The application of NASTRAN to seismic analysis by considering the example of a nuclear power plant control panel was considered. A modal analysis of a three-dimensional model of the panel, consisting of beam and quadri-lateral membrane elements, is performed. Using the results of this analysis and a typical response spectrum of an earthquake, the seismic response of the structure is obtained. ALTERs required to the program in order to compute the maximum modal responses as well as the resultant response are given. The results are compared with those obtained by using the SAP IV computer program

Pamidi, M. R.

Pamidi, P. R.

English

NASA Technical Reports Server

MODAL SEISMIC ANALYSIS OF A NUCLEAR POWER
PLANT CONTROL PANEL AND COMPARISON WITH SAP IV
by
M. R. Pamidi
Sargent and Lundy Engineers
Chicago, lllinois
and
P. R. Pamidi
Computer Sciences Corporation
Hampton, Virginia
SUMMARY
This paper deals with the application of NASTRAN to seismic analysis by
considering the example of a nuclear power plant control panel. A modal analy-
sis of a three-dimensional model of the panel, consisting of beam and quadri-
lateral membrane elements, is performed. Using the results of this analysis
and a typical response spectrum of an earthquake, the seismic response of the
structure is obtained. ALTERs required to the program in order to compute the
maximum modal responses as well as the resultant response are given. The re-
sults are compared with those obtained by using the SAP IV computer program.
INTRODUCTION
Current government and industry regulations [References 1 and 2] require
that the safety-related systems, structures and components of nuclear power
plants be designed to withstand specified seismic excitations without loss of
capability to perform their safety functions. This requirement is necessary
in order to ensure
(a) continued operation of the reactor without undue risk to the health
and safety of the public during an Operating Base Earthquake (OBE),
and,
(b) shutdown of the reactor and its maintenance in a safe shutdown con-
dition following a Safe Shutdown Earthquake (SSE).
The design of such equipment to withstand seismic disturbances involves
dynamic analysis, testing or a combination of both. Seismic qualification by
analysis alone is deemed sufficient provided the safety function of a structure
or component is assured by its structural integrity. Thus, for instance, most
mechanical equipment, such as heat exchangers, tanks, pressure vessels, etc.,
are usually qualified by analysis. Qualification by testing is recommended
J-LJ
https://ntrs.nasa.gov/search.jsp?R=19770013565 2020-03-20T07:35:59+00:00Z
in those cases where functional operability is not necessarily assured by
structural integrity. Thus, most electrical equipment, such as switchgears,
motor control centers, control panels, etc., are usually qualified by testing.
However, in many instances, testing is impractical either due to the size of
the equipment involved or due to the prohibitive cost entailed by such testing.
In such cases, a detailed dynamic analysis of the equipment, such as a control
panel, is performed and the various associated electrical instrumentation and
devices are then tested to acceleration levels determined by the analysis.
In this study, the application of NASTRAN to seismic analysis has been
discussed by considering the example of a nuclear power plant control panel.
A modal analysis of a three-dimensional model of the panel, consisting of beam
and quadrilateral membrane elements, is performed. Using the results of this
analysis and a typical response spectrum of an earthquake, the seismic response
of the structure is obtained. The results are compared with those obtained by
using the SAP IV computer program.
FORMULATION OF THE SEISMIC ANALYSIS PROBLEM
Obtaining the Modal Responses
The dynamic behavior of a system having multiple (n) degrees of freedom
and subjected to seismic excitation is described by a set of differential
equations represented by
[M] {u} + [C] {u} + [K] {u} : - [M] [D] {uf} (1)
where [M], [C] and [K] are the (n x n) mass, damping and stiffness matrices
respectively of the system; {u} is the (n x I) displacement vector of interest;
{uf} is a (3 x I) vector that represents the time-dependent floor acceleration
in the three component (X, Y and Z) directions; and [D] is an (n x 3) direction
cosine matrix consisting of ones and zeroes that selects the masses that are
involved in the motion in the three directions. The negative sign in this
equation merely indicates that the effective load due to the seismic distur-
bance is opposite to that of the floor acceleration.
