and the actual shape of the beam ; other 

 obscurer but not less important ones are the homogeneity and 

 ductility of the material and the treatment it has undergone 

 when being forged, rolled, or cast, etc. The ductility is roughly 

 measured by the percentage elongation that occurs, say, on an 8-inch 

 length when a tensile load great enough to break the rod is 

 applied ; this property though mentioned last is by no means the 

 least important, as even though its effect is not marked during 

 elastic extension or compression, yet when once the limit of 

 elasticity is exceeded its effect is very strongly shown in dis- 

 tributing the stress more evenly over the surface strained. A bar 

 with little ductility will break owing to an isolated fracture over 

 one small area spreading over the whole surface 1 , whereas a ductile 

 bar will allow the stress at the elastic limit to be considerably 

 exceeded before fracture. 



The effect of ductility is very plainly shown in the experiments 

 described in this paper, and its measure is indicated by the fact 

 that the mild steel rods used, when stressed to the extent of 

 40 tons per square inch, showed an elongation of 12 per cent, on 

 an 8-inch length. 



The simple theory of the bending of beams assumes that a 

 section of the beam originally plane remains plane during the 

 elastic deformation that occurs on loading, this section being taken 

 perpendicular to the plane of bending. In other words, the relation 

 between the distance of any fibre from the neutral axis and the 

 strain in that fibre is one of simple proportion. When the load 

 is increased to such an extent that the maximum stress exceeds 



1 The state of affairs in a non-ductile rod has been well compared to a " Bridge 

 structure in which several tension members have been replaced by Cast Steel 

 Ties." 



