ML20197D469
| ML20197D469 | |
| Person / Time | |
|---|---|
| Site: | Trojan File:Portland General Electric icon.png |
| Issue date: | 11/22/1978 |
| From: | Broehl D PORTLAND GENERAL ELECTRIC CO. |
| To: | Schwencer A Office of Nuclear Reactor Regulation |
| Shared Package | |
| ML20197D476 | List: |
| References | |
| TAC-07551, TAC-08348, TAC-11299, TAC-7551, TAC-8348, NUDOCS 7811280324 | |
| Download: ML20197D469 (35) | |
Text
{{#Wiki_filter:. _ _ - _ _ g b1 ' s l'ORTLAND CENEllAL 15LECTitIC COMI'ANY l2l S.W SALMON STREET PORTLAND, OREGON 972O4
- s s,sma vic e eme sio n wt 1
Novembe r 22, 1978 l Trojan Nuclear Plant Docket 50-344 f License NPF-1 Director of Nuclear Reactor Regulation ATTN: Mr. A. Schwencer, Chief l Operating Reactors Branch #1 l Division of Operating Reactors U. S. Nuclear Regulatory Commission l Washington, D. C. 20555
Dear Sir:
Attached is supplementary documentation in support of the floor response spectra provided in our submittals of October 27, 1978 and November 2, 1978, and in response to NRC Staff requests for additional information. Sincerely, 0 - 0 0\ q g l i 2 8 0 31y
, C' s s
SUPPLEMENTARY RESPONSE TO NRC OUESTIONS This response contains supplementary document'ation in sup+ port of the floor response spectra provided in the submit-tals of October 27, 1978 and November 2, 1978 in accordance with the following NRC staff request for information: Verify that the spectra are adequate to bound the responso of the safety related equipment, nystems, components and piping in the Control-Auxiliary-Fuel Building Complex con-sidering: l
- 1. Use of design f6 of 5000 psi rather than the as built fl of 6000-6500 psi
- 2. Poinson's ratio of 0.25 rather than a lower l more appropriate value j 1
- 3. And any other dif ferences between the design and on built properties.
Include in your consideration the effect of time on theco parameters and expected variation in these paremeters; variation in mass, variations due to analysis techniques, etc. Lint all parameters and variationn in thene parameters and provide the basis for these choices. State and justify the statistical adequacy of the methods used to account for the probable error (peak broadoning) on both the upper fregunney and the laver frequency bound j r of the response spectra. Also state and juntify any as-l numptions regarding damping vs. carthquake levels.
-l-
8 e verify that all the factors considered above (parameter , variation, stiffness degradation, etc.) would not advernely impact the vertical response spectra. l Included in the response to the above the ef fects of inter-action with regard to possible tensjon in the walls.
RESPONSE
The expected values and the variationn of the parameters that could produce structural frequency variations are described as follows: (1) Concrete and Masonry Strengths: The expected concrete and masonry strengths used to evaluate the modulus of clasticity of the walls are 6600 psi and 3680 psi respectively. This resulta in an ef fectivo nodulus of elasticity equal to 4.59 x l' 06 6 The basis pal with a variation of i 0.29 x 10 psi. for these values is given in Appendix A. (2) Poisson's natio Poisson's ratio used for thin evaluation is 0.22 with a variation of i 0.02. The basin for these valuen is given in Appendix D. l
f S (3) System Stiffness Reduction Factors The expected values of the stiffnens reduction fac-tors for the 0.25g SSE and a 0.114 lower level earth-quake are presented in Appendix C. These values are baned on the PCA and the Berkeley test results. The variations in the stiffness reduction factors are 111%. (4) Structural Mannes since detailed weight calculationn were performed in the process of developing the STARDYNE finite element model, a high confidence level wan achieved in the structural mann determination. However, a 15% varia-tion in the structural mass used in the STARDYNC analysis in assumed. (5) Other Uncertaintics Uncertainties in the structural modeling and anal-ysin techniquan have been minimized by using a finite element model, making a detailed weight estimate on the existing structure, and using concrete ntrength from actual tests. There are, however, some minor effects not specifically accounted for in the overall analysis. One such effect is the stiffness and capacity of some secondary block walls. All the walls that have been omitted from specific consideration are relatively thin with respect to their height and as such will not contribute nignificantly to the total structural stiff-ness. The St minimum variation in frequency specified BC-TOP-4A and Reg. Guide 1.122 will be adequate to cover thin and other negligible ef fects. The expected values of the first three parameters concidered above are based on the as-built structural properties with the effect of aging included. These values are dif ferent from the design values used in the STARDYNE analysis. As a result, the structural frequencies determined from the STARDYNR ana-lysis should be adjusted to correspond to the expected values of these parametern. The resulting frequencies, as adjusted, are-the expected frequencies of the structure for the as-built
> condition at the particular stress level considered. Varia-tions in all five parameters will result in variations in the expected frequencies. Since the variations in each of the pa-rameters result from independent sources and these variations are upper and lower bound values, the total frequency varia-tion due to the effect of individual variations can be com-bined using the SRSS method. This is consistent with the intent of the SRSS combination method and complies with the criteria stated in BC-TOP-4A and Reg. Guide 1.122.
