to Transverse Strain in Beams. 425 



given by equation (20), and the breaking weight may thence 

 be calculated. 



Mr. Barlow made experiments on six patterns of beams of 

 this description, four being tested of each pattern. In the 

 Table on p. 426 are given the mean dimensions for each 

 pattern, the breaking weights found by experiment, and 

 those calculated as above. 



Except in two instances (those of patterns 5 and 6, the 

 second of which should on any theory be considerably stronger 

 than the first, the breaking weights according to Mr. Barlow's 

 formula being 4935 and 5533 lb. respectively) the agreement 

 between the calculated breaking weights and those found by 

 experiment is very remarkable ; and it must be remembered 

 that these values are not obtained from an empirical formula 

 with arbitrary constants. 



For a bar of square section diagonally strained the height 

 of the neutral axis above the lowest point is determined by a 

 cubic equation 



i 7 /l ~7)—r,-y 2 , (23) 



where c = k—g. 2 od x ' 



c S 



But as j =1— ^— ,the value of h may readily be found by 



approximation when e 1 is given. Taking this as before at 

 •004 for the maximum elongation at breaking point, and S 

 and E as before, we find h = '5412^. 



And calculating the moment of stress on the same prin- 

 ciples as in the former examples, we obtain 2894 lb. for the 

 breaking weight of a bar 2*835 inch in depth and 60 inches 

 between the supports. 



Four such bars were tested by Mr. Barlow, and the weights 

 with which they broke varied from 2708 to 3268 lb.* 



The case of flanged girders would be of more importance if 

 any reliance could be placed for practical purposes upon the 

 element of strength in question. But as a test of the theory, 

 the correspondence of the results deduced from it with the 

 facts evinced by the three descriptions of beams already 

 noticed is amply sufficient. 



It may therefore be regarded as proved that the transverse 

 strength exhibited by cast-iron bars or beams can be accounted 

 for by tensile and compressive resistance without requiring 

 either to exceed those found to exist by experiment on direct 



* Experiments on similar, but smaller bars, showed in proportion con- 

 siderably greater strength, and the same result appears in comparing 

 experiments with square bars squarely strained, and also with round bars. 

 In fact it would seem as if the tensile strength of an iron casting must be 

 greater near the surface than in the interior, as was found by Mr. 

 Hodjfkinson to be the case in regard to its compressive strength. 



