‘230 
MR. W. H. BARLOW ON THE RESISTANCE OF FLEXURE 
double that produced by the same strain when excited by a weight applied trans- 
versely. 
From these and other considerations I was led to think it probable that the effect 
of the lateral action of the fibres or particles of a beam, tending to modify the effect 
of the unequal strains and opposite forces, and thus diminishing the amount of ex- 
tension and compression which would otherwise arise, constituted in effect a resist- 
ance to flexure-, and it will be found that the following experiments fully confirm the 
existence of this resistance as an additional element of strength in beams ; and that 
it explains the apparent anomaly in the amount of tensile resistance when excited by 
direct and by transverse strains. 
Assuming the probability of a resistance, acting independently of, or in addition 
to, the resistance of direct tension and compression, and varying with the flexure, it 
occurred to me that it might be exhibited experimentally by casting open girders of 
the forms shown figs. 2, 3 & 4, having the same sectional area in the upper and lower 
ribs ; the same number of vertical ribs, but the distance between the horizontal ribs, 
and consequently the deflections of the girders, different. 
In these girders the neutral axis would necessarily be (like that of the solid beam) 
in the centre, and the sectional area of the ribs subjected to tension and compression 
being the same in each, the circumstances under which rupture would ensue would 
be similar, except in the amount of flexure. 
The formula for the strength of a girder of this form is as follows ; — 
Let a=the united area contained in the upper and lower ribs ; 
a' = the intervening space; 
d=the total depth; 
c=the distance between the upper and lower ribs; 
/=:the length of bearing ; 
W=the breaking weight; 
and F=the force required to produce rupture in the extreme fibres or 
particles. 
Then 
or 
a+a'=the total area of the rectangle m, n, o, p, 
W=f‘(i+c+^). 
The formula may also be obtained by calculating the moments in the usual way. 
Using the same letters as before, we have, for the distance of the centres of com 
pression and extension, 