Por the 0.25g SSE, the frequency adjustmen t factors and the frequency variations are tabulated in Table 1. As shown in j this table, the total frequency variation is 8%. Using the ! t frequency adjustment factors and the +8% variation shown in ! Table 1, the expected major frequencies of the structure, and the upper and lower bound spectral peak frequencies are cal-culated and listed in Table 2. The spectral peak frequency rangen shown in thin table can be compared with those of the STARDYNC floor spectra as presented in the October 27, 1978 and November 2, 1978 submittals. The comparison shows, that the spectral peak frequrfncy ranges are within the STARDTNE response spectra provided in the October 27 and November 2, 1978 submittals in both N-S and E-W directions for the Con-trol Building and in the N-S direction for the Auxiliary and Puel Duildings. The comparison also shows a maximum 71 addi-tional widening on the high frequency side of the second peak j of the Auxiliary and Fuel Building spectra, between the fre-quency rangen of 13 cpn and 17 cps and a 4% additional widen-
~4-I l
1 - - ._-
_ _ _ _ __ _ __ ~ Ing on the major peak of the 0.57. E-W spectrum of the Auxiliary Building El. 61' in the frequency range of 9-12 cps. These additional wideningn are due to the use of more conservative higher stiffness reduction factors in the Fuel Building. The lower bound spectral peak frequencies are still covered by the lower bound STARDYNE spectral peak frequencies even with [ a ductility factor of 1.59 considered for the Control Building in the N-s direction. Consistent'with our response of October 16, 1978 and Novomber 1, 1978 we will take suitable corrective , action in all cases where the seismic capability of equipment, components or piping are ca13cd into question by this widen-ing of the spectra. For an earthquake having a ground acceleration lower than 1 0.259, the structural recponse will be lower and the stiff-noss reduction factor higher than those of the SSE. For the purpose of evaluating the adequacy of the STARDYNE floor re-sponse spectra for lower level earthquakes, a 0.11g earthquake
- , is connidered. The expected stiffnens reduction factors and ;
their variations for a 0.119 earthquake are discussed in Ap- 4 i pendix C. Using these values along with the previously dis- l cussed expected values and variations of parameters, the fre- : quency adiustment factors and the frequency variations associ- f ated with the 0.119 earthquake are calculated and presented in Table 3. The expected values of the major structural frequencies and the upper and lower bound spectral peak fre-quencios using a +8% peak widening criteria are tabulated in Tabic 4. Since a 0.119 earthquake will roralt in a struc-tural response about 0.73 of the 0.259 SSE risponse as ex-
- plained in Appendix C, the upper and , lower.b dund f requencies
.shown in Tabic 4 'should be compared to the STARDYNE spectral peak frequency ranges associated with a peak magnitude about
~ i 0.73 of the SSE peak magnitude. This comparison shows that -t the 'STARDYNE spectra are adequate f or the 0.11g carthquake. j i l 1 s e
+- - = , , y- .- ,- . , + -- . ,_m,-- ...e v,,, n-,, rv,-..,,ev-.m-,-..,,.~a,ew-wr,-e., w.w--.---.-, , . ,..- - , , , , - - +
t 6 Since the initial clastic stiffnessen calculated for the Trojan walls are valid only at a very low shear stress icvel (up to about 30% of the cracking shear stress), the structural complex will respond according to its initial stiffnesses only at an starthquake level much lower than the 0.119 carthquako. At such further reduced 1cvel, the peaks of the.STARDYNR spec-tra are wide enough to accommodate the higher structural fre-quencies as a result of less stiffne'ss reduction. It is thus concluded that the STARDYNB floor response spectra are ad-equate for any earthquake icvel up to and including the 0.25g ssE. The responne to Ouestion 6 submitted on November 2, 1978, discussed the vertical response spectra. In addition to the parameters considered there, the effect of using tho as-built strength of the concrete and the ef fect of aging are considered. The effect of aging is to strengthen the con-crete, resulting in an increase in the modulus of elasticity which increases the frequency. The slabs are constructed of concrete which has a design compressive strength of either 3000 psi or 5000 psi. The increase in s trength of the con-crete with a 3000 psi design strength is nimilar to that dis-cussed in Appendix A, therefore the change in frequency will be 12 % . This will be partially or totally offset by the de-crease in frequency considering the ef fect of wall flexibili- l ties as discussed in the response to Question 6. This change ,
.3 will not cause the responso to exceed original vertical re- !
