Page 168 - Pressure Vessel Design Manual

146 Pressure Vessel Design Manual

FORCES AND MOMENTS
CASE A CASE B CASE C

Outer 7 Outer

Inner Inner

I Loads at Lugs, Q

0 Basic equation for vertical load Q on 1t~g.s. Note: P is (+) for internal pressure and (-) for external
pressure. M is (+) or (-) depending on the direction of
w Mo
Q=Nhz load F or the location of the moment in the ring.
Allowable tensile stress = 1.5SE. Allowable compressive
Substituting F, for W: stress = 1.25s.
Fv
Q=-&- M,
N OB
Notes
Since M, = FhL, v, = F,/N, and vh = Fh/N, the basic
equation becomes: 1. Stresses due to radial loads are determined for a second
of shell, 1 in. in length (thus the “ring” analogy). The
bending stresses are a result of this “ring” absorbing
the radial loads.
2. Assume effects of radial loads as additive to those due
to internal pressure, even though the loadings may be
in the opposite directions. Although conservative, they
Stresses will account for the high discontinuity stresses imme-
diately adjacent to the lugs.
1. Find the maximum load bending moment, M, due to 3. In general, the smaller the diameter of the vessel, the
radial loads on ring from appropriate case of Table 3- further the distribution of stresses in the circumferen-
18. tial direction. In small diameter vessels, the longitudi-
2. Add localized stress due to bending to general mem- nal stresses are confined to a narrow band
brane stress due to pressure: (approximately 2 in. for a 24-in.-diameter vessel). The
6M
PR, +- opposite becomes true for larger-diameter vessels or
O@ = larger R,/t ratios.
t t2
~