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PIPE SHELL (Continued)

t = thickness of conduit shell, in inches
r = inside radius of conduit, in inches
p = maximum internal pressure, in psi
S = design stress, in psi
e = efficiency of longitudinal joints.

If a conduit is freely supported at a number of points, it will act as a continuous beam. If expansion joints are installed, the portion of the conduit between the center of the expansion joint and the nearest support is assumed to act as a cantilever. Reactions, moments, and stresses can be estimated by the use of appropriate beam formulas. Stresses resulting from frictional resistance at supports and in expansion joints when movement of the pipe is caused by temperature changes, should be estimated on the basis of the appropriate friction coefficients referred to in Paragraphs 2.18, 2.19, 2.20, and 2.24. At supports, circumferential and longitudinal stresses in the shell should be estimated by means of the formulas referred to in Paragraph 2.17. Where shell thicknesses based on stress considerations are less than thicknesses calculated from the following formulas, the latter should govern.

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Where conduits act as beams, the maximum equivalent unit stresses should not exceed the critical buckling stress which may be estimated from the formula, 3/

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Values of C, based on experimental determinations, vary from 0.20 to 0.26 for shell thicknesses of from 0.03 to 0.25 inch, respectively.

3/ Wilson and Newmark, “The Strength of Thin Cylindrical Shells as Columns,”

Bulletin No. 255, published in 1933 by the University of Illinois.


.16 Stiffener rings may be required to avoid excessive shell thicknesses under the STIFFENER following conditions: RINGS

A. Where conduits are subjected to uniform external pressure.

B. Where conduits are placed underground and subjëcted to earth pressure or concentrated loads.

C. Where conduits are embedded in concrete and subjected to pressure resulting from buoyancy while concrete is being placed.

For conduits subjected to uniform external pressure, stiffener rings should be designed on the basis of the formula, 4/

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Conduits placed underground may be subjected to (1) concentrated vertical loads, (2) distributed vertical loads, and (3) distributed vertical and horizontal loads. Maximum bending-moment formulas are as follows: 5/

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4/ “API-ASME Code for the Design, Inspection and Repair of Unfired Pressure Vessels for Petroleum, Liquids, and Gases,” Fourth Edition, 1943.

5/ “Handbook of Culvert and Drainage Practice,” published in 1931 by Armco Culvert Manufacturer’s Association, Middletown, Ohio, pp. 42-76.

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Values of q vary from 0.37 for rigid conduits to 0.85 for flexible conduits depending on the degree of flexibility and the condition of the backfill in the conduit trench. Where rings are installed, a value of about 0.75 may be used for g. Values of W may be obtained from Figures 17 and 18. Where stiffener rings are used, Q and W are assumed as being equal to the load per unit length of conduit multiplied by the distance between rings. In these cases d = 2R, the neutral diameter of the combined ring section illustrated in Figure 22. Stiffener rings for conduits embedded in concrete should be designed for the reactions resulting from the buoyant forces to be expected or the reactions resulting from the weight of the empty pipe, whichever is greater. Suitable structural steel supports to be attached to the rings may be provided with the pipe or furnished by the installation contractor.

Support rings are required at the supports where conduits are carried on rocker- or roller-type supports, on sliding-type supports, or on saddle-type Supports. Typical designs are shown in Figures 19, 20, and 21.

Circumferential stresses in support rings for use with both rocker- and
sliding-type supports can be computed from formulas and tables in Figures 22
and 23 when the columns carrying the vertical reactions are placed as shown.
These formulas apply when the conduit is precisely full or under pressure,
which are the usual normal operating conditions for which the support rings
are designed. However, stresses occurring in a partially filled conduit will
exceed those occurring when the conduit is full, the most unfavorable condition
being when the conduit is half full. To eliminate the possibility of failure
while the conduit is being filled or emptied, the half-full condition should be
considered and the support rings should be designed so that stresses under
this condition will not exceed the design stress by more than 50 percent. For-
mulas for estimating stresses when the conduit is half full and for all condi-
tions when the support columns are located other than as shown in Figure 22
can be found in Chapter III of the bulletin referred to in the figure. Longitudi-
nal stresses in the conduit shell may be estimated from the formula, 6/

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and other notations are as shown on Figure 22. It frequently happens that the moments at a support necessitate a greater shell thickness than that required between supports. In a case of this kind, the minimum length of the heavier plate at the support should be calculated from the formula,


L1 = minimum length of the support section, and the value of q
is as shown in Figure 22.

6/ Schorer, Hermann, “Design of Large Pipe Lines,” American Society of

Civil Engineers Transactions, 1931.

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2.18 DESIGN OF STEEL CONDUITS (Continued) STIFFENER RINGS AND SUPPORTS (Continued) Circumferential stresses in support rings for use with saddle-type supports can be computed by use of the formula and graph shown in Figure 24. A value for p of 120 degrees is usually used. A typical rocker-type support assembly and details of the different parts are ROCKERshown in Figures 25 and 26, respectively. Supports of this type offer little TYPE resistance to movements of the conduit resulting from temperature changes SUPPORTS

and are usually used for conduits over about 4 feet in diameter where conditions permit. An over-all friction coefficient of 0.15 may be assumed for design purposes. Vertical reactions, forces due to frictional resistance, wind loads, and concrete bearing values should be considered in the design.

A typical sliding-type support is shown in Figure 20. Supports of this type are SLIDINGused principally in open tunnels where clearances are restricted and where the TYPE sliding plates are not subject to abrasion by blowing sand or other causes. SUPPORTS Friction coefficients of 0.15 may be assumed for design purposes where selflubricating bronze plates are used for one of the contact surfaces. Where two nonlubricated steel plates are in contact, a friction coefficient of 0.50 may be assumed. Vertical reactions, forces due to frictional resistance, wind loads if the installation is outside of a tunnel, and concrete bearing values should be considered in the design.