sponse spectra. Considering the vortical forces on walls and the influence of these forces on the vertical response spectra, the compressive and possible tensile stressen were investigated. The maximum average compressive stresses from dead load, horizontal, and vertical carthquake on the major shear walls in less than l I l
)
.- . .. ._ --- ~. -- 500 psi. This is less than 10 porcent of the compressive strength; therefore, no change in stiffness is expected. The maximum average tensile stress could be expected to occur in the' South walls due to a North-South earthquake and has a magnitude of approximately 30 psi. The tensile strength of j concrete is approximately 10 percent of the compressive j strength, or 600 psi to 700 psi. Since the average tensile stress is Jess than 5 percent of the tensile strength, no change in the vertical responce will result. Further, the horizontal capacities of the shear walls where tensions may exist due to combined horizontal and vertical responses are about twice the horizontal shear loads. Therefore, no reduc ~ , 1 tion in vertical stiffness will exist. Sunmarizing the previous discussions, the floor response spectra for the Trojan Control-Auxiliary-Fuel Building Com-
. plex are adequate and conservative for the ovaluation of l safety related equipment, systems, components and piping'for any level of earthquake up to and including the 0.259-SSE.
The overall conservatism in these spectra is the result-of accumulating various built-in conservatioms in the total process of the spectra development. These conservatinms can be itemized as follows:
- 1. The combined application of the Trojan design ground spectrum input with a 5% structural damping and a 0.5%
equipment damping for the 0.25g SSE as specified in the Trojan FSAR, resultn in floor spectral peak magni-tudes which are higher than those which would result l from the combined application of the nequlatory Guide l 1.60 spectrum input at 0.259 and the Regulatory Guide I 1.61 ntructural and equipment damping values for the . SSE. l l I 1 l l
I
- 2. The STARDYNE floor response spectra for each floor in each huilding are the renuit of enveloping the spec-tra of many points on the floor with highest responsen.
Thus, the envelope spectra have connervative spectral peak magnitudes for each floor. Additionally, the en-velope spectra contain an inherent amount of peak wid-ening even before the final stage of peak widening.
- 3. The une of the more detailed finite element model of the structural complex in the STARDYNM analysis renults in a more accurate responne prediction and the higher degree of certainty in the response. Furthermore, the parameters considered in conjunction with the spectral peak widening criteria have more definitive valuen and lean uncertaintien associated with them such that a smaller amount of peak !
widening in warranted since these structuren have been l I throughly investigated. Ranges of variation in the valuen of these parameters have been considered and an +8% widen l ing of the peaks was used. In addition, the spectra as j widened were further broadened to the lower frequency side considering the effect of stiffness reduction and inelastic behavior. The neismic qualifications of nafety-related equipment, com-
' ponents and piping in the Trojan Plant have been described in previous submittals. There are added degreen of conserva-tism in the ability of safety-related equipment, components and piping to withstand seismic motion which are not credited in seinmic qualification criteria, but which should also be recognized.
Mechanical and electrical equipment components which are seinmica]1y qualified by generic testing are typically qualified to acceleration leveln much greater than would l
.g_
r_._,_.~~ . . _ . - - - ._ ~, _ r , v be required for a specific plant. Por example, the West-inghouse "High Seismic" Generic Test Spectra, used to qualify much of the Trojan Control Room equipment, exceedn the Control Room floor response npoetra in all cases and by large margins in most f requency ranges. Where generic test spectra are not used for neismic qualification, conservative floor response spectra are used, and some components are qualified to spectra which envelope all locations in the plant where the component might be installed such that component sparea can be inter-changed throughout. I Safety-related electrical cable trays for the Trojan Plant are seismically qualified to SSE accelerations using a combined material and structural damping ratio of 5%. Consideration of the actual energy abnorption characteristics of cable tray nystems suggest much larger available damping, and tests on cable tray systems have confirmed damping ratios on the order of twice the values used in the Trojan Seismic Qualification Analysis. The increase in damping from 5% to 10% would have the ef f ect of significantly reducing peak response accelera-tions. Safety-related piping systems for the Trojan plant are quali-fled by analysis, using a conservative damping ratio for SSE loadings toqcther with conservative loading combinations and allowable stress limits. The seismic analyses of Trojan l nafety-related piping of the SSC evaluation were based on a pipe allowable stress criteria for 1.8 times the materisl allowable stress as specified in the Trojan FSAR rather than 2.4 times the material allowable stresn permitted by the cur-rent code criteria for an SSC. These criteria result in an additional margin of 25% over the l I stress criteria permitted by the codes applicable to the originni design. Stresses on pipe supports generally do not 1 1 _9
~
8 f i 1 l govern the seismic capability of a piping syncer. In addi- i l tion there is an inherent conservatism built into the valves by the manufacturer so that his product een be broadly ap-plied without specific qualification for caen site. It has been our experience that valves can safely tolerate accelera-tion icvels 25% to 50% higher than those initially quoted by the manufacturer. Nozzle loadings for equipment and Vossels~ , have similar margins built in by their manufacturers. ! l l The added conservatisms 'for safety-related equipment, compo- l nents and piping described above are not credited in the scis - mic qualification criteria, but do provide a f urther degree of confidence in the ability of such equipment to withstand I any carthquake up to and including a .2Sg SSE with a consid-
. crobic margin of cafety.