The displacement vector {u} in Eq. (I) may be expressed in terms of the
normal coordinates as
{u} : } "i : {w} (2)
i =I
where {w} is an (n x I) vector that represents the normal (or generalized) coor-
dinates wi and [@] is an (n x n) matrix whose columns {@i } are the n eigenvectors
of the free, undamped system given by
[M] {u} + [KJ {u} : 0 (3)
516
By using the orthogonal properties of the eigenvectors and utilizing the
relationships that exist among the generalized mass, damping and stiffness
quantities at any mode, Eqs. (l) and (2) can be combined to give a set of n
uncoupled equations in the nomam coordinates as follows [Ref. 3]:
{_i + 2 _i miwi + m_ wi = - {Fi}T{uf }' i = I, 2, ..... , n (4)
where _i is the damping ratio and mi is the natural frequency of the i th mode.
{F i} is a (3 x 1) vector whose elements represent the so-called modal parti-
cipation factors in the three component directions for the i th mode and is given
by
{Fi}T= I_!xl T = {_i }T [M] [D]F!Ylz {@i} T [M] {@i} (5)
The denominator on the right hand side of the above equation is the generalized
th
mass for the i mode.
Equations (4) can be solved for significant modes by direct integration if
the time-history of the floor acceleration {_f} is known. The solutions for the
various significant modes can then be superimposed as per Eq. (2) to obtain the
total solution. However, from a design point of view, it is simpler and often
more convenient and economical to obtain the maximum displacements in any given
mode by response spectrum analysis. This approach involves the use of design
spectra derived from past earthquake data.
re reenh soera s acemens,or,ehmo e
_diy
(}_diz
for excitations in the X, Y and Z directions. The corresponding spectral velo-
cities {Svi} and spectral accelerations {Sai} are related to the spectral dis-
placements by
{Svi} {Sai}
{Sdi} - = _ (6)
The maximum response for the i th mode due to the individual spectral dis-
placements Sdi x, Sdiy and Sdi z in the X, Y and Z directions respectively is
D.I./
given by [Ref. 3]:
{Ui}xma x {@i } Fix Sdi x (7a)
{u i = {@i }}Ymax Fiy sdiy (7b)
{u i} = {@i } Fiz Sdi zZmax
(7c)
The maximum response for the i th mode due to simultaneous seismic exci-
tations in the three component directions is obtained by combining Eqs. (7a),
(7b) and (7c) and is represented by I
• + {u i + {u i{Ui}max = {Ul}xmax }Ymax }Zmax (8)
or {Ui}ma x = {@i } Gi (9)
where Gi is a scalar quantity given by the product
Gi = {Fi}T{Sdi} (10)
Eq. (9), which gives the maximum response for the i th mode, can be genera-
lized to give the maximum response for any of m modes (I !m _n) by the single
matrix equation
[U']max = [@'] diag[[F']T[s_]] (11)
where
[U']ma x = [{Ul}ma x {U2}ma x ..... {Um}ma x] (12a)
Eq. (8) gives a conservative estimate for the maximum response for the i th mode.
It is acceptable to the regulatory authorities to compute this response by tak-
ing the square root of the sum of the squares of the maximum responses in the
three component directions [Ref. 4].
518
and
[@'] = [{@l } {@2 } ..... {@m }]
[F'] = [{Fl} {F2} ..... {Fm} ]
[S_] = [{Sdl} {Sd2} ..... {Sdm} ]
Eq. (ll) can be rewritten as
(12b)
(12c)
(12d)
[U']ma x = [@'] [G']
where [G'] = diag[F']T[s_]
l 0 ..... 0-
G2 ..... 0
• _ e• •
• Io. •
0 0 ..... G_
-m
The elements of the (m x m) diagonal matrix [G'] are given by Eq. (10).
(13)
(14)
Combining the Modal Responses
The total response of the system can be obtained by combining the maximum
responses of the individual modes involved as given by Eq. (13). The exact
manner in which these modal responses are combined is, however, a matter of
judgment and there is no one way for obtaining the total response. When the
modes are not closely spaced, 2 current regulatory practice [Ref. 4] requires
that the resultant response (whether it be displacement, stress or other quan-
tity) be obtained by taking the square root of the sum of the squares (SRSS)
of the corresponding maximum responses for the individual modes involved. When
the modes are closely spaced, it is required that the total response be computed
by any one of three methods acceptable to the regulatory authorities. Referred
to as the Grouping Method, the Ten Percent Method and the Double Sum Method, the
details of these methods are given in Reference 4.
