ML20062K290
| ML20062K290 | |
| Person / Time | |
|---|---|
| Site: | La Crosse File:Dairyland Power Cooperative icon.png |
| Issue date: | 07/27/1982 |
| From: | Cao N, Finnian C, Mortien T NUCLEAR ENERGY SERVICES, INC. |
| To: | |
| Shared Package | |
| ML20062F993 | List: |
| References | |
| 81A0051, 81A0051-R00, 81A51, 81A51-R, NUDOCS 8208170112 | |
| Download: ML20062K290 (56) | |
Text
{{#Wiki_filter:'A mur DOCUMENT NO. 81A0051 iiEV. 0 NUCLEAR ENERGY SERVICES, INC.' PAGE nF I 26 SEISMIC AND STRESS ANALYSIS OF THE LACBWR 14" SHUTDOWN CONDENSER VENT PIPING SYSTEM PREPARED FOR DAIRYLAND POWER COOPERATIVE CONTROLLED COPY ED ON.Y J lHIS SW IS E f Project Application Prepared By Da e APP ROV ALS TITLE / DEPT. S I G N A T U ft E DATE al Encineerine d M I
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30 cia 2JL '7/ufg 7!2h !b2 M Project Engineer V.P. Engineering 7 _ L 7, 7!3L Service Operations \\ Quality Assurance Manager 7 Z/J [J, f/ f 8208170112 820722 DR ADOCK 05000
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81A0051 mur DOCUMENT NO. NUCLEAR ENERGY SERVICES. INC. TABLE OF CONTENTS PAGE 1.
SUMMARY
4 2. IN TROD UCTION........................... 4 3. PIPING SYSTEM DESCRIPTION.................... 6 l I 4. LO ADING C RITE RI A......................... 91 4.1 Dead Weight and Other Sustained Mechanical 1.oads......... 9 4.2 Internal Pressure...................... 9 4.3 Ther mal Loa ding........................ 9 4.4 Seismic Loading 9 5. STRESS ACCEPTANCE CRITERIA................... 10 5.1 Design Loadings 10 5.2 Level A Service Limits 11 5.3 Level B Service Limits...... 11 6. ANALYTIC AL M ETHODS....................... 11 6.1 Mathematical Model....................... 11 ) 6.2 Static Load Analysis.......... 12 6.3 Eigenvalue Analysis....... 13 6.4 Dynamic (Seismic) Analysis.................... 13 4 6.5 Stress Analysis......... 16 1 7. DISCUSSION OF RESULTS...................... 18 I-8. CONCLUSIONS AND RECOMMENDATIONS............. *.. 25 1 l 9. REFERENCES............................ 26 A P P EN DIC ES............................ Al A. Analytical Input Data...................... Al B. Tabulated Results of Analysis. B1 I i i I i l l l l l l l t l l l l \\ w' [ FORM # NES 205 2/80
[ 81A0051 DOCUMENT NO. 4 26 NUCLEAR ENERGY SERVICES, INC. 1.0
SUMMARY
~ his report, prepared for Dairyland Power Cooperative, presents the results of seismic stress analysis of the 14" Vent line of the shutdown condenser system. he shutdown condenser is a safety-related system at L A C B W P.. The analysis performed is in l accordance with the design requirements of the ASME Boiler and Pressure Vessel Code, Section Ill, Division I, Class 2 piping code of 1980. He original design of LACBWR's piping was to the ANSI B-31.1 piping code. Class 2 piping analysis methods are considered to be appropriate and conservative. I It was necessary to assume that the vertical support at node 110 will be modified so that it can resist lateral loads. With this simple modification, results of the analysis ~ indicate that the stresses are low compared to the allowable stresses. he bellows expansion joint included in this line undergoes an applied torque, which is considered an undesirable form of loading for expansion joints per Section 111 of the ASME 1980 code. The bellows' applied torques have been calculated to be 5034 lb-in and 8009 lb-in for OBE and SSE events respectively. However, an evaluation based on the bellows manufacturers recommendations (Ref. 6) shows that the bellows can withstand the l applied torque. The maximum allowable applied torque according to the formula given in Reference 6 is 94,000 lb-in.
2.0 INTRODUCTION
l l l At the LACBWR, the shutdown condenser system provides a backup heat sink for the reactor in the event that the reactor is isolated from the main condenser. The system l consists of a condenser, piping, valves and instrumentation equipment. he shutdown condenser system is automatically started when the reactor building steam isolation i l valve or turbine building steam isolation valve is not fully open, or when the reactor pressure exceeds 1,325 psi. Rese are emergency conditions that also provide a scram signal to the reactor safety system. t l
81A0051 5* DOCUMENT NO. NUCLEAR ENERGY SERVICES, INC. The shutdown condenser is a horizontal U-tube heat exchanger, with reactor steam condensing inside the tubes. Reactor coolant sensible and latent heat is transferred to boiling, demineralized water on the shell side. The shell side vapor is vented directly to the outside atmosphere via the 14" vent line. He hed.emoval capacity of the shutdown condenser is well in excess of reactor decay heat generation rate for all l times following reactor shutdown. De system provides adequate emergency shutdown I ~ cooling capability by cooling reactor water to 3000 F at a rate of 500 F/ hour. However, the normal mode of operation for reactor water cooling below 4700 F is the decay heat cooling system. Natural circulation is the driving force behind the system. Steam flows from the main steam lines into the shutdown condenser located ten feet above the main floor of the f containment building. Condensate is collected in the lower channel section and is returned to the feedwater lines by gravity flow. The shutdown condenser system has been designated as a safe shutdown system and, as such, it must be capable of operating during and after a seismic event. The 14-inch vent line to. atmosphere must remain intact to ensure proper system operation since a break in this line would: (a) interfere with transfer of reactor decay heat to an external heat sink (atmosphere) as require ~d; and (b) represent a breach of the containment boundary. l For the purpose of this analysis, the evaluation of the 14-inch atmospheric vent line is f performed in accordance with the requirements of the ASME Boiler and Pressure Vessel Code, Section III, Subsection NC (Class 2 components). These requirements are applied even though the vent line (and all other reactor plant piping) was originally designed and fabricated to ANSI B31.1 Power Piping code requirements. His is justified since the basic methodology and the allowAle sie'sses are the same for ANSI B31.1 and ASME Section III Classes 2 and 3. This approach also allows for overall consistency with previous NES and Gulf United piping stress analyses performed for LACBWR. l FMOrmN6 2/80
