SIGMA PHI STRESSES

SIGMA THETA STRESSES

Membrane

Inner

Outer

Membrane

Inner

Outer

9,905

-1,948

21,757

29,371

25,815

32,926

For this point the stresses can be categorized as follows:

Pm = 9.905 psi in [PHI] direction

PL = 29,371 psi in [theta] direction*

Pb = 0

Q

=

11,852 psi on the inner surface in the [PHI] direction

=

-3,555 psi on the inner surface in the [theta] direction

=

+11,852 psi on the inner surface in the [PHI] direction

=

+3,555 psi on the inner surface in the [theta] direction

We must also consider that there is a radial stress, [sigma]r, equal to the

pressure and considered as a compressive stress acting on the inner surface

and perpendicular to it. This is a surface stress and some thought must be

given as to where it is placed. For instance, at any point being considered

where there exists only a membrane stress, Pm, the [sigma] should be put

into the Q category. The same reasoning applies to where there are only Pm

and Pb stress components, as in the case of a flat head or some knuckle

positions. In such a case, it would be best to consider [sigma]r or a Pb

stress. For the example being discussed, we have additional Q stress

Q = 1000 psi on the inner surface in the r direction

Finally, the peak stress components must be considered. This is usually done

by denoting these as stress concentration factors, KPHI], and K[theta]B,

acting in the [PHI] direction and the [theta] direction, respectively. F

components are developed by multiplying the sum of the principal stresses in

that location in each direction by the factor (K[PHI] - 1.0) or (K[theta]

- 1.0), respectively. For instance, assume that the stresses as shown in the

computer printout line above, were calculated by hand or by some cruder

computer program incapable of accurately modeling the fillet radius. The

effect of the reentrant corner on the outside surface would have to be

determined in some manner. Assume that this geometry was estimated to induce

a K[PHI] of 1.6 and K[theta] of 0.0. Then

F = (K[PHI] - 1) (total principal stress in [PHI] direction

F = (1.6 - 1) (21,757) = 13,054 in the [PHI] direction on the

outside surface.

* This figure is a local membrane stress because the computer printout

shows that this stress decays very rapidly as distance is measured from

the geometric discontinuity.

Integrated Publishing, Inc. |