Two modes are said to be closely spaced if their frequencies differ from each
other by I0% or less of the lower frequency.
519
ANALYSIS
Analysis by NASTRAN Program
NASTRAN cannot directly perform seismic analysis, but can be adapted for
the purpose. The procedure employed here corresponds to the theoretical devel-
opment presented in the previous section. The method essentially involves two
major steps as indicated below3:
Step I. Perform a normal mode analysis using Rigid Format 3 and obtain the
significant modes."
Step 2. Once the significant natural frequencies are known, input the appro-
priate spectral displacement matrix [S_] [see Eq. (12d)] and the
direction cosine matrix [D] [see Eq. (I)] via DMI bulk data cards
and repeat the normal mode analysis using the following ALTERs to
Rigid Format 3 (Level 16) and employing N_RM = MASS (normalization
to unit value of the generalized mass) on the EIGR bulk data card
[Ref. 7]:
ALTER 106 $
MPYAD PHIA,MAA,/DUMMYA/C,N,I $
MPYAD DUMMYA,DIRCOS,/MODEPF/C,N,O $
MPYAD MODEPF,SEISMIC,/DUMMYB/C,N,O $
DIAGONAL DUMMYB/DUMMYC/C,N,SQUARE $
MPYAD PHIA,DUMMYC,/PHIASS/C,N,O $
ALTER I08 $
SDRI USET,,PHIASS,,,GO,GM,,KFS,,/PHIG,,QG/C,N,I/C,N,REIG $
ALTER 121 $
TRNSP PHIASS/PHIASST $
MPYAD PHIASS,PHIASST,/DUMMYD/C,N,O $
DIAGONAL DUMMYD/SRSSDISP/C,N,COLUMN/C,N,O.5 $
MATPRN SRSSDISP,,,,// $
ENDALTER $
The adaptation of NASTRAN for seismic analysis has also been discussed by
other users [Refs. 5 and 6].
For seismic analysis purposes, a mode is considered significant if its fre-
quency is less than or equal to 33 Hz.
520
The data blocks used in the above ALTER package have the following corres-
pondences to the matrices mentioned in the previous section:
PHIA - [¢']
MAA - [M]
DIRC(_S - [D]
M(_DEPF _= [F']T
SEISMIC _ [S'd]
DUMMYC z [G']
PHIASS _ [U']max
The so-called eigenvectors printed out by the above analysis actually repre-
sent the maximum modal responses (displacements) as given by Eq. (13). The
stresses obtained correspond to these displacements.
The output data block SRSSDISP in the above ALTER package is an (n x l)
vector that represents the resultant response obtained by taking the square
root of the sum of the squares (SRSS) of the maximum modal displacements. The
corresponding SRSS stresses can be obtained by combining the individual modal
stresses.
Analysis by SAP IV Program
SAP IV can perform seismic analysis directly without the need for a separate
intermediate run just to obtain the significant modes. The proportions of the
seismic excitations in the three directions are specified and the spectral infor-
mation (displacements or accelerations) is input as a table of spectral values
versus period. The maximum modal displacements and the resultant (SRSS) dis-
placements and stresses are automatically output. The details of the method
are explained fully in Reference 8.
FINITE ELEMENT MODEL
The basic details of the finite element model of the control panel considered
are shown in Figures l, 2 and 3. Beam elements of three different cross sections
and quadrilateral membrane elements of two different thicknesses are used to model
the structure. The beam elements are represented by the CBAR elements in NASTRAN
and by the three-dimensional beam elements (element type 2) in SAP IV; the mem-
brane elements are represented by the CQDMEM elements in NASTRAN and by the plane
stress quadrilateral membrane elements (element type 3) in SAP IV. A total of
265 active degrees of freedom are involved in the analysis. The complete details
of the model can be obtained from the authors.
521
RESULTS
Using essentially identical input data, the finite element model described
above was analyzed by both NASTRAN and SAP IV programs following the procedure
outlined earlier. Seismic excitations of equal magnitude in the three component
directions were assumed. The spectral data used was based on the El Centro
(Calif.) earthquake of 1940. A damping of 2% (see Reference 9 for guidelines
in this regard) was assumed.
The results of the analysis are presented in Tables I, 2 and 3. Table 1
lists the significant natural frequencies obtained by the two programs. Table
2 gives the corresponding modal participation factors. Table 3 shows some re-
presentative resultant (SRSS) displacements of significant magnitude.