l l l l t
Table 1 Frecuency Adiustment Factors and Frequency Variations for SSE 0.25g Value Used Expected Variation Frequency Variation Parameter in STARDYNE Value in Adjustment in Analysis Value Factor Frequency ] Elastic Modulus 3.67x10 6 4.59xld 10.29x10 6 1.12 13.1% Poisson's Ratio 0.25 0.22 10.02 1.01 10.8% Stiffness Reduction 1.0 See Table ~+11% Ste Table ~+5.4% Factor C-3 C-3 Mass Factor 1.0 1.0 10.05 1.0 +2.5% Other Uncertainties ----- ----- ----- 1.0 15% Frequency adjustment factor exceeding stiffness reduction factor
= (1.12)(1.01) = 1.13 SRSS Variation in frequency = 18.4%
4 11 . _________.__m_.m_- - -___________m_________mm-_____.._. _ _ _ _ _ _
Table 2 Spectral Peak Frequency Range for SSE 0.25g-STARDYNE Frequency + Expected Lower Bound
- Upper Bound ** ,
Direction Frequency Adjustment Frequency Spectral Peak Spectral Peak , (cps) Factor (cps) Frequency- Frequency (cps) (cps) - 6.8 0.90 6.12 5.63 6.61 N-S 9.49 1.00 9.49 8.73 10.25 12.05 1.07 12.89 11.86 13.92 16.22 0.95 15.41 14.18 16.64 8.63 1.01 8.72 8.02 9.42
. E-W 12.11 1.13 13.68 12.59 . 14.77
- Expected frequencies multiplied by 0.92
** Expected frequencies multiplied by 1.08
+ Frequency adjustment factor from Table 1 times the square root of the stiffness reduction factor from Table C-3 t'4 s .
.. .... - - - - , - , - - - . -- - - - . - nm
i l1 Table 3 Frequency Adiustment Factors and Frequency Variations for a 0.110 Earathquake Value Used Expected Variation Frequency Variation
, Parameter in STARDYNE Value in Adjustment in Analysis value Factor Frequency i
Elastic Modulus 3.67x106 4.59x10 6 0.29x10 6 1.12 13 .1 t-Poisson's Ratio 0.25 0.22 10.02 1.01 10.8% Stiffness Reduction 1.0 See Table 111% See Table 15.4% Factor C-3 C-3 Mass Factor 1.0 1.0 10.05 1.0 12.5% Other Uncertainties ----- ----- ----- 1.0 15% l# - l Frequency adjustment factor exceeding stiffness reduction factor
= (1.12)(1.01) = 1.13 .
SRSS Variation in frequency = 18.4% i t
- 13 j -
i
~
i Table 4 Spectral Feak Frecuency Range for 0.llg Earthquake STARDYNE Frequency + Expected Lower Bound
- Upper Bound **
Direction Frequency Adjustment Frequency Spectral Feak Spectral Feak (cps) Factor (cps) . Frequency Frequency (cps) (cps) 6.80 0.97 6.60 6.07 ^7.13 N-S 9.49 1.07 10.15 9.34 10.96 12.05 1.13 13.62 12.53 14.71 16.22 1.00 16.22 14.92 17.52 8.63 1.08 9.32 8.57 10.07 E-W 12.11 1.13 13.68 12.59 14.77
- Expected frequencies multiplied by 0.92
** Expected frequencies multiplied by 1.08
+ Frequency adjustment factor from Table 1 times the square root of the stiffness reduction factor from Table C-4 4
h % a
,t APPENDIX A CONCRETE MODULUS OF ELASTICITY i
The modulus of elasticity of the concrete in the core of the composite walls and in the cells of the concrete blocks is given by; ! E, = 57000 L
) fa (psi) (1) b ..
- j. The compressive streng th of the concrete, CL , has.boen j
- determined for an age of 6 to 7 years which corresponds to 1 l the age of the structure at of the end of 1979. The strength l variation with time is shown in Figure A-1. In this figure, 1
< three sets of information are presented. First is the com- ^l
, ~
- C. ..
pres'sive strength of concrete used in the cores of the-walls l j
- i. ; .