DOCUMENT NO. NUCLEAR ENERGY SERVICES, INC. Section 3.0 of this report describes the physical and geometrical properties of the shutdown condenser 14-inch vent line. The loading criteria, design criteria and analytical methods used in the analysis are given in Sections 4.0, 5.0 and 6.0 respectively. The results of the analysis are discussed in Section 7.0. The conclusions and recommendations are summarized in Section 8.0. PN 3.0 PIPING SYSTEM DESCRIPTION The 14" vent line, which consists of carbon steel pipe, is designed to supply a path for steam from the shell side of the shutdown condenser to leave the Containment Building. It originates at the nozzle of the shutdown condenser and terminates upon leaving the containment vessel. The layout of the shutdown condenser vent piping is shown in Figure 3.1. The mathematical model for the vent line is shown in Figure 3.2. A bellows expansion joint is included in the vent line. This accommodates thermal expansion following shutdown condenser initiation. i ll The governirg design specification used in the analysis of the 14" vent line piping system is given in Reference 3. The piping arrangement analyzed and piping suspension (support) characteristics have been taken from the drawings listed in Reference '4. Piping properties have been taken from the information given in Reference 3. Bellows properties have been taken from Reference 5. This information is summarized in Table A-1 and Table A-Il of Appendix A. hm FORM # NES 205 2/80
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81A0051 DOCUMENT NO. NUCLEAR ENERGY SERVICES, INC. 4.0 LOADING CRITERIA The load cases which must be considered in performing a Class 2 Stress Analysis include: Dead loads and sustained mechanical loads, internal pressure, thermal expansion loading and seismic loading. The static and dynamic load cases are summarized in Table A-III and A-IV of Appendix A. 4.1 DEADLOAD PLUS SUSTAINED MECHANICAL LOAD PLUS OPERATING - PRESSURE: (Static Load Case 1) The deadweight of the piping system is calculated assuming the system to be filled with evaporated water. The weight of expansion joint is also included in the analysis. Dimensions of expansion joint are taken from vendor drawings and specifications supplied by DPC and are given in Table A-II of Appendix A. 4.2 INTERNAL PRESSURE (Static Load Cases I and 3) System normal operating pressure, Load Case 1 and peak pressure, Load Case 3 used in the analysis are 40 PSI. This corresponds to the internal design pressure of the shutdown condenser shell. The pressure in vent line will not exceed this limit. 4.3 TliERMAL LOADING (Static Load Case 2) c_ Tne thermal expansion stresses are based on the thermal loading which could occur following a major primary system pipe rupture inside containment. A i maximum temperature of 2750 F ls used for the Vent line analysis. 1 4.4 SEISMIC LOADING (Load Cases 4 and 5) A dynamic analysis of the piping system is performed using the response spectrum ; method of analysis (Section 6.4). Two seismic loading events are considered: The Safe Shutdown Earthquake (SSE) and the Operating Basis l Earthquake (OBE). l FORM
- NES 205 2/80
DOCUMENT NO. 81A0051 10 op 26 PAGE NUCLEAR ENERGY SERVICES, INC. Seismic inertia loading is imposed on the piping system in the form of seismic acceleration spectra which were derived for the LACBWR plant (Ref.1). He ~ horizontal SSE and OBE acceleration spectra used for the Vent line are that corresponding to the crane support at an elevation of 726.5 ft. Le vertical response spectra for the SSE and OBE loading are taken as 2/3 of the respective horizontal crane support spectra. The spectra in the global X (horizontal), Y (vertical), Z (horizontal) are applied individually and the totalresponse is formed by the square root of the sum of the squares (SRSS) of those individual resultants. Load case 4 represents the SSE earthquake while load case 5 represents the OBE earthquake. The applicable response spectra used in the analysis for dynamic load cases are shown in Table A-V of Appendix A. SSE seismically induced anchor movements (static load case 7) for node 10 were estimated by taking the relative displacements of the Shutdown condenser platicrm with respect to the main floor (from the shutdown condenser platform analysis) added to the relative displacements of the crane support level with respect to the main floor (from the containment building analysis). For the OBE, seismic anchor movements (load case 6) were taken as one half of the SSE anchor movements. !A l 5.0 STRESS ACCEPTANCE CRITERIA lI il l Re requirements for acceptability of a Class 2 piping system are given in Paragraph l l NC-3611 of Reference 2. Calculated stresses resulting from specified load combinations must meet' the stress limits of equations 9 through 13 of Paragraph NC-3652 of Reference 2. For conservatism, stress limits no greater than those specified for Service Level B have been applied for acceptance of any combination of loads, including SSE, which are considered in the analysis. l 5.1 DESIGN LOADINGS l The sum.of stresses due to design internal pressure, weight, and other sustained loads shall not exceed S. This requirement is satisfied by meeting Equation (9), h NC-3652.1. l l
81A0051 DOCUMENT NO. .A nr NUCLEAR ENERGY SERVICES. INC. 5.2 LEVEL A SERVICE LIMITS The stress range due to thermal expansion shall not exceed S, or the sum of A stresses due to internal pressure, weight, other sustained loads, and the stress range due to thermal expansion shall not exceed the sum of SA and S. This h requirement is satisfied by meeting Equation (11) or (13), NC-3652.3. ~ 5.3 LEVEL B SERVICE LIMITS The sum of stresses due to internal pressure, live and dead loads, and those due to occasional loads such as wind or earthquake shall not exceed 1.2 times the allowable stress value S. This requirement is satisfied by meeting Equation h (10), NC-3652.2. 6.0 ANALYTICAL METHODS 6.1 MATHEMATICAL MODEL In order to perform static, dynamic and stress analyses, the continuous piping system is mathematically modeled as an assembly of elastic structural elements interconnected at discrete nodal points (Figure 3.1). Nodal points are located at all points of interest in the piping ' system such as elbows, valves, anchorages, hangers, tee intersection, load points, all structural and material discontinuities, etc. This three dimensional multidegree-of-freedom model of the piping system l is attached to the " ground"(structure) by means of rigid hangers, support springs, hydraulic snubbers and anchors. Stiffness characteristics of structural elements j are related to the moment of inertia and the axial and effective shear area of the pipe cross section. The stiffness characteristics of the elbows and tee connections are modified to account for local deformation by using the flexibility factors given in the ASME Code (Ref. 2). l l l For the seismic analysis the distributed mass of the piping system is lumped at the system nodal points. Masses are lumped so that the lumped mass, multidegree-of-freedom model represents the dynamic characteristics of the 1 i-M#6MM
