ML17117A457
| ML17117A457 | |
| Person / Time | |
|---|---|
| Site: | Beaver Valley  |
| Issue date: | 04/21/2017 |
| From: | FirstEnergy Nuclear Operating Co |
| To: | Office of Nuclear Reactor Regulation |
| Shared Package | |
| ML17117A433 | List:
|
| References | |
| L-17-029 | |
| Download: ML17117A457 (159) | |
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BVPS UFSAR UNIT 1 Rev. 19 B-1 APPENDIX B SEISMIC DESIGN TABLE OF CONTENTS Section Title Page B.1 SEISMIC DESIGN AND ANALYSIS OF STRUCTURES, SYSTEMS AND COMPONENTS B.1-1 B.1.1 Subgrade Properties B.1-2 B.1.2 Damping B.1-2 B.1.3 Containment Structure B.1-3 B.1.4 Other Seismic Category I Structures B.1-6 B.1.5 Amplified Response Spectra for Equipment Loading B.1-7 B.1.5.1 The Frequency Response Method B.1-7 B.1.5.2 Validation of the Frequency Response Method For the Beaver Valley Power Station B.1-9 B.1.5.3 The Soil Structure Interaction Method B.1-10 B.1.5.4 Qualification of Frequency Response Method ARS to the Soil Structure Interaction Method ARS B.1-10 B.1.6 Computer Programs Used for Structural Analysis B.1-11 ATTACHMENT "A" TO SECTION B.1 EMPIRICAL METHOD TO DETERMINE AMPLIFIED RESPONSE SPECTRA B.1-15 B.2 STONE
& WEBSTER B.2-1 B.2.1 Analyses and Design Criteria of Seismic Category I Piping B.2-1 B.2.1.1 Summary of Stone & Webster Piping Analysis procedures B.2-1 B.2.1.2 General Analytical Procedure B.2-1 B.2.1.3 Amplified Response Spectra B.2-2 B.2.1.4 Dynamic Analysis B.2-3 B.2.1.4.1 Mathematical Model B.2-3 B.2.1.4.2 Natural Frequencies and Mode Shapes B.2-4 B.2.1.4.3 Dynamic Response B.2-4 B.2.1.5 Piping Stress Limits B.2-5 B.2.1.6 Buried Seismic Category I Piping B.2-6 B.2.1.7 Interface Between Seismic Category I Piping and Non-Seismic Piping B.2-6 B.2.1.8 Pressure Relief Devices B.2-6 B.2.1.9 Simplified Seismic Analysis of Small Size Seismic Category I Piping (Generally Less than or Equal to 6 inches)
B.2-7 BVPS UFSAR UNIT 1 Rev. 19 B-2 TABLE OF CONTENTS (CONT'D)
Section Title Page B.2.1.10 Field Run Piping B.2-10 B.2.1.11 Computer Programs for Seismic Category I Piping Systems B.2-11 B.2.1.12 Use of ASME Code Case N-411 B.2-14 B.2.2 Summary of Stone & Webster Equipment Design Procedures B.2-16 B.2.2.1 Static Analysis B.2-17 B.2.2.2 Dynamic Analysis B.2-21 B.2.2.3 Testing B.2-23 B.2.2.4 Specification Requirements B.2-24 B.2.2.5 Computer Programs for Seismic Category I Equipment B.2-27 B.3 WESTINGHOUSE NUCLEAR STEAM SUPPLY SYSTEM B.3-1 B.3.1 Seismic Category Definitions B.3-1 B.3.2 Equipment List B.3-1 B.3.3 Design Philosophy B.3-1 B.3.4 Seismic System Analysis B.3-2 B.3.4.1 Analysis of Seismic Category I Mechanical Equipment B.3-2 B.3.4.2 Analysis of Reactor Vessel Internals B.3-2 B.3.5 Seismic Subsystem Analysis B.3-3 B.3.5.1 Analysis of Seismic Category I Mechanical Equipment B.3-3 B.3.5.2 Analysis of Reactor Vessel Internals B.3-4 B.3.5.3 Analysis of Fuel Assemblies, Control Rod Assemblies, and Control Rod Drives B.3-5 B.3.6 Criteria for Seismic Instrumentation Program B.3-5 B.3.7 Seismic Design Control Measures B.3-5 B.3.8 Code Classes B.3-6 B.3.9 Computer Programs used in Dynamic and Static Analysis B.3-6 BVPS UFSAR UNIT 1 Rev. 23 B-3 LIST OF TABLES Table Title B.1-1 Structures and Systems Requiring Design for Seismic Loading B.1-2 Distribution of Damping Values (Percent of Critical)
B.1-3 Damping Factors B.1-4 Comparison of Shear and Overturning Moment in External Structure of the
Reactor Containment OBE B.2-1 (Deleted)
B.2-2 (Deleted)
B.2-3 (Deleted)
B.2-4 Comparison of PITRUST With Franklin Institute Program "CYLNOZ" and Hand Calculation B.2-5 Comparison of PITRUST With Reference 1 Results
B.2-6 Comparison of PILUG Computer Program Output With Hand Calculations B.2-7 Summary of Comparison of Saval Computer Output With Hand Calculation As-Designed Condition B.2-8 Summary of Comparison of Saval Computer Output With Hand Calculation Reinforced Condition (1 1/4" Pad)
B.2-9 (Deleted)
B.2-10 Peak Broadening - Sample Calculation B.2-11 1 G Flat Response Dynamic Factor Study B.2-12 Modal Density, n* Dynamic Factor Study
B.2-13 Amplified Response Dynamic Factor Study B.2-14 (Deleted)
B.2-15 TAC2D - Sample Problem B.2-16 ASAAS Sample Problem B.2-17 Vessel Penetration Analysis - Sample Problem
BVPS UFSAR UNIT 1 Rev. 23 B-4 LIST OF TABLES (CONT'D)
Table Title B.2-18 Summary of Manual Calculations B.2-19 Summary of Computer Calculations
B.2-20 Shell 1 - Sample Problem B.2-21 Stress Analysis of Shells of Revolution Sample Problem B.2-22 Exact and Computer Stresses for Hollow Cylinder of Figure B.2-13 B.2-23 ST-167 - Sample Problem B.2-24 Load Combinations and Acceptance Criteria for Pressurizer Safety and
Relief Valve Piping and Supports - Upstream of Valves B.2-25 Load Combinations and Acceptance Criteria for Pressurizer and Relief Valve Piping and Supports - Seismically Designed Downstream Portion B.2-26 Definitions of Load Abbreviations
B.2-27 Load Combinations and Allowables for QA Category 1 Piping 2" Diameter and Smaller B.2-28 Load Combinations and Allowables for QA Category 1 Piping 2" Diameter and Smaller Attached to Containment Penetrations B.2-29 Load Combinations and Allowables for QA Category 1 Small Bore Piping Supports (2" Pipe Diameter and Less)
B.2-30 Load Combinations and Allowables for QA Category 1 Small Bore Piping (2" Diameter and Less) Equipment Nozzles and Active Component Supports B.2-31 Definition of Terms B.3-1 NSSS Fluid Systems Component Seismic Category List
B.3-2 Summary of Seismic Requirements B.3-3 Stress Limits for Various Load Combinations B.3-4 Loading Conditions and Stress Limits
B.3-5 Equipment Code and Classification List B.3-6 (Deleted)
B.3-7 (Deleted)
BVPS UFSAR UNIT 1 Rev. 19 B-5 LIST OF TABLES (CONTD)
Table Title B.3-8 (Deleted)
B.3-9 (Deleted)
B.3-10 (Deleted)
B.3-11 (Deleted)
B.3-12 (Deleted)
B.3-13 WESTDYN Test Problem Number 1 B.3-14 WESTDYN Test Problem Number 2
B.3-15 WESTDYN Test Problem Number 3 B.3-16 WESTDYN Test Problem Number 4 B.3-17 WESTDYN Test Problem Number 5 BVPS UFSAR UNIT 1 Rev. 19 B-6 LIST OF FIGURES Figure Title B.1-1 Seismic Analysis Containment Structure B.1-2 Vertical Dynamic Model for Seismic Analysis of Containment Structure
B.1-3 Comparison of Shell I vs Hand Calculation Sheet 1 B.1-4 Comparison of Shell I vs Hand Calculation Sheet 2 B.1-5 Comparison of Hand Calculations to MAT 5 Program B.1-6 Comparison of MAT 5 Output to Hand Calculations for a Ten Foot Thick Circular Mat B.1-7 Results of Time History Program Containment Structure-Operating Floor Level Time History of Structure Response B.1-8 Results of STRUDL II Analysis Containment Structure-Operating Floor Level Time History of Structure Response B.1A-1A Time History - Frequency Response Methods Comparison B.1A-1B Time History - Frequency Response Methods Comparison B.1A-1C Time History - Frequency Response Methods Comparison
B.1A-2A Time History - Frequency Response Methods Comparison B.1A-2B Time History - Frequency Response Methods Comparison B.1A-2C Time History - Frequency Response Methods Comparison
B.1A-2D Time History - Frequency Response Methods Comparison B.1A-2E Time History - Frequency Response Methods Comparison B.1A-3A Amplified Response Spectra B.1A-3B Comparison of Soil Shear Modulus at Charging Floor B.2-1 Representation of Family of Peak Response Curves Within Broadened Resonant Peak B.2-2 Hypothetical vs Actual Response of Multiple Modes Within Broadened Response Peak
B.2-3 Justification of Static Load Factor BVPS UFSAR UNIT 1 Rev. 23 B-7 LIST OF FIGURES (CONT'D)
Figure Title B.2-4 Amplified Response Spectra
B.2-5 Model Beams B.2-6 (Deleted)
B.2-7 Test Problem - SAVAL B.2-8 (Deleted)
B.2-9 Transient Temperatures in a Right Circular Cylinder - Comparison of TAC2D Results With Series Solution B.2-10 (Deleted)
B.2-11 (Deleted)
B.2-12 Ten Element Idealization of Thin-Wall Cylinder B.2-13 Four-Element Idealization of Hollow Cylinder B.3-1 (Deleted)
B.3-2 (Deleted)
B.3-3 Comparison Between Design and Collapse Conditions For Sy Hoop Stress of 0.9 B.3-4 Comparison Between Design and Collapse Conditions For Sy Hoop Stress of 0.0 BVPS UFSAR UNIT 1 Rev. 19 B.1-1 APPENDIX B SEISMIC DESIGN B.1 SEISMIC DESIGN AND ANALYSIS OF STRUCTURES, SYSTEMS AND COMPONENTS All structures, systems and components including instruments and controls where failure might cause or increase the severity of a loss-of-coolant accident or result in an uncontrolled release of excessive amounts of radioactivity, and those structures and components vital to safe shutdown of the reactor are defined as Seismic Category I. Note that the classification of Seismic Category I was previously designated as "Seismic Class I." These two terms are considered equivalent for which the above definition applies. Seismic Category I structures, systems and components are listed in Table B.1-1.
Those structures, systems and components which are important to reactor operation but not vital to safe shutdown of the reactor and whose failure could not result in the release of substantial amounts of radioactivity are defined as Seismic Category II. All other structures, systems or components not defined as either Seismic Category I or II are classified as nonseismic. The Nuclear Steam Supply System supplier also referred to this nonseismic category as Seismic Category III.
Seismic Category I structures are designed to resist seismic forces based on two ground response spectra which are described in Section 2.5:
- 1. The Operational Basis Earthquake (OBE)
- 2. The Design Basis Earthquake (DBE).
The OBE is based on 0.06 g maximum ground acceleration at zero period, and the DBE is based on 0.125 g maximum ground acceleration at zero period. Response spectra for each earthquake used for the analysis of Seismic Category I structures are given in Figures 2.5-1 and
2.5-2. The response of the structure is obtained through modal analysis of a multi-mass dynamic model which closely approximates the physical and response characteristics of the structure.
Masses are normally lumped at floor elevations and include the floor system, a portion of the walls above and the walls below the floor system, and major component and equipment loads.
In addition, masses are located at elevations where any other response values are required. Spring elements between masses represent building structural characteristics and are based on equivalent structural flexibilities. These structural representations provide for the inclusion of torsional effects as a part of the dynamic output.
The soil springs which support the dynamic model are based on the subgrade shear modulus. A range of shear moduli values is used in the dynamic analysis to envelope the variation of peak floor response periods. In addition, the containment peak response spectra periods are further enveloped by considering containment wall and dome structural properties which are based on uncracked to partially cracked reinforced concrete sections to account for normal and pressurized conditions. The undamped model is analyzed to determine characteristic mode BVPS UFSAR UNIT 1 Rev. 19 B.1-2 shapes, natural frequencies, and modal participation factors. The appropriate damped ground response spectra provides the relationship between frequency and force-displacement.
Modal responses from the dynamic model are combined using the square root of the sum of the squares (SRSS) method to establish Seismic Category I structure seismic loads. This is used even when modes have closely spaced frequencies, since no well established criteria to
combine modes under this condition was available.
The results of the seismic analysis provide the required information for structural component and equipment loading and interstructure "rattle-space." A 3-inch minimum width joint is provided between all structures not built integrally with each other. Components and equipment
are generally designed to withstand the static application of the SRSS method of the force or deflection values of all participating modes. For certain critical equipment and piping (e.g., the Nuclear Steam Supply System), amplified response spectra generated from total system response are used for detailed dynamic analysis.
All inputs and responses required by all design organizations for all Category I structural systems, components, and equipment are derived from the lumped mass dynamic models.
The dynamic model is also used to determine base overturning moments. These are calculated by taking the sum of each mass times its height above the base times its square root of the sum of the squares acceleration value. Overturning moments are combined with vertical acceleration forces in order to check structure overturning stability and subgrade reactions. B.1.1 Subgrade Properties The properties of the subgrade are discussed in Section 2.5.3.
B.1.2 Damping Structural damping is energy loss due to internal friction within the material and at connections between elements. The resulting damping forces are a function of the intensity of the motion and of the stress levels induced. The stress levels referred to are those resulting from the dynamic response only. However, structural makeup is also important in consideration of damping forces.
For the containment structure the major contribution to stress intensity is not from seismic loading but from other loading required by the load combination criteria. Loading due to internal pressure causes cracking of the concrete. The damping value of 2 percent for the structural components of response is considered valid because of high damping forces anticipated at the crack surfaces without consideration of the damping forces available from the internal equipment.
Damping for each significant mode of response is estimated by calculating the energy losses due to damping in each component of the mode. Component energy losses are summed and prorated to the total energy available in the mode with the system undamped.
This relationship establishes a damping value for the mode which is qualitatively correct and has some verification through test and observation.
(1)(2)(3) Based upon the calculated damping values determined in this way, conservative damping coefficients are established for the significant modes of response. For the soil-structure system, 5 percent and 7 percent of critical damping has been established for the OBE and DBE respectively, for all significant modes.
BVPS UFSAR UNIT 1 Rev. 19 B.1-3 These values are appropriately conservative as compared to the theoretical values obtained for this system.
A distribution of damping values calculated on a modal basis by the method described is outlined in Table B.1-2. A review of these values shows that total system damping is relatively insensitive to the values assumed for the structural components for the first two modes.
Structural damping begins to dominate in the higher modes but this does not have much effect because the contribution to system response from the higher modes is not significant.
For the design of the containment structure, a value of 2 percent of critical is assumed for the concrete for both the OBE and DBE. A value of 5 percent is used for the total soil-containment structure in response to the OBE because of energy dissipation due to interaction with the soil.
Because of a greater intensity of motion, a coefficient of 7 percent is used with the DBE for the total soil-containment structure system. B.1.3 Containment Structure Seismic response forces and stresses are determined for the containment structure from the simultaneous application of horizontal and vertical earthquake ground motions by the frequency response method (response spectrum technique). The motion of the containment structure in the vertical direction is uncoupled from the lateral motion. This necessitates two dynamic models. The earthquake ground motions are established in the form of frequency response spectra as the OBE and DBE for lateral loading. The derivation of these earthquakes and the response spectra are as shown in Section 2.5. The spectral intensity for vertical loading is assigned a value of 2/3 of the horizontal intensity for both earthquake loadings. The design loading conditions for combination with seismic loading and the allowable stress levels are stated in Section 5.2.1 and 5.2.2.
Originally, the containment structure was analyzed as a four-degree-of-freedom model. The cylindrical shell and dome and the internal structure were transformed to equivalent mass-spring systems mounted on the mat. A lumped mass model was later used to show the validity of the approach. This model incorporated the latest configuration and data and the results are used for seismic stress values.
The dynamic model of the containment structure for lateral motion is shown in Figure B.1-1. It consists of a system of spring-connected lumped masses coupled to the subgrade by soil springs. This multiple-degree-of-freedom model is established to determine the free, undamped vibrational characteristics of the structural system.
The dome is represented by one lumped mass. The cylindrical shell is modeled as 6 discrete
mass points. Masses Ml through M7 constitute the total real mass of the outer structure exclusive of a small tributary mass at the base of the shell which is lumped with the mass of the mat, M8.
BVPS UFSAR UNIT 1 Rev. 19 B.1-4 Translational and rocking spring constants, K8 and K14 respectively, are included to represent the subgrade. These constants are for a rigid circular base resting on an elastic half space.
Their values are given by:
32(1-M u)GR K8(translational) = (Bycroft 1956)
(4) (7-8M u) (B.1-1)
8GR 3 K14(rocking) =
(Borowicka 1943)
(4) (B.1-2) 3(1-M u) where: G = Shear modulus of subgrade R = Radius of foundation mat
M u = Poisson's ratio of the subgrade Beam Theory which accounts for distortion due to flexure and shear is used to establish the flexural characteristics of the cylinder and dome under inertial loading. Beam Theory is admissible since the shell cross-sections do not distort under inertial loading. The spring
elements Kl through K7 shown in Figure B.1-1 represent the outer structure. Spring Kl represents the dome and K2 through K7 represent the cylinder.
The internal structure consists of the primary shield wall and the crane wall interconnected by floors and radial walls. The lumped masses (M9 through M13) representing the internal structure and equipment are also shown in Figure B.1-1. The stiffness elements K9 through K13 are determined from Beam Theory, accounting for flexure and shear distortion.
Torsional effects in the containment were studied and due to symmetry were found to contribute only a negligible amount to the entire containment motion.
In determining the free vibrational characteristics of the dynamic model, the modal equation for a multi-degree lumped-mass system, written using matrix notation is:
FMq 1 W q n 2 (B.1-3) where: [F] = square flexibility matrix
[M] = a diagonal mass matrix containing the masses of the system
{q} = column matrix of displacement for the nth mode W n = natural frequency in radians per second for each mode
The solution of this equation determines the natural circular frequencies (W n) for each mode and the associated coordinate displacements.
BVPS UFSAR UNIT 1 Rev. 19 B.1-5 The modal participation factors are defined by the equation:
where: i = mass point
r = mode
IMH = rigid body mass moment of inertia due to lateral dimension only Damped modal response is established for each mode from the following equation:
A ir = (P r) (q ir) (A sr) (B.1-5)
where: A ir = ith coordinate response for the rth mode
A sr = ith damped spectral response for the rth mode
The total response at any mass point is determined by taking the square root of the sum of the squares of the coordinate response for each mass for all significant modes:
A i = (A)(A)...(A) i1 2 i2 2 ir 2 (B.1-6) where: A i = total response for mass point i for all significant modes The dynamic model of the containment structure for vertical motion is shown in Figure B.1-2. Masses Ml, M2 and M3 represent the dome, M4 through M8 the containment, M9 the foundation mat, and M10 through M14 the internal structures and major equipment. The structural spring elements Kl through K8 and K10 through K14 represent the vertical deformation characteristics of the structural elements. The soil stiffness K9 is determined by the following formula.
(5) K9 = 4GR(1M)u (B.1-7)
Mode shapes, modal participation factors, and structural response are determined by the previously described method.
Earthquake-generated forces are applied statically to the structure and the results are combined with other loadings following the combinations and factors listed in Section 5.2.2. (B.1-4)
BVPS UFSAR UNIT 1 Rev. 19 B.1-6 B.1.4 Other Seismic Category I Structures Seismic response forces and stresses are determined for Seismic Category I structures other than the containment by using the same approach described in Section B.1.3.
A lumped-mass, multiple-degree-of-freedom model is developed for each separate structure taking into account foundation conditions.
The free vibrational characteristics of the model are calculated. Acceleration and deflection values from the ground response spectra curves for the OBE and DBE (Section 2.5) are then combined to give the design loads. For the vertical model, ground response spectra values are taken as two-thirds of the horizontal. The resultant earthquake design load, depending upon the type and character of the structure or component, is either that resulting from horizontal acceleration, vertical acceleration, or a combination of both.
Earthquake-caused deflections are determined for both Seismic Category I structures and any abutting structures. The structures are then separated by a space sufficient to prevent unaccounted-for interaction between the structures.
Loading combinations for Seismic Category I structure s other than the containment, have seismic loading combined with dead, live, and other static loads. Normal wind or tornado loadings are not assumed to occur simultaneously with the earthquake loading.
Concrete sections of Seismic Category I structures are designed using Working Stress Design according to "Building Code Requirements for Reinforced Concrete," ACI 318-63. The different loading combinations used are as follows:
D.L. + L.L.
D.L. + L.L. + OBE
D.L. + L.L. + DBE
D.L. + L.L. + TOR
D.L. + L.L. + F
where: D.L. = Dead Load
L.L. = Live Load
OBE = Operating Basis Earthquake Load DBE = Design Basis Earthquake Load
TOR = Tornado Loads
F = Max possible flood loads
BVPS UFSAR UNIT 1 Rev. 19 B.1-7 Allowable stresses are increased accordingly to the specific loading conditions as follows:
- 1. for OBE = 33% increase
- 2. for DBE = 50% increase
- 3. for TOR = 66.7% increase in allowable concrete compres-sive strength (reinforced steel at .9 fy)
- 4. for F = 50% increase Structural steel sections of Seismic Category I structures are designed in accordance with the American Institute of Steel Construction (AISC) Manual of Steel Construction 1963 edition, Part 1 "Specification for the Design, Fabrication, and Erection of Structural Steel for Buildings,"
except that the seismic loading referred to in paragraph 1.56 is considered as the OBE.
Loading combinations for these structures are the same as listed previously for concrete
structures. Allowable stresses are increased as follows:
- 1. For OBE = 33% increase
- 2. For DBE or Tornado = 90% of the specified minimum yield strength for structural steel B.1.5 Amplified Response Spectra for Equipment Loading A response spectra modal analysis technique was initially used to design Seismic Category I equipment and piping for BVPS-1. Amendment 15 of the BVPS-1 PSAR and the Safety Evaluation by the Division of Reactor Licensing are cited for details regarding the matter. The frequency response method is described in Section B.1.5.1 below. A special report covering the validation of this method entitled "Empirical Method to Determine Amplified Response Spectra," is presented in Attachment "A" to Section B.1. B.1.5.1 The Frequency Response Method The response of a structural system, such as a nuclear containment building to seismic ground motion, is made up of harmonic components of frequencies equal to the natural frequencies of the structure. Components such as equipment and piping, mounted in the structure respond to the structural motion. The elastic behavior of the components is not considered in the analysis of the total structure. This does not, however, introduce a discernible inaccuracy in the dynamic
analysis of the structure because the mass of the equipment is small as compared to the mass of the structure. Component mass is included in the analysis of the structure. The analysis of
components must take into account the modification of the ground motion due to the response of the structure and the effects of the distortion of the structure itself.
Components mounted in the structure which are flexible as compared to the structure will respond essentially as though supported directly in the subgrade. Distortion of the structure is not considered important. On the other hand, components which are very stiff as compared to the structure experience seismic response which is the same as that of the structure at the point where the component is supported.
BVPS UFSAR UNIT 1 Rev. 19 B.1-8 When components have natural periods close to the natural periods of the structure, resonance will occur and support motion will be greatly amplified. The extreme would be the classical situation of an elastic system responding to a sinusoidal support motion. Because of the irregular characteristics of earthquake motion and damping in the combined structure-sub-grade complex, a steady state of support motion does not exist and the harmonic components of support response are considered to decay. Component damping also has a significant effect on the magnitude of the component release.
Using the damped ground response spectra to determine modal responses at points of interest in the structure, structural motion is idealized as a decaying time-dependent sinusoidal motion for each mode of structural response. These discrete, time-dependent, modal structural motions are used as support motions for damped single-degree-of-freedom (SDF) oscillators to calculate approximate amplified response spectra.
This is accomplished by determining the ma ximum time-dependent oscillator response to each mode of the structural response and combining these results as the square root of the sum of the squares. Noting that the terms oscillator and component can be used interchangeably, a mathematical description of the frequency response method is summarized below. A computer program has been developed to carry out the procedure.
The equation of motion for a damped SDF oscillator subjected to time-dependent support
motion described by F(t) is:
Mu" + ku + cu' = -MF(t) (B.1-8)
where: M = mass
k = spring constant
c = oscillator damping constant u = displacement of oscillator relative to the support
t = the time function
F(t) = the exponentially decaying sinusoidal support motion function which represents the idealized structural motion at equipment support point
For multiple-degree-of-freedom (MDF) oscillator system s such as piping and equipment:
F(t) = e
(-rBst) P i A iSIN(W it) (B.1-9) where: P I = modal participation factor for ith structural mode
A i = amplitude of structural response acceleration for the ith structural mode
Bs = structural damping r = an empirical factor which modifies the logarithmic decay of the forcing function to provide conservative results at resonance
BVPS UFSAR UNIT 1 Rev. 19 B.1-9 t = time
W i = natural frequency in radians per second for each mode
Dividing equation (B.1-8) by M and denoting f 2=k/M (where f = natural frequency of the oscillator) and c = 2MBe (where Be is a measure of oscillator damping):
u" + 2Beu' + f 2u = -F(t) (B.1-10)
The maximum response of the oscillator is determined for each mode of structural response. For each oscillator over the range of interest (1,2,..........n), the maximum responses to each structural mode of response are combined as the square root of the sum of the squares to generate the amplified response spectrum. Curves are developed for the required levels of
equipment damping for both the OBE and DBE. B.1.5.2 Validation of the Frequency Response Method for the Beaver Valley Power Station To validate the method, amplified response spectra developed by the frequency response method are compared to spectra obtained by the theoretically more rigorous time history approach. This serves to establish the factor "r" which controls the rate of amplitude decay of the sinusoidal forcing function F(t).
