192 Mr Wimperis, Some Experiments upon Beams 
the elastic limit, then this linear law no longer holds, and the 
applied bending moment is equilibrated by the inner layers taking 
more than what may be called their “ fair share ” of the load ; when 
this occurs the stress is no longer proportional to the strain. 
During the elastic deformation the section was everywhere plane 
and the stress diagram was of the form shown in Fig. 1 where the 
ordinates of the shaded triangles AFC and GEH represent the 
stress at different distances from the neutral axis ; when the elastic 
limit is exceeded the stress diagram takes the form indicated at 
ABODE. In the first case the equilibrating moment was just 
gre^t enough to balance the applied without deforming the “ plane 
section,” at the larger moment however the beam takes up the 
load by increasing the shaded area AFC to the area A FOB, and 
the limiting case is reached when the triangle AFC becomes a 
rectangle standing on A F for base and of height equal to FC (this 
is the limiting case for an infinitely ductile substance) as shown in 
Fig. 1 a. In that case the resisting moment will be at its maximum 
value, i.e. about 50 per cent, greater than that at the elastic limit 
(this is nearly true for mild steel or iron) and any further increase 
of the load must produce fracture. The moment is said to be 
