m BEAMS SUBJECTED TO TEANSVEESE STEAIN. 
485 
But c : ^ : D' : D. We have, therefore, for the whole resistance above and below the 
neutral axis, 
. (k+§'e')«. 
If now we represent by iv the breaking weight in any experiment of a beam of given 
dimensions, and by I the length, or rather the distance between the props, there is 
obtained the expression 
an equation from which, when w and I are given, t may be determined. Or if t be pre- 
viously experimentally determined, w may be found. 
In order to submit these equations to the test of experience, we have selected from 
the valuable and extensive series of experiments, by Eaton Hodgkinson, Esq., published 
in vol. V. of the Memoirs of the Literary and Philosophical Society of Manchester, 
Second Series, a few experiments in which the girders differ most from each other in 
section, dimensions, and bearing distance ; and the results we obtain from the foregoing 
formula are given in the following pages, with the form of section and linear dimen- 
sions. It will be seen that the value of t, or the direct tensile strength of cast iron, 
thus obtained, falls generally between the limits of i(=14,000 and ^=16,000. 
In the Beports of the Commissioners for inquiry into the ‘ Application of Iron to 
Bailway Structui’es’ (page 9, &c.), there are given the results of about fifty experiments 
on the direct tensile resistance of one-inch square cast-iron bars, under the direction of 
Mr. Hodgkinson ; these consisted of seventeen different kinds of iron, each set of three 
bars being of the hke quality and manufacture, and in several of these sets, which one 
might have expected to yield very nearly the same results, the difference is full as great 
as in the following Table, exhibiting in fact very nearly like numbers. This circumstance 
will, it is presumed, be considered satisfactory evidence of the general applicability of the 
principles developed in the preceding pages to cast-iron beams and girders of every variety 
of section. 
( 1 )* 
( 2 ) 
Distance of props. 
4 feet 6 inches. 
4 feet 6 inches. 
^ Depth of girder . . . . 6T25 inches. 
Upper flange . . . 1-75 by -42 inch. 
Lower flange . . . I ‘77 by '39 inch. 
Thickness of centre web . . -29 inch. 
L Breaking weight 6 6 7 8 lbs. 
Computed value of 14578. 
'' Depth of girder . . . . 5T25 inches. 
Upper flange . . . I'74 by '26 inch. 
Lower flange . . . I '78 by *55 inch. 
Thickness of centre web . . -30 inch. 
L Breaking weight 7368 lbs. 
Computed value of 141 28. 
* These numbers are those of the experiments selected from Mr. Hodgkixsok’s series. 
