468 
ME. W. H. BAELOW ON THE EESISTANCE OE FLEXHEE 
and including the equal resistance to compression 
which taken between the limits and x=d, becomes 
In the case of rectangular bars, if the breadth this expression becomes 
ifid’=iiw ( 1 .) 
In girders or bars of other forms, if ?/= the double ordinate con’esponding with the 
distance x, the general expression will be 
^"^yxdx ; 
and when the form of section is symmetrical above and below the neutral axis, 
2^'^~yxdx=ilW. 
From this general expression we obtain the following for the several forms experi- 
mented upon : — 
In the square bar broken on its angle, if 
d= half the depth, 
y=2{d—x), 
the complete integral of this between the limits ^=0 and x=d mil be 
f=im. 
( 2 -) 
In hke manner, in round bars, if 
then the complete integral is 
d— half-depth or radius, 
y — 2 \/{d^—x% 
x=3-1416... , 
(3.) 
In the open beam, the expression for the resistance is the same as in the rectangular 
bar, except that here denoting the half-depth by D, and the half-distance between the 
bars by d, the expression 
2hf^2^dx 
must be taken between the limits x=d and a^=D, which gives 
2bf/W-d^\ 