DOCUMENT NO. 81A0051 ja y PAGE 12 OF 26 NUCLEAR ENERGY SERVICES, INC. = " piping system. In order to reduce the number of dynamic degrees-of-freedom, only translational degre-s-of; freedom are considered at each mass point (the masses associated with the rotational degrees-of-freedom are set to zero). This assumption has been shown to be completely satisfactory for accurate analysis of seismic response. Special items such as valves and actuators are modeled by lum 9ing their masses at an appropriate offset from the center-line of the piping system. 6.2 STATIC LOAD ANALYSIS l The static load analysis involves the application of the following loading conditions and their combinations: Design Pressure Gravity Loading (dead weight) and Sustained Mechanical Loads Support Displacement Thermal Expansion For the pressure loadings, the hoop and longitudinal stresses in the affected piping are calculated using the formulae given in the Code (see Section 6.5). For the deadweight, support displacement, or thermal expansion loading conditions the following equations of equilibrium written in matrix form are solved: l l (K) { U } = {P} (1) where: l l System stiffness matrix K = U Nodal point displacement vector = P External forces, dead weight or equivalent thermal load vector. = The system stiffness matrix is obtained from element stiffness matrices using l direct stiffness methods. The unknown nodal displacements U are obtained as follows: FORM # NES 205 2/80
DOCUMENT NO. 81A0051 mv NUCLEAR ENERGY SERVICES, INC. = {U } = (K)-l $P} (2) ~ The inversion of the stiffness matrix is performed using the Gauss-Siedel { g technique. From the nodal displacements U, the member internal forces are determined using the member stiffness matrix. Finally, the member internal forces are used in calculating the stresses. 6.3 EIGENVALUE ANALYSIS The eigenvalues (natural frequencies) and the eigenvectors (mode shapes) for each of the natural modes of vibration are calculated by solving the following frequency equation: (K Un M) { &n } = { 0 } (3) where: ~ th mode Un Natural angular frequency for the n = System mass matrix M = r. Mode shape vector for the nth mode in = 0 Null vector = i, 1 The eigenvalue/ eigenvector extraction is performed using the Householder-QR l technique. l 6.4 DYNAMIC (SEISMIC) LOAD ANALYSIS j Considering only translational degrees of freedom and assuming viscous (velocity proportional) form of damping, the equation of motion in matrix form can be expressed as follows: ( 1l M ('6 + N ) +C t + KUt = l 0 (4) t gt l l FORM # NES 205 2/80
81A0051 DOCUMENT NO. 14 26 PAGE OF 5 NUCLEAR ENERGY SERVICES, INC. l where: G Relative acceleration time history vector = t G Ground acceleration time history vector = gt C Damping matrix = Q Velocity time history vector = t Ut = Relative displacement time history vector f Rearranging equation (4) -Mb Peff (5) M t +C t + KU t = = gt To uncouple equation (5), assume &Yt U = where: Characteristic free vibration mode shapes matrix. = Yt Generalized coordinate displacement time history vector. = Pre-and post-multiplying equation (5) by the transpose of 4 and by 4 respectively and using orthogonality conditions, the following uncoupled equations of motion { are obtained: i ( + 2w A nt + W n Ynt = M n-Rnb (6) nt n n gt l l l where: l l Ynt Generalized displacement coordinate time history for nth mode = l th An Damping ratio for the n mode expressed as percent of = critical damping Mn * = Generalized mass for the nth mode 1 l $ [ M$ n = M $ [n i = FORM # NES 205 2/80
81A0051 DOCUMENT NO. NUCLEAR ENERGY SERVICES, INC. The mode shape 4n is normalized such that Mn* = 1 Participation factor for the n h mode R t = n & [ MI = [ Mi & in = I Column vector whose elements are generally unity = The solution for the differential equation (6) is given by the Duhamel Integral -A Wn (t-T) Rn t.. n Ynt fU e Sin en (t-T) d T = gt M W n n Using the response spectrum method of analysis, the maximum values of the generalized response for each mode is given by: y = Rn San n max (7) where: Y Maximum generalized coordinate acceleration response = n max for the nth mode. S ectral acceleration value for the nth mode (from the S P = an applicable response spectrum curve) a From the maximum generalized coordinate response, the maximum acceleration (On max) and maximum inertia forces (Fn max) at each mass point are given by: O " *"
- i"
= n ex Fn max Mnb = n max s The inertia forces (Fn max) for each of the system natural modes are applied as external static forces, and the piping system response (displacements, member internal forces and stresses) are calculated using the procedure described in Section 6.2. total system response is then obtained by combining the individual FORM # NES 205 2/80
DOCUMENT NO. 81A0051 ,.u any NUCLEAR ENERGY SERVICES, INC. modal response values by the square-root of the sum of the squares method; lower modes having large contribution to the response (all modes having natural frequency under 30 cycles per second) are considered and higher modes with f negligible participation are neglected. 6.5 STRESS ANALYSIS ~ The design requirements of the ASME Code for Class 2 piping systems are satisfied when the calculated stresses in the piping system due to thermal expansion, weight, and other sustained and occasional loads are combined in i accordance with and meet the limitations of equations 9,10,11 and 13 of Subsection NC-3652 of Reference 2. These requirements are described below: (Note: Equation numbers below have been adjusted to correspond to the equation ilumbers used by the ASME Code 1980 Edition, Subsection NC.) A. Sustained Loads The effects of pressure weight and other sustained mechanical loads must meet the requirements of equation (9). SSL PDo 0.75iMA < l.OSh (9) + = 4tn Z where: l 'l P = Internal design pressure, psi i Do Outside diameter of pipe, in. = Nominal wall thickness, in. tn = MA Resultant moment loading on cross section due to weight and = I other sustained loads, in. (See NC-3652.4, Ref. 2) l Section modulus of pip'e, in.3 (See NC-3652.4, Ref. 2) Z = I i Stress intensification factor (NC-3673.2 (b), Ref. 2) = l The product of 0.751 shall never be taken as less than 1.0 l i Sh = Basic material allowable stress at design temperature FKoHM # NES 205 2/80
81A0051 DOCUMENT NO. 17 26 PAGE OF NUCLEAR ENERGY SERVICES, INC. B. Occasional Loads he effects of pressure, weight, other sustained loads and occasional loads including earthquake must meet the requirements of Equation (10). P axDo 0.75i (MA+M) 51.2Sh (10) m B SOL = 4tn where: P ax = Peak pressure, psi m Resultant moment loading on cross section due to occasional MB = loads such as earthquake loads C. Thermal Expansion The requirements of either Equation (11) or Equation (13) must be met. 1. The effects of thermal expansion must meet the requirements of Equation (11) STE C 5 SA (II) = where: Mc Range of resultant moments due to thermal expansion. Also = include moment effects of anchor displacements due to . l earthquake if anchor displacement effects were omitted from l l Equation (10) Allowable stress range for expansion stesses (NC-3611.2, Ref. SA = 2) or 2. The effects of pressure, weight, other sustained loads and thermal expansion shall meet the requirements of Equation (13) i STE = PDo 0.75i MA + iMc 5 (Sh+S) (13) + A l 4tn Z Z 1 FQRM # Ng$ 2QG g/SQ
i. 81A0051 r DOCUMENT NO. NUCLEAR ENERGY SERVICES. INC. The above mentioned static, dynamic and stress analyses are carried out using the PIPESD computer code. PIPESD was developed by URS/ John A. Blume and Associates, Engineers, San Francisco, California and has been extensively used in the seismic and stress analysis of piping system for a number of nuclear power plants. PIPESD is available to Nuclear Energy Services through the Control Data Corporation CYBERNET Service.