In the time-history analysis method, seismic analysis is executed by an exact step-by-step integration of the modal equations of motion using as input an artificial time history (denoted by C) in Table B.1-4 whose response spectrum (denoted by B) envelopes the smoothed site design response spectrum (denoted by A) for five percent of critical damping. Time-history of the modal responses are combined algebraically to provide the time-history of total response, overturning moment and shear, at any elevation in the structure. In the analysis, a constant modal damping of 5 percent of critical is assumed. Maximum shears and moments predicted by this approach are summarized in Table B.1-4 under column III.
By the frequency response method, the peak response of each mode is computed directly from a response spectrum, curve B, obtained from the time-history curve. The peak modal responses are combined, usually by the SRSS or some modification thereof, to provide the estimated total peak response. Estimated maximum force and moments as predicted by the spectral analysis are shown in Table B.1-4 under column II.
The results of the above studies indicate that the base shear force computed from the time-history analysis is exceeded by the base shear values calculated from the response spectrum curves A and B. The base overturning moment calculated from the time history exceeds the base overturning moments calculated from the response spectrum curves A and B by only 9.2
and 3.0 percent, respectively.
A direct comparison can really only be made between values determined from curve B and the time history C. The time history shear values exceed the response curve B shear values by only 20 percent at the spring line and are exceeded by the response curve B shear values from
45 ft above the top of the mat to the top of the mat.
BVPS UFSAR UNIT 1 Rev. 19 B.1-10 Comparisons were made of amplified response spectra determined by the frequency response method and the time history method for the containment structure. Three earthquake records were used, viz., Helena E.W. and Taft and El Centro. All three time histories were normalized to .125 g. The soil-structure system damping was 7 percent for all modes and oscillator
damping was 0.5 percent. It was demonstrated that a value of r = 0.3 controlled the assumed logarithmic decay of the F(t) function to give conservative results in the resonant bands as compared to the time history method.
The BVPS-1 PSAR states that if the values of amplified response spectra obtained by the frequency response method fall below the appropriate spectra obtained by the time history method away from resonant peaks, the former values would be arbitrarily raised to envelop the time history spectra. The time history record used for this control is Helena E.W. in accordance with Amendment 15 of the BVPS-1 PSAR.
The containment structure dynamic model has been tested for possible variations in soil shear modulus.
Examination of results shows that reasonable variation of the soil shear modulus (33.33 percent) would have a significant effect on the rocking and translational frequencies (-20 percent and +25 percent as measured against the nominal resonant periods). Accordingly, this is taken into account in the generation of amplified response spectra for components. For all
other Seismic Category I structures the same value of "r" is used. Using the value of "r" calculated as outlined above, amplified response spectra were developed using the ground response spectra for the site. These were compared to the amplified spectra obtained directly from the time histories stated to ensure that the frequency response method gives acceptable results. B.1.5.3 The Soil Structure Interaction Method As part of the re-analysis of Seismic Category I piping systems performed in 1979, Amplified Response Spectra (ARS) was developed using Soil Structure Interaction (SSI) methodology. Section B.2.1.3 discusses the SSI-ARS. Figure 2.5-4 represents the response spectra for 0.125G DBE and Figure 2.5-5 represents the response spectra for 0.06 OBE. The licensee now considers that the SSI-ARS forms the present and future design basis for the plant.
B.1.5.4 Qualification of Frequency Response Method ARS to the Soil Structure Interaction Method ARS Amplified response spectra using soil structure interaction (SSI) methodology was developed for the operational phase re-analysis of Seismic Category I piping systems. A review of the original plant ARS (Figures 2.5-1 and 2.5-2) on a building-by-building and elevation-by-elevation basis indicated that peak resonant responses occurred below 10 Hz and that amplification of ground motion principally occurred below 20 Hz for structures housing Seismic Category I equipment. For each building a "cutoff frequency" was selected (i.e., 10 to 20 Hz) in order to identify seismic acceleration levels above and below the cutoff frequency for calculational purposes. The "g" level identified below the cutoff frequency was a minimum of 1.3 times the peak ARS response.
At the cutoff frequency the rigid range g value was conservatively selected.
A comparison of the ARS used for the original plant design with the SSI-ARS indicates that the original plant ARS are conservative based upon the above seismic specification of static g values for qualification by static analysis and testing.
BVPS UFSAR UNIT 1 Rev. 23 B.1-11 It was noted that peaks of the SSI-ARS are significantly lower than the peaks of the original plant ARS. The SSI-ARS peaks occur in the 2 to 5 Hz region for all structures evaluated and there is little amplification of maximum floor acceleration above 10 Hz. In some isolated cases the SSI-ARS curves exceed the original plant ARS in the low frequency region (below 5 Hz) distant from peak original ARS responses. This breaching of the original ARS would only potentially affect equipment whose natural frequency is below 5 Hz. Further discussion of the
SSI-ARS is presented in Section B.2.1.3. No re-analysis of Seismic Category I structures was necessary as a result of the development of the SSI-ARS curves. B.1.6 Computer Programs Used for Structural Analysis The following programs are used in the structural analysis of seismic Category I structures.
A Description of each program follows.
STRUDL II
STRUDL, an acronym for Structural Design Language, is a series of computer programs for solving problems in structural engineering. It is applicable to both framed and continuous mechanics problems, either static or dynamic in nature. In frame analysis, the member stiffness
matrix is computed from beam theory, while in finite element analysis, the element stiffness matrix is computed from energy considerations.
STRUDL II(12) has been designed as a modified subsystem of the Integrated Civil Engineering System (ICES) which was designed and formulated at Massachusetts Institute of Technology, Department of Civil Engineering.
The finite element method (11) provides for the solution of a wide range of solids mechanics problems. Its implementation within the context of the STRUDL analysis facilities expands these for the treatment of plane stress, plane strain, plate bending, shallow shell, and three dimensional stress analysis problems. STRUDL II also provides a dynamic analysis capability for linear elastic structures undergoing small displacements. Either free or forced vibrational response may be obtained, and in the latter case the forcing function may be in the form of time histories or response spectra.
The three dimensional finite element capability of STRUDL II is used to analyze the primary containment at the region of the personnel and equipment hatches.
Seismic Category I structures are analyzed for seismic effect using the dynamic analysis capability of STRUDL II. The analysis yields frequencies of vibration, modes, shapes, displacements, velocities, accelerations, and forces. Category I structures additionally have been analyzed using the frame analysis capability of STRUDL II. The analysis provides twisting and bending moments, axial forces, shears, displacements, and joint rotations.
BVPS UFSAR UNIT 1 Rev. 19 B.1-12 SHELL I This computer program is a further development of a computer program written at AVCO Corporation. The program is based upon the general numerical procedure proposed by B.
Budiansky and P. P. Radkowski (7)(8) to analyze a shell of revolution subjected to arbitrary loadings. The analysis is based upon the general first order linear theory of thin shells by J. L.
Sanders, Jr.
(9)
The program is used to obtain the membrane forces and bending moments in the primary containment walls and shield walls due to pressure and temperature loads. Discontinuity forces at the foundation mat are obtained from the computer program called MAT 5.
The results of pressure loads on a shell of revolution from SHELL I have been checked against hand calculations based upon "Theory of Plates and Shells" by Timoshenko and Woinowsky-Krieger (Second Edition, 1957). For these test problems actual containments were used. A plot of the meridional bending moment, meridional shear, and radial deflection of the containment wall showning the comparison between SHELL I and hand calculations based on "Theory of
Plates and Shells" is given in Figures B.1-3 and B.1-4 for a containment structure subjected to uniform internal pressure.
MAT 5 This computer program analyzes a symmetrically loaded circular plate on an elastic foundation and maintains compatibility between:
- 1. The plate (foundation mat) and the subgrade
- 2. The plate and the circular walls supported thereon.
The program computes the discontinuity effects at the interface of the mat and circular walls and includes these effects in the analysis. The general method is described in "Practical Methods for Analysis of Beams and Plates on Elastic Foundations" by Boris N. Zhemochkin (Second Edition, 1962).
The program is used to analyze the foundation mat and to provide the contact pressure and the discontinuity forces at the junction of the mat and superstructure (i.e., primary and secondary containment walls, reactor support wall).
The solutions to test problems using MAT 5 are substantially identical to those obtained by hand calculations using Zhemochkin.
(11) It is to be understood that the complexity of the hand calculations tend to limit their accuracy. The test problems have been actual containment structures.
Figure B.1-5 shows plots of the radial and tangential bending moments and the radial shear in the mat for a MAT 5 solution vs. hand calculations. Also shown are the discontinuity forces at the interface of the mat and circular walls. This particular mat is on soil.
BVPS UFSAR UNIT 1 Rev. 27 B.1-13 Figure B.1-6 shows similar plots for a MAT 5 solution vs. a hand solution done in accordance with "Theory of Plates and Shells" by Timoshenko and Woinowsky-Krieger (Chapter 9) for a mat on rock. The comparison, particularly at the junction of the containment wall and mat is excellent. The hand calculations show a somewhat larger radial shear near the edge because the cantilever effect (5 ft) of the mat beyond the containment wall was not included. Other minor discrepancies occur at the lift-off point for the mat between the two solutions but these are due to the assumptions inherent in a Timoshenko solution (i.e., at the point of mat lift-off the radial moment, displacement, and slope of mat equal 0).
Time History The Time History computer program computes time history response and amplified response spectra at any mass point location of a lumped mass spring connected system due to a synthetic earthquake time-motion record input. The responses are computed by integration of the modal equations of the system by the Exact Method.
(10) The program's main application is the generation of Amplified Response Spectra used for design of Seismic Category I equipment
and piping.
Time history program's solution to a test problem is substantially identical to the solution obtained using STRUDL II. The test pr oblem utilizes an actual containment structure subjected to an earthquake time-motion record input of Helena East-West normalized to .06 g. The time history response of the structure was computed by the Time History program and STRUDL II.
The results of these analyses are shown graphically in Figures B.1-7 and B.1-8 respectively, the results of the analysis using the Time history program agree extremely well with those obtained
using STRUDL II.
ANSYS ANSYS is a general purpose finite element analysis program with structural and heat transfer capabilities. ANSYS is used for engineering analysis of Seismic Category I structures, equipment, and piping. It has been used for several applications, including the structural and thermal analysis of the replacement steam generators. ANSYS is a recognized program in the public domain.
Verification of the ANSYS software has been completed by performing a series of test problems. Results were compared to verified solutions from alternate methods and hand calculations provided by the vendor.
BVPS UFSAR UNIT 1 Rev. 19 B.1-14 References for Section B.1
- 1. N.M. Newmark, "Design Criteria for Nuclear Reactor Subject to Earthquake Hazards," Urbana, Illinois (1967).
- 2. N.M. Newmark, and E.Rosenblueth, Fundamentals of Earthquake Engineering, Prentice-Hill Inc. (1971).
- 3. R.V. Whitman, "Analysis of Foundation Vibration," Vibrations in Civil Engineering , Procedures of a Symposium Organized by the British National Section of the International Association of Earthquake Engineering.
- 5. Timoshenko and Goodier, Theory of Elasticity , New York (1951).
- 6. Deleted by Revision 0, January 1982.
- 7. B. Budiansky and P. P. Radkowski, "Numerical Analysis of Unsymmetrical Bending of Shells of Revolution" AIAA Journal (August 1963).
- 8. G. A. Greenbaum, Comments of "Numerical Analysis of Unsymmetrical Bending of Shells of Revolution" AIAA Journal (October 1963).
- 9. J. L. Sanders, Jr., "An Improved First Approximation Theory for Thin Shells", National Aeronautics and Space Administration, Technical Report R-24.
- 10. C. Nigam and C. Jennings; "Digital Calculations of Response Spectrum from Strong-Motion Earthquake Records", National Science Foundation (June 1968).
- 11. 0. C. Zienkiewicz and Y. K. Cheung "The Finite Element Method".
- 12. "ICES STRUDL II, The Structural Design Language Engineering Users Manual" Volume I, Frame Analysis, November 1968; Volume II, Additional Design and Analysis Facilities (Chapters III and IV) (June 1971).
BVPS UFSAR UNIT 1 Rev. 19 B.1-15 ATTACHMENT "A" TO SECTION B.1 EMPIRICAL METHOD TO DETERMINE AMPLIFIED RESPONSE SPECTRA Introduction
In accordance with the procedures described in Amendment 15 of the BVPS-1 PSAR, amplified response spectra were developed for seismic design of equipment and piping by an empirical frequency response method. A mathematical development of this procedure is contained in Amendment 15 of the BVPS-1 PSAR and Section B.1.5 of the FSAR. Amendment 15 and the Safety Evaluation by the Division of Reactor Licensing concerned with validation of this method are cited for specific details.
This attachment contains the following information:
- 1. A comparison of amplified response spectra obtained by the frequency response method using the exact ground response spectra of the El Centro, Taft, and Helena E-W earthquakes, and amplified response spectra by the Time History Method using the same three earthquakes. These comparisons are shown in Figures B.1A-1A, B.1A-1B, and B.1A-1C.
- 2. A comparison of amplified response spectra obtained by the frequency response method using the site ground response spectra, and amplified response spectra obtained by the time history method using the Helena E-W earthquake. This comparison is for five locations in the containment structure. Three locations are on the internal structure and two are on the containment shell.
These comparisons are shown in Figures B.1A-2A, B.1A-2B, B.1A-2C, B.1A-
2D, and B.1A-2E.
- 3. Amplified response spectra showing the effects of reasonable variations in the soil shear modulus G on the magnitudes of the spectra and the variation in resonant periods for the containment building. This information is shown in
Figures B.1A-3A and B.1A-3B. As stated in the PSAR and the FSAR, the soil shear modulus is established to be 18,000 psi. A realistic variation in this value is 33-1/3 percent. The plots in Figures B.1A-3A and B.1A-3B were obtained by the frequency response method using the site ground response spectra.
BVPS UFSAR UNIT 1 Rev. 19 B.1-16 Summary and Conclusions
A general study of the frequency response method using a six degree of freedom model of the containment was undertaken and documented in Amendment 15 of the BVPS-1 PSAR. The amendment also stipulated the following:
- 1. That the frequency response method would be validated for the actual dynamic model of the containment structure by comparisons with results obtained by the time history method for known earthquake records.
- 2. That the empirical value "r" which alters the structural damping and the logarithmic decrement of the modal sinusoidal forcing functions would be established to provide sufficient conservatism in the resonant sands.
- 3. Having established the value of "r", amplified response spectra would be developed by the frequency response method for all Seismic Category I structures using the site ground response spectra.
- 4. That values of amplified response spectra obtained by the frequency response method based upon the site ground response spectra would be used except where amplified spectra obtained from a known earthquake record by the time history method are greater. In such cases, the values obtained by the time history
method was used.
In Amendment 15 of the BVPS-1 PSAR, it was shown that a value of r = .5 was sufficient to provide conservatism in the resonant peaks for the general study of the six degree of freedom model that was used. During the course of the validation procedure with the actual dynamic model of the Beaver Valley containment, several comparisons of results from the time history method and the frequency response method were made wherein the value of "r" was varied. It has been determined that the more conservative value of r = .3 yields reasonable results for the three earthquakes which were studied.
Referring to Figure B.1A-1A , it can be seen that the method is conservative at fundamental resonance and somewhat underconservative in the third structural mode for El Centro. Between the first and second modes and at periods longer than the first, the frequency response method yields results which are somewhat underconservative.
For the Taft earthquake, Figure B.1A-1B, the results are acceptable at fundamental resonance, the second mode, and very conservative for the third mode. Between the first and third modes and at periods beyond the first mode, results are underconservative.
As shown in Figure B.1A-1C , for the Helena E-W earthquake, the results are very conservative for the first, second, and third structural periods. The results are slightly underconservative at
long periods and between periods of resonance.
Results of comparisons for other points in the containment show a similar degree of conservatism. The point for which these curves are made is at the top of the crane wall where maximum amplification would occur for the internal structure. All three comparisons show good agreement for short period oscillators which comprise the bulk of the equipment. It is
emphasized that the major effort in this study and in the general study shown in the BVPS-1 PSAR, is to account for resonance effects.
BVPS UFSAR UNIT 1 Rev. 19 B.1-17 In Figures B.1A-2A , B.1A-2B , B.1A-2C , B.1A-2D and B.1A-2E are shown comparisons of amplified response spectra for five locations on the containment. The comparisons are between amplified spectra calculated obtained by the frequency response method at r = .3 using the site ground response spectra and amplified response spectra obtained by the time history method using the Helena E-W earthquake. The DBE condition is used (.125g). Structural damping is
.07 critical for all modes and oscillator damping is .005 critical for both methods. The Helena E-W record was normalized to .125g. The results from the frequency response method are conservative with the exception of a few oscillator periods between structural modes. At the oscillator periods where the frequency response results are under conservative, the time history results govern in accordance with paragraph 4 of this summary.
The plots in Figures B.1A-3A , and B.1A-3B show the difference in the amplified response spectra obtained by the frequency response method using the site ground response spectra due to a 33.33 percent variation in the soil shear modulus G. In Figure B.1A-3A a plot is shown of amplified spectra for the charging floor for the established soil shear modulus G = 18,000 psi. The effects of variations in the established value of the shear modulus on the amplified spectra are shown in Figure B.1A-3B. The plots in Figure B.1A-3B should be compared to Figure B.1A-3A. It can be concluded that a reasonable variation in the soil shear modulus (33-1/3 percent) has a significant effect on the rocking and translational frequencies. Accordingly, a -20 percent and
+25 percent variation (as measured against the nominal resonant periods at G = 18,000 psi) is accounted for in the calculation of amplified response spectra for seismic design of equipment and piping (reference Appendix B, Section 1.5.2).
BVPS UFSAR UNIT 1 Rev. 19 B.2-1 B.2 STONE & WEBSTER B.2.1 Analyses and Design Criteria of Seismic Category I Piping B.2.1.1 Summary of Stone & Webster Piping Analysis Procedures Seismic analysis of piping systems in nuclear plants has also undergone an evolution consistent with the growth and development of seismic methods for the plant as a whole. In the 1970's, several major changes in methods of nuclear plant seismic analysis were made. The key changes were a standardization of design ground spectra, a requirement for three-directional analysis and use of increased damping values. The net effect was a more rational approach to seismic analysis.
At the time of the design phase of BVPS-1, Seismic Category I piping analysis was done in accordance with the ANSI B31.1 code, 1967 edition including the Summer 1971 Addendum.
The 1967 B31.1 code did not address seismic design in the sense of providing detailed rules for stress determination and load combinations. Further, the code did not deal with Normal, Upset, Emergency and Faulted Stress limits. Since that time, development of B31.7 and ASME III have addressed these rules and limits. The original seismic analysis was performed by the use of the SHOCK II computer code. The SHOCK II code, which combines intramodal responses algebraically, is no longer considered acceptable by the NRC. The PSTRESS computer code which developed input data for SHOCK II is also replaced by the NUPIPE computer code. The re-analysis performed in 1979, uses the NUPIPE computer code. NUPIPE incorporates a methodology which is currently acceptable to the NRC.
The NRC determined where design specifications and drawings are used to obtain input information for seismic analysis of safety-related piping systems, that it was essential for these documents to reflect the as-built configurations. All Seismic Category I piping 2 1/2 inches and greater were given a field verification of as-built conditions according to NRC IE Bulletin 79-14 requirements.
The new stress analysis of safety-related piping system did show some of the support stresses
to exceed code allowable levels. These supports were corrected by physical hardware additions. Generally, this was done by the addition of restraints or snubbers, or minor modifications to existing supports. B.2.1.2 General Analytical Procedure Analysis of Seismic Category I piping 2-1/2 inches and larger is performed by the use of the NUPIPE computer code. Both the commercial version, NUPIPE-II, and the Stone & Webster version, NUPIPE-SW, are used. Each piping system is mathematically modeled as linearly elastic structural model in three- dimensional space. Inertial characters of the piping systems are modeled by lumping the mass at various nodes through-out the piping included in each computer analysis. The stiffness matrix used in each analysis is computed based upon
the structural behavior of piping elements in NUPIPE.
BVPS UFSAR UNIT 1 Rev. 19 B.2-2 The seismic inertial response within each mode is computed as the square root of the sum of squares of the response due to the seismic excitation in each of the three orthogonal directions. The seismic inertial response among modes is computed as the square root of the sum of squares of responses due to each mode computed, except that the responses of all modes within a natural frequency band of 10 percent are added absolutely, and this sum is added by the square root of the sum of squares with the remaining computed nodes. This approach is in full compliance with Regulatory Guide 1.92 entitled "Combining Modal Responses and Spatial Components in Seismic Response Analysis".
The development of amplified response spectra used in the analysis of piping systems is described in Section B.2.1.3. Damping factors used for seismically designed piping and components are 0.5 percent for the OBE and 1.0 percent for the DBE. Refer to Section
B.2.1.12 regarding the use of alternate damping values in ASME Code Case N-411.
Where a piping system is subjected to more than one amplified response spectrum as when support points are located in different parts of the structure or different structures, the amplified response spectrum which is closest to and higher in elevation than the highest support on the piping system is applied to this system or multi ARS are used simultaneously in the analysis.
Relative seismic structural displacements between the piping supports and anchor points, that is, between floor penetrations and equipment supports at different elevations within a building
and between the buildings, are used as inputs of equivalent static boundary displacement conditions in the computations. Relative seismic displacements between the pipe support points at different buildings are always considered to be out of phase in order to obtain the most
conservative piping responses.
For the analysis effort, the effects of the seismic anchor displacements have been evaluated statically and separately from the inertia effect. Static analysis is performed for each direction of relative displacement and for each earthquake, leading to a total of six evaluations. Internal moments resulting from the three evaluations for each earthquake are combined by SRSS on a component level and are then combined with the inertia effects by absolute summation, also on a component level. B.2.1.3 Amplified Response Spectra The NUPIPE computer code uses an amplified response spectra (ARS) based on soil-structure interaction (SSI). The methodology used in SSI-ARS is based upon a layered elastic media model for soil and a lumped mass model for the structure. Analysis using these models involves:
- 1. The calculation of frequency-dependent stiffness at the surface of a layered medium using the program REFUND
- 2. Modification of a specified surface motion to account for embedment of the structure
- 3. The application of kinematic interaction principles to modify translational input specified at the surface to both a translational and rotational motion at the base of the rigid structure foundation using the program KINACT
- 4. Analysis of the structural model supported on frequency-dependent springs using the program FRIDAY.
BVPS UFSAR UNIT 1 Rev. 19 B.2-3 The resulting ARS developed from this methodology were compared with ARS developed using a detailed finite element representation of the underlying soil medium with a lumped mass representation of the containment structure using the program PLAXLY. The amplified values of acceleration computed using the REFUND/KINACT/FRIDAY method are generally 30 to 100 percent larger than values computed using the more rigorous PLAXLY approach.
Variations in soil properties have generally been accounted for by developing ARS using mean values of soil moduli and damping ratio values adjusted for strain levels associated with earthquakes, and peak spreading the resulting ARS.
The soil properties are developed from subsurface data into a soil profile, in which each stratum
has its own soil parameters. The required dynamic properties in each layer are described first by the small strain values of shear modulus, and then site response analysis is used to develop values of damping and shear modulus that are compatible with the strains to be expected during an earthquake.
Subsurface information was obtained from several sources, which include the BVPS-1 FSAR, the Geotechnical Design Criteria for BVPS-2, and the report on the Soil Densification Program for BVPS-2. The pre-construction boring logs for BVPS-1 under the Category 1 structures are found in Appendix 2F. Two seismic cross-hole surveys were performed by Weston Geophysical Laboratory, the first in 1968 and the second in 1977, in conjunction with the BVPS-2 Soil Densification Program.
The computer program SHAKE developed by Schnabel, Lysmer, and Seed (6) was used to calculate strain compatible shear moduli and damping from low strain values was determined from field testing and empirical formulae based on laboratory test data.
The amplified response spectra used in the analysis are based on the methodology described in the report entitled "Soil-Structure Interaction in the Development of Amplified Response Spectra for Beaver Valley Power Station, Unit No. 1." This report was submitted to the NRC by Duquesne Light Company on June 11, 1979.
The licensee now considers that the SSI-ARS forms the present and future design basis for the
plant.
