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SHELL THICKNESS (Cont.)
DESIGN OF STEEL CONDUITS (Continued)
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.
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/
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.
DESIGN OF STEEL CONDUITS (Continued)
.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/
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/
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.
DESIGN L CONDUITS (Continued)
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
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
6/ Schorer, Hermann, “Design of Large Pipe Lines,” American Society of
Civil Engineers Transactions, 1931.
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, BRANCH OUTLETS, AND WYES
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
DESIGN TEE ONDUITS (Continued)
unsupported pressure areas resulting from the removal of part of the material
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
C. The method of stress analysis used for branches and wyes is approximate.