Note that hoop stress will change with diameter and wall thickness throughout the piping system. Hoop stress is most commonly represented by the following formula:. Axial stress results from the restrained axial growth of the pipe. Axial growth is caused by thermal expansion, pressure expansion, and applied forces. If a pipe run can grow freely in one direction, there is no axial present—at least in theory.
When comparing axial growth caused by pressure, steel-pipe growth is minimal at over ft and can be ignored. Composite piping such as fiber re-enforced pipe FRP or plastic pipe will exhibit noticeable growth, as much as 2 to 3 in. The primary reason for the difference in growth rates under pressure is related to the modulus of elasticity.
Steel has a modulus of elasticity of approximately 30 x 10 6 psi, whereas composites will be 2 to 3 orders of magnitude or less. Axial stress is represented by the axial force over the pipes cross-sectional area:. Bending stress is the stress caused by body forces being applied to the piping. Body forces are the pipe and medium weight, concentrated masses valves, flanges , occasional forces seismic, wind, thrust loads , and forced displacements caused by growth from adjacent piping and equipment connections.
Body forces create a resultant moment about the pipe, for which the stress can be represented by the moment divided by the section modulus:. Torsional stress is the resultant stress caused by the rotational moment around the pipe axis and is caused by body forces. However, because a piping system most likely will fail in bending before torsion, most piping codes ignore the effects of torsion. Fatigue stress is created by continuous cycling of the stresses that are present in the piping.
For example, turning a water faucet on and off all day will create a fatigue stress, albeit low, because of the pressure being released and then built up. Fatigue stress results in a reduction of allowable strength in the piping system and is commonly caused by cycling of:.
Piping codes, such as those published by ASME, provide an allowable code stress, which is the maximum stress a piping system can withstand before code failure. A code failure is not necessarily a piping failure. This is because of safety factors built into piping codes. ASME codes consider three distinct types of stress: sustained stress, displacement thermal or expansion stress, and occasional stress.
Sustained or longitudinal stress is developed by imposing loads necessary to satisfy the laws of equilibrium between external and internal forces.
Sustained stresses are not self-limiting. If the sustained stress exceeds the yield strength of the piping material through the entire thickness, the prevention of failure is entirely dependent on the strain-hardening properties of the material. Displacement stress is developed by the self-constraint of the piping structure.
It must satisfy an imposed strain pattern rather than being in equilibrium with an external load. Displacement stresses are most often associated with the effects of temperature; however, external displacements, such as building settlements, are considered a displacement stress. As a pipe stress analyst, it is critical to understand how wall thickness is determined.
If the pipe wall is too thin, it will not matter how the pipe is supported; it will fail. The centroid acts as a hinge.
The directions of the coordinate axes are assumed opposite to the anticipated expansions. The latter are designated by Ax, Ay, and. In order to move the centroid back from the expanded to the original position, forces X, Y, and Z are applied so that their combined effort causes defiections equal to -Ax, -Ay, and -.
The actual end reaction X applied at the free centroid will cause a movement of X I,;i El. The actual end reaction Y applied at the free centroid will cause a movement of. The movement in the x-direction produced by a unit force acting in the z-direction is I,j EJ.
The actual end reaction Z applied at the free centroid will cause a movement of Z I"'. The algebraic sum of the foregoing movements is the total movement in the x-direction. Equating this sum with the expansion Ax furnishes the first of three equations 7 , the other two are obtained in similar manner and represent, respectively, the movements in the y- and z-direction. For explanation of signs, see the article on Single-plane Piping page Procedure: The line is successively projected into the three planes formed by the coordinate axes.
Branches that are normal to the plane of projection will appear as a point and are indicated by a heavy dot. Forces located in the plane of projection, such as theX and Y forces in the xy-plane, will cause torsion in all branches that are at right angles to that plane.
In calculating the position of the centroid, the length of members appearing as points is modified in order to account for the displacement due to torsion.
