.Nrn. L. N. (1. FTLOX ox AX APPFOXDrATE SOLUTIOX FOP BEXDIXC^ A 
1 ar. 
which gives a negative sheai’ oil the axis of y, as soon as we get away from the point 
of loading. 
It follows that there must be, on either side of the cross-section through the load, 
a locus of points of zero shear. 
It is easy to find the approximate form of this locus in the neighbourhood of the 
])olnt of loadlug. lletainiiig only the leading terms in the X’s in the expression for 
the shear, we find that S = 0 when 
= ^1^X2 (H, - H„), 
’ * Tf/y h 
TT r 
or 
h.. 
4(H,-H„)r" = .T«/A <■'-T 74, _ „ = 
_\/ JT] J ly 
These are tw<^ circles passing througli tlie point of loading and having their centres 
Iving on the up])er edge of tlm beam, at a distance from the point of loading ecpial 
to —yj = These give a kind of wedge-shaped area, similar to that 
4 v/ HI — 
Fig. ix. 
oncl(*sed l)y the cusp of a caustic curve, inside winch the shear is negative. This cusp 
is shown in fig. ix. 
Foi‘ liigher values y'/h tliis apjn'oximation will no longer hold, and the curve will 
deviate from the circle. 
^ ?)5. Distortiort of the Beam. 
An interesting feature of a stress-system of this type is the distortion suttei'ed by 
lines parallel to the axis of the beam. 
We have ah-eady seen that at a certain distance the axis itself suffered a bodily shift, 
being dejwessed in front of the acting load and raised behind it. 
