IN BEAMS SUBJECTED TO TEANSVEESE STEAIN. 
473 
Taking y = the double ordinate corresponding to the distance the general expres- 
sion, when the sections are symmetrical above and below the neutral axis, will be 
■■im. 
From this general expression the following are obtained for the several forms experi- 
mented upon: — 
First, in the case of the square or rectangular bar, 
2(i/+lf)M’=i-fW (7.) 
For the square when broken angleway s, 
( 8 -) 
For the round bars, 
('*•) 
For the open bar, since the resistance to flexure depends on the inequality of extension 
between the part nearest and that most remote from the neutral axis, if d' = the depth 
of the bar, and D the half-depth of the beam, the resistance to flexure at the moment 
d' 
of rupture will be (p^, or multiplied by d'b, 
d' 
and this resistance acting at the distance D — we have, for the whole resistance, 
( 10 .) 
In the case of section No. 15 (flg. 1), broken with the flanges horizontal, the expression 
for the centre part will be 
and for the flanges, 
and consequently for the whole section, 
2(i/+i?)JD’+25{®^+5(D-f)f}=iiW. . . . (11.) 
And lastly, for section No. 16 (flg. 2), broken with the flanges vertical, the expression 
for the flanges will be 
2(i/+i?>)»; 
and for the centre part, 
b'd'^ 
and therefore, for the whole section, 
2(i/+i?)(w+*-^°)=inv (12.) 
3 Q 
2b 
MDCCCLVII. 