- 7. DISCUSSION OF RESULTS l
A seismic analysis of the 14" vent line from shutdown condenser piping system with its i existing support modified in the lateral direction indicated that the stresses due to Operating Basis Earthquake and Safe Shutdown Earthquake would be lower than the allowable stress. Figures 7. ~ through 7.5 summarize the maximum calculated stresses for the various load combinations considered and illustrate compliance with ASME code requirements. The natural frequencies for the first 3 significant modes of vibration of the piping system are summarized in Table 7-1. The deflections at each node point due to the various load cases are summarized in i V e. Table B-1 of Appendix B. The maximum deflection due to the SSE seismic inertia loading (Load Case 4) is.0168 inches at node point 140. For a flexible piping system this deflection is acceptable. He maximum deflection due to thermal expansion (Load l Case 2) is.2282 inches at node 105. Table B-ll, pages B-ll through B-14 of Appendix !l B, summarizes the elastic support reaction forces. l l; The applied torque on the bellows due to dead load plus thermal load, plus pressure is 'i 1986 lb-in. SSE anchor movement + SSE seismic inertia forces apply an additional l 6023 lb-in of torque. Section 111 of the ASME Boiler and Pressure Vessel code l l recommends that bellows expansion joints be installed so that they do not undergo torsion. Nevertheless, the bellows manufacturer has stated that the bellows can withstand some torsion and has given a formula to compute the maximum allowable torsion value (Ref. 6). According to this formula, the maximum allowable torque which can be applied to the bellows is 94,000 lb-in. De actual applied torque (1986 + 6023 = 8009 lb-in.) is significantly lower than this value. l' sec-wvveResswe
i ,y ed l FIGURE 7.1 E P W 5 + m 8 a T g a e .O 8 $8 l
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m z gw@ COMPLIANCE WITil hSMS CODE EQ. :9 O De* sign Loadings O 3: Applied Loads H o Design Pressure A Y Dead Weight and Other Sustained Mechan.ical Loadr 5 8 Allowable Stress, 1.0.Sg3.- 15,000 psi m MaximumStr.cssat. Node.150=1,188 psi E X
g ..c, ! Y o S 5 c0 -{ l 8 T Q 5 b5 l FIGURE'7.2 j P @ @e e: e m 7 O a h 0 w - ~O8 $8 e .a g E h )d C COMPLIANCE WITil ASME CODE EQ. -[0 c h Level B Service Limit For OBE E n2 Applied Loads. mg 2 Peak Pressure Y 1 I]end Weight and Other Sustained Mechanical Loads X+Y+Z Earthquake,( SSE) c$ { X+Y+Z Anchor Movement (bSSE) c Allowable Stress, 1.2 Shy 18,000 p,si g* E X Maximum Stress at Node 140
- 1,785 psi
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- 0 s
av E d ro %' 4 D a eM 2 1 O o p C L mr = e t eo d Ei d Th Ao Mm e c S N S i i nn e A L l gA ,t p i s a l e p sl s i c T A ea e s i D m 'r s I .e Wv r t e r e S r E e h t C S T 'e S l, N 9 A A b m I a u l L w m e P o i ,lp v M l x e ,~ O l a L A M eh@O C 'I
I i. ~ 3 3 d E c3 n !b 3 i m . FIGURE 7.4 ZC P @h m m Z 4 m b g 9 Q a k o Owe O C0!jPLIANCE WITil ASME CODE EQ.13 Level A Service Limit C 3: m 2 Applied. Loads 2 S ,o Design Pressure and Temperature Ay Dead Weight and Other Sustained Mechanical Londs N o Thermal Anchor Movement Seismi.c Anchor Movement h E Allowable stress, S-h+SA ". 37,500 ps1 M Maximum Stress at Node 150 ='1821 psi
,.e, l d O 5 c:sd I$ 9' z .c FIGURE 7.5 o 7 r-n m z + b gll @e@@@ O OO l m -~ 5 -@ 3,, @ t COMPLIANCE WITH A51fE CODE EQ.10 Ccc Level B Service Limit For SSE-3n Applied Loads ~ a> 2 Peak Pressure O .C Y Dead Weight and Other Sustained McEhanical Loads i X+Y+Z Earthquake (SSE) U X+Y+Z Anchor Movements (SSE) l 0 w ? Allowable Stress, 1. 2 sh.. 18,000,ps'i-E .x }!aximum Stress at Node.140 =. 2,282 psi;
4 81A0051 DOCUMENT NO. 4 26 PAG F. OF NUCLEAR ENERGY SERVICES, INC. TABLE 7.1. VIBRATION FREQUENCIES (PERIODS) MODE FREQUENCY PERIOD MODE FREQUENCY PERIOD (CPS) (SEC) (CPS) (SEC) 1 20.5646 .0486273 16 480.4491 .0020814 2 26.0020 .0384585 17 505.8260 .0019770 3 39.7532 .0251552 18 534.5363 .0018708 4 46.3107 .0215933 19 625.9840 .0015975 5 46.9636 .0212931 20 625.9841 .0015973 6 76.0288 .0131529 21 674.5639 .0014824 7 116.3767 .0085928 22 690.4489 .0014483 8 147.7348 .0067689 23 729.4692 .0013709 9 160.7971 .0062190 24 909.3581 .0010997 10 204.7682 .0048836 25 1040.9931 .0009606 11 222.0870 .0045027 26 1282.9654 .0007794 12 227.3131 .0043992 27 ~1301.7684 .0007682 13 252.0619 .0039673 28 2074.0304 .0004822 l 14 276.6335 .0036149 29 2131.8670 .0004691 15 392.5377 .0025475 30 2255.6881 .0004433 NUMBER OF SIGNIFICANT MODES 3 = l l
81A0051 DOCUMENT NO. my M NUCLEAR ENERGY SERVICES, INC.