The original ARS is the design basis for work performed prior to NRC approval of the use of the SSI-ARS. B.2.1.4 Dynamic Analysis B.2.1.4.1 Mathematical Model For dynamic analysis, the mathematical model is described as a lumped mass, multi-degree of freedom model. The distributed piping mass is lumped at the system nodal points. The equation of equilibrium for the system is:
Mu" + Cu' + Ku = F (B.2-1)
where: M = Mass matrix for assembled system
C = Damping ma trix for assembled system BVPS UFSAR UNIT 1 Rev. 19 B.2-4 u" = Nodal acceleration vector = u"(t)
u' = Nodal velocity vector = u'(t)
u = Nodal displacement vector = u(t)
F = Applied dynamic forces = F(t) - Mu g for earthquake u g = Ground acceleration = u g (t) This equation is solved for the system dynamic response as follows. First, the frequency, obtained by removing the forcing and damping terms from equation (B.2-1), is solved for the system natural frequencies and mode shapes. Next, the natural mode shapes are used to affect an orthogonal transformation of equation (B.2-1), yielding a series of independent equations of motion uncoupled in the system modes. Then, the uncoupled equations are solved by either the step-by-step integration or the response spectrum method to obtain system response in each mode, and the individual modal results are combined to determine the total system dynamic response. The mathematical formulation of these steps is discussed below. B.2.1.4.2 Natural Frequencies and Mode Shapes The eigenvalues (natural angular frequencies W n) and the eigenvectors (mode shapes n) for each of the natural modes are calculated by solving the frequency equation
[K - W n 2 M] {n} = {0} (B.2-2) where: W n = Natural frequency in n th mode K = Stiffness matrix M = Mass matrix n = Mode shape vector in n th mode 0 = Null vector The eigenvalues and eigenvectors are obtained in NUPIPE using the Householder-QR algorithm (NUPIPE-11M) or subspace iteration (NUPIPE-11L). B.2.1.4.3 Dynamic Response Pre- and post-multiplication of equation (B.2-1) by [], the square matrix of mode shape vectors, constitutes an orthogonal transformation, from which the uncoupled equations of motion shown below are obtained.
Y n + 2W nn Y + W n 2 Y 2 = P n (B.2-3)
BVPS UFSAR UNIT 1 Rev. 19 B.2-5 where: Y n = Generalized (model) displacement coordinate for the n th mode (U n = n Y n) n = Damping ratio for the n th mode expressed as percent of critical damping P n = Generalized force for the n th mode = n T F Solution to these differential equations may be obtained by direct integration, or, for seismic ground motions, by the method of response spectrum superposition. B.2.1.5 Piping Stress Limits The calculated stress of computer analyzed piping are governed by the following allowables:
S LP + S DL S h (B.2-4)
S LP + S DL + (S OL 2 + S OBET 2)0.5 1.2S h (B.2-5) S LP + S DL + (S OL 2 + SDBEI 2)0.5 1.8S h (B.2-6) S E [(1.25S c + 0.25S h) + (S h - S LP + S DL)]f (B.2-7) where: S LP = Stress due to longitudinal pressure S DL = Stress due to moments caused by deadload S h = Allowable stress of material at maximum and/or minimum operating temperature S C = Allowable stress of material at 70F S OL = Stress due to moments caused by occasional loads such as are due to valve actuation, etc.
S OBET = Stress due to moments (half range) caused by the operating basis earthquake. The inertial effects and anchor movement effects are summed absolutely.
S DBEI = Stress due to moments caused by the inertial effects of the Design Basis Earthquake.
S E = Maximum stress due to all moments induced by the constraint of free thermal expansion. f = Fatigue factor based upon the number of thermal cycles. This factor is determined from ANSI B31.1. For the River Water System, a special 4-way fitting (piping cross) was evaluated seismically by combining the seismic anchor movements with S E. This is allowed per ANSI B31.1, 1973. For load combination and stress limits applicable to the pressurizer safety and relief valve piping from the pressurizer to the pressurizer relief tank see Tables B.2-24, B.2-25 and B.2-26. For additional information concerning the use of these equations see Reference 18.
BVPS UFSAR UNIT 1 Rev. 19 B.2-6 Load combinations and stress limits associated with the Reactor Coolant Gas Vent System (RCGVS) piping are in accordance with ASME III, 1989. For load combinations and stress limits applicable to QA Category I piping 2" diameter and smaller, see Tables B.2-27 , B.2-28 , B.2-29 , B.2-30 and B.2-31. B.2.1.6 Buried Seismic Category I Piping Responses of buried Seismic Category I piping to differential ground motion, due to particle motions caused by seismic wave propagations, are calculated by a method developed by N. M. Newmark.
(4) Reactions and bending moments of buried Seismic Category I piping, due to differential motion at structural penetrations, are calculated by considering buried pipe as a semi-infinite beam on elastic soil foundation with full restraint at structural penetrations. Using the maximum expected seismic displacements at structural penetration and the modulus of soil foundation, the stress thus calculated is superimposed with axial tension-compression stress meet the requirements defined in ANSI-B31.1 Code for Pressure Piping. If these stresses are found to be excessive, a seismic design of the underground piping within concrete or steel conduits (unattached to structure) combined with or without expansion joints has been incorporated in the system. B.2.1.7 Interface Between Seismic Category I Piping and Non-Seismic Piping The interface between seismic and non-seismic piping has been addressed in several ways. In general, large non-seismic piping has been routed so as not to create a hazard to smaller seismic piping. In certain cases where this approach was not possible, the normally non-seismic piping was redesignated as seismic and supported as such, e.g. raw water pump discharge piping in the intake structure. Where a seismic/non-seismic break occurs within a piping system, an interface anchor was normally provided to effect separation. Another method utilized was the imposition of building structure or rack steel as barriers between piping systems. B.2.1.8 Pressure Relief Devices The design criteria for most safety/relief valves are in accordance with the rules in paragraph 122.6 of ANSI-B31.1. Maximum stresses on each valve nozzle is calculated based upon its full discharge loads (i.e., thrust and bending) and internal design pressure is also computed by Stone and Webster "PITRUST" computer program. The "PITRUST" computer program is based on Bijlaard's method of calculating local stresses and experimental results.
(5) For Open Relief System
The total steady state discharge thrust load for an open system discharge will be expressed as the sum of the pressure and momentum forces as follows:
F = 144P + V 2 (B.2-8) A 2g where: F = total reaction force (lb)
A = exit flow area (ft
- 2) P = exit pressure (psig)
BVPS UFSAR UNIT 1 Rev. 19 B.2-7 V = exit fluid velocity (ft/sec)
= exit fluid density (lb/ft
- 3) g = 32.2 ft/sec 2 To ensure consideration of the effects of the suddenly applied load, a dynamic load factor is computed by dynamic analysis. The dynamic load factor is based on the relief/safety valve opening time and system characteristics in the absence of slug flow, to be applied to the forces and moments due to the reaction force (F). In the case of open safety or relief valve(s) mounted on a common header and full discharge occurring concurrently, the additional stresses induced in the header is combined with the previously computed local and primary membrane stresses to obtain the maximum stress intensity.
For Closed Relief System For relief valve discharging into closed system, an analytical model of one-dimensional transient flow characteristics following the blow-off of the upstream safety/relief valve into the discharging piping system is established. The time-dependent pressure, temperature, density, velocity, and hence the momentum of the downstream pipe flow, is computed from this conservative hydrodynamic/thermodynamic flow model. Because of the complexity in the valve body structure, such phenomena as flow restrictions and frictional resistance, are considered. This model also considers the influence of valve opening time and the effect of loop seal water contained in the upstream valve seat. The Westinghouse proprietary computer codes ITCHVALVE and FORFUN were used to develop the hydraulic forcing function. This computer code is described in Section B.2.1.11. See Reference 18 for a more detailed description of this
analysis. The unbalanced transient hydraulic forcing function acting on the piping system computed from the flow model is used to determine the transient dynamic responses of the piping structural model. Adapting the lumped-parameter method incorporated with the modal analysis of piping
system, the time history modal response is computed.
B.2.1.9 Simplified Seismic Analysis of Small Size Seismic Category I Piping (Generally less than or equal to 6 inches)
Code Requirements
BVPS-1 is designed to the USAS B31.1 Code for Power Piping (ANSI B31.1.0-1967 including Addenda through and including June 30, 1971). The Code, at that time, contained few specific seismic design rules, essentially requiring that the designer consider the effects of earthquake but falling short of supplying any significant guidance for detailed design.
The Code recognizes the existence of simplified methods within the thermal expansion and flexibility section, and specifically allows their use as follows: approximate or simplified methods may be applied only if they are used for the range of configurations for which their adequate accuracy has been demonstrated. The Code also allows that systems can be qualified without analysis if the system duplicates a successfully operating installation or can be adjudged
adequate by comparison with previously analyzed systems.
BVPS UFSAR UNIT 1 Rev. 19 B.2-8 Development of Simplified Methods for Seismic Category I Piping This section is being maintained in the UFSAR to provide a historical record of the simplified methods performed by Stone and Webster during original plant design and construction.
During the 1979 re-analysis, Seismic Category I piping 2-1/2" diameter to 6" diameter was analyzed in accordance with Section B.2.1.2.
Stone & Webster, largely for economic reasons, initiated during the period 1968-1969, development of simplified piping analysis methods for application to 6 inch and smaller Seismic Category I systems. These rules consisted of (a) seismic methods and (b) flexibility methods. Seismic methods were based on Kellogg, and were intended to keep seismic loads felt by the system low by keeping the fundamental piping frequencies out of the range of the fundamental structural (building) frequency, avoiding the possibility of resonance. Calculations were based on simple beam formulations and control of the piping fundamental frequency was effected by establishing the span length (between supports) of the piping during application of the method. Flexibility methods were similarly based on simple cantilever beam methods, and provided the length of pipe necessary to absorb a given deflection at the free end. The formulations of both methods were available to the analyst in "chart" form (actually nomographs), and were also available in tabular form. Calculation of stress in the pipe was slightly different for each case in that the methodology of application followed a slightly different procedure.
For seismic, if the nomograph indicated that the piping was out of the resonance band of the structure, a "g" value equal to one-half the peak acceleration of the appropriate spectra was applied statically to the system. Tabulations relating various spans, nominal pipe sizes, and acceleration levels to actual pipe stress levels were provided for use by the analyst. The "resonant band" was defined as plus or minus 50 percent of the fundamental structural frequency. In 1971 the "resonant" band concept was revised to address the piping fundamental frequency for a simply supported beam model. Pipe span frequency, taken from nomograph or
manually calculated, was compared to structural frequency. The desired piping frequency was greater than or equal to one and one-half the structural frequency, where a piping acceleration of one-half the peak acceleration was applied. Where this proved impractical or not feasible, the pipe frequency was allowed to fall in the area less than one and one-half the structural frequency but the peak acceleration from the appropriate spectra was applied. Calculated seismic stress was based on an assumed 3 component earthquake. Still later in the design of BVPS-1, a further refinement of the simplified procedure specified the use of a piping span based on deadweight support spans (in accordance with B31.1 Code) and utilized an applied acceleration equal to one and one-half times the peak spectral acceleration if pipe frequency fell into the area below one and one-half times the structural frequency.
For flexibility the nomograph was based on an allowable stress range of 15,000 psi, derived from B31.1 material allowables at temperature, so that the resulting span lengths were "prequalified" for stress.
Support and restraint loadings were based on standardized loadings enveloping the various loading conditions. Equipment nozzle loads were calculated based on similar, simplified
methods.
BVPS UFSAR UNIT 1 Rev. 19 B.2-9 When it is judged practical, computer methods will be used in place of the simplified techniques.
Detailed Application This section is being maintained in the UFSAR to provide a historical record of the stress analysis methods performed by Stone and Webster during original plant design and construction. During the 1979 re-analysis, Seismic Category I piping 2-1/2" diameter to 6" diameter was computer analyzed in accordance with Section B.2.1.2.
For BVPS-1, piping was typically analyzed as follows, with the option of utilizing more rigorous methods available to the analyst.
Nominal Pipe Size Method Where Performed 8 inches and above Rigorous (Computer) Engineering Office 2 1/2 to 6 inches Simplified Engineering Office 2 inches and below Simplified Field Piping 2 inches and below was shown on the piping drawings "diagrammatically" (i.e., without detailed dimensions). The stress engineers located supports during the installation process working at the site with erection isometric sketches. The piping dimensions, including pipe support locations, were added to the piping isometrics.
Simplified Method for QA Category I Piping 2" Diameter and Smaller Simplified methods are used for the evaluation of QA Category I piping 2" diameter and smaller. The methods are similar to those used during original plant design. The methods consist of determining piping span requirements based on deadweight spans as well as seismic spans. Tables are developed utilizing beam formulas and static analysis which define the span requirements. The seismic span criteria for static analysis considers an applied acceleration equal to one and one-half times the peak spectral acceleration for that building and elevation.
If a piping frequency check is performed, and the piping frequency falls above the structure frequency experiencing the peak acceleration, the static evaluation can be performed based on one and one-half times the actual acceleration at that frequency. If the piping is determined to be rigid, (frequency > 33 Hz) the evaluation can be performed based on the actual acceleration at that frequency. The static 1.5 factor does not have to be applied where it can be shown that the entire frequency content and modal participation has been adequately accounted for.
Flexibility methods determine the length of piping offset necessary to absorb a given amount of expansion or deflection. The flexibility tables are based on an allowable stress range derived from material allowables at the operating temperature. The tables follow the expansion stress equation from the 1967 ANSI B 31.1 Code.
Support and equipment loadings are conservatively calculated for use in the support evaluations.
BVPS UFSAR UNIT 1 Rev. 19 B.2-10 It is also permissible to perform computerized analysis on QA Category I piping 2" diameter and smaller. Both simplified methods and computerized analysis will utilize the load combinations presented in Tables B.2-27 , B.2-28 , B.2-29 , B.2-30 and B.2-31. B.2.1.10 Field Run Piping This section is being maintained in the UFSAR to provide a historical record of the field run piping installed during original plant construction. Portions of the piping systems listed below are analyzed using the criteria of Tables B.2-27 , B.2-28 , B.2-29 , B.2-30 and B.2-31. All piping in nominal pipe sizes 2 inch and smaller are field run, with exception of Seismic Category I stainless steel piping in sizes 2 inch and 1 1/2 inch with wall thickness schedule 80 and heavier, which are shop fabricated. Materials for all other 2 inch and smaller piping are designed, fabricated, welded, tested, inspected, and erected at the jobsite in accordance with the requirements of ANSI B31.1-1967 and addenda through and including June 30, 1971. The simplified design analysis procedure for field run piping are described in Section B.2.1.9. None of the Seismic Category I systems are com pletely field run because each system consists of various pipe sizes. Portions of the following Seismic Category I piping systems that are 2 inch NPS and smaller which are field run are listed below:
- 2. Safety Injection
- 3. Containment Depressurization
- 4. Containment Vacuum
- 5. Charging and Volume Control
- 7. Boron Recovery
- 8. Component Cooling
- 9. River Water
- 10. Sample System
- 11. Fuel Pool Cooling and Purification
- 12. Process Radiation Monitoring
- 13. Area Radiation Monitoring
- 14. Fire Protection
- 15. Fuel Handling
- 16. Auxiliary Steam and Air Removal
- 19. Steam Generator Blowdown
- 20. Main Steam
- 21. Feedwater
- 22. Gaseous Waste.
The stress analysis design of field run piping has been initially performed by engineers and
designers located at the site and subsequently independently verified by engineering at Stone & Webster project headquarters in Boston. B.2.1.11 Computer Programs for Seismic Category I Piping Systems The following computer programs were used by Stone and Webster in dynamic and static stress analyses of Seismic Category I piping systems.
A description of each program follows:
NUPIPE NUPIPE-SW, the Stone & Webster version of NUPIPE, was used to re-analyze the Seismic Category I piping systems. NUPIPE-SW performs linear elastic analysis of three-dimensional piping systems subject to thermal, seismic, and dynamic time-history loads. The basic method of analysis used in NUPIPE-SW is the finite element stiffness method. In accordance with this method, the continuous piping is mathematically idealized as an assembly of elastic structural members connecting discrete nodal points.
Nodal points are placed in such a manner as to isolate particular types of piping elements, such as straight runs of pipe, elbows, valves, etc., for which force-deformation characteristics can be categorized. Nodal points are also placed at all discontinuities, such as piping supports, concentrated weights, branch lines, and changes in cross-section. System loads such as weights, equivalent thermal forces, and earthquake inertia forces are applied at the nodal points. Stiffness characteristics of the interconnecting members are related to the effective shear area and moment of inertia of the pipe. The stiffness of piping elbows and certain branch connectors is modified to account for local deformation effects by the flexibility factors suggested in the ASME Section III Code, Articles NB-3600 (Class 1 piping analysis), NC-3600 (Class 2 piping analysis), and ND-3600 (Class 3 piping analysis), and the ANSI B31.1 - 1967
and 1973 Code version piping.
BVPS UFSAR UNIT 1 Rev. 23 B.2-12 The program NUPIPE has been verified for flexibility and stress analysis of nuclear piping by comparison with hand calculations and other computer program analytical solutions. A complete report on the verification was prepared by the Nuclear Services Corporation.
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PITRUST PITRUST is a program to calculate local stresses in the pipe caused by cylindrical welded attachments under external loadings. This program uses the Bijlaard method as published in
WRC-107 (5) to calculate local stresses in the pipe wall caused by cylindrical welded attachments under external loadings, including pressure, dead load, and combinations of maximum seismic
reactions.
Program PITRUST has been verified by comparing its solution of a test problem to the solution of the same problem by an independently written piping local stress program, CYLNOZ, in the public domain. The CYLNOZ piping local stress program was written by Franklin Institute (Philadelphia, PA), and is presently used by engineering companies. The test problem is of a
72.375 inch O.D. x .375 inch thick run pipe, reacting under an external in-lbs. bending and torsional moments transmitted by a 16 inch O.D. nozzle. A comparison of results is tabulated in Table B.2-4 solution of a test problem to the experimental results obtained in Reference 10. A comparison of these results is tabulated in Table B.2-5. PILUG PILUG is a program to calculate local stresses in the pipe wall caused by rectangular welded attachments under external loadings. This program uses the Bijlaard method as described in Reference 5 to calculate local stresses in pipe wall caused by rectangular welded attachments under external loadings, including pressure, dead load and combinations of maximum seismic reactions.
Program PILUG has been verified by comparing its solution to a test problem, to results obtained by hand calculations using the formulations specified in Reference 5. A comparison of results is tabulated in Table B.2-6.
SAVAL SAVAL is a program to calculate stress levels at the junction of a run pipe and safety/relief valve nozzle during discharge of the valve. This program incorporates a subroutine to compute the dynamic load factor for each problem. The combined primary local stresses in the run pipe are obtained from Equation 9 of ANSI-B31.1 Power Piping Code (1973 proposed Summer Addendum). A design option is available which adds reinforcement, if necessary, to reduce stresses to allowable levels.
Program SAVAL has been verified by comparing its solution of a test problem to results obtained by hand calculations. The test problem is illustrated in Figure B.2-7. A comparison of results is tabulated in Table B.2-7 and B.2-8.
BVPS UFSAR UNIT 1 Rev. 23 B.2-13 GAPPIPE The GAPPIPE computer program is a general purpose piping analysis program. GAPPIPE performs both linear and nonlinear elastic analyses of three-dimensional piping systems subject to thermal expansion, imposed displacements, internal pressure, externally applied loads, seismic and fluid transient loads or motions.
GAPPIPE includes the capability to analyze piping systems containing gaps. Two analysis methods are included to compute the dynamic responses of such systems. The first method is nonlinear time history analysis by modal superposition and pseudoforce representation of gap responses. This method is most suitable for the simulation of piping responses induced by fluid transient loads or excitations where the input cannot be easily or adequately characterized by response spectra.
For excitations defined by response spectra, GAPPIPE offers a second analysis method that uses the response spectrum analysis technique and the method of equivalent linearization to account for the nonlinear behavior of gaps. In this method, GAPPIPE can use either uniform enveloped response spectra or different spectra at different supports using the independent support motion technique.
The program GAPPIPE has been verified for stress analysis of nuclear piping. The verification process included comparison to NRC benchmark problems (NUREG/CR-1677) as well as
comparison to test data.
RELAP5/MOD RELAP5/MOD was used to develop the forcing functions for analysis of the piping associated with the pressurizer safety valves and power operated relief valves in event of pressurizer overfill due to spurious operation of the Safety Injection System at power (refer to Section 14.1.16).
The light water reactor (LWR) transient analysis code, RELAP5, was developed at the Idaho National Engineering Laboratory (INEL) for the U.S. Nuclear Regulatory Commission (NRC). The Code uses include analyses required to support rulemaking, licensing audit calculations, evaluation of accident mitigation strategies, evaluation of operator guidelines, and experiment planning analysis. RELAP5 has also been used as the basis for a nuclear plant analyzer. Specific applications have included simulations of transients in LWR systems such as loss of coolant, anticipated transients without scram (ATWS), and operational transients such as loss of feedwater, loss of offsite power, station blackout, and turbine trip. RELAP5 is a highly generic code that, in addition to calculating the behavior of a reactor coolant system during a transient, can be used for simulation of a wide variety of hydraulic and thermal transients in both nuclear and non-nuclear systems involving mixtures of steam, water, noncondensables, and solute.
BVPS UFSAR UNIT 1 Rev. 23 B.2-14 RELAP5/MOD3.3 has been developed jointly by the NRC and a consortium consisting of several countries and domestic organizations that were members of the International Code Assessment and Applications Program (ICAP) and its successor organization, Code Applications and Maintenance Program (CAMP). Credit also needs to be given to various Department of Energy sponsors, including the INEL laboratory-directed discretionary funding program. The mission of the RELAP5/MOD3.3 development program was to develop a code version suitable for the analysis of all transients and postulated accidents in LWR systems, including both large-break and small-break loss of coolant accidents (LOCAs), as well as the full range of operational transients.
The code includes many generic component models from which general systems can be simulated. The component models include pumps, valves, pipes, heat releasing or absorbing structures, reactor point kinetics, electric heaters, jet pumps, turbines, separators, accumulators, and control system components. In addition, special process models are included for effects such as form loss, flow at an abrupt area change, branching, choked flow, boron tracking, and noncondensable gas transport.
B.2.1.12 Use of ASME Code Case N-411 As stated in Section B.2.1.2, the initial design damping values used at Beaver Valley Power Station Unit No. 1 for seismically designed piping and components are 0.5 percent for the operating-basis earthquake (OBE) and 1.0 percent for the design-basis earthquake (DBE).
NUREG 1061, "Report to the USNRC Piping Review Committee" has shown that the use of such low damping values for seismic piping analysis are overly conservative, and recommended the damping values given in ASME Code Case N-411 "Alternative Damping Values for Seismic Analysis of Classes 1, 2 and 3 Piping Sections". These damping values are: five percent below a frequency of 10 Hz; linear reduction from five percent to two percent between 10 Hz and 20 Hz; and two percent above 20 Hz. These damping values would apply for both OBE and DBE cases. The NRC staff has conditionally approved the use of the damping values in ASME Code Case N-411 for piping modifications and future piping stress analyses at Beaver Valley, Unit 1 by letter dated April 8, 1987.
The alternate damping values in ASME Code Case N-411 may be used at Beaver Valley, Unit 1 provided the following conditions are met:
- 1. The alternate damping criteria of this Code Case will be used for seismic analysis in cases where new piping is added, existing systems are modified, existing systems are re-evaluated for new requirements and where existing numbers of snubbers are to be reduced provided that the response mode frequencies are
limited to 33 Hz and below.
- 2. When these alternate damping values are used, they will be used in a given analysis completely and consistently in which current seismic spectra and procedures are employed.
- 3. The damping values will be used in seismic analysis using response spectrum methods and not for seismic analysis using time-history analysis methods.
BVPS UFSAR UNIT 1 Rev. 23 B.2-15 4. When used for reconciliation work or for support optimization of existing designs, the effects of increased motion on existing clearances and on line mounted equipment will be reviewed.
- 5. The alternate damping values will not be used in seismic analyses of piping systems using supports designed to dissipate energy by yielding or piping in which stress corrosion cracking has occurred.
- 6. When these alternate damping values are used, the +
15 percent peak broadening criteria of Regulatory Guide 1.122, "Development of Floor Design
Response Spectra for Seismic Design of Floor-Supported Equipment or Components" will be used.
- 7. When the damping values of Code Case N-411 are used, they will be used in their entirety in a given analysis and shall not be a mixture of Regulatory Guide 1.61 criteria and the alternate criteria of this Code Case.
- 8. For equipment other than piping, the damping values specified in Regulatory Guide 1.61, "Damping Values for Seismic Design of Nuclear Power Plants," should
be used.
- 9. The damping values specified in Code Case N-411 may be used only in analyses which assume an upper bound envelope of the individual response spectra for all support locations to calculate maximum inertial responses of multiply-supported items.
- 10. Where predicted maximum piping displacements using Code Case N-411 criteria exceed the current design calculations by an amount greater than acceptable tolerance levels, a physical verification of the availability of adequate clearance
with adjacent structures, equipment and components must be performed. For equipment mounted on piping, such as valves with extended structures, proper account must be taken for both rotation and translation in arriving at the predicted maximum displacement at the extreme ends of the pipe mounted equipment.
- 11. It must be verified that the operability qualification level of pipe mounted equipment is not exceeded by the predicted response using Code Case N-411.
- 12. Where the existing design loads of piping supports are exceeded by the new loads predicted by the use of Code Case N-411, it must be verified that the new loads do not exceed the design capacity of the supports.
- 13. It must be verified that the cumulative effect of the changes of loads on piping supports that are in turn supported by a structural element of a building, such as
walls, slabs, beams and columns does not exceed the load carrying capacity of the affected structural element.
- 14. A listing of all applications of Code Case N-411 will be maintained by engineering, and the individual files of pipe stress packages re-analyzed using Code Case N-411 will be maintained with its respective Design Change Package (DCP) or Technical Evaluation Report (TER) records.
