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 CEH 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 

 great enough to balance the applied without deforming the " plane 



4 



Fia.2a. 



section," at the larger moment however the beam takes up the 

 load by increasing the shaded area AFC to the area AFGB, and 

 the limiting case is reached when the triangle AFC becomes a 

 rectangle standing on AF 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 