- 8. CONCLUSION AND RECOMMENDATIONS 1.
The results of the subject analysis, which includes the effects of additional lateral restraint at the existing support, indicate that the deflections of the 14" vent line piping system, due to dead load, thermal load and seismic load are ~~ nominal. In addition, the stress resulting from these loadings, as calculated and combined in accordance with the rule given in sub-article NC-3652 of Section III of the ASME Code'(Reference 2), satisfy tiie design requirements of class 2 piping systems. 2. It is therefore recommended that the support near the bellow of 14" vent line be modified to provide restraint in the lateral direction. 1 FORM # NES 205 2/80
81A0051 DOCUMENT NO. NUCLEAR ENERGY SERVICES, INC.
- 9. REFERENCES 1.
Gulf United Services Report No. SS-1162 " Seismic Evaluation of the I.aCrosse Boiling Water Reactor", dated January 11, 1974. 2. ASME Boiler and Pressure Vessel Code, Section III, Division I,1980 Edition, Nuclear Power Plant Components. 3. Sargent and Lundy Engineers " Specification for Piping System - Lacrosse Boiling ~ Water Reactor" LACBWR No. 256. 4. Sargent and Lundy Engineers "LACBWR" Project Drawing Nos. 41-503362, 503370,303372. 5. DPC Letter LAC-8244 dated April 28,1982, Attachment 11, pg.12 of 13. 6. Standards of the Expansion Joint 7'anufacturers Association, Inc.1980 Ed., pg. 79. UNCITED REFERENCES 1. U.S. Atomic Energy Commission - Regulatory Guide 1.60, Rev.1, December 1973. 2. U.S. Atomic Energy' Commission - Regulatory Guide 1.61, October 1973. .r FQAM O NES 205 2/80
81A0051 ~ DOCUMENT NO. y PAGE Al OF A7 NUCLEAR ENERGY SERVICES, INC. APPENDIX A LACBWR 14" VENT LINE PIPING ANALYSIS ANALYTICAL INPUT DATA TABLE PAGE A-! Pipe Properties A-2 A-Il Bellows Properties A-3 A-III Static Load Cases A-4 through A-5 A-IV Dynamic Load Cases A.6 A-V Seismic Response Spectra A7 I l l l l l wm#wsmsm
81A0051 DOCUMENT NO. ^ ^ PAGE OF NUCLEAR ENERGY SERVICES, INC. TABLE A-I-PIPE DATA Run1 Run 2 I' I From Point 10 105 To Point 100 210 n O.D. (in) 14 14 [ ( Wall Thickness (in.) .438 .438 Matt. ASTM A106-B A106-B Fluid Steam Steam Wt. of Pipe and Fluid (Ib/in) 5.28 5.28 Design Temp. (OF) 275 275 Design Pressure (psia) 40 40 Elastic Modulus (psia x 10-6) 29 29 l l l FORM # NES 205 2/80_. _.
~ 81A0051 DOCUMENT NO. ^ A7 PAGE OF NUCLEAR ENERGY SERVICES, INC. TABLE A-II-BELLOWS DATA (FROM MANUFACTURER) Beam No.1 From Point 100 i To Point 105 O.D. (in) 14 i Wall Thickness (in), (2 plies) .076 Matt. ASTM A321 Fluid Steam Wt. of Bellows and Fluid (Ib/in) 4.067 Axial Spring Rate (Ib/in) 548 1 l Lateral Spring Rate (Ib/in) 2845 l Bending Angular Spring Rate (ib/in) 335 Area (in )* 32.75 x 10-5 2 I (in ) * * .01737 4 4 3 (in ) * *
- 860 Area is computed from Axial Spring constant A = KL E
Iis taken as the average value of I calculated from Lateral Spring rate cnd I from Bending Angular Spring rate. l According to the bellows manufacturer, the bellows is very s;iff with respect to I torsion. A value of 3 equal to that of the attached pipe is used in the analysis. l l l' L mamass me
8kA0051 s DOCUMENT NO. NUCLEAR ENERGY SERVICES, INC. PAGE OF TABLE A-111 - STATIC LOAD CASES. I 1. STATIC LOAD CASE : 1 i LOAD CASE TITLE DEADLOAD t SUSTAINED L3AD + OPERATING PRESSURE l l 5 INGLE JOINT FORCE AND MOMENT LOADit4G JGINT LOAD LOAD LOAD ~ l ID TYPE DIRECTION 1AGNITUDE 170 F O.(C E' ~~ ~~~ -69.3000 ~~ X ~ ~ - ~ ~ ' ~ ~ ~ ~ i THERMAL-AND PRESSURE LOADINGS FOR ALL PIPE RUNS DESIGN TEMPERATURE TEMPERATURE TEMPERATURE PRES $URE RUN P?. ES SUR E CHANGE GRAGIE4T GRADIENT STRESS ID PSI DEG. DEG. DEG. 1 40.00 G.0 3.000 ~ ~ ~'~~ ~2 40.00 ~ ' O. 0 ?s 0.000 ~~ 0.000 (ES ~ 0.000 YE5 2. 5TATIC LDAD CASE : 2 i LOAD CASE TI TLE THERM AL EXP ANSION E ANCHOR MOVEtsENT SUPPORT DISPLACEMENTS l JOINT LOAD DI SP LACE ME NT DISPL ACEMENT I ID TYPE DIRECTION MAGNITUDE t l { ._X __. _..0506... _... - - j 10 TRANS. j 10 TRANS. Y .1136 i 10 TRANS. 2 .0350 l l THERMAL AND PRESSURE LDADINSS FDR ALL PIPE RUNS i i i 1 LINEAR NONLINEAR 0NG. DESIGN T E ". P E R A T U R E TEMPERATURE RUN P7. E 5 S U R E CHANGE GRA3IENT ~ TEMPERATURE PRESSURE GR ADIENT STR6SS ID tl S I DEG. DEG. DEG. 1 0.00 203.03 0.000 0.000 NO 2 0.00 205.00 0.000 0 000 ND
m DOCUMENT NO. ^ ^ NUCLEAR ENERGY SERVICES, lNC. PAGE OF l 3. STATIC LOAD' CASE : 3 l LOAD CASE TITLE MAXIMUM PRESSURE THERMAL AND PRESSURE LOADINGS FOR' ALL PIPE RUNS LINEAR NONLINEAR LONG. DESIGN TEMPERATURE TEMPERATURE TEMPERATURE PRESSURE ~~ RUN PRESSURE CHANGE GRADIENT GRADIENT STRESS ID ~ PSI ~~~.DEG. ~~~~ DEG. DEG'. 1, 40.00 0.00 0.000 0.000 YES 2 40.00 0.00 0.000 0.000 YES ~. -
- 4. STATIC LOAD CASE :
6 ~ LOAD CASE TITLE 1/2 SSE ANCHOR MOVEMENT SUPPORTD((SPUCEMENTS ~ ~ ~ JOINT LOAD DISPLACEMENT DISPLACEMENT ID TYPE DIRECTION MAGNITUDE 10 TRANS. X .0902 10 TRANS. Y .0598 ~ ~ 10 TRANS. Z .0818