. i'n the Control-Auxiliary-Fuel Duilding complex, . mix'es D1 and D2. The age of the' concrete cy1'inders at testing was 7', ' 28,
~
f-J and 90 d'ye. a Second, in order to extend this data, the com- '! c'. S' , pressive strength of the concrete used in the containment (Reference 1 mixes El and R2,)* is presented which had an
. age at testing of 7, 28,.90, 180, and 365 dayn, (Referenco l 4
7 1). Third, to extend the data even further, a set of curves f rom Reference 2 is used. The curve labeled " Ordinary" was l 1
$* obtained from concrete made with ordinary Portland cement j l
- whereas the " Pozzolan" curve was obtained from concrete made from a cement which included pozzolan. )
The test data from mixes El and 87 show virtually no increase i in compressive strength beyond 90 days. The general informa-l 4 tion from Reference 2 shows a slight increase for the con- j crete containing pozzolan and a smaller increase for ordinary '[ ' }
---- ~. ,
4
- Mixes D1, D2, and El, E2 differ only in amount of cement. All the mixes used the same aggregate and contained pozzolan. Mixes
~
i- D1'and 81.had a 3/4-inch maximum size aggregate and D2 and E2 had a 1 1/2-inch maximum size aggregate. A-1 9
s.. ,
=> ,
concrete. Using this information, the compressive strength of
, the concrete in approximately 6600 psi at 6 to 7 years,which
.gives an clastic modulus of 4.63x106 psi. ,
4 The variation in the modulus of elasticity can also be'asse's- .i
^ i- sed by using the variation in f'c. For mix D1 and D2'the standard deviation of' the compressive strength test data is )
800 psi. This results in a change of +5.9 and'-6.3 percent j (' .in the modulus. For the purposes of this evaluation, the l variation is taken as 6.3 percent. The elastic modulus of the block is, according to the UBC,
' l':- 'given by1 :
Em = 1000 fd (psi)
. where f' is the compressive strength of the masonry block based on the not area. Data on the' concrete block concern-ing the change in strength with age was not available but.
lf the indications are that the change is negligible. The change.
, in the olantic modulus of the composite wall due to possible changes in block strength is negligible, since the net' area of the block is a small' portion of the total crosssectional
-area of the wall.
, The compressive strength of the two types of block us'ed',
/, o '
heavy weight (130 lbs/cu.ft.) and light weight (115 lbs/cu~. d' ft.) are 4100 psi and 2700 psi respectively. Since about
~ '
~ '
30 percent of the walls' use the light weight blocks, an average strength was obtained by:
-(fy ) = 0.3(2700) + 0.7(4100)
= 3680 put The. variation in the modulus of elasticity of the composite
' wall, due to variation in f 'm in taken an.the same percentage i
as for the concrete discussed above. l 4 g 3
- l:, h~2 . . . .
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;1n the STARDYtm finite analysis, the compressive strength of ~ ' '
concreto, Ifght blocks, and heavy block was taken as 5dob psi, 2000 pai, and 2500 poi. Using t.ho as-built aged informdtion
' ,,'. 1. .
the adjustment factor for t.he modulus of clasticity.is as . , , ..o . .
-,Y. follown: ,
- 1 g 600)'(0.75) + 3680 - *(0.25)'= 1'.2$. . ,
,,,.. g (S000) .3(2000) + .7(2500)
~
~ ~
The weighting factor of 0.75 for the. concrete core and' con-7./I .
'I crete cells and 0.25 for the block I's-based on relativo arease ,
' Doing the above adjustment' f oetor, the ef fectivo modulu's is ;
'. i
~1.25 (3.67 X 106 ) = 4.59 x 106 psi.
j: l/ j f'
.s .
+
. References
- 4. . .
~. (: , ~1 " Studies of concrete for Trojan Nuclear Containment: Ves-a . sol-Pinal Report" by David Pirtz, University of Califor- , , [l . nia, Berkeley, June 20, 1973. k., . .
- 2. Nev.illo,.A.M., P.roperties of Concrete, Halsted Press, , ?; 1973, pp. 73
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APPENDIX B
.,t T- -
_ POISSON'S RATIO FOR CONCRETE In general, 'the variation of Poisson's ratio with time in 'small, increasing during the first 2 years after which the value becomes stable (Ref. 1). Although testing of concrete used in the Contro3 I Building did not include determination of Poisnon's natio, repre- j sentative data is availabic from tests performed on the concreto l used in the Trojan Containment. Test data for the concrete. mix used in the Trojan containment (Mix E, f' = 6000 psi) shows the Poisson's ratio between 0.21 and 0.22 (Reference 2). The only '.,' , dif ference between this mix and th'e mix used for.the Control-
,I
- Auxiliary-Fuel Building Complex walls is the cement content. '
Since the aggregate of the respective mixes'is the sameLand , l this in the most important factor in' determining Poisson's ratic for concrete, the mixes w311 have the same Poisson's ratio. The time variation of Poisson's ratio given in Table B-1 shows l Insignificant change. For purposes of this evaluation, the expected value is 0.22 with a variation of +0.02. These values are supported by the information in Reference 1 and data in l l 1 Reference 2. For the concrete used to construct the block, Poisson's ra-I' tio was assumed to be equal to the value for the concrete die-cussed above.
