BEAM OF EECTANGULAR CROSS-SECTION UNDER ANY SYSTEM OF LOAD. 127 
It we calculate the values of So and for Ijb = tt/G, tt/S, 7r/2, we find 
lib. 
Si. 
S 2 . 
tt/G 
1-9862 
3*9475 
^/3 
1-2585 
- 3235 
v/2 
— 
--0591 
From these values and from the known behaviour of these functions near Ijb = 0 
and Ijb = co we can draw a rough diagTam illustrating their variations. Fig. vii. 
Fig. vii, 
gives the curves of Sq, 2 S|, and So as we increase J. It will he seen from the figure 
that So and 2Si Intersect when //fi = -52 nearly. 
Hence, when the arm of the couple is about half the height of the beam the shear 
is stationary at the centre, a horizontal straight line havino’ contact of the third 
Older With the curve. Curve (c), fig. vi., shows the distribution of shear, roughly 