- 5. STATIC LOAD CASE :
7 l LOAD CASE TITLE SSE ANCHOR MOVEMENT SUPPORT DISPL CEMENTS ~ JOINT LOAO DISPLACEMENT DISPLACEMENT ID TYPE DIRECTION MAGNITUDE 10 TRANS. X .1803 l 10 TRANS. Y .1195 10 TRANS. Z .1636 l FORM = NES 205 2/80
051 DOCUMENT NO. ^ NUCLEAR ENERGY SERVICES, INC. TABLE A-IV - DYNAMIC LOAD CASES Load Case No ' Load Description Spectrum ids
- Spectrum Multipliers X
Y Z X Y Z 4 X+Y+Z Earthquake (SSE) 1 I 1 386, 257.3 386. 5 X+Y+Z Earthquake (OBE) 2 2 2 386. 257.3 386. f I l l' - SSE Horizontal l 2 - OBE Horizontal a t l l l l l l
81A0051 DOCUMENT NO. PAGE OF NUCLEAR ENERGY SERVICES. INC. TABLE A-V - SEISMIC RESPONSE SPECTRA SEISMIC RESPONSE SPECTRA SPECTRUM FREQUENCY PERIOD ACCELERATION ID (CPS) (SEC.) (G) 1 50.000 .020 .59000 15.000 .067 .59000 10.000 .100 .72000 8.000 .125 1.10000 5.000 .200 1.54000 4.500 .222 1.74000 3.600 .278 1.64000 3.000 .333 1.50000 2.400 .417 2.29000 2.000 .500 4.09000 l 1.700 .588 5.42000 1.500 .667 4.09000 1.300 .769 2.30000 1.000 1.000 .91000 .800 1.250 .54000 .500 2.000 .25000 2 40.000 .025 .33100 20.000 .050 .33100 10.000 .099 .45700 8.580 .117 ' .80000 6.930 .144 .96200 5.610 .178 1.08500 4.590 .218 1.16000 3.650 .260 1.02200 2.860 .350 1.04800 2.640 .379 1.43400 2.280 .439 1.77100 1.870 .535 3.96000 1.530 .654 3.96000 1.197 .835 1.11400 .900 1.111 .45700 .450 2.222 .14300 .250 4.000 .14300 .100 10.000 .14300 l l ~ FORM # NES 205 2/80
DOCUMENT NO. 81A0051
== = NUCLEAR ENERGY SERVICES, INC. APPENDIX B LACBWR 14" VENT LINE PIPING ANALYSIS TABULATED RESULTS TABLE PAGE B-I JOINT DISPLACEMENTS B-2 through B-8 B-Il ELASTIC SUPPORT REACTIONS B-9 through B-13 B-III CLASS 2 PIPING STRESS
SUMMARY
B-14through B-23 l l { t e i I r l l l ~ rsonsores 7x6e s/so
~ m{ - a00K$H $* hI k E u i E s N m$* w* Om Om E u E $P I $ga4 $E5$hO. ~ ) / 1 0168734502995650007106 0054722560036497328100 E 0599011119973746002300 S 0000111112222110000000 A 2 0000000000000000000000 C 0000000000000000000000 ) S 0000000000000000000000 D N A A O I L D ( A 0845322378613725859700 R 0266033450000011120000 0000111110000000000000 ( Y 0000000000000000000000 S 0000000000000000000000 N 0000000000000000000000 E O 0000000000000000000000 R I U T.,. S A S S T T E O 0745541597983883727300 N E R R 0700933649048982901200 M P - X 0488888779084328708600 E 0000000000100011110000 C G 0000000000000000000000 A N 0000000000000000000000 I 0000000000000000000000 I P S T I A D R / E T S P / N I O 0612550338007068214800 O T 0397457284626115171200 J + 0488269309311087022100 N 0244869796654431000000 D 0000011220000000000000 E A 3 Z 0000000000000000000000 O 0000000000000000000000 1 M L B E D E N EL C N I 0098221372202013684700 B I ( 0373139033345935881401 A A A 0814719741462684887002 T T S 01236212581 72859172900 L S TY 0011233334010001311000 U N 0000000000012221000000 P S E 0000000000000000000000 M S + E C I D A A L 0235195790191291030708 D O P 0496220280276228145509 L S 0067938877322102516207 D I X 0366137826654463221100 A D 0000122340000000000000 T E 0000000000000000000000 D 0000000000000000000000 N I / ~ 0 ~ ~ T) J ~ ND 0000000005o00005000000 I I 1345678900l23455678901 ~ O G. 11l1111111112R J( ~ 7 IAm y $
l g L., and. s .ari E J 0 I NT DI SP LA CEMENTS (LOAD. CASE. 2) p ~ THERMAL EXPANSION E ANCHOR MOVEMENT 3 / --' --ROTATIONS (RADIANS) - - -/ m -~ JOINT /----DISPLACEMENTS (IN. 1-----/ (GID) X Y Z X Y Z ~~ 10 .0606000 1136000 .0350000 1000000 .0000000 .0000000 m 30 .0567261 .1262940 .0308503 0000682 .0000185 .0000266 E 40 .0477390 .1306885 0211056 .0001093 .0000542 .0000485 y
- _50,
.0468627 .1305749 .0201507 .0001095 .0000544 .0000486 p 60 .0379896 .1347048 .0100762 .0001205 .0000716 .0000539 y 70 .0338951 .1470895..0049443 .0001036 .0000697 .0000553 0 80 .0336782 .1522738 .0045281 0001027 .0000699 .0000556 90 .0290805 .1651885 .0072634 .0000643 .0000658 .0000745 100 .0191822 .1702459 .0157136 .0000376 .0000626 .0000951 105 .2282011 .0014663 .2170402 .0000090 .0004397 .0001190 110 .2060330 0000677 .2060767 .0001110 .0004392 .0001122 120 .1538084 .0025175 .1800903 .0000192 .0004287 .0000925 a 130 .1091611 .0041633 .1572027 .0000231 .0004054 .0000787 0 140 .1034987 .0042487 .1524464 .0000356 .0003486 .0000683 0 150 .1004011 .0041013 .1458232 .0'000437 .0002903 .0000645 K 155 .0858628 .0016978 .0752900 .0000427 .0002482 .0000440 H 160 - .0751600 .0001232 .0154323 .0000346 .0002189 .0000265 m 170 .0680164 .0002471 .0032343 .0'000158 .0001398 .0000265 o* 180 .0546708 .0001258 .0011707 .0000159 .0000469 .0000077 190 .0416591 .0000649 .0007234 .0000121 .0000384 .0000053 200 .0000000 .0000000 .0000000 .0000000 .0000000 .0000000 w m 210 .0273368 .0000000 .0000004 .0000000 .0000000 .0000000 7 8 E O w
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- 81A0051, DOCUMENT NO.