References:
- 1. Troxell, George F.., Harmer E. Davin, and Joe W. Kelley, Composition and Properties of Concrete, McGraw-Hill, New York, 1968, pp. 331.
- 2. Studies of Concrete for Trojan Nuclear Containment Vessel-Final Report by David Pirtz, University of California, nerkeley, June 20, 1973 P 4 n-1
. .nin l l
l I l l Table B-1 Poisson's Ratio for Mix E 1
- s. . . .
Age, Maximum Size Aggregate, Days Inches i
! l 3/4 1-1/2 ;
l 28 0.21 0.22 P e 180 0.22 0.20 365 0.22 0.22 I e e 0
=
4* 4 g ' 'k '
'r, ,
o 9 6 9 h 4 4 e# 7 4
*'O ,
e
, .. [3 2' 4
9
1
- APPENDIX C l l
d
. I
- STIFFNESS REDUCTION FACTORS j !
' Due to the inherent nonlinearity of concrete, the shear Jood i i vs. displacement relationship of reinforced concreto and com- !
) posite shear walls shows nonlinearity even before the onset i of major inelastic behavior (such as the formation of major ! shear cracks in the shear wall). This is exemplified in tents I such as the PCA reinforced concrete shear wall tests (Reference , 1), and the nerkeley block wall tests (Reference 2). Typical ; shear force vs. displacement envelope curves f rom the PCA 1 , tests and the Berkeley tests are shown in Figures C-1 and C-2. ; An enlarged portion of the curve in Figure C-1 below the major in . terms of the chear stress; shear crack is shown in Figure C-3, and strain. It i s clear from this figure that a significant . reduction of shear modulus occurs between the initial ( tan-gent) shear modulus G, and the " secant" shear modulus G at : the cracking stress. The 1.nitial shear . modulus G , is the up -
. . . . .- o
'per bound modulus which'is' applicable only for a very~1ow '
shear stress range, below about 30% of the cracking stress. i The cracking shear modulus GEr is the lower bound modulus for i the shear stress up to the cracking shear stress vEr . Thus, i for a shear stress between 0 and ver , the " secant" shear modu-lus G varies between G o and Ger . For a shear stress greater C-1 t t 2
than v e r, the lower bound G er is uned, since the offect of the i inelastic behavior is considered separately based on the duc-tility factor concept. The shcar modulus reduction factor ! is defined to be the ratic G/qn. This factor varies between I 1.0 and Gc7 /Co depending upon the shear s tress (or strain) i level. The value of the initial shear modulus G can be determined I baned on the following formula: I Gn = E 2(1+v) Where: 1 E = Modulus of elasticity based on tho appl.icable. code (the ACI code for concrete and the UBC e for masonry)~ . ,
' ' M ...g ,
, s y . .
'- -i-
- y.
, ','s,L
.',l
,' c , .
V' = Poisson'~s' ratio -
- s. o ,
Using the same methodology as used in Appendix D of'" Trojan- 'I Control Building Supplemental Structural Evaluation" dated September 19, 1978, the values of Gcr for the composite walls of the Trojan Control Building can bo determined based on the PCA test results (Reference 1) and the Berkeley test results (Reference 2). C-2
.' l N
I e Table C-1 shows the values of G er and v er based on the PCA tests. These values are used to determine the average, high,
}
l and low bound values of G c , as shown in the table. The value. k i of G er f r the block walls (including the effect of cell grout) l z from the Berkeley tests was determined to be 0.09 x 106 psi l
.in Appendix D. Although the test data show scattering, this f
value is used as a representative value, since the contrihu- I tion of the block stiffness to the total stiffness of the 1 Trojan composite wall is small. i The Trojan componite wall has a representative cross-ce'ctional a 4 geometry as shown in Figure C-4. The thickncas of the concrete core is about equal to the thickness of the block (with cell grout). Thus, the value of G f r the componite wall can er be determined by averaging the values of Ger from the PCA tests and the Berkeley tests as was done in Appendix D. The resulting values are shown in Table C-2. # 3 h The STARDYNC finite element analysin used the effective thich-ness which in equal to the concrete core thickness plus one half the block thickness. Thus, the values of G corresponding y er k' to the effective thickness can be calculated from the values for the gross thickness using tF a ratio of t /t = 4/3. The re-g off sulting valuen of G cr for tne ef fective thicknenn are also [; shown in $uo'c C-2. The values of v for the composite wall !! cr 3 shown in Table C-2 are calculated from the cracking stresses > l C-3 i V'
. - . . ..... . . . . . . . - - - c . _ .