While flexura! Thus the angular distortion of a straight member subjected to torsion can be expressed by the modulus of elasticity if the true length is multiplied by 1. The mechanics of the method can be readily followed in the numerical problem 9, which covers the case of a line consisting of straight branches only.
The successive projections into the three planes formed by the coordinate axes show which of the members are subjected to torsion by the forces located in the plane of projection. For example, branch cd in the xy-plane is subjected to torsion by the X and Y force. Its actuallength is 84 ft. Its modified length is 84 X 1. This length is used in determining the position of the centroid, the moments of inertia, and the product of inertia. It will be noted that the moment of inertia of the line consists of two parts obtained from two different planes.
For instance one I, is obtained from the xy-plane and one from the xz-plane. Their sum is the total moment of inertia, which is the coefficient for X in the first of the three equations 7. The reaction forces X, Y, Z obtained from these equations are transferred to the actual end, which in this case is at point f. The reaction moments at end f.
Bending moments at any point are obtained quickly by multiplying the forces at the centroid by their offsets from the point in question. The bending moment at point b is -1, lb.
Piping stress calculations involve the use of large figures. It is therefore advisable to express dimensions and pipe properties in feet. However, the structure of the equations is of a special type. The left side is symmetrical about the upper left to lower right diagonal, and for this case the process of solution can be simplified. The 1L W. Kellogg Company has developed a method that reduces the working time and practically eliminates the possibility of errors.
It is published in "Expansion Stresses and Reactions in Piping. At the top of the columns inscribe X, Y, Z, Constant, and in the row marked 1 place the coefficients of the unknowns and the constant, the latter with opposite sign.
The unknowns X, Y, Z, instead of being placed beside the coefficients, are placed in the heading of the table, the constant is on the left side of the equal sign, and "equals zero" is omitted from the table. In the same manner place the second and third equation in the rows marked 2 and 3. Thus far 3 rows are filled, 8 rows are blank. Thereafter fill the rows in the order indicated by the numbers at the left side of the table as follows: Row 4 is obtained by dividing the figures in row 1 by the negative coefficient of X, i.
Row 4 then reads. Row 5 : Each number in row 1 is multiplied by the coefficient of Y in row 4. For example: , X 0. Row 6 is the sum of the figures in rows 2 and 5. Row 7 is obtained by dividing the figures in row 6 by the negative coefficient. Row 8 : each number in row. Row 9 : Each number in row 6 is multiplied by the coefficient of Z in row 7. Row 10 is the sum of the figures in rows 3 , 8 , and 9.
Row 11 is obtained by dividing the figures in row 10 by the negative coefficient of Z resulting in. The moment that acts in the plane at right angles to the pipe axis causes torsion; the other two cause bending. The resultant of the latter is obtained by vectorial addition. For instance, if. In order to find the point of highest stress, the moments are tabulated in planes of projection, and, if desirable, bending-moment diagrams may be drawn for each plane.
Of the three moments obtained for each point, mark the one that causes torsion, thus leaving the other two for vectorial addition. A brief inspection will show which of the two combinations will cause the greatest effect.
With S the section modulus of the cross-sectional area of the metal, the bending stress is. In this case it is necessary to increase Sb and st by multiplying these values by the ratio Ec:Bh. The expansion stress Sg must be based on modulus E0 The maximum stress condition from the table for moments is found in the e1bow at point.
Converting to modulus E0 by multiplying by the ratio E0 :Eh. The stress intensification factor for a 24" long radius elbow is 1. The vectorial sum of the 1atter two moments is ,!
The stresses are: Bending stress Torsional stress. The allowable stress range SA is less than the eombined stress. The tenns that give the deflections dueto the end reactions have the product El in the denominator as shown on page In the case of piping with constant cross section and the same modulus E, the work in solving numerical problems is materially reduced by moving this product to the right of the equation sign as in equations 7 Page 67 For lines with variable cross sections or piping with variable flexibility, this simplification is lost, for the line inertias of each branch must be divided by the moment of inertia of its own cross-sectional area.