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g i l! N 5 d' i r'h U 8 . o 2C J0 I N T DI S P L A C. E M E N T S (LOAD CASE 6) P ~ T 1/2 SSE ANCHOR MOVEMENT 2 mz JOINT /---D I S PL A C E M E N T S (IN. ) --- / /------R O T A T I O N 5 ( R A D I A N S ) -----/ Q (GID) X Y Z X Y Z O 10 .0902000 .0598000 .0818000 .0000000 .0000000 .0000000 S 30 .0902113 .0598679 .0816017 .0000348 .0000159 .0000029 _k 40 .0904775 .0601675 .0811689 .0000574 0000551 .0000036 Q 50 .0905161 0602045 .0811299 .0000576 .0000554 .0000036 ? 60 .0910382 .0606773 .0803000 .0000845 .0000953 .0000005 2 70 .0913815 .0609476 .0709825 .0001145 .0001119. .0000104 9 80 .0914188 .0609469 .0785209 .0001149 .0001135 .0000108 90 .0912399 .0605263 .0769642 .0001292 .0001193 .0000236 100 .0904584 .0593766 .0755242 .0001385 .0001319 .0000316 105 .0002133 .0001924 .0011777 .0000566 .0000343 .0000434 110 .0006504 .0000244 .0007410 .0000515 .0000301 .0000413 120 .0013362 .0001262 .0000558 .0000383 .0000170 .0000374 o 130 .0016628 .0000727 .0002702 .0000285 .0000094 .0000326 140 .0016798 .0000839 .0002636 .0000215 .0000009 .0000353 c 150 .0016485 .0001306 .0002788 .0000101 .0000102 .0000364 155 .0009301 .0004289 .0002760 .0000019 .0000152 .0000287 z d 160 .0001907 .0004126 .0002737 .0000018 .0000160 .0000221 g 7 170 .0000442 .0002964 .0002154 .0000021 .0000123 .0000195 g ,o 180 .0000014 .0001568 .0001263 .0000015 .0000048 .0000067 190 .0000011 .0000948 .0000792 .0000011 .0000040 .0000053 200 .0000000 .0000000 .0000000 .0000000 .0000000 0000000 u m " { 210 .0000000 .0000000 .0000000 .0000000 .0000000 .0000000 ? U w
~ ~ unut umul-0 8 9 l 5 J 0 I NT D I 5 P LA CEME N TS (LOAD C ASE 7) p T SSE ANCHOR MOVEMENT 3 JOINT /- DISPLACEMENTS (IN. 1-----/ /-------ROTATIONS ( R AD I A N S ) -----/ m (GIDI X Y Z X Y Z r 4 10 .1803000 .1195000 .1636000 .0000000 .0000000 .0000000 30 .1803224 .1196358 .1632035 .0000696 000033A .0000057 E 40 .1808547 .1202352 1623380 .0001148 .0001102 .0000071 5 50 .1809319 .1203093 .1622600 .0001152 .0001108 .0000072 5 60 .1819757 .1212549 .1606005 .0001691 .0001905 .0000010 h 70 .1826617 .1217954 .1579662 .0002289 .0002238 .0000208 o 80 .1827361 .1217941 .1570432 .0002298 .0002270 .0000216 90 .1823,781 .1209533 .1539306 .0002582 0002386 .0000471 100 .1808153 .1186551 .1510514 .0002770 .0002637 .0000632 105 .0004270 .0003842 .0023553 .0001131 .0000687 .0000368 110 .0013009 .0000489 .0014820 .0001029 .0000602 0000826 120 .0026724 .0002514 .0001119 .0000766 .0000339 .0000748 g 130 .0033257 .0001439 .0005402 .0000569 .0000188 .0000651 o 140 .0033596 .0001662 .0005669 .0000430 .0000016 .0000706 150 .0032970 .0002597 .0005574 0000203 .0000204 .0000728 E 155 .0018602 .0008569 .0005519 .0000038 .0000304 .0000574 160 .0003814 .0008249 .0005472 .0000035 .0000321 .0000443 m H 170 ~ .0000884 .0005928 .0004305 .0000041 .0000246 .0000390 180 .0000029 .0003135 .0002526 .0000030 .0000097 .0000134 190 .0000022 .0001895 .0001583 .0000023 .0000081 .0000107 '200 .0000000 .0000000 .0000000 .0000000 .0000000 .0000000 m 210 .0000000 .00000'01 .0000001 .0000000 .0000000 .0000000 5 g 8 ? E 5 m I
