716 
MR. FAIRBAIRN’S EXPERIMENTAL INQUIRY 
It may be further worthy of remark, that experiments 2 and 3, 8 and 7, show that 
when the flanches of the beams are placed upwards the deflections are considerably 
greater than what they are when the flanches are placed downwards ; thus in expe- 
riments 2 and 3, we have 
Weight on the beams, 
lbs. 
6055 
6727 
7399 
and in experiments 8 and 7 
2470 
2739 
3008 
Deflections when the flanch is 
upwards, 
inch. 
•43 
•68 
•88 
1 
•66 
1-22 
2-20 
Deflections when the flanch is 
downwards, 
inch. 
•26 
•34 
•47 
•59 
•90 
1-35 
k!.. 
vl 
Beams with a Double Flanch. 
Let ABFE be a section of a beam having two flanches AB&a and El^e formed by 
angle-irons riveted to a vertical plate CD, the material 
being symmetrically distributed with respect to the ver- 
tical line CD. Let O be the neutral axis, and KVG a 
line passing through the centre V of the vertical line 
CD parallel to AB or EF. Put A= the area of the sec- 
tion of the material, Aj= area ABFE or 2 area ABGK, 
A 2=2 area mjsi, A 3=2 area jghG, ^2=2 area mjqv, 
a 3=2 area^ir/G, Di=GB=GF, D 2 =.y, D 3 = 6 G, d^=jq., 
d^=fGy X=OV, Ii=: moment of inertia about KG, 1 = 
moment of inertia about O, W= the breaking upon the 
centre of the beam, 1= the distance of the supports, e u v 
S, S,= the resistance of the material per square inch at the edges EF and AB re- 
spectively. 
Tojind the Neutral Axis. 
Taking KG as the axis of moments, 
A X X. — 2 V A 2 D 2 “|~ A 3 D 3 a^d^ ~ a^d ^') , 
X=- 
I -A-gDg ct^d‘ 
3"'3 
where 
2A 
A=Ai— A2— A3— ^2 
( 6 .) 
(7.) 
To Jind the Moments of Rupture, 8fc. 
Taking the moments of inertia with respect to the line KG, 
I,= moment inertia ABFE — 2 moment inertia space hgsiqf 
=1 ( A,Df - A 2 DI - AjD^ - afl—a^l) ( 8 .), 
