XV
265
STRESSES IN A RIGHT CIRCULAR CYLINDER
and for the axis of y
Xx
=
P 3R 2R2y2-y
-
Rπ R+2R2y²+y+
Yy
=
P/R2-y²
RT R2+y2
2
All the elements of the axes suffer compression in the direction
and extension in the perpendicular direction. At the
centre the pressure in the direction of x is 6/7 times what it
would be if the pressure P were distributed uniformly over the
whole section 2R. Even in this simplest case it appears that
the distribution of stress is extremely complicated.