B4 Stress_ (6)

STRESS ANALYSIS OF PIPING SYSTEMSB.210 GENERIC DESIGN CONSIDERATIONS or microcomputer pipe stress program by breaking the buried portions into elements of convenient length and then imposing a transverse spring at the center of each element to simulate the passive resistance of the soil. The entire pipe can be divided into spring-restrained elements in this manner; however, the only regions of the pipe that really need to be modeled in this manner are the lengths entering and leaving elbows or tees. The analyst should refer to the program users’ manual for guidance in modeling soil springs. All pipe stress computer programs with buried piping analysis options require that the following factors be calculated or estimated: 1. Location of the virtual anchor (dimension L⬘ or L ⬙) 2. Soil spring rate ki, j, which is a function of the modulus of subgrade reaction k. 3. Influence length, also a function of k. Some programs ignore the friction at the pipe/soil interface; this is conservative for calculating bending stresses on the buried elbows and branch connections, but may be unconservative for calculating anchor reactions. Determination of Element Lengths. The element lengths and transverse soil spring rates for each element are calculated by the following procedure: 1. Establish the element length dL and the number n of elements, as follows: (A) Set the element length to be equal to between 2 and 3 pipe diameters. For example, dL for a NPS 6 may be set at either 1 ft or 2 ft, whichever is more convenient for the analyst. (B) Establish the number n of elements by: (B4.81) This gives the number of elements, each being dL inches in length, to which springs are to be applied in the computer model. The number n of elements is always rounded up to an integer. 2. Calculate the lateral spring rate ki, j to be applied at the center of each element. (B4.82) where k = the modulus of subgrade reaction calculated from Eq. (B4.72). 3. Calculate the equivalent axial load necessary to simulate friction resistance to expansion. The friction resistance at the pipe/soil interface can be simulated in the computer model by imposing a single force Ff in a direction opposite that of the thermal growth. (B4.83) 4. Incorporate the springs and the friction force in the model. The mutually orthogonal springs ki, j are applied to the center of each element, perpendicular to the pipe axis. Shorter elements, with proportionally smaller values for the springs on these elements, may be necessary in order to model the soil restraint at elbows and bends. The friction force Ff for each expanding leg is imposed at or near the elbow tangent node, opposite to the direction of expansion. Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Since buried piping stresses are secondary in nature.digitalengineeringlibrary. higher total stresses may be permitted FIGURE B4. Stresses at building penetrations can be calculated easily after the reactions due to thermal expansion in the buried piping have been determined. An expansion joint must be considered as a relatively free end in calculating stresses on buried elbows and loads on anchors. then the stress due to the axial force Fmax and the lateral bending moment M can be found by (B4.84) If the penetration is not an anchor. Downloaded from Digital Engineering Library @ McGraw-Hill (www. B4. Since incorporation of expansion joints or flexible couplings introduces a structural discontinuity in the pipe. References 61. Allowable Stress in Buried Pipe Buried piping under axial stress can theoretically fail in one of two ways: either by column buckling (pipe pops out of the ground at midspan) or local failure by crippling or tensile failure (much more serious than column buckling). such as the modulus of subgrade reaction k.211 Determination of Soil Parameters. . and since the piping is continuously supported and restrained (see Fig. it is necessary to determine the stiffness affects of the water seal material in order to calculate the stress in the pipe at the penetration. If the penetration is an anchor. Stiffer springs can result in higher elbow stresses and lower bending stresses at nearby anchors. All rights reserved.31). Calculation of such stresses is beyond the scope of this section. Differential movement due to building or trench settlement can generate high theoretical stresses at piping penetrations to buildings. values for elemental spring constants on buried pipe runs can only be considered as rational approximations. but is instead a simple support with a flexible water seal. Soil parameters are difficult to establish accurately due to variations in backfill materials and degree of compaction. and 66 discuss soil stiffness and recommend procedures for estimating values for k which are consistent with the type of soil and the amount of pipe movement expected. but becomes less stiff as the pipe movements increase.com) Copyright © 2004 The McGraw-Hill Companies. the effects of the unbalanced pressure load and the axial joint friction or stiffness must be superimposed on the thermal expansion effects in order to determine the maximum pipe stresses and anchor loads. Consequently. The analyst should consult the project geotechnical engineer for assistance in resolving any uncertainties in establishing soil parameters.31 Plan of example buried pipe. while softer springs can have the opposite effects. testing has shown that soil is stiffest for very small pipe movements.STRESS ANALYSIS OF PIPING SYSTEMS STRESS ANALYSIS OF PIPING SYSTEMS B. and coefficient of friction µ. Any use is subject to the Terms of Use as given at the website. Pipe with Expansion Joints. confining pressure pc. Backfill is not elastic. 63. Pipe Stresses at Building Penetrations. “Secondary Stress Indices for Integral Structural Attachments to Straight Pipe. Stress Intensification Factors. and Kalavar. 6.” and Dodge. ASME B31. Bonney Forge Bulletin No.E. and Woods. Wichman. 16. 572 and 573). All rights reserved. Rodabaugh. 39–43. and Moore. 21...H.E.” 6. Downloaded from Digital Engineering Library @ McGraw-Hill (www. Tables 29 (p. Refrigeration Piping Code. 9. Process Piping Code. 1992 edition.. 1987. 785. 13. Stress Intensification Factors and Stress Indices.5. Bijlaard. Section III.. 1998 edition. no. and Mershon. 1995.1. 18. R. ASME. 1988. “Latrolet. Roark’s Formulas for Stress and Strain.5a1989 addenda.R. G. 2. Basavaraju. 1996 edition.L. Division 1. J. Sadd. D. August 1955. 15. Welding Research Council Bulletin #329.. C. 1983..R.P. 1987 edition. PA.C.3. Power Piping Code. and Rodabaugh.digitalengineeringlibrary.. REFERENCES 1.” Trans. E.. S. 17. 6th ed.L. 102. K. 22. “Finite Element Analysis of Eccentric Reducers and Comparisons with Concentric Reducers. 1979. McGraw-Hill. Addendum No. W. 789. ASME B31.” Welding Research Council Bulletin 107. S. ASME B31. 7. September 1974.212 GENERIC DESIGN CONSIDERATIONS as follows: (B4. . Bonney Forge Bulletin No. 1995 edition. 14.1. Allentown. March 1979 revision of August 1965 edition. P. Dodge. vol. 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