a of the PCA tests, adjusted by the core to gross thickness ratio and a f actor of 1.11/1.5 or 0.74, then adding the con-P ibution from the block. The factor of 0.74 accounts for ' the different maximum nominal shear stress ratios between the rectangular section of the Trojan walls and the web and flange section of the shear walls in the PCA test. The initial shear modulus for the composite walls used in the STARDYNE analysis in conjunction with the effective thickness 6 6 Using this is 1.47 x 10 psi [3.67 x 10 / 2(1 + 0.25)]. I value, the shoar modulus reduction factor og at tho cracking stress can be calculated as shown in Table C-2. As shown in thin tabic the average value of a o ic 0.46, and the upper and lower bound values are 0.51 and 0.41, respectively. The 'l
!l upper and lower bound values have a variation of +11% with respect to the average value. Although the variation of the shear modulus at a stress level lower than the cracking stress l if is not available f rom the test data, the variation of t'eh shear modulus can be plotted schematically as srown in Figure C-5.
.y (l
In the previous development of the STARDYNE floor response spectra, the calculation of the reduced stiffness for the SSE condition used a value ofag=.38 and a cracking nominal shear stress v,, of 170 ps.i as the basis for deriving the other reduction factors shom. In Table 4 of the October 27, 1978 submittal. The use of these values resulted in shif ts of the structural f requencies to lower values as shown in Tabic 3 of the October 27, 1978 submittal. l l C-4 i l l
li Thene frequency shifts reflect a system stiffness reduction factor for each mcde equal to the squaro of the frequency 1 ratio. Table C-3 shows the system stiffness reduction fac-H( I tors for the major struetural moden. Corresponding to the use of the average value of ac=0.46 and v er =132 psi as the l, basis, the nystem reduction factorn will be higher by a fac-l' tor of not more than the ratio of 0.'46/0.38 or 1.2, depend-l i ing upon modes. The use of v e, =132 psi instead of the 170 g psi ~ used previously will reduce the factor of 1.2, but the amount of reduction will not be significant. Thus, for the purpose of a conservative evaluation of the floor spectra on l the high frequency side, the upper bound factor of 1.2 is applied to each mode, resulting in on increase in the system stiffness reduction f actors as shown in the last column of
, Table C-3. The adjusted system reduction factors shown in this table with a variation of +11% are the values to be used for the 0.25g SSE.
Por an earthquake having a maximum ground acceleration lower than 0.25g, the structural responnes will be lower and the stiffness reduction factors will be higher than those for the 0.25g SSE. In order to assess the stif fnenn reduction f actors associated with a lower level earthquake, a 0.11g carthquake is considered. The 0.11g figure is about the earthquake level i where the structural damping of 2%,as specified in the Trojan FSAR for the'ODC,is available. In the major structural fre-C-5 : i o
. . h.
I quency' range, the Trojan design ground spectra show that the 0.15g OBE at 2% structural damping results in about the same , i structural damping. I structural response as the 0.25g SSR at 5% Therefore, a 0.llq earthquake with 2% structural damping will , have a structural response of about 0.73 of the SSE response (i.e. the ratio of 0.11g to 0.15g or 0.73). This results in l a shear stress of 0.73 x 215 = 157 psi in Wall 1 at EL. 45'-61' in the control Building. At this shear stress level, the value of a g, determined by the same methodology as used for deriving the reduction factors in Table 4, is 0.43. Scaling this up by the ratio of 0.46/0.38 or.l.2, this value becomes 0.52. Using ag u 0.52, the system reduction factors for the major structural moden for the 0.11g earthquake are shown in Tabic C-4. The values of the system reduction factors shown in the last column of this table with a variation of +11% are to be used for the lower level earthquake of 0.11g. i References l
- .s..
J.M., and Corley, W.G., " Shear Strength
- 1. Barda, F., Hanson, of Low-Rise Walls with Boundary Elements", ACI, SP53-8.
'I
(
- 2. Mayes, R.L., Clough, R.W., Hidalgo, P.A.,
and McNiven, (
- i ji H.D., " Seismic Research on Multistory Masonry Buildings", !