BVPS UFSAR UNIT 1 Rev. 19 B.2-16 B.2.2 Summary of Stone & Webster Equipment Design Procedures The seismic adequacy of Seismic Category I equipment has been documented. Depending upon equipment location, the basic source of seismic design data will be either the ground response spectra or the amplified response spectra to be derived through a dynamic analysis of the relevant structure (subparagraph B.1.5). New analysis will use the SSI ARS.
These spectra are developed and used for equipment consistent with the damping factors tabulated in Table B.1-3 or as justified by test. The uncertainties in the calculated values of fundamental structural frequencies due to reasonable variations in subgrade and structural properties are taken into account. The peak resonant period value(s) in the amplified response spectra developed as described in Subsection B.1.5 are subject to variations of plus 25 percent and minus 20 percent for this plant and site. Accordingly, equipment designed using these amplified response spectra having modal periods within plus 25 percent and minus 20 percent of the peak resonant period(s) are assigned the peak resonant response value(s). Beyond this range, the amplified response spectra are utilized exactly as shown.
As was discussed in Section B.1.5.3, a review of the original plant ARS with the SSI-ARS indicated that the original plant ARS are conservative based upon the seismic specification of static g values for qualification by static analysis and testing. The review of the original plant ARS indicated that peak resonant responses occurred below 10 Hz and that amplification of ground motion primarily occurred below 20 Hz for structures housing Seismic Category I
equipment. For each building a "cutoff frequency" was selected (i.e., 10 or 20 Hz) in order to identify seismic acceleration levels above and below the cutoff frequency for calculational purposes. The "g" level identified below the cutoff frequency was a minimum of 1.3 times the
peak ARS response.
Equipment having a natural frequency below the cutoff frequency was qualified to an equivalent static acceleration of 1.3 times the peak ARS response. When equipment frequency characteristics were rigid (above the cutoff frequency) the maximum rigid range g values were used. For tested equipment, the maximum rigid range g levels were conservatively used for qualification.
These requirements pertain to all Seismic Category I equipment regardless of industry code.
The requirements for seismic qualification are intended to either supplement existing industry
analytical requirements where applicable, or to provide documentation of component adequacy to combined normal plus earthquake loads where no documentation requirements existed at the time of the qualification.
All acceleration ("g") factors and analyses are based on elastic analysis exclusively.
Stress limits for Stone & Webster supplied Seismic Category I piping systems are specified in B.2.1.5.
Stress limits as outlined above were utilized in the qualification of all Seismic Category I components. No limits were imposed which allowed inelastic deformation on any Code Class A
or B component.
BVPS UFSAR UNIT 1 Rev. 23 B.2-17 Generally, no distinction is made for normal, upset, emergency, and faulted plant conditions in accordance with ASME III requirements for Class A, B, and C components. The combination of normal operating loads and Operating Basis Earthquake loads, which may be considered analogous to the normal and upset plant conditions, were kept within applicable code limits. Specification requirements for the combination of normal operating loads and Design Basis Earthquake loads, which may be considered analogous to the emergency and faulted plant conditions, allowed stress level to reach 90 percent of the minimum yield strength of the
material as an upper limit.
The three principal categories of documentation considered are:
- 1. Static Analysis
- 2. Dynamic Analysis
- 3. Testing B.2.2.1 Static Analysis Static analysis is utilized for equipment that can be characterized as a relatively simple structure. This type of analysis involves the multiplication of the equipment or component total weight by the specified seismic acceleration component (direction dependent loading) to produce forces that are applied at the center of gravity in the horizontal and vertical directions.
A stress analysis of equipment components such as feet, hold-down bolts, and other structural
members, is performed to determine their adequacy.
In the specification of equipment for static analy sis, two or more sets of acceleration data are provided, the choice of which set to use being dependent upon the fundamental equipment natural frequency. For the particular or "worst" equipment location, the relevant response curves are reviewed to determine a "cutoff frequency" which bounds the rigid range from the resonance range of the response curves. Components having fundamental natural frequencies above the cutoff frequency are analyzed to rigid range response accelerations. For components having a fundamental natural frequency below the cutoff frequency, analysis is based on response accelerations that are not less than those indicated by the curves over the full frequency range of the component. If the fundamental mode of the component falls within any of the "broadened" resonant response peaks existing in the component frequency range, the resonant response acceleration is increased by 30 percent as an arbitrary factor for conservatism in order to account for all significant dynamic modes under a resonant situation.
Method of Analysis
Those components which are considered relatively simple or rigid are designed, by virtue of natural frequency calculations, to withstand the effects of amplified seismic acceleration values dependent upon frequency and amplitude ranges associated with the relevant amplified response spectrum. Analysis of components to the peak value of resonant response is considered conservative since fundamental natural frequencies do not generally coincide with the frequency at resonance of the relevant response curve. Components having fundamental natural frequencies within the broadened response peak are designed to peak acceleration values, increased by a factor of 1.3, or as justified to account for the contribution of all significant dynamic modes under a resonant condition. Generally, the vibratory characteristics of the components qualified by "resonant static analysis" (relatively simple) is such that no possibility BVPS UFSAR UNIT 1 Rev. 19 B.2-18 exists for adjacent or multiple modes to exist within the relatively narrow peak of the response spectrum.
Peak broadening is intended to reflect a range of uncertainty in the precise location of the resonant peak of the response curve and not to indicate that the multiple peak resonant response is possible within this broadened range. What is concluded is that there is a fairly equal chance that the peak of the curve (singular) would fall in the specified range and thus what, in fact, exists is a "family" of resonant response curves, each having only one point of peak resonant response (Figure B.2-1). If more than one system or component mode of vibration falls within the broadened peak, one and only one mode (a presumed "worst case")
can be presumed at an actual response peak value (Figure B.2-2). All other possible modes would realistically respond to lower values. Using the simple vibration theory and some simplifying assumption, it is shown that a factor of 1.3 is conservative.
A simple damped oscillator responds with a transmissibility:
TR1(2W/W)[1(W/W)][2W/W]
n 2 n 22 n 2 (B.2-9)
The value of TR is sensitive to both the damping value and the assumed placement and spacing of the number of modes around the peak considered.
For instance, if only one mode is considered, the value of TR is as defined above and is equal to the value of the peak of the amplified response spectrum curve (single degree of freedom system).
As more modes are added around the nominal W n mode K will increase. It is easily concluded that the most conservative placement of assumed modes is with one mode on the "peak" and others centered around this peak.
Data is presented in Figure B.2-3 which proves that the factor 1.3 is conservative for all potential equipment applications. The curves are developed for two "planes" representing five modes, and nine modes assumed acting within broadening resonant peak. These numbers are intended to show an upper bound for general equipment application. Equipment damping values of 0.5 percent and 1.0 percent are used for static analyses. Higher damping is shown to indicate the trend and the full conservatism of this approach.
As further conservatism, all modes are considered equally participating. This is never the case in dynamic analysis. The higher frequencies of the component are given equal weight to the fundamental resonant frequency and the modes are centered on the "nominal" response curve. If the fundamental frequency were placed on the peak of the nominal curve, the results would show even lower transmissibilities.
As has been stated, the factor 1.3 is applicable only for those components whose fundamental natural frequency falls within the broadened response peak. Broadening generally spans ranges from +10 percent to 25 percent. A sample calculation of this method is given in Table B.2-10.
BVPS UFSAR UNIT 1 Rev. 19 B.2-19 It is shown that for the range of values associated with component and system static analysis, use of the 1.3 factor is conservative. In fact for a predominant number of likely cases a value far less than this can and should be justified on the bases of this data. For example, a value of 1.1 could easily be justified for most components which present only a few significant modes of vibration within the broadened response peak. It is further emphasized that, in reaching these conclusions, the most conservative (and generally improbable) assumptions regarding the location of the nominal response curve and the placement of response modes for the arbitrary
component, have been made.
Verification of Analysis As a conclusive supplement to the discussion above a study was performed utilizing rigorous dynamic analysis of models closely representative of typical components. This investigation consisted of computing the ratio of maximum dynamic stress to maximum static stress; i.e., the factor denoted by K for several model beams subject to a flat response and typical amplified response spectra. Since bending stress is dominant for frame/equipment constructions, the actual ratio employed equals KMaxdynamicmomentMaxstaticmoment Both the square root of the sum of the squares (SRSS) and absolute (ABS) moments are computed for comparison purposes, but conclusions are based solely on SRSS moments because they most closely represent actual dynamic stress.
Maximum static moment corresponds in the case of the l "g" flat response, to a l "g" static load.
In the case of a typical amplified response, the maximum static load is based upon the following frequency relationships (refer to Figure B.2-4).
f o f p, g = max (peak acceleration) (B.2-11) f o > f p, g = acceleration at f o (B.2-12)
where: f o = the fundamental frequency of the model beam f p = the peak frequency; i.e., the frequency at which the peak acceleration occurs. The effect of "peaking spreading" is investigated by using a flat response, thus giving all modes the same acceleration. This is equivalent to infinite peak spreading. The importance of the uncertainty in the location of the peak acceleration with respect to the fundamental mode of the model beams is examined by adjusting the fundamental frequency from well below to well above the peak resonant frequency of a typical response spectrum.
The model beams selected for this verification are shown in Figure B.2-5. These beams are typical of the frames and equipment combinations used in nuclear power plants. All dynamic analyses were conducted using the STRUDL computer program. Static analyses were carried out by hand, except for the simple/fixed beam with overhang. Consistent with design practice, all mountings are assumed rigid.
BVPS UFSAR UNIT 1 Rev. 19 B.2-20 Table B.2-11 summarizes the results for l "g" flat response applied to the model beams of Figure B.2-5. Three K factors were computed for comparison purposes:
Ks/cMaxSRSSdynamicmomentMaxstaticmomentfromconcentratedload (B.2-13)
Ks/uMaxSRSSdynamicmomentMaxstaticmomentfromuniformload (B.2-14)
Ka/uMaxABSdynamicmomentMaxstaticmomentfromuniformload (B.2-15)
All conclusions are based on K s/u because it most closely represents the actual ration of dynamic moment to static moment. K a/u was not so chosen because, as can be seen in Table B.2-12 modes are so widely spaced that no more than one modal frequency lies within a +
10 percent frequency band. K s/c is shown since this is the K factor which represents a typical simplification used in component analysis (concentrated static loads at component center of
gravity).
The 1 "g" flat response was selected to give infinite peak spreading. As can be seen, K s/u was never significantly greater than unity.
Table B.2-13 presents the results for the simply supported/fixed model beam with 33 percent overhang subjected to the response spectra of Figure B.2-4. The column entitled 1st Mode in Table B.2-13 gives the fundamental frequency (f o) and response acceleration (g o) at f o. Note that f o was adjusted (by density variation) from well below to well above the peak frequency (f p) of the response spectra to determine the effect on K of the uncertainty in the location of the peak frequency with respect to the fundamental frequency of the model beam. Since all values of K s/u were less than equity, it is concluded that this uncertainty has no important effects on the K factor.
It was concluded from the verification study that:
- 1. Peak acceleration times 1.3 applied as a static load to equipment whose fundamental natural frequency is within the broadened peak of the amplified
response spectra curve is conservative.
- 2. No amount of peak spreading can itself result in a K s/u factor significantly greater than unity.
- 3. Uncertainty in the frequency at which the peak response acceleration occurs itself has no important effects on the K factor.
- 4. Multiple supported continuous spans are not included in the scope of this study. Components or equipment which make up a system of continuous multiple span supports will utilize a factor no less than 1.5 times peak acceleration as in Item 1
above, if applicable.
BVPS UFSAR UNIT 1 Rev. 19 B.2-21 B.2.2.2 Dynamic Analysis A detailed dynamic analysis is performed when component complexity or dynamic interaction precludes static analysis, or when static analysis is too conservative.
Modeling To describe fully the behavior of a component subjected to dynamic loads, infinite number of coordinates would be required. Since calculation at every point of a complex model is impractical, the analysis is simplified by a judicious selection of a limited number of mass points. The "lumped mass" of the "consistent mass" approach is employed in the dynamic analysis. In the lumped and in the consistent mass idealization, the main structure is divided into substructures and the masses of these substructures are concentrated at a number of discrete points. The nature of these substructures and the stiffness properties of the corresponding modeling elements determine the minimum spacing of the mass points and the degrees of freedom to associate to each point. In accordance with the minimum spacing requirements, the analyst can then choose for the model, particular mass points which reflect predominant masses of components which are believed to give significant contribution to the total response.
In cases for which some dynamic degrees of freedom do not contribute to the total response, static or kinematic condensation is employed in the analysis.
Method of Analysis
The normal mode approach is employed for seismic analysis of components. Natural frequencies, eigenvectors, participation factors, and model member-end forces and moments of the undamped structure are calculated. The system of equations which describe the free vibrations of an n-degree of freedom, undamped structure is
[M] {x"} + [K] {x} = 0 (B.2-16) where: [M] = mass matrix
[K] = stiffness matrix
{x}, {x"} = displacement, acceleration vectors The mode shapes and frequencies are solved in accordance with:
[KWM]{}0 n 2 n (B.2-17)
W n = frequency of the n th mode {}n = mode shape vector for the n th mode Eigenvector, eigenvalue extraction routines such as Householder-QR, Jacobi Reduction and Inverse Iteration are used depending upon the total number of dynamic degrees of freedom and
the number of modes desired.
BVPS UFSAR UNIT 1 Rev. 19 B.2-22 For each mode, the participation factor for the specific direction is defined by:
n{}[M]{D}i{}[M]{}i T T (B.2-18) where: {}T = transpose of mode shape vector for the n th mode {D} = earthquake direction vector referring to direction i The modal member-end forces and moments are determined by:
{F M}n = [KM] {}n (B.2-19) where: [KM] = member stiffness matrix
For each modal frequency, the corresponding response acceleration is determined for a given level of equipment damping from the applicable response curve.
The maximum response for each mode is found by computing:
{x"}nRn{}iin (B.2-20)
{x'}1 W{x"}n n (B.2-21)
{x}1 W{x"}n 2 n (B.2-22)
{F}Rn W{F}n ni n 2 mn (B.2-23) where: {x"}
n 1 {x'}n 1 {x}n {F}n are the modal acceleration, velocity, displacement and member-end force and moment vectors respectively. Rn is the spectral acceleration for the nth mode in the i direction.
Before combining seismic response, a search is made for modes with adjacent closely spaced
frequencies.
If no such modes are found, the total combined seismic results are obtained by taking the square root of the sum of the squares (SRSS) of each parameter under consideration.
BVPS UFSAR UNIT 1 Rev. 19 B.2-23 B.2.2.3 Testing Equipment that is tested is qualified in accordance with Stone & Webster general instructions for Earthquake Requirements. For tested equipment these S&W Requirements either supplement
other applicable industry standards (such as "IEEE Guide for Seismic Qualification of Class I Electric Equipment for Nuclear Power Generation Stations," STD-344-1971) or provide guidance for testing where no such codes are available. Equipment packages or components are shown adequate either by being tested individually, as part of a simulated structural section, or as part of an assembled module or unit. In any case, the minimum acceptance criterion must
include:
- 1. No loss of function, or ability to function, before, during, or after the proposed test
- 2. No structural/electrical failure (i.e., connections and anchorages) which would compromise component integrity
- 3. No adverse, or dysfunctional, operation before, during or after the proposed test that could result in an improper safety action.
Equipment vendors and suppliers are required to formulate a program for qualifying the equipment in accordance with the conditions specified in Stone & Webster's general instructions for Earthquake Requirements. The vendor must submit a summary of the proposed effort to
Stone & Webster for approval.
General testing guidance criteria specified for components include the following:
- 1. A frequency scan (standard logarithmic sweep) at a constant acceleration level is performed for as much of the range between 2 and 100 Hz as practicable or justified. The objective of this test is to determine the natural frequencies and amplification factors of the tested equipment and its critical components or appurtenances and to assure general seismic adequacy over the full frequency range of interest. The acceleration inputs used are the maximum rigid range accelerations indicated by the relevant response spectrum curves (damping)
independent.
BVPS UFSAR UNIT 1 Rev. 23 B.2-24 2. A "dwell test" of the equipment at its fundamental natural frequency is included at the acceleration values specified in Item 1 above. Additionally, other frequencies are selected if amplification factors of 2.0 or more are indicated. A 20 to 60 second duration is considered acceptable for each "dwell." 3. The test is conducted in three orthogonal directions individual or in a manner that adequately represents vertical and horizontal forcing simultaneously for each of two orthogonal horizontal directions.
Qualification programs for random or sinusoidal beat excitation are considered acceptable alternatives to the sinusoidal vibration test criteria outlined above. Also given consideration are laboratory shock results, in-shipment shock data, or adequate historical dynamic adequacy data (i.e., previous relevant test or environmental data). The method of test selected must demonstrate the adequacy of principal structural and functional components of the equipment. B.2.2.4 Specification Requirements Within these three general categories, all Seismic Category I equipment furnished will be shown to meet the requirements for the Operational Basis Earthquake and Design Basis Earthquake. There is no requirement that a Design Basis Earthquake (DBE) and a Design Basis Accident (DBA) be considered simultaneously for accident analysis purposes. The following discussion
applies to safety-related SSC design considerations only.
Operating Basis Earthquake (OBE)
Equipment is designed to be capable of continued operation with the normal operating loads acting simultaneously with both horizontal and vertical components of the Operating Basis seismic loadings. Horizontal and vertical seismic loads are added considering a horizontal direction earthquake acting concurrently with the vertical direction earthquake. One more direction of the horizontal earthquake is considered on a "most severe basis." The stress levels due to these combined loading conditions are kept within maximum working stress limits
permitted under applicable design standards, AISC Manual of Steel Construction, ASME Boiler and Pressure Vessel Code, AWWA Standards, or other codes or specifications. If no codes are used, the stress level under the combined loading is limited to 90 percent of the minimum yield
strength of the material per the ASTM relevant Specification.
The equipment is designed to withstand the combined effects of the normal operating loads acting simultaneously with DBE loads without loss of function or structural integrity. Horizontal and vertical seismic loads are added considering a horizontal direction earthquake, again on the "most severe basis." It is permissible to allow strain limits in excess of yield strain in safety-related components during the DBE and under postulated concurrent conditions, provided the necessary safety functions are maintained. These limits would be defined and utilized only with reference to specific design codes, such as ASME Section III, which allow such limits for this
loading.
BVPS UFSAR UNIT 1 Rev. 19 B.2-25 Coupled Items In the course of analysis, a comparison of relative mass and stiffness properties between connected components is performed. If this comparison indicates that the possibility of dynamic interaction is small, the interface is assumed to be an anchor. In order for this to be valid, the natural frequencies of connected components must be separated by a factor equal to or greater than 2, and the floor connected component (related to amplified response curve) be nonresonant.
If, however, adverse dynamic coupling is concluded to be possible, the problem is resolved by two general methods. Either additional restraints are provided to suitably alter stiffness parameters, and thus dynamically uncouple the system, or the analytical model is formulated to include the connected components interface loads (specifically nozzle loads) for inclusion in
component adequacy documentation.
Seismic Design of Category I Instrumentation and Electrical Equipment
Seismic Category I instrumentation and electrical equipment are designed to maintain their capability to:
- 2. Withstand seismic disturbances during post accident operation Instruments and electrical equipment are seismically qualified in accordance with Stone &
Webster's general instructions for Earthquake Requirements. These Stone & Webster Requirements generally impose the requirements of the IEEE Codes, such as IEEE STD-344-1971 even though this code was nonexistent during the purchase cycle of most Seismic Category I electrical equipment. Equipment of this type may be tested as an individual component, as part of a simulated structural section, or as part of a completely assembled module or unit.
The response of racks, panels, cabinets, and consoles is considered in assessing the capability of instrumentation and electrical equipment. Mounted components are tested, as a minimum, to acceleration levels consistent with those transmitted by their supporting structure. A design objective is to minimize amplification of floor acceleration by supporting members to mounted
components.
Determination of amplification and seismic adequacy of instruments and electrical equipment is implemented by the analysis and testing methods outlined previously.
Dynamic System Analysis and Testing
All Seismic Category I mechanical equipment such as fans, pumps, and heat exchangers are qualified as seismically adequate in accordance with the criteria and procedures outlined previously. Generally all equipment is specified for qualification in the operating mode unless it can be shown that an alternative condition is a more severe case. Compliance with these criteria is intended to assure that the equipment will function when subjected to seismic loading.
BVPS UFSAR UNIT 1 Rev. 19 B.2-26 In Generic Letter 87-02 (19), the NRC staff set forth the process for resolution of Unresolved Safety Issue (USI) A-46 and encouraged licensees to participate in a generic program to resolve the seismic verification issues associated with USI A-46. As a result, the Seismic Qualification Utility Group (SQUG) developed the "Generic Implementation Procedure (GIP) for Seismic Verification of Nuclear Plant Equipment," Revision 2. Beaver Valley Unit 1 committed (Reference 21) to follow the SQUG commitments set forth in GIP-2, including clarifications, interpretations and exceptions identified in the NRC Supplemental Safety Evaluation Report.(20) Reference 22 provided a summary report of the implementation results of the USI A-46 program at BVPS-1. The NRC concluded (Reference 23) that the Beaver Valley Unit 1 USI A-46 Implementation Program, in general, met the purpose and intent of the criteria in GIP-2 and the NRC SSER(20) for the resolution of USI A-46.
Air handling cooling units are specified to be furnished in accordance with ARI and AMCA Codes and Standards. Fans are specified to be furnished in accordance with AMCA Standards. Damper assemblies are not furnished in accordance with any code or standard.
Safety related cooling units, fans, and damper assemblies are analyzed or tested to specified seismic criteria to confirm structural integrity and functional capability during earthquake conditions. Electrical components are subject to ambient temperature limited to 104F. This type of equipment is of standard industrial design and has proven reliable over many years of use. Operating conditions for the equipment will not exceed past performance criteria as there are no safety related cooling units, fans, or dampers assemblies located within the
containment.
Seismic Category I cranes have been dynamically analyzed to ensure structural adequacy. In addition, restraints have been designed and installed to prevent cranes from becoming dislodged during an earthquake.
Seismic Design Control
Components and equipment requiring seismic input are specified in Table B.1-1. When equipment specifications are prepared a check is made to ensure that they are in full compliance with the FSAR. All designers and vendors of Seismic Category I equipment are provided with the necessary seismic information for the design and verification of components and equipment. This information is either amplified (floor) acceleration data (in the form of either response spectra or acceleration "g" constants) or dynamic model data necessary to incorporate coupling effects.
Stone & Webster designed and purchased components not specifically affecting structural response are specified in accordance with these Stone & Webster procedures. All vendor-supplied documentation is reviewed by Stone & Webster to insure component adequacy with
respect to current criteria. The vendors proposed methods for documenting seismic adequacy are reviewed prior to implementation and reviewed in detail for approval upon submittal of completed documentation.
BVPS UFSAR UNIT 1 Rev. 23 B.2-27 B.2.2.5 Computer Programs for Seismic Category I Equipment The following computer programs were used by Stone & Webster in dynamic and stress analyses for Seismic Category I Stone & Webster designed equipment:
A description of each program follows.
TAC2D TAC2D is a general purpose two-dimensional heat transfer computer code. It is a finite difference computer code. It can be used to determine steady-state and transient temperatures in two-dimensional problems. The configuration of the body to be analyzed is described in the rectangular, cylindrical, or circular (polar) coordinate system by orthogonal lines of constant coordinate called grid lines. These grid lines specify an array of nodal elements. Nodal points are defined as lying midway between the bounding grid lines of these elements. A finite-difference equation is formulated for each nodal point in terms of its capacitance heat generation, and heat flow paths to neighboring nodal points. The equations for all the nodal points are assembled and solved using an implicit alternating gradient algorithm. TAC2D(11) is a recognized program in the public domain.
A sample problem is presented to compare the results from TAC2D with an analytical solution in Table B.2-15. The objective is to show that the TAC2D program yields the correct solution.
A comparison of the output from the code with the series solution is shown in Figure B.2-9. The temperature versus time function is plotted at three representative points within the cylinder. It can be seen that the results from TAC2D are almost identical to the series solution results. The maximum difference between the two sets of results is about 2F out of a mean magnitude of 100F.
BVPS UFSAR UNIT 1 Rev. 19 B.2-28 ASAAS This is a finite element computer code. It can be used to determine stresses and displacements in arbitrary axisymmetric solids, including problems involving asymmetric mechanical and thermal loads and asymmetric temperature-dependent mechanical properties. All dependent variables, including the mechanical properties, are input by "Fourier Series" expansions of the circumferential coordinate. The mechanical loads can be surface pressures, surface shears, and nodal point forces.
The explicitly defined stiffness relations for the axisymmetric solid ring elements of triangular cross section are based on the classical theorem of potential energy and the assumption that within any element the displacement variation in the R-Z plane is linear. All dependent variables, including the material properties, are expanded into "Fourier Series." The harmonics are coupled and all the equilibrium equations are solved simultaneously. The algorithm used to solve the equations is a block modified square root "Cholesky Method with Iterative Refinement." ASAAS(12) is a recognized program in the public domain.
A sample problem is presented in Table B.2-16. The computer results are very close to the exact results. Therefore, this problem serves to verify that the accuracy of ASAAS for mechanical loading problems where material properties are not variable.
Vessel Penetration Analysis
This computer code performs various analyses on tanks and pressure vessels. All of the analyses are concerned with local stresses at penetrations. Typical problems which can be handled include the following:
- 1. Applied load stresses at vessel-nozzle junction for:
- a. Rigid attachment to cylinder
- b. Rigid attachment to sphere
- c. Hollow attachment to sphere
- 2. Pressure discontinuity analysis for thin shell interaction
- 3. Allowable load functions on nozzles for each case
- 4. Area compensation analysis in accordance with ASME Code
- 5. Maximum forces on supports of vessel based on allowable loads on nozzles.
