IN BEAMS SUBJECTED TO TEAliSVEESE STEAIN. 
471 
transverse strain, the beam being supposed to be supported at the centre f, and loaded 
at its extremities. 
In this change of figure it will be observed that there are three effects : — 
First, an extension of the fibres or particles, commencing at the neutral axis Inm, 
and increasing to the upper portion of the beam. 
Secondly, a compression of the fibres or particles from the neutral axis to the lower 
portions of the beam ; and 
Thirdly, the planes or surfaces ale and hnd are forced downwards to the distance 
no and fy. 
There are, in fact, two distinct changes of figure : — 
There is the change produced by the tension and compression, which, if acting alone, 
would result in the figure efhg ; and there is the change produced by curvature, which, 
if acting alone, would result in the figure Ipnorm. The effect produced by the curva- 
ture is, to cause the sides or planes bd and ac to descend parallel to themselves ; the 
effect produced by the tension and compression is, to cause these planes to turn about 
the neutral axis. The combination of these effects is necessary to produce the figure 
which a beam assumes when placed under transverse strain ; and the changes of figure 
point out distinctly the nature of the resistances. For as it was shown by the measure- 
ments taken in the experiments on the neutral axis, that the lines or planes corre- 
sponding to ac and hd remained straight, whatever was the amount of their angular 
motion, it follows that the tensions and compressions will increase in an arithmetical 
ratio from the neutral axis to the outer portions of the beam. But the effect of ffexure 
causes the planes corresponding to ac and bd to descend an equal extent throughout 
their surfaces ; the resistance to this change of figme will therefore be a force distributed 
evenly over the whole surface. 
If abed were a series of horizontal laminae, these two changes of figure might be 
obtained separately ; efhg being the result of the strains applied in the direction of the 
length, and Inom that of a strain applied at right angles to the length. 
But if the laminae are all united together, the elastic reaction of the mass causes 
certain fixed relations to be estabhshed between the curvature and the angles formed 
by the planes which were at right angles to the length, prior to the strain being 
apphed. 
Of these relations, it is sufficient for the present purpose to point out that which sub- 
sists between the degree of extension and compression, and the amount of curvature. 
