IN BEAMS SUBJECTED TO TRANSVERSE STRAIN. 
229 
supposed to be capable of taking up the same degree of extension and compression 
from the same force as if it acted separately, and independently of the adjoining fibres. 
But it is well known as a practical fact, that there is a powerful lateral action which 
tends to modify the effect of unequal strains. 
If, for example, a bar, ahcd, have a strain applied at efdh, the portion 
defb will not be extended so much as it would be if separated from 
acef, unless an equal strain is applied to the portion acef. And if a 
portion of a bar cannot be extended in proportion to the force applied to 
it, unless the contiguous part is equally strained, it follows that the outer 
portions of a beam subjected to transverse strain will not be extended in 
proportion to the force applied, because the part nearer the neutral axis ^ 
is not equally strained. The measurements made for obtaining the posi- 
tion of the neutral axis afford direct evidence on this point. 
In the first beam, a strain of 5786 lbs. caused an extension of twenty- 
eight divisions of the micrometer; the points measured were j-^ths of 
the depth of the beam. The extension at the outer fibres was therefore 
28XTf=30 divisions. The micrometer reading before the strain was ap- 
plied was 211 1, and the total distance of the points measured was 2111 -1-51661=53772. 
The effect of the strain caused therefore an extension of of the length. The 
beam was 7 feet 4 inches long, 6 inches deep, and 2 inches thick ; and as 
W-— ^ 
. 3^W 
d 2ad 
or/= 
3x88x5786 
2x 12x6 
= 10,608 lbs.; 
so that, with a strain of 10,608 lbs. at the outer fibres, the extension produced was 
of the length. 
But in referring to the experiments made by Mr. Hodgkinson, it will be seen that 
a force of 10,538, applied by direct tensile strain, extends cast iron r^s-eth of its 
length, being nearly double that exhibited by the beam. 
In the second beam, a weight of 8000 lbs. (from the mean of two results) produced 
an extension of forty divisions, which at the extreme fibres will be 40^=44 divisions. 
The mean reading of the micrometer, previous to the strain being applied, was 
1439 ; therefore the extension was 
44 1_ 
51661 + 1439~1207‘ 
The strain at the outer fibres produced by this weight was 14,666 lbs. ; so that 
14,666 lbs. to the inch caused an extension of xrorfh of the length. 
But referring again to Hodgkinson’s experiments on direct tensile strain, a weight 
of 14,793 lbs. produced an extension of of the length ; which is again nearly 
2 I 2 