Since calculating moments of inertia of pipe lengths involves squaring or cubing of lengths and distan ces, precaution must be taken, in introducing numerical values of area inertias, that 1 is carried along in the first power and not accidentally included in the process of squaring or cubing. For instance, in problem 5, which presents the case of a in. The factor converts 1 into feet 4 When line moments of inertia are calculated, these numbers are set in front of the parentheses containing the line inertia calculated in the usual manner.
This problem shows the procedure for pipe lines ha. Two branches of a in. The effect of corrugating as established by tests is as follows: In bending the ftexibility of a corrugated bra. This is expressed mathematically by assigning to the corrugated length when engaged in bending one-fifth of the moment of inertia of the. In torsion, however, the corrugated pipe has the same ftexibility as the plain pipe, and therefore I is not altered when this action is accounted for.
Sum of I. SOOZ- 1. S f 'Jwv. MO THifU. S ,,2-l- 5. GI 38Q 5. JrJ 8. ZlJ 6. LS ZO J 6. JO JJ. S 8Y US 01' EL. Seamless Red brass Copper2 in.
Allowable S valuea for lntermedlate temperatureamay be obtained by intarpolation. Carbon atael above F; carbon-molybdetwal ateel abovo IJ75 F; chrome-motybdenum atoel with chromlwn undor 0. J F; 'caton-molybdetw. Jm aloel abovo 11! J F; ch10m. See also apecific requlrementa for aervice conditions contemplated.
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Si ICilled O. Uhd cwbon otee! T'Iwt "oo of " - '! I'IO Si JC illed 1. IL or F.. Si JCilled. Allowoble S Valu. O 13, 13, 12, 9, 8, 4, 11, fl. Where th operatlona ar not cwried out. Spectfi Grade or cation 'elded. Jft'P'Ir jol,. STW No. Whete th op. X proldea fot hlcher yteld atrencth by bet-en -ducer cona..
S for u.. U u-a the yteld U thlclr. HOT1t: Por electrlc-,. Oa atrancth -cl. The typea ancl 1ad ol pipe tabu.
Allowabla S l. P'or electrlc Iclecl pipa for appllct Uahecl TM verai ypea and erad ol ptp41 tabulated abOYe ahflll noc: be I. Aaed at: temperac,. Y be obtlned by. The vluea tabulated l01t. For Cl. Seamless 1 Per Cmt Ouomium, 0. The decimal thickneues lisced for che respective pipe aizes repreaent their nominal or aYerae wall dimeosiona. For tOlerancu on wall! Thicknuaea showo in bold face type for Schedule 40 are identical with thicknesses sho- in baid face rype for Standard WoUipe in Tab.
All dimensiooa ate given in oches. The decimal thicknuaes li ated for da reapecti Yll pipe a us repreaen theu nomiaal or averasl! For toleraacn on wall dli c:k. Thicknnaea aho.. YPe for Sdudule 40 in Tabie 2. Tboae aho- in bold face rype for f:;,lra Slitons lfiaJl are idenlical with correapoadins dlicknuaes ahown in bold face rype in Schedulea 1'0 and 80 in Table 2. Sec lauoductory Notes, Par. AJI dimeru. Weipua are. All d. The decimal thickneaaea liatad forme reapeCYe pipe aizes repre- t their DOm1oal or aYera1e dimeasioos.
For rolerucea oo wa. Thicknuaes of sil of me aizes ahowa abcne are alihdy rncer man those of correapoad.
Sec hurodvctory "'Norca, Pv. AJI dimeaaiona are in io inchea. Thoae shown in boid fac:e rype lor :t. TacC deootea pipe wit. According to the theorem of Castigliano, the partial derivative of W with respect to any one of the externa! The partial derivative of W with respect to an externa! Figure 42 shows a cantilever structure fi. The fi. Let m. In this form the equation for the displacement permits a convenient interpretation which may be expressed as follows: To find the displacement ata specified point andina specified direction apply on the unloaded cantilever and at the point in question an amciliary unit force in the desired direction and compute the moments m for all branches of the line.
