484 
ME. W. H. BAELOW OX THE EESISTAXCE OE FLEXHEE 
and the sum of those due to curvature or change of figure, ; or calling the 
whole direct resistance of this central web below x will be ^mxtb. Again, since the direct 
tensile resistance of the unsupported fiange varies as the distance from the neutral axis, 
if we consider x as representing a constant quantity, and y any variable distance from the 
neutral axis, (taken between y—x and y—x—d) becomes the sum 
of all the direct tensile resistances ; the resistance to change of figure being expressed 
simply by dht. 
The total direct resistance below the neutral axis is therefore 
(^x+2hd—Yj^t- 
In like manner, the total direct resistance to compression above the neutral axis is 
which must be made equal to the former expression. 
But we must here observe, that the compression of the upper fibre c, is to the corre- 
sponding tension of the lower fibre t, as x' to x', substituting accordingly, rejecting the 
common factor and observing that x'=a — x, we find 
+ Ad'b'a + — d'%' 
^ Gma + A{db -\-d’b’) 
Having thus determined the position of the neutral axis, we have now to take the 
moments of these several direct forces both above and below that hne, the formula for 
which are however already given in the preceding pages ; that for the lower part of the 
central web being (D now representing x, the distance above found), and that for 
the unsupported flange being the same as in the open beam, viz. 
3D <2^d)dbt. 
This latter is, however, reducible to a more convenient form for numerical calculation, 
viz. to 
(d-A)®. 
We have therefore 
the resistance below the neutral axis, and 
>D'^c+ 
the resistance above the neutral axis. 
* In the preceding paper, Mr. W. H. Baelow, by obtaining from experiments a mean value of t, has, by 
means of his original equation lor rectangular bars, i. e. and his other equations for beams 
ol other forms when broken transversely, endeavoured to find a mean value of cp, and he finds the latter to 
be to the former as about 9:10; but from the difficulty of obtaining the mean value of t within certain wide 
limits, I have not hesitated in assuming t and 0 equal to each other in the case of cast iron. 