A typical saddle-type support is shown in Figure 21. Supports of this type may SADDLEbe used where clearances are restricted. The frictional resistance may be TYPE reduced by using two layers of graphited asbestos sheet packing between the SUPPORTS flange of the support ring and the bearing plate, with the graphited surfaces in contact. Although this type of support when new has a friction coefficient of about 0.25, a coefficient of 0.40 should be used for design purposes on the assumption that the sheet packing may deteriorate or become dislodged by temperature movements of the pipe.

Transverse earthquake loads of from 0.10 to 0.20 of the gravity load, depending EARTHon local records, should be included for installations to be made in locations QUAKE subject to seismic disturbances. When a pipe line is located close to an earth- LOADS quake-producing fault zone the above seismic coefficients should be increased in accordance with local records.


Bends (or elbows) are required where changes in direction, either horizontally BENDS or vertically, occur in a conduit. Plate-steel bends are made up of short segments of pipe with mitered ends. Wherever possible, bends should be designed with deflection angles between segments of from 5 to 10 degrees and with radii of from 3 to 5 diameters. For penstocks where the conservation of head is very important, deflection angles of from 4 to 6 degrees may be used. Where the point of intersection of a horizontal angle coincides with that of a vertical angle, or where these points can be made to coincide, a single bend, called a combined or compound bend, designed to accommodate both angles should be used. The combined bend should have a pipe angle equal to the developed angle (X) obtained by the use of the appropriate formula shown in Figure 27. Reducing bends designed in accordance with the layout and formulas shown in Figure 28 combine the functions of a uniform-diameter bend and a reducer, and should be used where practicable. Typical uniform-diameter bends are shown in Figure 29.

Branches and wyes are used where the flow in a conduit diverges into two or BRANCHES more streams or where the flows in two or more conduits converge into a sin- & gle stream. The most important features to be considered in the design of WYES

fittings of this type are structural safety and hydraulic efficiency. For safety, reinforcement of some type must be provided to offset the effect of the

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unsupported pressure areas resulting from the removal of part of the material
from the conduit walls. The locations of these areas, and the loading diagrams
assumed for design purposes are shown on Figures 30 and 31 which illustrate
a number of different types of branches and wyes. Several different methods
of reinforcement are also shown.

A. Right-angle branches and cylindrical outlets or inlets should be avoided where hydraulic efficiency is important or where the question of cavitation is involved. The use of conical connections with side-wall angles so equal to from 6 degrees to 8 degrees reduces hydraulic losses to about one-third of those resulting from the use of cylindrical connections. Hydraulic losses may be further reduced by joining the branch pipe to the main pipe at an angle 9 less than 90 degrees as shown in Figure 30(c). This deflection angle varies in practice from 30 to 75 degrees. For branch outlets (Figure 30) it should not be less than 45 degrees and the corresponding angle for wyes (Figure 31) should not be less than 22-1/2 degrees or 45 degrees between two branches, as smaller angles introduce fabrication difficulties. Branches and wyes are usually designed so that the longitudinal axes meeting at a common point will lie in the same place.

B. Branches as shown in Figure 30 (a), (b), and (c) may be reinforced with a
simple curved plate designed to meet the requirements of the API-ASME
Code referred to in Paragraph 2.16. Branches and wyes of the types
shown on Figure 30 (d) to (g) inclusive, and on Figure 31 (b) to (f) inclusive,
may be reinforced by the use of one or more girders or by a combination
of girders and tie rods. The type and size of reinforcement to be used
depends upon the pressure in the vessel, the extent of the unsupported
pressure area, and clearance restrictions. When branch outlets intersect
in a manner as shown in Figure 30 (d) and (e) and wyes as shown in Fig-
ure 31(f), three or four exterior horseshoe girders may be used, the ends
of which are joined by welding. This welding will be facilitated by insert-
ing a round bar at the junction. For wyes used in pipes with low-velocity
flow an internal horseshoe girder, also called a splitter, as shown in Fig-
ure 31(a) may be used. The splitter is structurally effective, being sub-
ject to direct tension and bending loads, but will cause disturbance if the
flow is unequally divided. Branches of the type shown on Figure 30 (f) and
(g) are not desirable when D1 is over about three-fourths of D, as the
lateral curvature of the reinforcing girder becomes very sharp under this
condition. In these cases, the design indicated on Figure 30(e) is prefer-
able. Wyes reinforced as shown on Figure 31(a) are satisfactory for con-
verging flows, but should be used for diverging flows only in exceptional
cases where it is impracticable to place reinforcement on the outside of
the wye.

C. The method of stress analysis used for branches and wyes is approximate.
Simplifying assumptions are made in the analysis which yield results of
sufficient accuracy for practical design purposes. The reinforcement is
proportioned to carry the entire unbalanced load as indicated by the shaded
areas in Figures 30 and 31. A portion of the pipe Shell is considered to be
acting monolithically with the girders as in the case of stiffener rings.
Excess material within the area of reinforcement may be considered as
load-carrying. In the analysis of the ring girder type of reinforcement
shown in Figures 30 (f) and (g), it is assumed that the curved girder is
acting Similar to a plane ring, that the loads in both directions are uni-
formly distributed, and that the ring is circular. The first assumption is
believed to be reasonably accurate because the ring girder is supported
along its entire perimeter by the pipe shell and cannot be appreciably
twisted or deflected laterally. Assumption of a uniform load distribution
is on the side of safety. As to the assumption of circularity for the ring,
however, it should be noted that the ring girder becomes egg-shaped for
branch outlets with small deflection angles, but for larger deflection
angles the assumption of circularity is nearly correct.

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