AND STEEL.

BY GENERAL NICHOLAS KALAKOUTZKY.


NO. I.

_Determination of the Influence of Internal Stresses on the Strength of
Materials._--We call internal stresses those which exist within the mass
of any hollow cylinder or other body, when it appears to be in a state
of repose, or not under the influence of external forces. When pressure
is applied to a hollow cylinder, either externally or internally, the
interior layers into which its walls may be conceived to be divided are
subjected to a new series of stresses, the magnitude of which is
independent of those already existing. These additional stresses combine
with the former in such a manner that at every point of the thickness of
the cylinder they have common resultants acting in various directions.
Thus, if we call t the internal stress existing at a distance r_x
from the axis of the cylinder, and in a direction tangential to its
cross section, and T the additional stress due to pressure inside the
cylinder acting at the same point and in the same direction, then the
newly developed stress will be t + T.

If R and r0 be the external and internal radii of the cylinder, and
if we suppose the external pressure _nil_, then, if the pressure inside
the bore be P0, the stress on the radius r_x is determined by the
following expression deduced from the well-known fundamental formulæ of
Lame:[1]

r0² R² + (r_x)²