Displacement in Direction of Force. In the case of Fig. Displacement Normal to Force. A similar procedure will give the displacement. There the auxiliary unit force is applied in the y-direction,. Sin ce m,. Maxwell's law of reciprocity of deflections.
Angular Displacement Due to Force. The angular displacement at B caused by force X is found by applying a unit moment 1ft lb at B. S-:e is the statical moment of the line about the x-axis. Thus the angular displacement due to X is T:z:m. Angular Displacement Due to Moment. The angular displacement due to an external moment 1l1 at Bis obtained by combining the moments dueto an auxiliary unit moment at B with the externa!
Translatory Displacement Due to Moment. The displacement along tne :t-axis due to an external moment 1l1 at B is obtained by applying a unit force along the x-aXlS. Note the law o reciprocity between translatory and rotary displacement by comparing equations 9 and Rights: Public Domain, Google-digitized. Get this Book. Trove: Find and get Australian resources.
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Piping stress calculations simplified by Siegfried Werner Spielvogel Thank you I need this book can you help me. Piping Systems work under different temperature and pressure conditions which place lot of stress on its various components. Systems must be thoroughly analysed using latest Stress Analysis Softwares and supported in such a manner that no detrimental stresses occurs in the system, which can cause system failure.
Various software used for pipe stress analysis are [ ]. The applications of piping design are widely accepted and procedure for designing piping is very complex. A simplified and handy procedure is there for needed. Hence, here in this paper we presented the analytical method of calculating two important components of piping design i. File Size: 1MB. Basic Pipe Stress Analysis Tutorial Good, relevant and non-overwhelming technical information on pipe stress analysis is hard to come by.
So, we decided to provide a simple tutorial on the basics of piping stress analysis. At present, there are many. Piping stress calculations simplifiedAuthor: Siegfried Werner Spielvogel.
All piping systems shall be evaluated and, if appropriate, analyzed for applicable conditions in accordance with. The designer shall be qualified in. ASME B Process Piping: For piping systems used in process plants, such as petrochemical plants, this is the code that covers almost all the requirements to design, erection, testing of piping stress analysis requirements are detailed in this code can be applied to all the plants designed according to this Size: 1MB.
Open Library is an open, editable library catalog, building towards a web page for every book ever published. For thermal analyses, Norm gave me a copy of Spielvogel's Piping Stress Calculations Simplified to read and to help me develop a good understanding of what piping flexibility analysis was all about. It turns out I didn't actually employ very many of the manual techniques in the book. The concept underlying this rule is very well described in the famous book by S.
The attention given to pipe stress analysis has increased in the last decades, due to the high security requirements of the modern process plants. Piping stress calculations simplified download pdf book. Download Piping stress calculations simplified here. Circumferential Through-wall Bending Stress. Ring Buckling Analysis resulting from external pressure. Ovality resulting from external pressure. Chart section of this application enables user to see the behavior of each mentioned parameters with their criteria if desired on one chart.
Report section provide users with input and outputs results of analysis in ax excel sheet. Sheet 1: Local Stress Calculation In order to calculate the local stresses which are introduced in the related technical papers, find how sensitive the local stresses are to design parameters of attachments and finally calculate safety factors in discontinuity area, this calculating sheet has been developed.
Briefly, it includes the following parts: Local stresses calculators for trunnion and three types of structural profile attachment Local stress calculator for saddle supports and bare supported pipes Interactive graphs which demonstrate local stress sensitivity to design parameters of the attachments. Calculation Sheets. This section consists of some calculation sheets to illustrate some results from the methods which are explained in the technical papers part.
The presented calculations give users an opinion about the application of formulas, criteria, assumptions and limitations on which some common engineering methods or codes are based on. Besides, some designed graphs help users to compare the introduced methods with each other.
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