Local stresses due to nozzle loads are found by the method of P.P. Bijlaard.
(5) The method of "Johns and Orange" is used for pressure discontinuity stresses.
BVPS UFSAR UNIT 1 Rev. 23 B.2-29 A sample problem, described in Table B.2-17, consists of a thin-walled cylindrical vessel subjected to applied loads from a rigid cylindrical attachment. A solution of this problem may be obtained by the use of Reference 5. A summary of the manual calculations is presented in Table B.2-18. The computer calculations are summarized in Table B.2-19. As can be seen, the computer results are very close to the exact results. Therefore, this problem serves to verify the accuracy of "Vessel Penetration Analysis."
SHELL 1 This is a finite-difference stress analysis computer code. It can be used to determine the forces, moments, shears, displacements, rotations, and stresses in a thin shell of revolution subject to arbitrary loads expanded in "Fourier Series" of up to 150 terms. Single-layer shells with up to 30 simply connected branches may be analyzed. Poisson's Ratio may change at discontinuity points, and Young's Modulus and the thermal coefficient of expansion may be different at each point. The allowed types of loading include elastic restraints, pressures in three orthogonal directions, temperature changes which may have a gradient through the shell thickness, and simplified input for weight of the shell or earthquake forces.
The equilibrium equations for a thin shell are based on the linear theory of Sanders. Sanders' equations are expanded and modified slightly to handle a broader range of problems. All pertinent load, stresses, and deformation variables are expanded into Fourier Series. The individual Fourier components of stress and deflection are found separately by solution of the finite-difference forms of the appropriate differential equations. The algorithm used to solve these equations is a minor modification of the Gaussian elimination method.
A sample problem is described in Table B.2-20. The cylinder is idealized by 10 elements as shown in Figure B.2-12. The computer results compared to exact calculations in Table B.2-20 were favorable. As can be seen, the problem serves to verify the accuracy of SHELL 1.
Stress Analysis of Shells of Revolution
This is a finite element computer code. It can be used to determine the forces, moments, shears, displacements, rotations and stresses in a thin shell of revolution subject to axisymmetric loads. Different orthotropic material properties may be input for each element in a model. The allowed types of loading include internal pressure, temperature changes which may have a gradient through the shell thickness, and simplified input for weight of the shell.
The explicit stiffness relations for the axisymmetric shell elements are based on the classical theory of potential energy and the usual approximations of thin shell theory. The direct stiffness method (a simple modification of the displacement method) is employed to assemble the equilibrium equations. The algorithm used to solve these equations is derived by applying the "Gauss-Jordan" method of elimination to a Tri-diagonal System of equations.
A sample problem is described in Table B.2-21. The cylinder is idealized by 10 elements as shown in Figure B.2-12. The computer results compared to hand calculations in Table B.2-21 were favorable.
BVPS UFSAR UNIT 1 Rev. 19 B.2-30 SAAS III This is a finite element computer code. It can be used to determine displacements, stresses, and strains in axisymmetric and plane solids with different orthotropic, temperature-dependent material properties in tension and compression including the effects of internal pore fluid pressures and thermal stresses. The mechanical loads can be surface pressures, surface shears, and nodal point forces, as well as acceleration or angular velocity.
The explicit stiffness relations for the two-dimensional solid elements of triangular cross section are based on the classical theorem of potential energy and the assumption that within any element the displacement variation in the place is linear. The stiffness matrix is assembled in a band form. A simplified "Gaussian Elimination Method," which takes advantage of the concentration of the elements of the stiffness matrix along the main diagonal, is the algorithm
used to solve the equilibrium equations. SAAS III (14) is a recognized program in the public domain.
The well-known Lame cylinder solution for an elastic isotropic material is used to check the answers obtained by use of the SAAS III program. The cylinder is idealized by four elements as
shown in Figure B.2-13. The computer results are shown on Table B.2-22 along with the exact results obtained by the use of Reference 15. As can be noted from the table, the computer results are very close to the exact results. Even better results, however, can be obtained by the use of more elements in the radial direction.
STARDYNE The STARDYNE Structural Analysis System, written by Mechanics Research, Inc., of Los Angeles, California, is a fully warranted and documented computer program available at Control Data Corporation's 600 data centers. The latest version of this program became available
September 1, 1972.
The MRI STARDYNE Analysis System consists of a series of compatible digital computer programs designed to analyze linear elastic structural models. The system encompasses the full range of static and dynamic analyses. The static capability includes the computation of structural deformations and member loads and stresses caused by an arbitrary set of thermal, modal applied loads, and prescribed displacements. Utilizing the normal mode technique, dynamic response analyses can be performed for a wide range of loading conditions, including transient, steady-state harmonic, random and shock spectra excitation types. Dynamic response results can be presented as structural deformations and internal member loads.
PISCES The PISCES, written by Physics International Scientific Codes and Engineering Services of San Diego, California, is a fully supported and well-documented computer code available at Control
Data Corporation.
Physics International's PISCES computer program utilizes state-of-art techniques to solve complex problems in fluid-structure interaction, explosion effects, gas and fluid dynamics, and impact and penetration. The unique and powerful feature of the PISCES is the ability to apply the most accurate and efficient numerical schemes to the different regimes of a given problem and then couple them together in space and time.
BVPS UFSAR UNIT 1 Rev. 19 B.2-31 ST-167 Free Vibration Analysis of Undamped Systems This computer program, written at Stone & Webster Engineering Corporation, is designed to calculate eigenvectors, eigenvalues, and participation factors of vibrating systems whose mass matrix contains off-diagonal terms.
Free vibration analysis of undamped systems is represented by the following system of equations:
[M] {(t) } + [K] {(t) } = 0 (B.2-28) Assuming that (t) = eiwt , the above equation can be written as
[M] -1 [K] {} = W 2 {} (B.2-29) which is in the form of the classical characteristic value problem. However, if [M] contains off-diagonal elements, the matrix [M]
-1 [K] is, in general, a nonsymmetric matrix.
Eigenvalues are extracted by transforming matrices to the upper Hessenberg form and using the QR transformation by Francis. Eigenvectors are extracted using J. H. Wilkinson's approach. Participation factors are calculated using eigenvectors and the mass matrix as shown by J. M. Biggs in his book "Introduction to Structural Dynamics." A sample problem comparing the results of hand calculations and the ST-167 output is presented in Table B.2-23.
BVPS UFSAR UNIT 1 Rev. 19 B.2-32 References for Section B.2
- 1. American National Standard Code for Pressure Piping ANSI-B31.1 American Society of Mechanical Engineers (1971).
- 2. Deleted by Revision 0, January 1982.
- 3. Deleted by Revision 0, January 1982.
- 4. N. M. Newmark and E. Rosenblueth, Fundamentals of Earthquake Engineering, Section 10.6 and 16.5, Prentice-Hall (1971).
- 5. K. R. Wichman, et al, "Local Stresses in Spherical and Cylindrical Shells due to External Loadings," Welding Research Council Bulletin WRC-107 (December 1968).
- 6. P. B. Schanbel, J. Lysmer, and H. B. Seed, "SHAKE: A Computer Program for Earthquake Response Analysis of Horizontally Layered Sites," Earthquake Engineering Research Center, Report No. EERC72-12 (December 1972 as modified for SWEC Computer System in Program ST211 Version 2 Level 0).
- 7. "NUPIPE Computer Program Verification" Revision 1, Nuclear Services Corporation (August 3, 1976).
- 8. "Nuclear Power Plant Components," American Society of Mechanical Engineers, Boiler and Pressure Vessel Code,Section III, (1971, including all addenda up to Winter, 1972).
- 9. Deleted by Revision 15, January 1997.
- 10. "Experimental Elastic Stress Analysis of Cylinder to Cylinder Shell Models and Comparison with Theoretical Predictions," J. M. Corum and W. L. Greenstreet, First International Conference on Structural Mechanics in Reactor Technology, Berlin, Preprints Volume 3, Part G, (1971).
- 11. J. F. Peterson, "TAC2D - A General Purpose Two-Dimensional Heat Transfer Computer Code," GA-9262, Gulf General Atomic Inc. (September 6, 1969).
- 12. T. G. Crose, "ASAAS Asymmetric Stress Analysis of Axisymmetric Solids with Orthotropic Temperature-Dependent Material Properties that Can Vary Circumferentially," Air Force Report No. SAMSO-TR-71-297 Aerospace Report No. TR-
0172 (S2816-15)-1 (December 29, 1971).
- 13. Deleted by Revision 15, January 1997.
- 14. J. G. Grose and R. M. Jones, "SAAS III Finite Element Stress Analysis of Axisymmetric and Place Solids with Different Orthotropic, Temperature-dependent Natural Properties in Tension and Compression," Air Force Report No. SAMSO-TR-71-103, Aerospace
Report No. TR0059 (S6816-53)-1, (June 22, 1971).
BVPS UFSAR UNIT 1 Rev. 19 B.2-33 References for Section B.2 (CONTD)
- 15. S. Timoshinko and J. N. Goodier, Theory of Elasticity, McGraw-Hill Book Company, Inc., New York, N. Y., pp 58-60 (1951).
- 16. A Reanalysis of Safety-Related Piping Systems, Interim Report for Beaver Valley Power Station Unit 1; Submitted to the NRC April 20, 1979.
- 17. Program Verification on File at Stone & Webster Engineering Corporation, Boston, Mass.
- 18. Duquesne Light Company to NRC submittal concerning NUREG-0737, Item II.D.1, Pressurizer Safety and Relief Line Piping and Support Evaluation, dated June 24, 1983.
- 19. NRC Generic Letter 87-02, "Verification of Seismic Adequacy of Mechanical and Electrical Equipment in Operating Reactors, Unresolved Safety Issue (USI) A-46," dated February 19, 1987.
- 20. USNRC "Supplemental Safety Evaluation Report No. 2 on Seismic Q ualification Utility Groups Generic Implementation Procedure, Revision 2, corrected February 14, 1992,"
dated May 22, 1992.
- 21. Duquesne Light Company letter to USNRC, "Response to Supplement 1 to Generic Letter 87-02, SQUG Resolution of USI A-46," dated September 22, 1992.
- 22. Duquesne Light Company letter to USNRC, "Generic Letter 87-02, Summary Report for Resolution of USI A-46," dated January 31, 1996, and Attachment 1, "Beaver Valley Power Station, Unit 1, USI A-46 Seismic Evaluation Report."
- 23. USNRC letter to Duquesne Light Company, "Safety Evaluation for USI A-46 Program Implementation at Beaver Valley Power Station, Unit No. 1 (BVPS-1)," dated December 9, 1998.
BVPS UFSAR UNIT 1 Rev. 19 B.2-34 Bibliography for Section B.2.2.5
- 1. R. H. Johns, T. W. Orange, "Theoretical Elastic Stress Distributions Arising from Discontinuities" and "Edge Loads in Several Shell-Type Structures," National Aeronautics and Space Administration Technical Report R-103 (1961).
- 2. J. L. Sanders, Jr., "An Improved First Approximation Theory for Thin Shells," National Aeronautics and Space Administration Technical Report R-24.
- 3. B. Budlansky, P. P. Radkowski, "Numerical Analysis of Unsymmetrical Bending of Shells of Revolution," AIAA Journal 1 , 1833 (March 1964).
- 4. G. Greenbaum, "Comments on Numerical Analysis of Unsymmetrical Bending of Shells of Revolution," AIAA Journal 2 , 590 (March 1964).
- 5. P. E. Grafton and D. R. Strome, "Analysis of Axisymmetric Shells by the Direct Stiffness Method," AIAA Journal 1 , No. 10 (1963).
- 6. J. H. Percy, T. H. H. Pian, S. Klein and D. R. Navaratna, "Application of Matrix Displacement Method of Linear Elastic Analysis of Shells of Revolution," AIAA Paper No.65-142 (January 1965).
- 7. R. Anderson, Fundamentals of Vibration, The MacMillan Company, New York, p. 774 (1967).
BVPS UFSAR UNIT 1 Rev. 19 B.3-1 B.3 WESTINGHOUSE NUCLEAR STEAM SUPPLY SYSTEM B.3.1 Seismic Category Definitions Equipment and equipment supports of the Nuclear Steam Supply System are classified into seismic categories equivalent to those contained in Section B.1. This category assignment is considered in the design, material aspects, manufacture and fabrication, and assembly stages.
A single system may have components in more than one category. B.3.2 Equipment List Components are listed in Table B.3-1 according to the seismic category definitions of Section B.1. The ASME Code is mandatory.
A summary of the seismic requirement for each category is provided in Table B.3-2. B.3.3 Design Philosophy In addition to the loads imposed on the system under normal operating conditions, the design of equipment requires that consideration also be given to abnormal loading conditions such as an earthquake. Two types of seismic loadings are considered: Operational Basis Earthquake (OBE) and Design Basis Earthquake (DBE).
For the OBE loading condition, the Nuclear Steam Supply System is designed to be capable of continued safe operation. Therefore, for this loading condition, equipment is required to operate within design limits. The design for normal plus DBE and the normal plus DBE plus DBA loading condition is intended to provide a margin in design that ensures capability to shutdown
and maintain the nuclear facility in a safe condition.
In this case, it is only necessary to ensure that critical equipment does not lose capability to perform its safety function. This has come to be referred to as the "no-loss-of-function" criteria and the loading condition as the "Design Basis Earthquake" loading condition.
Not all critical components have the same requirements to ensure no loss of function. For
example, rotating equipment must not seize and piping and vessels must retain their contents
and allow fluid flow.
The seismic design of Seismic Category I mechanical components is covered in the remainder of this Appendix. The seismic evaluation of Seismic Category I instrumentation and electrical equipment is covered in Section 7.2.1.
Seismic Category II equipment is not covered because it is not essential to safe shutdown and isolation of the reactor and its failure would not result in the release of substantial amounts of radioactivity. Non-seismic equipment is not designed for seismic disturbance.
It should be noted that BVPS-1 equipment was designed to the 1965 and 1968 versions of Section III of the ASME Code. A simple approach was sought to evaluate the adequacy of forces or stresses obtained from a conservative elastic analysis for Faulted Condition loadings. The stresses therein obtained frequently exceed yield values for relatively short periods of time. These brief excursions into the plastic range do not affect the integrity of the system. The
design "Stress Limits for Various Load Combinations" and the "Loading Conditions and Stress
Limits" are presented in Tables B.3-3 and B.3-4.
BVPS UFSAR UNIT 1 Rev. 23 B.3-2 B.3.4 Seismic System Analysis B.3.4.1 Analysis of Seismic Category I Mechanical Equipment The seismic response of Seismic Category I piping and component within Westinghouse scope of responsibility is determined as part of a multi-degree of freedom model which includes the support characteristics. This model is a multi-mass mathematical representation of the system.
A sufficient number of masses are included to ensure an accurate determination of the dynamic response. A single mass model is used to determine vertical response loads for the seismic design when justified by the equipment design characteristics and/or the conservatism of the assigned loadings.
Horizontal and vertical seismic umbrella spectra are generally prepared which encompass the floor response spectra at the elevations where the piping system attaches to the building structure. The system is analyzed for the simultaneous occurrence of these horizontal and vertical seismic input motions. The results for the vertical direction are added absolutely to the results of the worse of those for the North-South and East-West directions. The umbrella spectra are compared with the horizontal and vertical floor response spectra developed to assure conservatism of the spectra used in the analysis.
In a coupled system with different structural elements, either the lowest damping value of the system is used for all modes, or equivalent modal damping values are determined according to the energy distribution in each mode. Damping values used are given in Table B.1-3.
The materials employed in systems under Westinghouse scope of supply are standard. The material properties which can effect a variation in modal period are well known, and the known variation in these properties does not account for any measurable or significant shift in period or increase in seismic loads.
Details of the response spectrum analysis are described in Section B.3.5. B.3.4.2 Analysis of Reactor Vessel Internals Nonlinear dynamic analysis of the Reactor Pressure Vessel (RPV) system (RPV, internals, and fuel) includes the development of the system finite element model and the synthesized time history accelerations.
The basic mathematical model for seismic analysis is essentially similar to LOCA models in that the seismic model includes the hydrodynamic mass matrices in the vessel/barrel annulus to account for the fluid-solid interactions. The RPV system finite element model for the nonlinear time-history seismic analysis consists of three concentric structural sub-models connected by nonlinear impact elements and linear stiffness matrices. The first sub-model represents the reactor vessel shell and its associated components. The reactor vessel is restrained by reactor vessel supports and by the attached primary coolant piping. The reactor vessel support system in the system finite element model is represented by stiffness matrices.
The second sub-model represents the reactor core barrel, thermal shield, lower support plate, tie plates, and the secondary support components. These sub-models are physically located inside the first, and are connected to them by stiffness matrices at the vessel/internals interface.
Core barrel to reactor vessel shell impact is represented by nonlinear elements at the core barrel flange, upper support flange, core barrel outlet nozzles, and the lower radial restraints.
BVPS UFSAR UNIT 1 Rev. 23 B.3-3 The third and innermost sub-model represents the upper support plate assembly consisting of guide tubes, upper support columns, upper and lower core plates, and the fuel. The fuel assembly simplified structural analysis model incorporated into the RPV system model preserves the dynamic characteristics of the entire core. For each type of fuel design the corresponding simplified fuel assembly model is incorporated into the system model. The third sub-model is connected to the first and second by stiffness matrices and nonlinear elements.
As mentioned above, fluid-structure or hydroelastic interaction is included in the reactor pressure vessel model for seismic evaluations. The horizontal hydroelastic interaction is significant in the cylindrical fluid flow region between the core barrel and the reactor vessel annulus. Mass matrices with off-diagonal terms (horizontal degrees of freedom only) attach between nodes on the core barrel, thermal shield, and the reactor vessel. The diagonal terms of the mass matrix are similar to the lumping of water mass to the vessel shell, thermal shield, and core barrel. The off-diagonal terms reflect the fact that all the water mass does not participate when there is no relative motion of the vessel and core barrel. It should be noted that the hydrodynamic mass matrix has no artificial virtual mass effect and is derived in a straightforward, quantitative manner.
The matrices are a function of the properties of two concentric cylinders with the fluid in their cylindrical annulus, the density of the fluid, and the length of the cylinders. Vertical segmentation of the reactor vessel and the core barrel allows inclusion of radii variation along their heights and approximates the effects of beam mode deformation. These mass matrices were inserted between the selected nodes on the core barrel, thermal shield, and the reactor vessel. The seismic evaluations are performed by including the effects of simultaneous application of time-history accelerations in three orthogonal directions. The WECAN computer code that is used to determine the response of the reactor vessel and its internals is a general purpose finite element code. In the finite element approach, the structure is divided into a finite number of discreet members or elements. The inertia and stiffness matrices, as well as the force array are first calculated for each element in the local coordinates. Employing appropriate transformations, the element global matrices and arrays are assembled into global structural matrices and arrays, and used for dynamic solution of the system equations.
B.3.5 Seismic Subsystem Analysis B.3.5.1 Analysis of Seismic Category I Mechanical Equipment The typical Westinghouse supplied Category I mechanical components are checked for seismic adequacy as follows:
- 1. If a component falls within one of the many categories which has been previously analyzed using a multi-degree-of-freedom model and shown to be relatively rigid, then the equipment specification for that component is checked to ensure that the specified values are smaller than those used in the previous analysis.
- 2. If the component cannot be categorized as similar to a previously analyzed component that has been shown to be relatively rigid, then an analysis is
performed as described below.
BVPS UFSAR UNIT 1 Rev. 23 B.3-4 Seismic analysis of typical Westinghouse supplied Seismic Category I mechanical equipment including heat exchangers, pumps, tanks, and valves are analyzed using a multi-degree-of-
freedom modal analysis. Appendages, such as motors attached to motor operated valves, are included in the models. The natural frequencies and normal modes are obtained using analytical techniques developed to solve eigenvalue-eigenvector problems. A response spectrum analysis is then performed using horizontal and vertical umbrella spectra that encompass the appropriate floor response spectra developed by Stone & Webster. The simultaneous occurrence of horizontal and vertical motions are included in the analyses. The combined modal seismic response is obtained by adding the individual modal responses by the square root of the sum of the squares method. Combined modal response for closely spaced modal frequencies whose eigenvectors are orthogonal are handled in the above mentioned manner. In the rare event when two significantly closely spaced modal frequencies
occur and their eigenvectors are parallel, the combined modal response is obtained by adding the square root of the sum of the squares of all other modes to the absolute value of one of the closely spaced modes.
Hydrodynamic analysis of tanks is performed using the methods described in Chapter 6 of the "U.S. Atomic Energy Commission - TID-7024." Bridge and trolley structures are designed so that restraints prevent derailing due to the DBE. The manipulator crane is designed to prevent disengagement of a fuel assembly from the gripper under the DBE.
The reactor coolant system components and supports, except piping, which is addressed in Section 2 of this Appendix, are designed for the loading combinations and stress limits given in Table B.3-3. The loading conditions are categorized with respect to Normal, Upset, Emergency and Faulted condition. Stress intensity limits for each of the loading conditions is presented in Table B.3-4. Valves in sample lines are not considered to be part of the reactor coolant system boundary because nozzles connect to the reactor coolant system through a 3/8 inch hole. This hole restricts the flow such that loss through a severance of one of these lines can be made up by normal charging. B.3.5.2 Analysis of Reactor Vessel Internals The core internals are dynamically analyzed using the methods described in Section B.3.4.2.
Results of the nonlinear Design Basis Earthquake (SSE) dynamic analysis include the transient displacements and impact loads for various elements of the mathematical model. These displacements, impact loads, and linear component loads (forces and moments) are then used for detailed component evaluations to assess the structural integrity of the reactor vessel, reactor internals, and the fuel. Note that the linear component forces and moments are not the direct output from the modal superposition analysis, but rather are obtained by post-processing the data saved from the nonlinear time-history analysis. From the modal analysis (free vibration analysis), the system eigenvalues (frequencies) and eigenvectors (modal shapes) are stored for later use in the modal superposition analysis. The validity of a complex system structural model is generally verified by comparing the calculated fundamental frequency of the system with the available test data frequency.
BVPS UFSAR UNIT 1 Rev. 19 B.3-5 The criterion for normal plus OBE loadings is that the stresses are limited to those given by the ASME Nuclear Power Plant Components Code for upset conditions. These limits are intended to assure that the reactor will be able to continue or resume operation. For the normal plus DBE and the normal plus DBE plus Design Basis Accident loading conditions, the criteria core coolant and core shutdown must be assured. This implies that the deformation of the reactor internals must be sufficiently small so that the geometry remains substantially intact.
Consequently, the limitations established on the internals are concerned principally with the maximum allowable deflections and/or stability of the parts in addition to a stress criterion to assure integrity of the components. The deflections and stresses caused by the DBE are small in comparison to those caused by the DBA. B.3.5.3 Analysis of Fuel Assemblies, Control Rods Assemblies, and Control Rod Drives Fuel assembly component stresses induced by horizontal seismic disturbances are analyzed through the use of computer modeling. The time history floor response, based on a standard seismic time history normalized to Design Basis Earthquake levels is used as the seismic input. The reactor internals and the fuel assemblies are modeled as spring and lumped mass systems. The seismic response of the fuel assemblies is analyzed to determine design adequacy.
Detailed discussion of the analyses performed for a typical fuel assembly may be found in
WCAP 7950 (2). The control rod drive mechanisms (CRDM) are seismically analyzed to confirm that system stresses under seismic conditions do not exceed allowable levels as defined by the ASME Boiler and Pressure Vessel Code,Section III for "Upset" and "Faulted" conditions. Based on these stress criteria, the allowable seismic stresses and resultant bending moments in the structure are determined. The CRDM is mathematically modeled as a system of lumped and distributed masses. The model is analyzed for the applicable seismic loads and bending moments along the length of the CRDM. These values are then compared to the previously calculated allowable seismic bending moments for the equipment to assure adequacy of the
design. B.3.6 Criteria for Seismic Instrumentation Program Seismic instrumentation is discussed in Section 5.2.8.1. B.3.7 Seismic Design Control Measures The following procedure is implemented for Westinghouse supplied Seismic Category I mechanical equipment that fall within one of the many categories which have been analyzed as described in Sections B.3.4 and B.3.5 and has been shown to be relatively rigid with all natural
frequencies greater than 30 Hz:
- 1. Equivalent static acceleration factors for the horizontal and vertical directions are included in the equipment specification. The vendor must certify the adequacy of the equipment to meet the seismic requirement as described in Section B.3.5.
- 2. The floor response spectra are developed and the cognizant engineer responsible for the particular component checks to ensure that the acceleration values are less than those given in the equipment specification.
BVPS UFSAR UNIT 1 Rev. 23 B.3-6 Design control generally is discussed in detail in Appendix A. B.3.8 Code Classes A tabulation of components and applicable code classes is shown in Table B.3-5 "Equipment Code and Classification List". B.3.9 Computer Programs used in Dynamic and Static Analysis The following computer programs have been used in dynamic and static analysis by Westinghouse to determine mechanical loads, stresses, and deformations of Seismic Category I components and equipment.
A description of the basis, capabilities, and extent of application of each program follows. A series of solutions of test problems is included for the WESTDYN program along with comparisons to hand calculations, other computer programs, and/or experimental results. Verification of the remaining programs was provided in the form of a topical report which was submitted in early April 1974.
