Mr W imperis, 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structure in which several tension members have been replaced by Cast Steel 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.” 
