The document discusses seismic analysis methods for nuclear assets according to Russian methodology. It describes analyzing structural response to seismic loads using time history and response spectrum methods. The Russian approach models systems as spatial structures and uses SRSS and CQC methods to combine modal responses. Pipelines are modeled as 3D rod systems and damping is assumed to be 2% of critical. The methodology is similar to American approaches but with some differences like a lower cut-off frequency for static analysis.

1. INDIAN STRUCTURAL INTEGRITY SOCIETY
Workshop on Structural Integrity
Assessment of Nuclear Energy Assets
9th – 10th May 2018
AERB Auditorium, Niyamak Bhavan-B, Mumbai

2. Seismic Analysis
By : Mohammad Salman
Engg-LWR, NPCIL-HQ
WORKSHOP
AS PER “PNAE G-7-002-86”
Structural Integrity Assessment of Nuclear Energy Assets

3. Presentation Outline
• Introduction
• Russian Methodology as per PNAE G-7-002-86
• Cyclic Strength Calculation
• Use of equivalent static load method of analysis
• Procedure used for modelling
• Interaction of other pipelines with seismic category I
piping
• Combination of modal response
• Analysis procedure for damping
• Summary

4. Introduction
• “DYNAMIC ANALYSIS“ of Systems, Structures and
Components of NPP is one of the essential requirement.
• Dynamic means time varying.
• One of the Dynamic load could be “SEISMIC LOAD”.
• Response of SSC could be displacement, deformation,
velocity, acceleration, strain and stress.
Load (t) Response (t)“Nuclear Component”
■ Equation of motion for Earthquake loading for MDOF system:
        )()()()( txMtxCtxKtxM g
 
Damping
Force
Inertia
Force
Due to internal
stresses.

5. • Equation of motion of forced vibration of damped SDOF
system:
)()()()( tPtxctkxtxm  
k
c
m
P(t)Fs(t)
Fd(t)
)(tx
■ Equation of motion for Earthquake loading for MDOF system:
        )()()()( txMtxCtxKtxM g
 
Damping
Force
Inertia
Force
Due to internal
stresses.
Continued…

6. Seismic Analysis Methods
• Time History Method
1) Method of Modal Superposition
2) Direct Integration Method
• Response Spectrum Method
1) Modal Combination Method

7. Continued…
Direct Integration Methods
Implicit methods
Require iteration
Eg. Central Difference
method, Runge – Kutta
method
Explicit methods
Do not require
iterations
Eg. Newmark Beta
method, Wilson theta
method.

8. Which one is better?
• In Response Spectrum Method, the peak values of
response (displacement, deformation, acceleration
etc.) are determined for each mode and then modal
combination is done.
• In Modal Time History method, the instantaneous
values of response (displacement, deformation,
acceleration etc.) are determined for each mode
then modal combination is done.
• Response Spectrum Method: More Conservative
• Modal Time History: More Accurate

9. Russian Methodology as per
PNAE G-7-002-86
• The basic document regulating rules and norms of seismic
design of the NPP equipment and pipelines is NP-031-01
(STANDARDS FOR DESIGN OF SEISMIC RESISTANT NUCLEAR
POWER PLANT).
• AERB/NPP-PHWR/SG/D-23.
• The basic document regulating strength estimation of the
NPP equipment and pipelines is “Regulations for Strength
Calculation of Equipment and Pipelines of Atomic Power
Plants. PNAE G-7-002-86, Moscow, Energoatomizdat,
1989”.

10. • Selection of the seismic analysis method:
As per Table A9.2 of Appendix-9 of PNAE G-7-002-86,
selection of seismic analysis methods are done on following
basis.
• Mode extraction in modal analysis is only valid for linear
systems. Therefore response spectrum method is only
applicable for linear analysis.
Table A9.2

11. • Response spectrum method with floor response spectra as
input are used for analysis of equipment and piping.
• Non-linear analysis is not performed for any of the
structures, systems and equipment of the reactor plant.
• Seismic qualification:
- For seismic category I : Safe Shutdown Earthquakes (SSE) and
Operating Basis Earthquakes (OBE)
- For the seismic category II : only for OBE.

12. Cyclic Strength Calculation
• As per PNAE G-7-002-86 the cyclic strength calculation is done
by using maximum amplitude of stresses, determined by
combination of loads from NOC+OBE.
• No of Loading Cycles for OBE : 50 cycles ( 10 loading cycles in 5
OBE events)
• Exemption: Cyclic strength analysis for seismic loads is not
required to be performed, If the total damageability (from the
loads, acting on the equipment and pipelines without regard
for seismic loads in the course of NPP operation) does not
exceed 0.8.

13. Use of equivalent static load method of
analysis
• It is only applicable for seismic category II equipment.
• In addition this method is not applied for piping system of
any seismic category as detailed dynamic analysis is carried
out.
• If first natural frequency > 20 Hz.
• Calculation using static method is performed by means of
multiplication of accelerations, obtained from response
spectrum, by the factor of 1.3 for the frequencies within the
range of 20…33 Hz.
• and by a factor of 1.0 for the frequencies exceeding 33 Hz.
• For the equipment and piping, the first natural frequency of
which is below 20 Hz, the calculation is performed by
dynamic methods only.

14. Procedure used for modeling
• Calculation model is selected in such a way as to provide
more exact representation of the main dynamic properties
of the equipment and pipelines under consideration. The
considered systems are represented in the form of spatial
models with the assigned stiffness and inertia characteristics
simulating the properties of actual system.
• The pipeline is modeled by the calculation software as a
linear elastic 3-D rod system.
• Distributed mass of pipelines is condensed in nodes of
calculation model, the discrete masses of equipment could
have both linear, and angular (moments of inertia) degrees
of freedom.

15. Procedure used for modeling

16. Interaction of other pipelines with seismic
category I piping
■ Pipelines of other categories connected to them up to their
first immovable support are considered in the common
calculation model.
■ Example: In discharge pipeline of pressurizing system,
pipelines from pressurizer to PSD (Pulse Safety Device) is of
seismic category I and the pipelines from PSD to relief tank
is of seismic category II.

17. Three components of earthquake motion
• Seismic loads on the structure, as well as displacements,
accelerations and internal force factors in their components
are determined by two independent horizontal and vertical
effects.
• The resulting value is evaluated as the square root of sum of
squares of values of the studied factor under seismic impact
along the corresponding axis.

18. Combination of modal response
• SRSS (Square-Root-of-Sum-of-Squares)
• CQC (Complete Quadratic Combination): all terms are
summed up with regard of their signs
• CQC method is used to combine the responses due to closely
spaced modes
• Then the response due to the missing mass is determined
and combined with the response due to lower modes of
vibrations by SRSS rule.

19. Analysis procedure for damping
• Damping in the equipment and piping seismic analysis is
considered using method of internal friction.
• The value of relative damping is assumed as per PNAE G-7-
002-86 equal to 2 % of critical damping.
• This damping value is assumed to be constant at OBE and
SSE for the equipment and pipelines irrespective of diameter
and natural frequency.
• As ASME Appendix N:

20. Summary
• Basic methodology for Seismic analysis is same in
American and Russian approach.
• Cut off frequency for equivalent static analysis is 20Hz
in PNAE G-7-002-86 instead of 33Hz.
• The value of relative damping is assumed as per PNAE
G-7-002-86 equal to 2 % of critical damping.

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