WESTDYN (or WESDYN-7)
WESTDYN, a Westinghouse adaption of the A. D. Little Company program (3), is a special purpose program for the static and dynamic analysis of redundant piping systems with arbitrary loads and boundary conditions. It computes, at any point in the piping system, the forces, deflections, and stresses that result from the imposed anchor or junction loads, thermal gradients in the system, and gravity loads, in any combination of the three orthogonal axes.
The piping system may contain a number of sections, a section being defined as a sequence of straight and/or curved members lying between two network points. A network point is:
- 1. A junction of two or more pipes
- 2. An anchor or any point at which motion is prescribed
- 3. Any arbitrary point.
Any location in the system may sustain prescribed loads or may be subject to elastic constraint in any of its six degrees of freedom. For example, hangers may be arbitrarily spaced along a section and may be of the rigid, flexible, or constant force type.
The response to seismic excitation is analyzed by normal mode, response spectral superposition technique with a lumped mass system. The eigenvalue routines used are the Jacobi rotation and the Givens-Householder schemes (4). The maximum spectral acceleration is applied for each mode at its corresponding frequency from response spectra to obtain the amplitude of the modal coordinate for each mode. A basic assumption is that the maximum modal excitation of each mode occurs simultaneously. The forces, deflections, support reactions, and stresses are calculated for each significant mode. The total response is computed by combining the contributions of the significant modes by several methods, one of
which is the square root of the sum of the squares method.
BVPS UFSAR UNIT 1 Rev. 23 B.3-7 The applicability and validity of the WESTDYN program has been demonstrated by running test problems and comparing the results from this program with the results of hand calculations, other programs, etc. A summary of five test problems are presented in Tables B.3-13, B.3-14, B.3-15, B.3-16 and B.3-17. A complete verification of this program was supplied in a topical report of April, 1974.
FIXFM FIXFM is a digital computer program which determines the time-history response of a three-dimensional structure excited by arbitrary, time varying forcing functions. The input for FIXFM (obtained from the WESTDYN program) consists of normalized mode shapes, natural frequencies, forcing functions, and an initial deflection vector. The program sets up the modal
differential equations of motion. The modal differential equations are solved numerically by a predictor-corrector technique of numerical integration. The modal contributions are then summed at various mass points throughout the structure to obtain the actual time-history response. FIXFM, like WESTDYN, is applied to redundant piping systems.
WESDYN-2 WESDYN-2 is a slightly modified version of the WESTDYN program. The program treats the input of time-history displacement vectors at mass points (from FIXFM) as an imposed deflection condition and proceeds to a usual WESTDYN static solution. In addition to the usual stress solution, the program also calculates axial stress, shear stress, and stress intensity.
STHRUST The STHRUST code computes hydraulic loads on primary loop components from the blowdown information calculated by the SATAN (5) code, i.e., density, internal energy, and mass flow rate. The entire primary system, including special elements such as the reactor core, pressurizer, and accumulators, is represented by the same two-loop model employed in the SATAN blowdown calculation.
BVPS UFSAR UNIT 1 Rev. 19 B.3-8 The force nodes are selected along the two-loop geometric model of a reactor plant where the vector forces and their components in a global coordinate system are calculated. Each force node is associated with a control volume which may contain one or two blowdown (SATAN) control volumes depending on the location of the force node in the system. Each force control volume, in turn, has one or two associated apertures (flow areas). STHRUST calculates the
time-history of forces at locations where there is a change in either direction or area of flow
within the RCL.
The major input information required for the code is:
- 1. Blowdown hydraulic information which is read directly from the SATAN result tape
- 2. The orientation of the force node in the system which is input as three projection coefficients along the three coordinate axes of the global coordinate system.
STRUDL STRUDL, part of the ICES Civil Engineering Computer System (6), is a general purpose matrix structural analysis program which can solve for stresses and deflections of structures subjected
to static or thermal loads. The basis of the program is the general beam finite element. It is applicable to linear elastic two- and three-dimensional frame or truss structures, e.g., steam generator lower, steam generator upper lateral, and reactor coolant pump lower support structures. STRUDL employs the stiffness formation and is valid only for small displacements.
Structure geometry, topology, and element orientation and cross-section properties are described in free format. Member and support joint re leases, such as pin and rollers, are specified. Otherwise, six restraint components are assumed at each end of each member and at each support joint.
The STRUDL system performs structural stability and equilibrium checks during the solution process and prints error messages if these conditions are violated. However, the system cannot detect geometry or topology errors. Type, locations, and magnitude of applied loads or displacements are specified for any number of loading conditions. These can be combined as desired during the solution process.
One important feature of STRUDL is that any desired changes, deletions, or additions can be made to the structural model during the solution process. This produces results for a number of structure configurations, each with any number of loading conditions.
The output includes member forces and distortions, joint displacements, support joint reactions, and member stresses.
BVPS UFSAR UNIT 1 Rev. 23 B.3-9 THESSE The THESSE computer program was developed by Westinghouse to accomplish RCL equipment support structures analyses and evaluation. Two versions are used:
- 1. One for normal and upset condition loading using AISC-69 allowable stress equations
- 2. One for faulted condition loading which LOCA loads are read in time-history form and ultimate stress equations are used.
Westinghouse has expanded the output capabilities of STRUDL to include selective punched
card data that is used as input in the THESSE program. The input includes:
- 1. Six components of forcing acting on the support structure for each of the thermal, weight, pressure, seismic, and LOCA loadings
- 2. Member geometry and material
- 3. 6 x 6 member influence coefficient array for each end of each member.
Loads on the structure are combined, transformed to the structure-coordinate system, and multiplied by member influence coefficients. The resulting member forces are then used with member properties in stress and interaction equations to determine the adequacy of each member in the structure. THESSE calculates all member internal forces and moments and determines when the highest stresses occur in each member. These maximum stresses are expressed as a ratio of the maximum stress to the limiting values.
WECAN & WECAN PLUS WECAN, a one-, two-, and three-dimensional finite element program capable of solving elastic-plastic static structural problems, transient and steady-state thermal problems, and linear and nonlinear dynamic structural problems. Its library of finite elements includes spars, beams, pipes, plane and axisymmetric triangles, three-dimensional solids, plates, plane and axisymmetric shells, three-dimensional shells, friction interface elements, springs, masses, dampers, thermal conductors, hydraulic conductors, convection elements, and radiation elements.
WECAN is capable of predicting mode shapes and natural frequencies, maximum response to harmonic excitation, or complete time-history response to arbitrary forcing functions. The matrix displacement method is applied to each finite element in the idealized structure. A "wave front" direct solution technique is employed to give accurate results in a minimum of computer time.
The analysis solution output includes geometry plots, nodal displacements, element stresses, and nodal forces.
BVPS UFSAR UNIT 1 Rev. 23 B.3-10 ITCHVALVE and FORFUN The Westinghouse proprietary computer code ITCHVALVE was used to perform the transient hydraulic analysis for the pressurizer safety and relief valve piping system. This program uses the Method of Characteristics approach to generate fluid parameters as a function of time. One-dimensional fluid flow calculations applying both the implicit and emplicit characteristic methods are performed. Using this approach the piping network is input as a series of single pipes. The network is generally joined together at one or more places by two- or three-way junctions. Each of the single pipes has associated with it friction factors, angles of elevation, and flow areas.
The computer program possesses special provisions to allow analysis of valve opening and closing situations.
Fluid acceleration inside the pipe generates reaction forces on all segments of the line that are bounded at either end by an elbow or bend. Reaction forces resulting from fluid pressure and momentum variations are calculated. These forces can be expressed in terms of the fluid properties available from the transient hydraulic analysis performed using program ITCHVALVE.
Unbalanced forces are calculated for each straight segment of pipe from the pressurizer to the relief tank using program FORFUN. The time-histories of these forces are stored on tape to be used for the subsequent structural analysis by Westinghouse using the FIXFM3 and WESDYN2 proprietary computer programs for the pressurizer safety and relief lines.
ITCHVALVE and FORFUN were compared with test data. Piping load data has been generated from the tests conducted by EPRI at the Combustion Engineering Test Facility. Pertinent tests simulating dynamic opening of the safety valves for representative commercial upstream environments were carried out. The resulting downstream piping loadings and responses were measured. Upstream environments for particular valve opening cases of importance, which envelope the commercial scenarios, are:
- 1. Cold water discharge followed by steam - steam between the pressure source and the loop seal - cold loop seal between the steam and the valve, 2. Hot water discharge followed by steam - steam between the pressure source and the loop seal - hot loop seal between the steam and the valve, 3. Steam discharge - steam between the pressure source and the valve.
Specific thermal hydraulic and structural analyses have been completed for the Combustion Engineering Test Configuration.
The applicability of the ITCHVALVE and FORFUN computer programs for calculating the fluid-induced loads on the piping of the pressurizer safety and relief valves has been demonstrated. For a more detailed description of ITCHVALVE and FORFUN see Reference 7.
ANSYS ANSYS is a general purpose finite element program with structural and heat transfer capabilities. ANSYS was used for structural and thermal analysis of the replacement steam generators. The code is a commercial software product.
BVPS UFSAR UNIT 1 Rev. 23 B.3-11 References for Section B.3
- 1. Deleted by Revision 23.
- 2. L. T. Gesinski, "Fuel Assembly Safety Analysis for Combined Seismic and Loss-of- Coolant Accident", WCAP-7950, Westinghouse Electric Corporation (July, 1972).
- 3. Dingwell, I. W. and Bradshaw, R. T., "Static, Thermal, Dynamic Pipe Stress Analysis Operating Manual," Arthur D. Little, Inc.
- 4. Greenstadt, J., "The Determination of the Characteristic Roots of a Matrix by the Jacobi Method," Chapter 7 of Mathematical Methods for Digital Computers , John Wiley, New York, (1959).
- 5. Bordelon, F. M., "A Comprehensive Space-Time Dependent Analysis of Loss of Coolant," (SATAN-IV Digital Code), WCAP 7750, Westinghouse Electric Corporation (August 1971).
- 6. Logcher, R. D., and Flachsbart, B. B., "ICES STRUDL-II, The Structural Design Language Frame Analysis," MIT-ICES-R68-91, Volume 1, Massachusetts Institute of Technology (November 1968).
- 7. Duquesne Light Company to NRC submittal concerning NUREG-0737, Item II.D.1. Pressurizer Safety and Relief Line Piping and Support Evaluation, dated June 24, 1983.
BVPS UFSAR UNIT 1 TABLES FOR APPENDIX B
BVPS UFSAR UNIT 1 Rev. 19 1 of 7 Table B.1-1 STRUCTURES AND SYSTEMS REQUIRING DESIGN FOR SEISMIC LOADING The following Seismic Category I structures and components are designed to resist the seismic loading described in Appendix B:
STRUCTURES
Containment Structure
Reinforced Concrete Substructure Reinforced Concrete Superstructure Reinforced Concrete Interior Shields and Walls Steel Plate Liner Piping, Duct, and Electrical Penetrations and Shield Wall Personnel Access Hatch Equipment Access Hatch Cable Vault and Cable Tunnel
Pipe Tunnel to Containment from Auxiliary Building
Main Steam Valve Area Pump Room below Main Steam Valve Area
Safeguards Areas
Safeguards and Main Steam Valve Area Ventilation Rooms
Primary Auxiliary Building
Reinforced Concrete Substructure Steel Superstructure Fuel Building
Reinforced Concrete Substructure Steel Superstructure Spent Fuel Storage Racks Fuel Handling Trolley Support Structure
Duct Lines and Manholes to Intake Structure and Diesel Generator Building
BVPS UFSAR UNIT 1 Rev. 27 2 of 7 Table B.1-1 (CONT'D)
STRUCTURES AND SYSTEMS REQUIRING DESIGN FOR SEISMIC LOADING Portions of Service Building
Main Control Room Emergency Switchgear and Relay Room Battery Rooms Cable Tray Area in Service Building Cable Tunnel Air Conditioning Equipment Room for Control Room Diesel Generator Building Primary Grade Water Pump Room (adjacent to diesel enclosure)
River Water Pumps and Engine-Driven Fire Pump Intake Structure Waste Gas Storage Area Coolant Recovery Tank Structure Demineralized Water Storage Tank Enclosure and Mat Refueling Water Tank Mat Caustic Tank Mat (note: Caustic Tank retired in place) Quench Spray Chemical Addition Building
SYSTEMS AND COMPONENTS Containment Isolation Valves - Containment Isolation Valves and Associated Piping
Reactor Coolant System Steam Generators Steam Generator Supports Reactor Coolant Pumps Reactor Coolant Pump Supports Reactor Coolant Pump Oil Collection System Pressurizer and Pressurizer Heaters Pressurizer Support Top Segment of Pressurizer Thermal Insulation Pressurizer Safety Valves Inlet Piping Insulated Enclosures Reactor Vessel Reactor Core Support Structure Reactor Control Rod Guide Structure Fuel Assemblies Control Rod and Drive Shaft Assemblies Incore Instrumentation Thimbles Reactor Vessel Supports and Neutron Shield Tank Control Rod Drive Mechanisms Reactor Coolant Piping, Valves, and Supports Reactor Coolant Bypass Piping, Valves, and Supports Pressurizer Surge Line Pressurizer Spray Lines, Valves, and Supports Pressurizer Safety and Relief Valves Piping BVPS UFSAR UNIT 1 Rev. 27 3 of 7 Table B.1-1 (CONT'D)
STRUCTURES AND SYSTEMS REQUIRING DESIGN FOR SEISMIC LOADING Safety Injection System
Accumulators and Supports Boron Injection Tank Low Head Safety Injection Pumps and Piping All Other Piping, Valves, and Supports
Containment Depressurization System
Quench Spray Subsystems Refueling Water Storage Tank Quench Spray Pumps Chemical Addition Tank (retired in place) Quench Spray Chemical Injection Pumps (retired in place) All Piping, Valves, and Supports Associated with and Connecting above Components (portions retired in place)
Recirculation Spray Subsystems Recirculation Spray Pumps and Piping Recirculation Spray Heat Exchangers Reactor Containment Sump and Screens All Other Piping, Valves, and Supports
Containment Vacuum and Leakage Monitoring System
Open Pressure Taps up to and Including Capped Tubing Outside Containment
Chemical and Volume Control System Boric Acid Tanks Boric Acid Transfer Pumps Boric Acid Blender Charging/Safety Injection Pumps Regenerative Heat Exchanger Nonregenerative Heat Exchanger Reactor Coolant Filter Volume Control Tank Seal Water Heat Exchanger Seal Water Filter Seal Water Injection Filters Excess Letdown Heat Exchanger Piping, Valves, and Supports Associated with above Components
Residual Heat Removal System
Residual Heat Removal Pumps BVPS UFSAR UNIT 1 Rev. 19 4 of 7 Table B.1-1 (CONTD)
STRUCTURES AND SYSTEMS REQUIRING DESIGN FOR SEISMIC LOADING Residual Heat Exchangers All Piping, Valves, and Supports
Component Cooling System Primary Plant Component Cooling Water Heat Exchangers Primary Plant Component Cooling Water Pumps Component Cooling Surge Tank Piping, Valves, and Supports Associated with above Components and Following:
Lines to and from Residual Heat Exchangers and Residual Heat Removal Pump Seal Coolers Lines to and from Fuel Pool Heat Exchangers 8 In., 18 In., and 24 In. Headers and in Lines to and from Components not Listed above up to and including Second Automatic Isolation Valve
Fuel Pool Cooling System
Fuel Pool Pumps Fuel Pool Heat Exchangers Piping, Valves, and Supports Associated with above components
River Water System River Water Pumps All River Water Piping, Valves, and Supports to Seismic Category I Components
Sample System Primary Coolant and Blowdown Sample Lines to and including Containment Isolation Valve Outside Containment
Fire Protection System
Engine Drive Fire Pump and Line with Associated Valves and Supports to River Water System
Fuel Handling System Manipulator Crane in Containment Movable Platform with Hoist in Fuel Building Fuel Handling Trolley in Fuel Building Fuel Transfer Tube with Blind Flange Reactor Cavity Seal (installed position) Refueling Cavity Cofferdam in Containment BVPS UFSAR UNIT 1 Rev. 26 5 of 7 Table B.1-1 (CONTD)
STRUCTURES AND SYSTEMS REQUIRING DESIGN FOR SEISMIC LOADING Auxiliary Steam and Air Removal System
Containment Isolation Valves and Piping in between
Vent and Drain System
Containment Isolation Valves and Piping in between
Ventilation and Air Conditioning Supplementary Leak Collection and Release System Containment Purge System Isolation Valves and Duct Work Between Valves River Water Pump Area Ventilation System Diesel Generator Building Ventilation System Air Conditioning System for Control Room Area Ventilation Vent Stack
Main Steam System
Steam Piping from Main Steam Lines to Turbine Driven Steam-Generator Auxiliary Feedpump Main Steam Piping from Steam Generators to and including Main Steam Nonreturn Valve, including Trip Valves Feedwater System
Primary Plant Demineralized Water Storage Tank Steam Generator Auxiliary Feedpumps Following Piping, Valves and Supports: From Primary Plant Demineralized Water Storage Tank to Steam Generator Auxiliary Feedpumps From Steam Generator Auxiliary Feedpumps to Steam Generator Feed Lines Steam Generator Feed Lines Inside Containment to and including First Containment Isolation Valve Outside Containment
Steam Generator Blowdown System
Steam Generator Blowdown Piping, Valves, and Supports Inside Containment to and including Containment Isolation Valves Outside Containment and Piping/Components Up to the First Pipe Support in the Cable Vault (El. 722'6")
BVPS UFSAR UNIT 1 Rev. 20 6 of 7 Table B.1-1 (CONTD)
STRUCTURES AND SYSTEMS REQUIRING DESIGN FOR SEISMIC LOADING Gaseous Waste Disposal System
Charcoal Delay Beds Decay Tanks Compressors Surge Tank Waste Gas Piping, Valves, and Supports from the Charcoal Delay Beds inlet and bypass valve up to and including Isolation Valve Downstream of Decay Tanks Process Radiation Monitoring System
Recirculation Spray Heat Exchanger River Water Monitors Fuel Building Ventilation Exhaust Monitors Containment Purge Exhaust Monitors
Area Radiation Monitoring System
Main Control Room Monitor Main Control Room Radiation Monitoring System Cabinets Instrumentation and Control
All Instrumentation and Control Required During a Design Accident or Controlled Shutdown Reactor Protection Safety Injection Containment Isolation Phases A and B Feedwater Isolation Steam Line Isolation Steam Generator Water Level Control System Electrical System
Emergency Diesel Generators Station Service Batteries and Chargers for Seismic Category I Components Vital Bus and Vital Bus Inverters 480 V Emergency Unit Substation for Seismic Category I Components 4160 V Emergency Station Service Switchgear for Seismic Category I Components Control Panel Boards for Seismic Category I Components D-C Switchboards and Distribution Panel for Seismic Category I Components Emergency Motor Control Centers
BVPS UFSAR UNIT 1 Rev. 26 7 of 7 Table B.1-1 (CONTD)
STRUCTURES AND SYSTEMS REQUIRING DESIGN FOR SEISMIC LOADING Motors for Seismic Category I Components Emergency Shutdown Panel Main Control Board Heat Tracing of Seismic Category I Piping and Tanks All Cable to Components, Instruments, and Controls Required During a Design Accident or Controlled Shutdown
Emergency Diesels
Fuel Oil Day Tanks Fuel Oil Transfer Pumps Underground Fuel Oil Storage Tanks Emergency Diesel Generator Cooling System Fuel Oil Piping, Valves, and Supports to Emergency Diesel Generators, except Fill Lines for Underground Fuel Oil Storage Tanks
Hydrogen Analyzers
Hydrogen Analyzers (0-10%) including Tubing, Valves and Supports inside the Cable Vault Areas
Miscellaneous
Reactor Containment Crane (not operating) Fuel Building Crane (not operating) Reactor Cavity Seal Storage Rack (vertical & horizontal positions)
Reactor Containment Jib Cranes (not operating) -
CR-42 and 44 Reactor Containment Auxiliary Crane (not operating)
(See also, Table B.3-1 for NSSS Fluid Systems/Components)
BVPS UFSAR UNIT 1 Rev. 19 1 of 1 Table B.1-2 DISTRIBUTION OF DAMPING VAL UES (PERCENT OF CRITICAL)
Contribution from Summation of Contribution from Rigid Body Motion Modal Mode Flexural Motion in Subgrade Damping Containment Internal Structure Structure Translation Rocking 1 0.11 0.0089 6.69 3.62 10.4 2 ---
--- 34.7 2.1 36.8 3 1.32 0.62 0.017 0.58 2.5 4 0.57 1.36 1.10 0.73 3.8
BVPS UFSAR UNIT 1 Rev. 19 1 of 1 Table B.1-3 DAMPING FACTORS Type and Condition Percentage of Stress Level of Structure of Component Critical Damping 1. Low stress, well below proportional limit.
Stresses below 0.25 yield point a.Steel, reinforced concrete; no cracking and no slipping at joints 0.5 to 1.0
- 2. Working stress limited to 0.5 yield point. a.Welded steel, well reinforced concrete (with only slight
cracking) 2.0 b.Reinforced concrete (with considerable cracking) 2.0 c.Bolted steel 5.0 3. At or just below yield point a.Welded steel 5.0 b.Reinforced concrete 5.0 c.Bolted steel 7.0 4. Vital piping 0.5 OBE
- systems 1.0 DBE Total systems damping for structures including damping from motion in subgrade is assigned to be 5.0 percent for the Operational Basis Earthquake and 7.0 percent for the Design Basis
- Refer to Section B.2.1.12 regarding the use of alternate damping values in ASME Code Case N-411.
BVPS UFSAR UNIT 1 Rev. 23 1 of 1 Table B.2-4 COMPARISON OF PITRUST WITH FRANKLIN INSTITUTE PROGRAM CYLNOZ AND HAND CALCULATION Franklin Institute Source of Corrected Output from Hand Stress Values PITRUST Calculation Circumferential p(Normal) 395. 399. 399.99 p(Bending) 1875. 1883. 1887.3 Mc(Normal) 35.85 35.85 36.06 Mc(Bending) 364.7 366.6 354.3 ML(Normal) 79.05 79.66 79.54 ML(Bending) 90.52 80.57 79.42 Axial p(Normal) 813. 812. 814.8 p(Bending) 812.3 827. 810.6 Mc(Normal) 91.79 105. 95.45 Mc(Bending) 158.8 160. 158.8 ML(Normal) 37.06 37.0 37.12 ML(Bending) 117.9 105. 103.85 Shear Stress by M 6.63 6.63 6.63 Shear Stress by Vc 106.1 106.1 106.1 Shear Stress by VL 106.1 106.1 106.1 BVPS UFSAR UNIT 1 Rev. 23 1 of 1 Table B.2-5 COMPARISON OF PITRUST WITH REFERENCE 1 RESULTS
Location & Cause PITRUST Results Exp. Results (Ref. 1)
Element "A" Longt. Moment Circumf. Stress 20438.9 psi 20000 psi (Fig. 16, Axial Stress 26292.6 psi 25000 psi Ref. 1)
Element "B" Circumf. Moment Circumf. Stress 22016.2 psi 24000 psi (Fig. 15, Axial Stress 13105.8 psi 13000 psi Ref. 1)
Reference:
- 1. J. M. Corum and N. L. Greenstreet "Experimental Elastic Stress Analysis of Cylinder to Cylinder Shell Models and Comparison with Theoretical Predictions",
International Conference on Structural Mechanics in Reactor Technology , Berlin, Preprints Vol. 3, Part G (1971).
BVPS UFSAR UNIT 1 Rev. 23 1 of 2 Table B.2-6 COMPARISON OF PILUG COMPUTER PROGRAM OUTPUT WITH HAND CALCULATIONS Test Problem: Run Pipe 0.D.=17 in.; Run Pipe Thickness=0.812 in.
Axial Length of LUG-12 in.;
Width of LUG along Circumf=3 in.
Loads: P-3399 lb; Vc=-1788 lb; Vl=2478 lb; Mc=81834 in-lb; Ml=103320 in-lb Mt=76284 in-lb Stress in Circumferential Direction (all units are in psi):
PILUG Computer Fig. B Stress From Hand Calculation Output Remarks 3C .5485 387 330 Membrane Stress due to P lC .326 2165 2160 Bending Stress due to P 3A .294 671 629 Membrane Stress due to Mc lA .388 18976 19904 Bending Stress due to Mc 3B .467 3014 2961 Membrane Stress due to
M L lB .416 6143 5969 Bending Stress due to M L Stress in Axial Direction:
4C .4447 683 690 Membrane Stress due to P 2C .4632 773 792 Bending Stress due to P 4A .294 1897 1864 Membrane Stress due to Mc 2A .550 6357 5942 Bending Stress due to Mc
BVPS UFSAR UNIT 1 Rev. 23 2 of 2 Table B.2-6 Cont.
COMPARISON OF PILUG COMPUTER PROGRAM OUTPUT WITH HAND CALCULATIONS Computer Fig. B Stress From Hand Calcul.
