14-01-2013, 04:13 PM
Stresses in Large Horizontal Cylindrical Pressure Vessels on Two Saddle Supports
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INTRODUCTION
The design of horizontal cylindrical vessels with dished
heads to resist internal pressure is covered by existing
codes. However, the method of support is left pretty
much up to the designer. In general the cylindrical shell is
made a uniform thickness which is determined by the
maximum circumferential stress due to the internal
pressure. Since the longitudinal stress is only one-half of
this circumferential stress, these vessels have available a
beam strength which makes the two-saddle support
system ideal for a wide range of proportions. However,
certain limitations are necessary to make designs
consistent with the intent of the code.
The purpose of this paper is to indicate the approximate
stresses that exist in cylindrical vessels supported on two
saddles at various locations. Knowing these stresses, it is
possible to determine which vessels may be designed for
internal pressure alone, and to design structurally adequate
and economical stiffening for the vessels which require it.
Formulas are developed to cover various conditions, and a
chart is given which covers support designs for pressure
vessels made of mild steel for storage of liquid weighing
42 lb. per cu. ft.
HISTORY
In a paper1 published in 1933 Herman Schorer pointed
out that a length of cylindrical shell supported by
tangential end shears varying, proportionately to the sine
of the central angle measured from the top of the vessel
can support its own metal weight and the full contained
liquid weight without circumferential bending moments in
the shell. To complete this analysis, rings around the entire
circumference are required at the supporting points to
transfer these shears to the foundation without distorting
the cylindrical shell. Discussions of Schorer's paper by H.
C. Boardman and others gave approximate solutions for the
half full condition. When a ring of uniform cross section is
supported on two vertical posts, the full condition governs
the design of the ring if the central angle between the post
intersections with the ring is less than 126°, and the
half-full condition governs if this angle is more than 126°.
However, the full condition governs the design of rings
supported directly in or adjacent to saddles.
MAXlMUM LONGlTUDlNAL STRESS
The cylindrical shell acts as a beam over the two
supports to resist by bending the uniform load of the vessel
and its contents. The equivalent length of the vessel (see
Figs. 2 and 3) equals (L + (4H/3)), closely, and the total
weight of the vessel and its contents equals 2Q. However,
it can be shown that the liquid weight in a hemispherical
head adds only a shear load at its junction with the
cylinder. This can be approximated for heads where H R
by representing the pressure on the head and the
longitudinal stress as a clockwise couple on the head
shown at the left of Fig. 3. Therefore the vessel may be
taken as a beam loaded as shown in Fig. 3; the moment
diagram determined by statics is also shown. Maximum
moments occur at the mid-span and over the supports.
TANGENTIAL SHEAR STRESS
Figure 4 (d) shows the total shear diagram for vessels
supported in saddles away from the heads.
Where the shell is held round, the tangential shearing
stresses vary directly with the sine of the central angle ,
as shown in Section B-B of Fig. 4, and the maximum
occurs at the equator.
However, if the shell is free to deform above the saddle,
the tangential shearing stresses act on a reduced effective
cross section and the maximum occurs at the horn of the
saddle. Fig. 4. The summation of the vertical components of these
assumed shears must equal the maximum total shear.
DESIGN OF RING STIFFENERS
When the saddles must be located away from the heads
and when the shell alone cannot resist the circumferential
bending, ring stiffeners should be added at or near the
supports. Because the size of rings involved does not
warrant further refinement, the formulas developed in this
paper assume that the added rings are continuous with a
uniform cross section. The ring stiffener must be attached
to the shell, and the portion of the shell reinforced by the
stiffener plus a width of shell equal to 5t each side may be
assumed to act with each stiffener. The ring radius is
assumed equal to r.