418 



Mr. R. C. Nichols on the Resistances 



two 



pression of the fibres varies directly with the amount of 

 extension or compression. 



When this condition does not continue to the point of rup- 

 ture, but, as in the case of cast iron, the limit of elasticity 

 has been passed for tensile, but not for compressive, strain 

 before rupture takes place, the maximum tensile stress is that 

 which will produce rupture by direct tensile strain. But this 

 maximum stress will exist, after the limit of elasticity is 

 passed, not only at the lower margin, but for some distance 

 within the substance of the beam. The form of the areas of 

 equal maximum stress will be that shown in fig. 7, and the 

 position of the neutral axis will be raised above the centre of 

 gravity of the section. 



The same considerations will lead to the 

 conclusion that when the limit of elasticity is 

 passed before rupture for compressive, but not 

 for tensile strain, the form of these areas will 

 be that shown in fig. 9, and the position of 

 the neutral axis will be depressed. When 

 it is passed for both tensile and compres- 

 sive strain, the form will be one of the 

 fig. 10 ; and the position of the 

 neutral axis will be raised or 

 depressed according as the limit 

 of elasticity is first passed for 

 tensile or compressive strain, or 

 as the maximum compressive or 

 tensile stress is the greater. 



In each case the maximum tensile stress is supposed to be 

 measured by the base of the section, and to be the unit of 

 stress for both of the areas. 



The same principles will apply to beams of any other 

 section. In all cases the effect will be the same as if the 

 dimensions of the section were reduced for some distance on 

 each side of the centre of the beam, and the stress continued 

 to increase proportionally to the strain without limit up to the 

 point of rupture. 



The results of four experiments made by Mr. Barlow on the 

 deflexion of bars or girders of rectangular section under 

 various loads increased by degrees to the breaking weight are 

 recorded in his paper of 1855. In the following Tables the 

 figures of the first and third columns are the loads and corre- 

 sponding deflexions given by Mr. Barlow as the results of his 

 first two experiments, the other quantities being calculated 

 from them. The irregularity of the deflexions observed to 

 be produced by the smaller loads renders it difficult to deter- 



TyglO 