It can be seen from Table 1 that the agreement between the significant
natural frequencies obtained by the two programs is excellent. The modal part-
icipation factors given in Table 2 agree well too, except when their magnitudes
are small; this is due to small differences that exist in the various eigenvector
components (not shown) obtained by the two programs. The representative resultant
(SRSS) displacements of significant magnitude shown in Table 3 also agree well,
but the same is not true when they are of smaller magnitude. This is due not
only to the small differences in the modal participation factors involved, but
also to the different manner in which the spectral data is input to the two
programs. The agreement in the results, on the whole, is quite good.
SUMMARY AND CONCLUSIONS
The application of NASTRAN to seismic analysis has been discussed by con-
sidering the example of a nuclear power plant control panel. A modal analysis
of a three-dimensional model of the panel, consisting of beam and quadrilateral
membrane elements, is performed. Using the results of this analysis and a typi-
cal response spectrum of an earthquake, the seismic response of the structure
is obtained. ALTERs required to the program in order to compute the maximum
modal responses as well as the resultant (SRSS) response are given. The results
are compared with those obtained by using the SAP IV program. The agreement, on
the whole, is quite satisfactory.
The paper demonstrates the adaptability and suitability o£ NASTRAN for seis-
mic analysis. The greater choice of elements offered by NASTRAN as well as the
availability of such desirable features as the CNGRNT capability (which can re-
sult in significant reductions in running times particularly for large problems)
[Ref. 7] and Guyan reduction [Ref. lO] make this versatile program an attractive
tool for seismic analysis of large structures.
522
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REFERENCES
Regulatory Guide 1.29, Seismic Design Classification, U. S. Atomic Energy
Commission, Directorate of Regulatory Standards, Washington, D. C., Revision
l, August 1973.
IEEE STD 344-1975, IEEE Recommended Practices for Seismic Qualification of
Class IE Equipment for Nuclear Power Generating Stations, IEEE, New York,
1975.
Wiegel, R. L., (ed.), Earthquake Engineering, Prentice-Hall, Englewood
Cliffs, N. J., 1970.
Regulatory Guide 1.92, Combining Modal Responses and Spatial Components in
Seismic Response Analysis, U. S. Nuclear Regulatory Commission, Office of
Standards Development, Washington, D. C., Revision l, February 1976,
Go, J. C., "Seismic Analysis of Nuclear Power Plant Structures", NASTRAN:
Users' Experiences, NASA TM X-2893, September 1973, pp. 243-249•
Setlur, A. V. and Valathur, M., "Some Studies on the Use of NASTRAN for
Nuclear Power Plant Structural Analysis and Design", NASTRAN: Users'
Experiences, NASA TM X-2893, September 1973, pp. 585-594•
The NASTRAN User's Manual, (Level 16.0), NASA SP-222(03), March 1976.
Bathe, K. J., Wilson, E. L., and Peters•n, F. E., SAP IV: A Structural
Analysis Program for Static and Dynamic Response of Linear Systems, Uni-
versity of California, Earthquake Engineering Research Center, Berkeley,
California, June 1973.
Regulatory Guide 1.61, Damping Values for Seismic Design of Nuclear Power
Plants, U. S. Atomic Energy Commission, Directorate of Regulatory Standards,
Washington, D. C., October 1973.
The NASTRAN Theoretical Manual, (Level 16.0), NASA SP-221(03), March 1976.
J_J
Table I. Natural Frequencies of Significant Modes
Mode
no.
1
2
3
4
5
6
7
8
9
I0
II
12
13
Natural frequencies (Hz)
NASTRAN results
0.6352E+01
0.6563E+01
0.6699E+01
0.I013E+02
0,I180E+02
0.1401E+02
0.1648E+02
0.1652E+02
0.1665E+02
0.1706E+02
0,2371E+02
0.2578E+02
0.3082E+02
SAP IV results
0.6352E+01
0.6563E+01
0.6700E+01
0.I013E+02
0.I180E+02
0.1401E+02
0.1649E+02
0.1652E+02
0.1665E+02
0,1706E+02
0.2370E+02
0.2579E+02
0.3082E+02
524
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Modal seismic analysis of a nuclear power plant control panel and comparison with SAP 4

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