Output Remarks 4B .467 2365. 2328 Membrane Stress due to M L 2B .582 4989.7 4842 Bending Stress due to M L
Shear Stress:
1304.8 1304.8 Shear Stress due to M -366.99 -366.99 Shear Stress due to Vc 127.15 127.15 Shear Stress due to V L
BVPS UFSAR UNIT 1 Rev. 23 1 of 1 Table B.2-7
SUMMARY
OF COMPARISON OF SAVAL COMPUTER OUTPUT WITH HAND CALCULATION AS-DESIGNED CONDITION Hand Variable Calculation SAVAL Valve & Nozzle Weight (lb) 714.09 714.09 Run Pipe Stiffness (in-lb/Rad.) 37,950,000 38,083,056 Nozzle Stiffness (in-lb/Rad.) 1,120,000,000 1,120,619,008 Equivalent Stiffness (in-lb/Rad.) 36,700,000 36,831,376 Nat. Rotational Frequency (cps) 22.0 22.19 Time Ratio 1.11 1.11 Dynamic Load Factor 1.22 1.22 Circumferential Moment x D.L.F. (in-lb) 314,760 314,760 Net Vertical Force (lb) 14,423 14,436 Nozzle Stress (psi) 6,600 6,597
- PITRUST Stress Intensity (psi) 62,782 62,789
- Stress Intensifi-cation Factor 5.6 5.608 Equation (9) Stress (psi) 36,651.9 36,681 *
- Allowable Stress=1.2 Sh=1.2 (15,490) = 18,588 psi
BVPS UFSAR UNIT 1 Rev. 23 1 of 1 Table B.2-8
SUMMARY
OF COMPARISON OF SAVAL COMPUTER OUTPUT WITH HAND CALCULATION REINFORCED CONDITION (1 1/4" PAD)
Hand Variable Calculation SAVAL Valve & Nozzle Weight (lb) 714.09 714.09 Run Pipe Stiffness (in-lb/Rad.) 181,500,000 181,490,256 Nozzle Stiffness (in-lb/Rad.) 1,120,000,000 1,120,619,008 Equivalent Stiffness (in-lb/Rad.) 156,200,000 156,193,808 Natural Rotational Frequency (cps) 45 45.7 Time Ratio 2.27 2.29 Dynamic Load Factor 1.13 1.13 Circumferential Moment x D.L.F. (in-lb) 291,540 291,540 Net Vertical Force (in-lb) 14,436 14,436 Nozzle Stress (psi) 6,144 6,144 PITRUST Stress Intensity (psi) 17,046 17,046 Stress Intensifi-cation Factor 2.59 2.59 Equation (9) Stress (psi) 16,186 16,200 BVPS UFSAR UNIT 1 Rev. 19 1 of 1 Table B.2-10 PEAK BROADENING - SAMPLE CALCULATION An example of the method of data calculation described in Section B.2.2.1 is given below.
- a. Number of modes within peak = 5, B = 1.0 percent, Wn = 10 Hz if broadening is 20 percent (Wn), mode spread = 10 percent Wn, Hz TR 8. 2.775 9. 5.241 Ratio TR SRSS
= K = 50.634 = 1.012 10. 50.010 TR PEAK 50.010
- 11. 4.737
- 12. 2.270
- b. Number of modes = 9, B = 1.0 percent, Wn = Hz if peak broadening is 20 percent (Wn), mode spread = 5 percent Wn, Hz TR 8. 2.775 8.5 3.597 9. 5.241 9.5 10.069 Ratio TR SRSS
= K = 52.717 = 1.054 10. 50.010 TR PEAK 50.010 10.5 9.560 11. 4.737 11.5 3.094 12. 2.270
BVPS UFSAR UNIT 1 Rev. 19 1 of 1 Table B.2-11 1G FLAT RESPONSE DYNAMIC FACTOR STUDY Maximum Dynamic Moment Maximum Static Moment Model Beam Fundamental Frequency Sum Moment, In-Lb Load Type Moment, In-Lb Location Ks/c Ks/u Ka/u Cantilever 1 *SRSS Absolute 620,000 694,900 Concentrated
Uniform 700,000 700,000 Fixed end .89 .89 .99 Simple-Simple 1 SRSS Absolute 179,000 186,000 Concentrated
Uniform 348,000 174,000 Midspan .51 1.03 1.07 Fixed-Fixed 1 SRSS Absolute 103,000 112,000 Concentrated
Uniform 174,000 116,000 Fixed end .59 .89 .97 SF - No overhang 1 SRSS Absolute 152,000 169,000 Concentrated
Uniform 261,000 174,000 Fixed end .58 .87 .97 SF - 16% overhang 1.34 SRSS Absolute 83,200 114,000 Concentrated
Uniform 162,000 111,000 Fixed end .51 .75 1.03 SF - 33% overhang 1.04 SRSS Absolute 57,000 890,000 Concentrated
Uniform 77,400 77,200 Fixed end .74 .74 1.15 SF - 50% overhang .62 SRSS Absolute 152,000 176,000 Concentrated
Uniform 174,000 174,000 Simple support .87 .87 1.01
- Square root of the sum of the squares
BVPS UFSAR UNIT 1 Rev. 19 1 of 1 Table B.2-12 MODAL DENSITY, N
- DYNAMIC FACTOR STUDY Simple Fixed Simple Simple Fixed Mode Cantilever Fixed Fixed Simple 33% Overhang No. Freq.,Hz Freq., Hz Freq., Hz Freq., Hz Freq.
1 1.0 1.0 1.0 1.0 1.0 2 5.8 2.7 3.2 3.8 2.9 3 15.3 4.9 6.3 8.2 6.5 4 28.0 7.5 10.2 13.6 8.4 5 43.2 10.2 14.0 19.5 13.3 6 59.6 - - - -
- Modal density is 1 based on a 10% criterion. Resultant modes are spaced such that any adjacent mode does not fall within 10% of the object mode.
BVPS UFSAR UNIT 1 Rev. 19 1 of 1 Table B.2-13 AMPLIFIED RESPONSE DYNAMIC FACTOR STUDY Maximum Dynamic Moment Maximum Static Moment Model Beam First Mode Dynamic Load High Low Summation Technique Moment, In-Lb Location *Uniform Load, In-Lb Ks/u Ka/u SF - 33% overhang g o f o g max f g c f c Model 6a .10 .70 2.87 3-4 .33 20 SRSS Absolute 20,000 30,000 Fixed end
Fixed end 222,000 .09 .13 Model 6B .10 1.0 2.87 3-4 .33 20 SRSS Absolute 148,000 157,000 Fixed end
Fixed end 222,000 .67 .71 Model 6C 2.87 3.3 2.87 3-4 .33 20 SRSS Absolute 102,000 118,000 Simple Simple 222,000 .45 .53 Model 6D .40 10 2.87 3-4 .33 20 SRSS Absolute 22,000 32,000 Fixed end
Fixed end 31,000 .71 1.03 Model 6E .33 20 2.87 3-4 .33 20 SRSS Absolute 20,000 27,000 Fixed end
Fixed end 25,700 .78 1.05 Model 6F .30 33 2.87 3-4 .33 20 SRSS Absolute 18,000 25,000 Fixed end
Fixed end 23,400 .77 1.07
- gmax (peak acceleration) if f o (fundamental frequency) f p (peak frequency); g = acceleration at f o if f o f p BVPS UFSAR UNIT 1 Rev. 23 1 of 3 Table B.2-15 TAC2D - SAMPLE PROBLEM PROBLEM DESCRIPTION The problem is to determine the transient temperature distribution in a right circular cylinder which is initially at temperature T
- 1. At time t = 0, the temperature at the surface is instantaneously changed to T 2 and maintained at that value. Mathematically the problem is defined by the following equations:
Rr0;t T K 1 z T t T rrr l 2 2)( (1)
T(r,z,0) = T 1 (2) T(R,z,t) = T 2 (3) T(r,L 2 ,t) = T 2 (4) where: t = time r = radius z = axial coordinate R = outside radius of the cylinder L = length of the cylinder and the diffusivity and K k c (5) where: K = thermal diffusivity k = thermal conductivity p = density c = specific heat capacity.
BVPS UFSAR UNIT 1 Rev. 23 2 of 3 Table B.2-15 (CONT'D)
TAC2D - SAMPLE PROBLEM For the specific problem analyzed, the following numerical values were used:
R = 12.0 in. c = 40.0 Btu/ft 3-F L = 48.0 in.
T 1 = 0.0 F K = 20.0 Btu/hr-ft-F T 2 = 1000.0 F ANALYTICAL SOLUTION It may be shown (1) that the solution is TT TT1f(z,t)g(r,t) 1 2 1 (6) 2)12(1 1)12(cos)12()1(4),(t L n k n n e L z n ntzf (7) tk m m R r n m m e J Jtrg o 2)(2),(1 1 (8) where the m are the roots of J 0 (m) = 0 (9)
The roots m of Equation 9 and the functions J 1 (m) have been tabulated(2) and need not be computed.
From the definition of the problem there is symmetry about the geometry center of the cylinder and the origin of the coordinate system taken at that point, as is reflected in the boundary conditions, Equations (3) and (4).
BVPS UFSAR UNIT 1 Rev. 23 3 of 3 Table B.2-15 (CONT'D)
TAC2D - SAMPLE PROBLEM NUMERICAL SOLUTION WITH TAC2D A cross section of the problem model for TAC2D is shown in Figure B.2-8. The model extends only to the axial midplane of the cylinder where an adiabatic boundary may be specified by virtue of the symmetry condition described above. The solid material is represented by one material block. The boundary conditions on the four external boundaries are described by Coolants 1 through 4 (specifically, Coolant Blocks 1 through 4). The material and coolant thermal parameters, as specified by the input functions, are given in tabular form. All coolants have the standard specific heat of 1.0 Btu/lb-F. Coolants 1 and 2, which represent the adiabatic external boundaries, have the standard heat transfer coefficient of 10
-6 Btu/hr-ft 2-F and the standard flow rate of 10 6 lb/hr. INPUT THERMAL PARAMETER FUNCTIONS FOR TAC2D SAMPLE PROBLEM
- 1. Material Thermal Parameters: SPECl (X) = 40.0 RCONl (X) = 20.0 ACONl (X) = 20.0
- 2. Coolant Thermal Parameters: H3A (X) = 1.0E+08 FL03A (X) = 1.0E+08 TIN3A (X) = 1460.0 H4A (X) = 1.0E+08 FL04A (X) = 1.0E+08 TIN4A (X) = 1460.0
References:
- 1. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids , Oxford at the Clarendon Press, p. 227. (1959)
- 2. E. Jahnke and F. Ende, "Tables of Functions," Dover Publications, Fourth Edition, (1945)
BVPS UFSAR UNIT 1 Rev. 23 1 of 1 Table B.2-16 ASAAS SAMPLE PROBLEM PROBLEM DESCRIPTION An infinitely long, solid, circular cylinder is subjected to cos and cos 2 pressure distributions. A closed-form solution of this problem may be obtained by the A.E.H. Love Methodology (1). The pertinent parameters of the cylinder are:
Dimension and Properties Loading and Boundary Conditions r o = a r = p o (cos + cos 2) = a r = p o sin E = 10 x 10 6 psi u z = o = 0.25 u r = 0 r = o a = 1 inch p o = 10000 psi The following solution can be verified by consulting Reference 1.
rprcoscos2o () (1)
][2cos aa2rcos3rp 222o (2)
][2sin sin 222rarrPor (3)
])([2cos 3ar2 r E 1 cos 2Ear)(1)4(1pu 2 3 2 r~ (4)
}])[({2sin 3 2 1 1 sin 2)1)(45 2 3 2r a r E Ea rPu o (5)
References:
- 1. A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity , Dover Publications, New York, N.Y., (1944)
BVPS UFSAR UNIT 1 Rev. 19 1 of 1 Table B.2-17 VESSEL PENETRATION ANALYSIS - SAMPLE PROBLEM PROBLEM DESCRIPTION
A thin-walled cylindrical vessel is subjected to applied loads from a rigid cylindrical attachment. A solution of this problem may be obtained by the use of Reference 1.
The pertinent parameters of the problem are:
Dimensions Loading T = .375 in P = 1,000 lb r = 8.0 in Mc = 1,000 in-lb Rm = 19.1875 in M L = 1,000 in-lb M T = 1,000 in-lb V c = 1,000 in-lb
V L = 1,000 in-lb
Reference:
- 1. K. R. Wichman, A. G. Hopper, J. L. Mershon, "Local Stresses in Spherical and Cylindrical Shell Due to External Loadings," Welding Research Council Bulletin 107 (December 1968)
" "
BVPS UFSAR UNIT 1 Rev. 23 1 of 1 Table B.2-20 SHELL 1 - SAMPLE PROBLEM PROBLEM DESCRIPTION
A long thin-walled circular cylinder is subjected to a constant internal pressure distribution. A solution of this problem may be obtained by the use of Reference (1).
The pertinent parameters of the cylinder are:
Dimension and Properties Loading and Boundary Conditions R = 25 in Fr = M =
z = 0 Z = 0 Z = 0 Z = 0 1 = 20 in t = 0.5 in Fr = M = Fz = 0 z = 1 z = 1 z = 1 E = 28 x 10 6 psi v = 0.3 P i = 75 psi The following solution can be verified by consulting Reference 1.
R 2 pR Et (1) pR t (2)
PROBLEM RESULTS Variable Exact Shell 1 R 3.348 x 10
-3 in 3.342 x 10
-3 in 3,750 psi 3,750 psi
Reference:
- 1. R. J. Ruark, Formulas for Stress and Strain, McGraw-Hill Book Company, Fourth Ed., New York, N.Y., (1965)
BVPS UFSAR UNIT 1 Rev. 19 1 of 1 Table B.2-21 STRESS ANALYSIS OF SHELLS OF REVOLUTION SAMPLE PROBLEM PROBLEM DESCRIPTION
Dimensions and Properties Loading and Boundary Conditions R = 25 in F R = M = z = 0 z = 0 z = 0 z = 0 1 = 20 in t = 0.5 in F R = M = Fz = 0 z = 1 z = 1 z = 1 E = 28 x 10 6 psi ! = 0.3 P OUT = 75 psi
The following solution can be verified by consulting Reference 1.
R 2 t pR E (1) pR t (2)
PROBLEM RESULTS
Stress Analysis of Variable Exact Shells of Rev.
R 3.348 x 10
-3 in 3.361 x 10
-3 in 3,750 psi 3,764 psi
Reference:
- 1. R. J. Roark, Formulas for Stress and Strain, McGraw-Hill Book Company, Fourth Ed., New York, N.Y., (1965)
BVPS UFSAR UNIT 1 Rev. 19 1 of 1 Table B.2-22 EXACT AND COMPUTER STRESSES FOR HOLLOW CYLINDER OF FIGURE B.2-13 PROBLEM DESCRIPTION
The pertinent parameters of the cylinder are:
i = 5000 psi r i = 1 in. o = 10,000 psi r o = 2 in. E = 30 x 10 6 psi ! = 0.3 PROBLEM RESULTS Stress at Element Center (psi) r r Element EXACT SAAS EXACT SAAS 1 -7400 -7329 -15,933 -16,032 2 -9490 -9473 -13,844 -13,840
BVPS UFSAR UNIT 1 Rev. 23 1 of 1 Table B.2-23 ST-167 - SAMPLE PROBLEM The equations of motion to be solved are:
Results of hand calculations of this problem are as follows:
- 1. The three eigenvalues, W 2, are: 2.535898 K m 6.0 K m 9.464102 K m 2. The three eigenvectors are:
For comparison, the results of computer program ST-167 solution are as follows: 1. The three eigenvalues are: 2.536577 K m 6.006006 K m 9.499567 K m 2. The comparable eigenvectors are:
BVPS UFSAR UNIT 1 Rev. 19 1 of 1 Table B.2-24 LOAD COMBINATIONS AND ACCEPTANCE CRITERIA FOR PRESSURIZER SAFETY AND RELIEF VALVE PIPING AND SUPPORTS - UPSTREAM OF VALVES Plant/System Piping Operating Allowable Stress Combination Conditions Load Combination Intensity l Normal N 1.0 S h 2 Upset N + OBE + SOT U 1.2 S h 3 Emergency N + SOT E 1.8 S h 4 Faulted N + MS/FWPB or DBPB 2.4 S h + SSE + SOT F 5 Faulted N + LOCA + SSE + SOT F 2.4 S h
NOTES: (1) See Table B.2-26 for SOT definitions and other load abbreviations. (2) The bounding number of valves (and discharge sequence if setpoints are significantly different) for the applicable system operating transient defined in Table B.2-26 should be used.
(3) Verification of functional capability is not required, but allowable loads and accelerations for the safety-relief valves must be met.
(4) Use SRSS for combining dynamic load responses.
(5) Combinations to be made with components of applicable moments.
BVPS UFSAR UNIT 1 Rev. 19 1 of 1 Table B.2-25 LOAD COMBINATIONS AND ACCEPTANCE CRITERIA FOR PRESSURIZER AND RELIEF VALVE PIPING AND SUPPORTS - SEISMICALLY DESIGNED DOWNSTREAM PORTION Plant/System Piping Operating Allowable Stress Combination Conditions Load Combination Intensity 1 Normal N 1.0 S h 2 Upset N + SOT U 1.2 S h 3 Upset N + OBE + SOT U 1.8 S h 4 Emergency N + SOT E 1.8 S h 5 Faulted N + MS/FWPB or DBPB 2.4 S h + SSE + SOT F 6 Faulted N + LOCA + SSE + SOT F 2.4 S h
NOTES: (1) This table is applicable to the seismically designed portion of downstream non-Category I piping (and supports) necessary to isolate the Category I portion from the non-seismically designed piping response, and to assure acceptable valve loading on the discharge
nozzle.
(2) See Table B.2-26 for SOT definitions and other load abbreviations.
(3) The bounding number of valves (and discharge sequence if setpoints are significantly different) for the applicable system operating transient defined in Table B.2-26 should be used.
(4) Verification of functional capability is not required, but allowable loads and accelerations for the safety-relief valves must be met.
(5) Use SRSS for combining dynamic load responses.
(6) Combinations to be made with components of applicable moments.
BVPS UFSAR UNIT 1 Rev. 19 1 of 1 Table B.2-26 DEFINITIONS OF LOAD ABBREVIATIONS N = Sustained loads during normal plant operation SOT = System operating transient
SOT U = Relief valve discharge transient SOT E = Safety valve discharge transient(1)
SOT F = Maximum of SOTU and SOTE
- or transition flow OBE = Operating basis earthquake SSE = Safe shutdown earthquake
MS/FWPB = Main steam or feedwater pipe break DBPB = Design basis pipe break
LOCA = Loss-of-coolant accident
S h = Basic material allowable stress at maximum (hot) temperature
(1) Although certain nuclear steam supply systems design transients (for example, loss of load) which are classified as upset conditions may actuate the safety valves, the extremely low number of actual safety valve actuations in operating pressurizer water reactors justifies the emergency condition from the ASME design philosophy and a stress analysis viewpoint. However, if actuation of safety valves would occur, a limitation must be placed to shut down the plant for examination of system integrity.
BVPS UFSAR UNIT 1 Rev. 19 1 of 1 Table B.2-27 LOAD COMBINATIONS AND ALLOWABLES FOR QA CATEGORY I PIPING 2" DIAMETER AND SMALLER Load combinations and allowable stress limits for small bor e piping are shown in the following table. Either equation set (A) or (B) must be met in its entirety.
Load Combination Allowable (A) 1) P + D S H 2) P + D + SRSS{E, H}
1.2 S H 3a) T + R + A S A 3b) P + D + T + R + A S A + S H 4) P + D + SRSS{E', H}
1.8 S H (B) 1) P + D S H 2) P + D + SRSS{(E + A), H}
1.2 S H 3a) T + R S A 3b) P + D + T + R S A + S H 4) P + D + SRSS{E', H}
1.8 S H
Notes: 1. For definitions of terms, see Table B.2-31.
- 2. Equation 3a or 3b may be utilized.
- 3. For piping attached to containment penetrations, see Table B.2-28. 4. For piping that is supported from the containment wall, the effects of R' shall be considered.
BVPS UFSAR UNIT 1 Rev. 19 1 of 1 Table B.2-28 LOAD COMBINATIONS AND ALLOWABLES FOR QA CATEGORY I PIPING 2" DIAMETER AND SMALLER ATTACHED TO CONTAINMENT PENETRATIONS (CONTAINMENT PRE SSURE BOUNDARY)
Load combinations and allowable stress limits for small bore piping attached to containment penetrations (containment pressure boundary) are shown in the following table. Either equation set (A) or (B) must be met in its entirety.
Load Combination Allowable (A) 1) P + D S H 2) P + D + SRSS{E, H}
1.2 S H 3a) T + R' + A S A 3b) P + D + T + R' + A S A + S H 4) P + D + SRSS{(E' + A'), H}
1.8 S H (B) 1) P + D S H 2) P + D + SRSS{(E + A), H}
1.2 S H 3a) T + R' S A 3b) P + D + T + R' S A + S H 4) P + D + SRSS{(E' + A'), H}
1.8 S H Notes: 1. For definitions of terms, see Table B.2-31.
- 2. Equation 3a or 3b may be utilized.
BVPS UFSAR UNIT 1 Rev. 19 1 of 1 Table B.2-29 LOAD COMBINATIONS AND ALLOWABLES FOR QA CATEGORY I SMALL BORE PIPING SUPPORTS (2" PIPE DIAMETER AND LESS)
Load combinations and allowable stress limits for small bore pipe supports are shown in the following table.
Load Combination Allowable Normal Stress Allowable Shear Stress 1) D + T + R 0.6 S Y 0.4 S Y 2) D + T + R + SRSS{(E + A) + H}
0.8 S Y 0.52 S Y 3) D + T + R + SRSS(E' + H) 0.8 S Y 0.52 S Y Notes: 1. For definitions of terms, see Table B.2-31. 2. Member allowable normal and shear stress are shown in the above table. For load combinations which include seismic loading, allowable normal and
shear stresses have been increased by 33% as shown in the table.
However, the AISC code check for compression and buckling remains
unchanged.
- 3. For supports on active components, see Table B.2-30.
BVPS UFSAR UNIT 1 Rev. 19 1 of 1 Table B.2-30 LOAD COMBINATIONS AND ALLOWABLES FOR QA CATEGORY I SMALL BORE PIPING (2" DIAMETER AND LESS) EQUIPMENT NOZZLES AND ACTIVE COMPONENT SUPPORTS Load combinations and allowable stress lim its for equipment nozzles and supports on active components of small bore piping are shown in the following table.
Load Combinations Allowables
- 1) D + T + R
- 2) D + T + R + SRSS{(E + A) + H}
See Notes Below
- 3) D + T + R + SRSS{(E' + A') + H}
Notes: 1. For definitions of terms, see Table B.2-31.
- 2. For equipment nozzles the loads are limited to vendor approved allowables or are accepted by comparison with the loading used in the equipment qualification or by alternate analysis. 3. For active component supports the allowables are the same as for pipe supports, see Table B.2-29. The active component qualification includes
the effect of the above loadings. 4. In Equation 2, replace R with R' for equipment or active components on piping that either penetrate the containment or is attached to the containment.
BVPS UFSAR UNIT 1 Rev. 19 1 of 1 Table B.2-31 DEFINITION OF TERMS The following table provides the definitions of the terms for Tables B.2-27 , B.2-28 , B.2-29 and B.2-30.
D - Sustained mechanical loads, including deadweight of piping, components, contents, and insulation. P - Longitudinal pressure stress. T - Loads due to Thermal Expansion of the system in response to the system fluid operating temperature.
R - Loads induced in the piping due to the thermal growth of equipment and/or structures to which the piping is connected. R' - Loads induced in the piping due to the growth of the Reactor Containment Building as a result of BVPS-1 plant faulted conditions. E - Loads due to OBE Seismic Inertia.
E' - Loads due to DBE Seismic Inertia. A - Loads induced in the piping due to OBE Anchor Movements including Orbital Motion (1/2 range of moments to be used).
A' - Loads induced in the piping due to DBE Anchor Movements including Orbital Motion (1/2 range of moments to be used).
H - Loads induced in the piping due to fluid transient loads. S H - Allowable material stress at maximum operating temperature. S C - Allowable material stress at room temperature (70F).
S A - Allowable material stress range for expansion stress = f(1.25S C + 0.25S H).
f - Stress range reduction factor due to cyclic conditions (= 1 for 7000 cycles and less).
S Y - Yield Strength of material.
BVPS UFSAR UNIT 1 Rev. 23 1 of 2 Table B.3-1 NSSS FLUID SYSTEMS COMPONENT SEISMIC CATEGORY LIST COMPONENT
REACTOR COOLANT SYSTEM SEISMIC CATEGORY Reactor Vessel I Full Length CRDM Housing I Reactor Coolant Pump Assembly I Reactor Coolant Pump Casing I Reactor Coolant Pump Internals I Reactor Coolant Pump Motor I Steam Generator I RC Stop Valves I Pressurizer I Reactor Coolant Piping, Fittings I and Fabrication Surge Pipe, Fittings and Fabrication I Pressurizer Sprayline I Loop Bypass Line I RC Narrow Range Temperature Detectors Thermowells I RC Wide Range Temperature Detectors Thermowells I Safety Valves I Relief Valves I Valves to RC System Boundary I Piping to RC System Boundary I
BVPS UFSAR UNIT 1 Rev. 26 2 of 2 Table B.3-1 (CONT'D)
NSSS FLUID SYSTEMS COMPONENT SEISMIC CATEGORY LIST COMPONENT
CHEMICAL AND VOLUME CONTROL SYSTEM Regenerative HX I Letdown HX I Mixed Bed Demineralizer II Cation Bed Demineralizer II Reactor Coolant Filter I Volume Control Tank I Charging Pumps I Seal Water Injection Filter I Letdown Orifices I Excess Letdown HX I Seal Water HX I Boric Acid Tanks I Boric Acid Filter I Boric Acid Transfer Pump I Boric Acid Blender I Boric Acid Batching Tank II RESIDUAL HEAT REMOVAL LOOP
Residual Heat Removal Pump I Residual Heat Exchanger I Residual Heat Removal Piping I Residual Heat Removal Valves I
SAFETY INJECTION SYSTEM
Accumulators I High Head SIS Pumps I Low Head SIS Pump I Boron Injection Tank I
BVPS UFSAR UNIT 1 Rev. 19 1 of 1 Table B.3-2
SUMMARY
OF SEISMIC REQUIREMENTS TYPE OF ANALYSIS LIMITS ANALYSIS DBE + NORMAL + DBA NLSF, Permanent Dynamic + Deformation Blowdown Permitted (Faulted Condition)
DBE + NORMAL NLSF, Permanent Deformation Dynamic Permitted (Faulted Condition)
OBE + NORMAL Applicable Code Stresses Dynamic (Upset Condition)
DBE The "Design Basis Earthquake" is that earthquake giving rise to the maximum vibratory ground acceleration at a site which can be reasonably predicted from geologic and seismic evidence.
