1903]. Stress and Strain in the Cross- section of a Beam. 25 



by dividing the numbers in Table X by the magnification and the 

 breadth of the beam, and multiplying the result by the scale unit. 



By comparing these strains with Tables VI and VII (Appendix), or 

 with the curve in fig. 6, we can find the direct stresses which must 

 have accompanied them. These are given in Table XII for loads up 

 to 1J tons. 



Proceeding in a similar way for Cast-iron Beam No. 2 and for the 

 wrought-iron beam, we obtain the second column of Table XIII and 

 the last two columns of Table V for the actual strains per J ton, 

 and comparing these with fig. 6, we get the stresses given in the 

 Appendix in the third column of Table XIII for the cast-iron beam, 

 and in Table XIV for the wrought-iron beam. 



The degree in which these stresses agree with those obtained by 

 the ordinary theory of the bending prism, as given by Coulomb 

 and generalised by Saint Venant, may be taken as a measure of the 

 applicability of that theory. Thus Table XIV contains the theoretical 

 values of the stresses calculated for the wrought-iron beam, and it will 

 be seen that the agreement with the experimental results is not very 

 good at the higher stresses. 



The theoretical stresses for the cast-iron beams are given in 

 Tables XV and XIII (Appendix). 



Discussion of the Results for Cast Iron. 



The theoretical stresses are not calculated for loads higher than 

 1J tons, as above that point some of the values obtained would be 

 greater than the actual tensile strength of the material. 



At the lower loads the lateral strains, and the stresses inferred from 

 them, are generally lower than those obtained theoretically. 



The amount of this discrepancy can best be seen by comparing 

 Tables XII and XV. 



It is also noteworthy that as the load is increased the results show 

 a distinct shifting of the position of the neutral axis from the tensile 

 towards the compressive side of the beam. 



For loads over 1J tons not only is the theoretically calculated 

 maximum stress greater than the ultimate stress the material will 

 stand before fracture, but the values obtained by measuring the 

 strains are also considerably greater than the maximum lateral strain 

 which occurs in a tensile specimen. 



The strain at fracture of a tensile specimen is about 35 x 10~ 5 . This 

 is nearly equalled by the lateral strain noted at 2\ tons load on the 

 beam, whilst the maximum lateral strain at fracture would be greatly 

 in excess of this value. 



Saint Venant* assumes that, since all materials are capable of a small 



* See Saint Venant's ' Navier' (Paris, 1864), p. 178. 



