to Transverse Strain in Beams. 407 



which is about the average. It must be remembered that the 

 extension measured by Mr. Barlow is that of 12'25 inches of 

 the length of the beam, and that the maximum extension at 



the centre is therefore 1*078 times this amount or - ., „„ rt n . 



looz'o 



Taking the modulus of elasticity at 17,270,000 the extension 



due to a stress of 10,608 lb. applied by direct tension is 



10608 1 , ., . , 



17 270 0O0 = 1626' ° r Verj nea J Same ( l uantlt ^* And 



the extension above deduced from Mr. Barlow's measurements 



with this load of 5786 lb. is '000633, or , which is greater 



than that due to the direct tension if the modulus be as here 

 supposed. 



At all events Mr. Barlow's conclusion that the extension 

 produced by direct tensile stress is nearly double of that caused 

 by an equal calculated stress in the outer fibres in transverse 

 strain, is not supported by the results of his own experiments. 

 On the contrary, it appears that with moderate loads the 

 extension is very nearly the same in both cases. But with 

 extreme loads this is no longer true. The extension of the 

 lower fibres will then be found considerably to exceed that 

 which would be caused by a direct tensile stress equal to that 

 calculated from the load on the supposition of the indefinite 

 elasticity of the material, if such a stress could be applied 

 without causing rupture. 



It is, however, inconceivable that any such tensile stress 

 exceeding that which is found by direct experiment to pro- 

 duce rupture can exist within the material. What, then, is the 

 true explanation of the facts disclosed by the experiments ? 



In what Mr. Barlow terms " the existing theory of beams/' 

 as well as in the arguments upon which he bases his own 

 theory, it is assumed that up to the point of rupture the 

 elasticity of the material is unlimited ; in other words, that the 

 tensile or compressive stress always varies with the strain. 



Now it is well known that this is not the case. It was 

 found by Hodgkinson that with cast iron, although between 

 a limit of about 5 tons tensile to 15 tons compressive stress 

 the stress varied very nearly with the strain, when these 

 stresses were exceeded the proportion of stress to strain 

 diminished with increasing rapidity. Even within these limits 

 the strict proportion which existed for either tensile or com- 

 pressive strain of very small amount was not absolutely main- 

 tained, but with increasing stress the proportion of stress to 

 strain gradually, though at first only very slightly, diminished. 