I 1 3 TABLE B ELASTIC SUPPORT REACTION ELA S T I C S UP P QRT R E"A CT I ON S (LOAD C ASE 1) DEADLOAD + SUSTAINED LOAD + OPERATING PRESSURE I SUPPORT /------- F O R C E (LB. l - --- -- / /--- - - MOMENT ( IN-LB l - ----/ JOINT X Y Z X Y Z z 8 10 6.14 388.81 4.64 -4648.00 -132 73 5713.67 ~ l'10 0.00 630.11 0.00 0.00 0.00 0.00 5g 200 69.48 965 89 1.68 -18632.17 315.70 -23729.23 m M 8 INCLINED AXIS SUPPORT REACTIONS g x /----DIRECTION COSINES----/ y SUPPORT REACTION REACTION (INCLINED AXIS) m JOINT TYPE MAGNITUDE X Y Z -[z 110 FORCE -8 932 .7071 0.0000 .7071 P ELA ST I C SUP P 0RT REA CT I ON S (LOAD C ASE 2) THERMAL EXPANSION E ANCHOR MOVEMENT SUPPORT / - ----F O R C E (LB. 1 -------- / /------- M O M E N T t IN-LB l-- ----/ O JOINT X Y Z X Y Z 8 C 10 106 86 259.01 -135 27 -6299.94 5408.42 3041.19 k ~~ 110 0.00 -297.86 0.00 0.00 0.00 0.00 200 -35.02 38.86 207.11 -3622 31 18240.47 1453.48 3 z E .o INCLINED AX,IS SUPPORT REACTIONS g /- --DIRECTION COSINES----/ 8 o m SUPPORT REACTION REACTION (INCLINED AXISI JOINT TYPE MAGNITUDE X Y Z U 110 FORCE -101.599 .7071 0.0000 .7071
m Y Y maa - G 8v M B z C P s'x E ELA S T I C SUP P 0RT R E A'C T I ON S (LOAD CASE '3) mxo MAXIMUM PRESSURE SUPPORT /--------FORCE (LB. ) --------/ / --MOMENT ( IN-LB 3 --- ---- / y JOINT X Y Z X Y Z 5 0 10 .52904 .27572 .21357 -13.02803 10.46359 -12 73117 110 0.00000 .32267 0.00000 0.00000 0.00000 0.00000 200 .07952 .04695 ,.66309 -1.74104 56.94293 -2.23403 ~ INCLINED AXIS SUPPORT REACTIONS \\ /----0IRECTION COSINES- --/ 8 SUPPORT REACTION REACTION (INCLINE 0 AXIS) JOINT TYPE MAGNITUDE X Y Z g m, 110 FORCE .636 .7071 0.0000 .7071 ,k >z O .O B O Ti 5=
I e ~ i E .ma - [I z C ELA S T I C S UP P.0 R T R E. A CT I ON S (LOAD CASE 41 p 9 SRSS (X+Y+Z) SSE EARTHQUAKE m m ~ EARTHQUAKE RESPONSE = TOTAL X,Y AND Z RESPONSES COMBINED BY SOSS SUM. ' SUMMATION OF 3 MO DES. TOTAL X, Y AND Z RESPONSES WERE FORMED BY CSF ~ 'SOPP0RT ~ /-- -F OR CE (LB. 1--------/ /-------MOMENT ( IN-LB ) --- --- - / JOINT X Y Z X Y Z 5 10 97.0 7.9 105.1 3515. 3805. 3427. 200 327.8 166.4 285.7 6676. 5477. 4187. 1 10 0.0 116.2 0.0 0. O. O. ~ INCLINED AXIS SUPPORT REACTIONS /---D I R E CT I O N C0 5 I NE S---/ O SUPPORT REACTION REACTION (INCLINED AXIS) y JOINT TYPE MAGNITUDE X 'Y Z g 110. FORCE 255.3 .7071 0.0000 .7071 H 2 O .O I w co W 8 E e.
g ~ 3 j ind - rii U 8 ^$ I b EL A S T I C S U P P OR T R EA CT I ON 5 (LOAD CASE 51 p T SRSS (X+Y+Z) 1/2 SSE EARTHOUAKE m E m EARTHOUAKE RESPONSE = TOTAL X, Y AND Z RESPONSES COMBINED BY SOSS SUM. TOTAL X, Y AND Z RESPONSES WERE FORMED BY CSF SUMMATION OF 3 MODES. j SUPPORT / - - --- = - F O R C E (LB. 3-- -/ /- --- -MOMENT ( IN-LB l ------ / JOINT X Y Z X Y Z 5 1U 54.43 4.41 58.95 1972. 2135. 1922. 110 0.00 65.20 0.00 0. O. O. 200 183.91 92.20 160.29 3746. 3073. 2349. ^ INCLINED AXIS SUPPORT REACTIONS /----DIRECTION COSINES----/ 0 SUPPORT REACTION REACTION (INCLINED AXISI JOINT TYPE MAGNITUDE X Y Z E S 110 FORCE 143.2 '.7071 0.0000 .7071 H m> z .O m i N = 1 g o l g M l 1 e w l
I ~ ,p i i unut I amul' 3s ELA S T I C S U P P OR T R E A CT I ON S (LOAD CASE 6) 1/2 SSE ANCHOR MOVEMENT SUPPORT /--------FORCE (LB. 3 -/ /-------MOMENT ( IN-LB l--------/ JOINT X Y Z X Y Z 9 T 10 130.400 89.803 121.453 3188.369 -3643.144 -873 530 2 110 0.000 -107.568 0.000 0.000 0.000 0.000 200 18.630 17.755 27.577 341.920 2011.977 -2360.166 M INCLINED AXIS SUPPORT REACTIOMS $5 /----0!RECTION COSINES----/ 5 SUPPORT REACTION REACTION (INCLINED AXIS) E JOINT TYPE MAGNITUDE X Y Z 9 E' L A S T I C SUP P Q R. T RE A CT I ON5 (LOAD CASE 7) SSE ANCHOR MOVEMENT SUPPORT /-- - -FORCE (LB. )---------/ /-------MOMENT ( IN-LB 1--- --/ O JOINT X Y Z X Y Z C 10 260.697 179.457 242.860 6376 159 -7285.185 -1748.373 M 110 0.000 -214.963 0.000 0.000 0.000 0.000 2 200 37.265 35.50$ 55.103 684.908 4021.505 -4719 349 3 2 S P INCLINED AXIS SUPPORT REACTIONS g g = /----0IRECTION COSINES----/ 3 o SUPPORT REACTION REACTION (INCLINED AXIS) 'n JOINT TYPE MAGNITUDE X Y Z U 110 FORCE -421.383 .7071 0.0000 .7071 w
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