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STRESSES BEYOND THE ELASTIC LIMIT. Art. 80. 



strength, on account of the contraction of area. In a beam there 

 is very little contraction on the tension side, or expansion on 

 the compression side. 



The adequacy of this explanation is disputed by some 

 authorities, because certain experiments have shown that the 

 neutral axis moves very little in a cast iron beam, and that the 

 ultimate strength in bending does not differ greatly from that 

 in tension, for stone and concrete, provided the latter is de- 

 termined accurately, which is a difficult matter to do. 1 



Equations applicable beyond the elastic limit have been 

 developed, but for the sake of simplicity, the form of equation 

 (10) is used to compare the ultimate strengths of beams. Thus, 

 if a beam having a certain length and cross section is loaded 

 until rupture occurs in the extreme fiber, the moment may be 

 calculated from the breaking load and length, and v and / are 



known; from these may be calculated s u = j- . s u is an exper- 

 imental constant, for a certain kind of material, and may be 

 used to calculate the breaking load for other beams of the same 

 material, having different lengths and cross sections. If the 

 forms of the cross sections are different, the results may be 

 largely in error, particularly for cast iron. s u is called the 

 modulus of rupture in cross-breaking. 



Steel and iron really have no modulus of rupture in cross- 

 breaking, because they do not rupture like stone, wood, and 

 cast iron, but bend indefinitely; for them the elastic limit is 

 the proper limit of strength. 



Foppl's Technische Mechanik, Vol. Ill 22a. 