OBE The "Operating Basis Earthquake" is that earthquake which is of sufficient probability of occurrence to require its resulting ground accelerations at the site to be considered for operational loadings.
NORMAL Those normal operation occurrences which are expected frequency and regularly in the course of power operation, refueling, maintenance, or maneuvering of the plant.
DBA The "Design Basis Accident" is the double ended rupture of the largest pipe in the reactor coolant system.
NLSF No loss of safety function. Permanent deformation permitted to the extent there is no loss of safety function.
DYNAMIC A response spectrum analysis or other dynamic analysis or test.
BLOWDOWN Loads caused by the DBA which are to be combined with the seismic loads for safety equipment.
BVPS UFSAR UNIT 1 Rev. 19 1 of 2 Table B.3-3 STRESS LIMITS FOR VARIOUS LOAD COMBINATIONS LOAD COMBINATION STRESS LIMIT (NOTE 1)
- 1. Normal (deadweight, thermal and pressure) Normal Conditions
- 2. Normal and Operational Basis Earthquake Upset Condition
- 3. Normal and Design Basis Earth-quake Faulted Condition
- 4. Normal and Pipe Rupture Faulted Condition
- 5. Normal, Design Basis Earthquake, and Pipe Rupture Faulted Condition Note 1: Definition of Terms from Summer 1968 Addenda to the ASME Boiler and Pressure Vessel Code,Section III.
The Operating Condition categories are defined as follows:
- 1. Normal Condition - Any condition in the course of system startup, operation in the design power range and system shutdown, in the absence of Upset, Emergency or Faulted Conditions.
- 2. Upset Condition - Any deviations from Normal Conditions anticipated to occur often enough that design should include a capability to withstand the conditions without operational impairment. The Upset Condition includes those transients caused by a fault in a system component requiring its isolation from the system, transients due to a loss of load or power and any system upset not resulting in a forced outage.
The estimated duration of an Upset Condition shall be included in the Design Specifications. The Upset Conditions include the effect of the specified earthquake for which the system must remain operational or must regain its operational status.
- 3. Emergency Condition - Any deviations from normal conditions which require shutdown for correction of the conditions or repair of damage in the system. The conditions have a low probability of occurrence but are included to provide assurance that no gross loss of structural integrity will result as a concomitant effect of any damage developed in the system. The total number of postulated occurrences for such events shall not exceed twenty-five (25).
BVPS UFSAR UNIT 1 Rev. 19 2 of 2 Table B.3-3 (CONT'D)
STRESS LIMITS FOR VARIOUS LOAD COMBINATIONS
- 4. Faulted Condition - Those combinations of conditions associated with extremely low probability postulated events whose consequences are such that the integrity
and operability of the nuclear energy system may be impaired to the extent where considerations of public health and safety are involved. Such considerations require compliance with safety criteria as may be specified by jurisdictional authorities.
Among the Faulted Conditions may be a specified earthquake for which safe
shutdown is required.
BVPS UFSAR UNIT 1 Rev. 19 1 of 2 Table B.3-4 LOADING CONDITIONS AND STRESS LIMITS
A. PRESSURE VESSELS
where: P m = primary general membrane stress intensity PL = primary local membrane stress intensity PB = primary bending stress intensity Q = secondary stress intensity S m = stress intensity from ASME B&PV Code,Section III, Nuclear Vessels Sy = minimum specified material yield (ASME B&PV Code,Section III, Table N-421 or equivalent)
STRESS LIMIT LOAD COMBINATION
- 1. Normal Condition (a) Pm Sm (b) Pm (or PL) + PB 1.5*Sm (c) Pm (or PL) + PB Q 3.0*Sm 2. Upset Condition (a) Pm Sm (b) Pm (or PL) + PB 1.5*Sm (c) Pm (or PL) + PB + Q 3.0*Sm 3. Emergency Condition (a) whichever is larger (b) whichever is larger
- 4. Faulted Condition Design Limit Curves as discussed in the text and as shown in Figure B.3-3 and Figure B.3-4 (4)
BVPS UFSAR UNIT 1 Rev. 19 2 of 2 Table B.3-4 LOADING CONDITIONS AND STRESS LIMITS B. EQUIPMENT SUPPORTS STRESS LIMIT LOAD COMBINATION
- 1. Normal Condition Working Stresses or Applicable Factored Load Design Values 2. Upset Condition Working Stresses or Applicable Factored Load Design
Values 3. Emergency Condition Within Yield After Load Redistribution
- 4. Faulted Condition Permanent Deflection of Supports Limited to Maintain Supported Equipment Within Design Limit Curves as discussed in the text and attached
NOTES Note 1: The limits on local membrane stress intensity (PL 1.5*Sm) and primary membrane plus primary bending stress intensity (Pm (or PL) + PB 1.5*Sm) need not be satisfied at a specific location if it can be shown by means of limit analysis or by tests that the specified loadings do not exceed 2/3 of the lower bound collapse load as per paragraph N-417.6(b) of the ASME B&PV Code,Section III, Nuclear Vessels.
Note 2: In lieu of satisfying the specific requirements for the local membrane (PL 1.5*S) or the primary plus secondary stress intensity (PL + PB + Q3*Sm) at a specific location, the structural action may be calculated on a plastic basis and the design will be considered to be acceptable if shakedown occurs, as opposed to continuing deformation, and if the deformations which occur prior to shakedown do not exceed specified limits, as per paragraph N-417.69a) (2) of the ASME
B&PV Code,Section III, Nuclear Vessels.
Note 3: The limits on local membrane stress intensity (PL1.5*Sm) and primary membrane plus primary bending stress intensity (PM (or PL) + PB1.5*Sm) need not be satisfied at a specific location if it can be shown by means of limit analysis or by tests that the specified loadings do not exceed 120 percent of 2/3 of the lower bound collapse load as per paragraph N-417.10(c) of the ASME B&PV Code,Section III, Nuclear Vessels.
Note 4: As an alternate to the design limit curves which represent a pseudo plastic instability analysis, a plastic instability analysis may be performed in some specific cases considering the actual strain-hardening characteristics of the material, but
with yield strength adjusted to correspond to the tabulated value at the
appropriate temperature in Table N-424 or N-425, as per paragraph N-417.11(c) of the ASME B&PV Code,Section III, Nuclear Vessels. These specific cases will
be justified on an individual basis.
BVPS UFSAR UNIT 1 Rev. 23 1 of 4 Table B.3-5 EQUIPMENT CODE AND CLASSIFICATION LIST Component Code Code Class Addenda Case Reactor Coolant System Replacement Reactor Vessel Closure Head ASME III, 89 1 None 2142-1 2143-1 N-525 N-474-1 Reactor Vessel ASME III, 68 A Thru W 68 1332-3 1335-2 1336 Full Length CRDM Housing ASME III, 68 A Thru W 69 NA Steam Generator (tube side) ASME III, 89 1 NA N-20-3 N-71-16 N-411-1 N-474-2 (shell side) ASME III, 89 2 NA NA Reactor Coolant Stop Valves ASME III, 68 A (Body & Bonnet) Thru W 68 NA Pressurizer ASME III, 65 A Thru W 66 1401 Reactor Coolant Piping, Fittings, and Fabrication** ANSI B31.1, 67 NA NA NA Surge Pipe, Fittings, and Fabrication ANSI B31.1, 67 NA NA NA Loop Bypass Line ANSI B31.3, 67 NA NA NA Reactor Coolant Narrow Range Temperature
Detector Thermowells
ASME III 1
NA NA Reactor Coolant Wide Range
Temperature Detector Thermowells
ANSI B31.1, 67
NA NA NA BVPS UFSAR UNIT 1 Rev. 23 2 of 4 TABLE B.3-5 (CONT'D)
EQUIPMENT CODE AND CLASSIFICATION LIST
Component Code Code Class Addenda Case Reactor Coolant System (Contd) Safety Valves ASME III NA Thru S 68 NA Relief Valves ASA 16.5 NA NA NA Valves to Reactor Coolant System Boundary ASA 16.5, MSS-SP 66A NA NA NA Pressurizer Relief Tank ASME VIII NA Thru S 68 NA CRDM Head Adapter Plugs ASME III, 89 NA NA NA Reactor Coolant Pump Standpipe Orifice No Code NA NA NA Reactor Coolant Pump Standpipe ASME VIII NA NA NA Reactor Coolant Pump Casing ASME III, 68 A NA 1355 Main Flange ASME III, 68 A NA NA Thermal Barrier ASME III, 68 A NA NA No. 1 Seal Housing ASME III, 68 A NA NA No. 2 Seal Housing ASME III, 68 A NA NA Pressure Retaining Bolting ASME III, 68 A NA NA Remaining Parts ASME III, 68 A NA NA Reactor Coolant Pump Motor NEMA MG1, 67 NA NA NA Shaft Coupling NEMA MG, 67 NA NA NA Armature NEMA MG1, 67 NA NA NA Flywheel ASTM A-533, Grade B Class 1 + E Spec
Provisions
NA
NA
NA Motor Bolting NEMA MG1 NA NA NA Upper Oil Cooler TEMA*** C NA NA Lower Oil Cooler TEMA*** C NA NA BVPS UFSAR UNIT 1 Rev. 19 3 of 4 TABLE B.3-5 (CONT'D)
EQUIPMENT CODE AND CLASSIFICATION LIST
Component Code Code Class Addenda Case Chemical and Volume Control System Regenerative Heat Exchanger ASME III C NA NA Nonregenerative Heat Exchanger ASME III C Tube Side NA NA ASME VIII C Shell Side NA NA Mixed Bed Demineralizers ASME III C NA NA Reactor Coolant Filter ASME III C NA NA Volume Control Tank ASME III C NA NA Seal Water Heater Exchanger ASME III C Tube Side NA NA ASME VIII C Shell Side NA NA Excess Letdown Heat Exchanger ASME III C Tube Side NA NA ASME VIII C Shell Side NA NA Chemical Mixing Tank ASME VIII (Not Stamped) NA NA Cation Bed Demineralizer ASME III C NA NA Boric Acid Tanks ASME VIII (Not Stamped) NA NA Batching Tank ASME VIII (Not Stamped) NA NA Seal Water Injection Filters ASME III C NA NA Boric Acid Filter ASME III C NA NA Seal Water Filter ASME III C NA NA Resin Fill Tank ASME VIII (Not Stamped) NA NA Valves USAS B31.1** NA NA ANSI B16.5 NA NA BVPS UFSAR UNIT 1 Rev. 19 4 of 4 TABLE B.3-5 (CONT'D)
EQUIPMENT CODE AND CLASSIFICATION LIST
Component Code Code Class Addenda Case Emergency Core Cooling System Accumulators ASME III C NA NA Boron Injection Tank ASME III C NA NA Valves ASA B16.5 or MSS-SP-66
NA NA NA NA NA Residual Heat Removal System Residual Heat Exchangers - Tube Side ASME III C NA NA Shell Side ASME VIII NA NA NA Residual Heat Removal Valves ANSI B31.1 ASME III, 68 NA NA NA NA NA NA ASA B16.5 NA NA NA Residual Heat Removal Pumps No Code NA NA NA
- Under USAS B31.1 - 1967, there is no Class as such.
- TEMA - Tubular Exchangers Manufacturers Association
NA - Not Applicable
BVPS UFSAR UNIT 1 Rev. 19 1 of 1 Table B.3-13 WESTDYN TEST PROBLEM NUMBER 1 A.D. Little Hand Calc./WESTDYN Comparison Object: Determine the ability of WESTDYN to calculate the deflections of a cantilever with a concentrated load and moment at the free end. See if transfer matrices develop any round off error when this same cantilever is divided into five sections with ten members each.
Result: Deflections and moments along the cantilever from WESTDYN were compared to those found in a hand calculation by I. W. Dingwell (A. D. Little Company). The comparisons indicate that WESTDYN computations are accurate, and that no round off error is incurred through the 50 transfers from member to member.
Deflections A.D. Little WESTDYN WESTDYN (in Inches)
Point Hand Calc. Case A Case B D y 10 -.103 -.103 -.103 20 -.303 -.301 -.301 30 -.534 -.531 -.531
40 -.733 -.729 -.729 50 -.836 -.832 -.832 Moments (Inch-Kips) M z 0 25,000.025,000.4 24,000.4 25 0.00.0 -.80 50 25,000.025,000.0 25,000.0
___________________
Case A = Cantilever split into 5 sections - 1 or 2 members per section
Case B = Cantilever split into 5 sections - 10 members per section
BVPS UFSAR UNIT 1 Rev. 19 1 of 1 Table B.3-14 WESTDYN TEST PROBLEM NUMBER 2 AISC/WESTDYN COMPARISON Object: To determine if WESTDYN correctly calculates piping loads and support reactions for a straight pipe under distributed (deadweight) loading.
Result: The forces and moments obtained from WESTDYN were compared to the answers given on Page 2-133, example 37 of the AISC Manual of Steel Constuction.
Fy Mz Position AISC West AISC West 1 BEG 38.00 37.95 0.0. 2 END 60.30 62.05 -14,460.-14,462. 2 BEG 62.00 60.26 14,460.14,462. 3 END 39.70 39.74 -2,148.-2,145. 3 BEG -4.00 -4.02 2,148.2,145. 4 END 4.00 4.02 -6,960.-6,963. 4 BEG 55.80 55.80 6,960.6,963.
5 END -44.20 -44.20 0.-3.
6 END -3.30 -3.30 11,724.11,655.
7 END 0.00 0.00 11,700.11,720.
8 END 44.20 44.20 0.0.
BVPS UFSAR UNIT 1 Rev. 19 1 of 4 Table B.3-15 WESTDYN TEST PROBLEM NUMBER 3 Object: Determine the ability of WESTDYN to find thermal and deadweight loads and movements.
PARAMETERS
- 1) Joint Coordinates - The coordinate system origin is located at the intersection of the tangents through node points 4 and 5.
Node X Y Z Point (in.)(in.)(in.)
1 -108.3-145.20.0 2 -108.3-36.30.0 3 -72.00.00.0 4 -36.30.00.0 5 0.00.035.3 6 0.00.077.3
- 2) Physical Properties:
Diameter = 7.288 in.
Thickness = 0.241 in.
Bend Radius = 36.3 in.
Unit Weight = 2.581 lb/in.
T = 850 F " = 0.300 E = 24 x 10 6 psi # = 7.1565 x 10
-6 in./in. F
BVPS UFSAR UNIT 1 Rev. 19 2 of 4 TABLE B.3-15 (CONT'D)
WESTDYN TEST PROBLEM NUMBER 3 KELLOGG/MEC-21/WESTDYN THERMAL LOAD COMPARISON:
Forces (Kips And Node Point 1 Node Point 6 Inch-Kips)
Kellogg MEC-21 WESTDYN Kellogg MEC-21 WESTDY N F x -1.75 -1.74-1.721.751.74 1.72 F y -1.71 -1.69-1.681.711.69 1.68 F z -0.64 -0.64-0.630.640.64 0.63 M x -56.04 -55.66-55.2495.0493.90 93.59 M y 14.40 14.5014.20-80.52-80.01 -79.02 M z 133.08 132.57130.60-63.36-63.08 -62.52 MEC-21/WESTDYN THERMAL LOAD DEFLE CTION COMPARISON:
Deflections (In Inches Node Point 1 Node Point 2 Node Point 3 And Radians)
MEC-21 WESTDYN MEC-21 WESTDYN MEC-21 WESTDYN Dx 0.000 0.000 -0.517 -0.515 -0.322 -0.319 Dy 0.000 0.000 0.661 0.661 0.777 0.777 Dz 0.000 0.000 -0.242 -0.243 -0.407 -0.408 Rx 0.0000 0.000 -0.0029 -0.0028 0.0005 0.0005 Ry 0.0000 0.000 0.0026 0.0025 0.0025 0.0025 Rz 0.0000 0.000 -0.0052 -0.0050 -0.0074 -0.0073 Node Point 4 Node Point 5 Node Point 6 Dx -0.106 -0.102 0.059 0.062 0.000 0.000 Dy 0.483 0.484 0.075 0.077 0.000 0.000 Dz -0.483 -0.483 -0.249 -0.249 0.000 0.000 Rx 0.0027 0.0026 0.0031 0.0030 0.0000 0.000 Ry 0.0016 0.0016 -0.0023 -0.0022 0.0000 0.000 Rz -0.0087 -0.0085 -0.0042 -0.0042 0.0000 0.000
BVPS UFSAR UNIT 1 Rev. 19 3 of 4 TABLE B.3-15 (CONT'D)
MEC-21/WESTDYN DEADWEIGHT LOAD COMPARISON:
Node Point MEC-21 1 2 3 4 5 6 F x kips -0.036 -0.036 -0.036 -0.036 -0.036 -0.036 F y -0.511 -0.230 -0.083 0.009 0.156 0.262 F z 0.002 0.002 0.002 0.002 0.002 0.002 M x inch-kips 0.797 -1.045 -1.128 -1.128 2.609 11.191 M y -0.476 -0.476 -0.393 -0.311 1.092 2.583 M z 1.420 -2.540 1.090 2.404 0.127 0.127 D x inches 0.000 0.001 0.007 0.007 0.002 0.000 D y 0.000 0.000 -0.010 -0.019 -0.008 0.000 D z 0.000 -0.007 -0.009 -0.005 -0.000 0.000 R x radians 0.0000 -0.0001 -0.0003 -0.0003 -0.0003 0.0000 R y 0.0000 -0.0001 -0.0001 -0.0001 -0.0001 0.0000 R z 0.0000 -0.0001 -0.0003 -0.0002 -0.0000 0.0000 B31.1 186. 347. 191. 327. 353. 1,262.
Stress (psi) WESTDYN F x kips -0.04 -0.04 -0.04 -0.04 -0.04 -0.04 F y -0.51 -0.28 -0.08 0.01 0.16 0.26 F z 0.00 0.00 0.00 0.00 0.00 0.00 M x inch-kips -0.80 -1.04 -1.12 -1.12 2.58 11.15 M y -0.47 -0.47 -0.39 -0.31 1.09 2.58 M z 1.40 -2.56 1.08 2.41 0.16 0.16 D x inches 0.000 0.001 0.007 0.007 0.002 0.0000 D y 0.000 0.000 0.010 0.020 0.009 0.0000
BVPS UFSAR UNIT 1 Rev. 19 4 of 4 TABLE B.3-15 (CONT'D)
MEC-21/WESTDYN DEADWEIGHT LOAD COMPARISON:
WESTDYN Node Point (CONTD) 1 2 3 4 5 6 D z 0.000 0.007 0.009 0.005 0.000 0.000 R x radians 0.0000 0.0001 0.0003 0.0003 0.0003 0.0000 R y 0.0000 0.0001 0.0001 0.0001 0.0001 0.0000 R z 0.0000 0.0001 0.0003 0.0002 0.0000 0.0000 Results: A multi-plane pipe bend problem proposed by W. Hovgaard was used and compared with an M.W. Kellogg hand calculation and the MEC-21 computer code. This example problem was first proposed by W. Hovgaard to illustrate an algebraic method of calculating the stress in multi-plane pipe bends(1). It has since been used as a benchmark in the piping industry.
In the first, a comparison of forces is made from two sources; the MEC-21/7094 piping flexibility analysis program (2), and the M.W. Kellogg general analytical method (3). In the latter, the MEC-21 displacements and stresses are given.
Comparison shows a variation in forces, moments, deflections, and rotations of less than 5 percent from Kellogg and MEC-21 for both thermal and deadweight analyses.
References
- 1. W. Hovgaard, "Stress in Three-dimensional Pipe Bends," Trans.
ASME, Volume 57 , paper FSP-57-12, pp. 401-416, (1935).
- 2. J. H. Grifin, "MEC-21/7094," LA-2229, Engineering and Equipment TID-4500 (31st Edition).
- 3. Design of Piping Systems , M. W. Kellogg Company, 2nd Edition, John Wiley & Sons, New York (1956).
BVPS UFSAR UNIT 1 Rev. 19 1 of 3 Table B.3-16 WESTDYN TEST PROBLEM NUMBER 4 Object: Determine the ability of WESTDYN to calculate fre- quencies and influence coefficients.
FREQUENCIES IN ORDER:
Neubert Calc.
Neubert Meas. WESTDYN 109.0 110 112.03 115.9 117 116.61 135.0 134 138.16 212.5 214 216.37 352.4 357 404.29 394.6 382 423.09 422.2 416 451.92 532.1 553 549.05 655.8 - 735.71 684.9 697 761.02 760.7 - 852.46 821.1 821 892.55 849.3 852 895.71 873.2 885 914.27 903.5 898 937.52 928.2 927 959.39 935.6 - 965.96 939.0 - 973.31
BVPS UFSAR UNIT 1 Rev. 19 2 of 3 Table B.3-16 (CONT'D)
NEUBERT/WESTDYN COMPARISON OF INFLUENCE COEFFICIENTS:
Neubert Influence Coefficients x 10 5 in/lb Calculated Measured Calculated Measured 1 x 0.820 0.822 1 z 0.133 0.115 2 x 0.835 0.810 2 z 0.925 0.89 3 x 0.310 0.330 2 z 0.914 0.947 4 x 0.311 0.295 4 z 0.134 0.124 5 x 0.740 0.740 5 z 0.305 0.260 6 x 1.304 6 z 0.305 7 x 1.861 7 z 0.305 0.280 8 x 1.874 1.83 8 z 0.810
9 x 1.891 9 z 1.486
10 x 1.906 1.88 10 z 1.994 2.08 11 x 1.327 11 z 1.981
12 x 0.740 0.655 12 z 1.967 2.05 13 x 0.740 13 z 1.466 14 x 0.740 14 z 0.802 WESTDYN Influence Coefficients x 10 5 in/lb 1 x 0.814 1 z 0.138
2 x 0.834 2 z 0.950
3 x 0.317 3 z 0.937 4 x 0.308 4 z 0.134 5 x 0.712 5 z 0.305
6 x 1.232 6 z 0.305 7 x 1.753 7 z 0.305
BVPS UFSAR UNIT 1 Rev. 19 3 of 3 Table B.3-16 (CONT'D)
WESTDYN Influence Coefficients x 10 5 in/lb (Cont'd)
Calculated Measured Calculated Measured 8 x 1.768 8 z 0.792
9 x 1.784 9 z 1.496
10 x 1.798 10 z 1.984
11 x 1.255 11 z 1.969
12 x 0.712 12 z 1.955 13 x 0.712 13 z 14.76 14 x 0.712 14 z 0.734 Results: The Neubert problem, a well documented three- dimensional frame problem, was used. Frequencies from WESTDYN were compared to those obtained by Neubert. Frequencies less than 200 cps varied by less than 2 percent. This variation increased as frequencies became larger, with variations up to 15 percent. It should be noted that at these higher frequencies, the frequencies which are closest do not necessarily represent the same
mode.
In comparing influence coefficients, forces in the x and z directions were applied at Node Point 10. Variation from Neubert's results was less than 5 percent in all cases and usually much less.
Reference:
- 1. E. Neubert, "Dynamic Behavior of a Foundation-like Structure, Mechanical Impedance Method", ASME (1958).
BVPS UFSAR UNIT 1 Rev. 19 1 of 1 Table B.3-17 WESTDYN TEST PROBLEM NUMBER 5 Object: Determine the ability of WESTDYN to calculate individual and cumulative modal response to shock spectra input. Combination by both absolute sum, and square root of the sum of the squares, is calculated for transverse displacements and bending moments in a lumped mass cantilever. Comparison is then made between WESTDYN, and hand calculations based on Response of Structural Systems to Ground Shock, by D. Young, Yale University.
Results: The response given by WESTDYN agrees very well with that found by the hand calculations. The maximum deviations from Young are 0.4 percent for displacements, 1.5 percent for bending moments, for the absolute sums.
Freq Point 1 Point 2 Point 3 Point 4 Point 5 Hand 3.0 4.230 2.767 1.421 0.406 0.000 Calc. 17.6 -0.417 0.114 0.346 0.190 0.000 46.7 0.065 -0.071 0.020 0.077 0.000 81.5 -0.009 0.016 -0.025 0.025 0.000 WESTDYN 3.0 4.229 2.768 1.423 0.407 0.000 17.49 -0.417 0.113 0.346 0.192 0.000 45.75 0.065 -0.070 0.019 0.078 0.000 78.27 -0.009 0.016 -0.024 0.024 0.000 Total System Response Hand ABS SUM X 4.721 2.967 1.811 0.698 0.000 Calc. ABS SUM MZ 0 1169. 1363. 1468. 2586.
RMS X 4.252 2.770 1.463 0.456 0.000 RMS MZ 0 647. 776. 877. 1463. WESTDYN ABS SUM X 4.720 2.967 1.812 0.701 0.000 ABS SUM MZ 0 1163. 1361. 1474. 2595.
RMS X 4.250 2.771 1.465 0.457 0.000 RMS MZ 0 643. 782. 890. 1484.
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