North American Masonry Conference, Boulder, CO, Augunt i 14-16, 1978. _
' - 1 C-6 l :
1 _ _ _ _ _ . . _ _ _ _ _ _ _ _ _ _ _ _ . . _ , . _ _ . ____ __ _ . _ . _ _ . _ . . _ - _ . _ .. . . . . .- l
.b . ' ) k 4 1 P i' Tablo C-1 PCA Test Results { t> , si i A ! Specimen ' Cracking ' Cracking Cracking i 2
- Shear Stress Shear. Strain Shear Modulus
, Ver(PSI)- Y er (in/in) Ci cr IPUI) k k 6 B4-3 320 0.00040 0.80 x 10 ' 3) j B5-4 330 0.00032 1.03 x 10 6 4 B6-4 280 0.00035 0.80 x 10 6 I B7-5 330- 0.00032 1.03 x 10 6 g h k
- Average Y er = 0.00035 I
L , Upper bound Ger a 1.03 x 106 pgi g i 1 , Average G.r r = 0.91 x 106 p31 Lj Lower bound G er = 0.8 x 106 pai l' 4 Y q. W 4 ll ll
!j l
L I, C-7 f i s
- ._----.~~+ -- - = = =
3 , 1 .
, t d
- r
. Table C-2 Cracking Shear Modulus Ger for Composite Wall 4 Effective Thickness 4
-Grons Thickness .-
vgp ** G cr
- Ger "G" G cr/Go (psi) (psi) (psi) 137 0.56'x-10 6 0.75 x 10 6 0.51 High bound Average 132 0.50 x 10 6 0.67 x 10 0.46 119 0.45 x 10 6 0.6 x 10 6 0.41 Low bound _
j. o 6 Go = 1.47 x 10 pgi
**v c of PCA tents divided by 2 and adjusted by l
a factor of 0.74, then adding the contribu- , tion from the block of IS psi (1/2 of 0.09 x 10 6 l timon the averago concrete cracking shear strain) l l
- Averg'ge pnioffor thethePCA testwall block values from and thetho 0.09 Derkeley x 10 test.
1 t a-C-8
- +- .- -
+-me -+vr.w
. s Table C-3 Stiffness _ Reduction Factor for SSE 0.25g i fy f 2 s
"* ""s *'l*2
, Direction (cps) (eps0 NS 6.80 4.96 0.53 0.64 9.49 7.63 0.65 0.78 12.05 10.35 0.74 0.89 16.22 12.31 0.58 0.70 EW 8.63 7.09 0.67 0.80 12.11 11.03 0.83 1.00 Notes:
fy = Linear clastic structural f requencies f rom the STARDYtIE analysis. f Structural frequencies using the stiffness reduct' ion f actor of ,; 2 = Table 4 of the October 27, 1978 s ubmi t ta.l . ;
"s = System stif fness reduction f actor for each mode = ( 2f /f1) Il a0 = System stif fness reduction f actor for each modo adjusted by [
" a factor of 1.2 which is the ratio of 0.46/0.38;n* 1.0. l 1
C-9 l ' ' ,
,i I
I Tabic __C-4_ System Stiffness Deduction for a 0.11g Earthquake f y f 0
"* "s 1.2 2
Direction (eps) (cps 0 NS 6.80 4.96 0.53 0.73 9.49 7.63 0.65 0.89 12.05 10.35 0.74 1.00 16.22 12.31 0.58 0.79 EW 8.63 7. ' 9 0.67 0.92 12.11 2 .C3 0.83 1.00 Notest 1 1 = 1inear elastic structural f requencies f rom the STARDYNE analysis. f 2 = Structural f requencien using the stif fness reduction factor of Table 4 of the actober 27, 1978 submittal.
"3= System stiffness reduction f actor for each mode = ( f2/f 1 uj = System stif fness reduction f actor for each modo adjusted by a f actor of 1.37 which is the ratio of 0. 52/0. 3 8 ; a *< 1.0.
I I \ l C-10
' Shear Stress 1000 (psi) 500 ,
-Vcr
/
/
/
/
/ ' '
0' 0.2 0.3 o 0.1 Deficction (in) EIGURE C-1 Shear Force - Dicplacement Envelope l Curve of PCA Tests (Reference 1) ,. 1 100
- 208 g t
n n e G t o, e ! o,
*d ~ ~
$ 80 0
u o o 60
. 104 Il y m N cr ,
I y N 40 I - 52 20 f
'l ' '
O '- O 0.2 0.4 0.6 0.8 Doflection (in) FIG _UR_E C-2 Shear Force - Dicpincoment Envelope Corvo of ntrkeley Test.n (Reference 2) I' - C-11 ..
FIGURE C-3 Shear
! [
Stress ' (psi). g g c V i cr - l l l v- -- g i I i i I
! l l I !
I i
. I i i 1 i i i f _
l - P j! I . cr Shear Strain (in/in) .. Shear Stress - Strain Envelope (below the Cracking Shear Stress) l1 j. Il l c-12.
)
., ., . . o FIGURE C-4 !.
l' v j' h s
- 1+ ; 2 - #- - -- 1+
t Block i; Block core m - ;- -_.
. ll i.
tu
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- N N *l..
> Dioek
. .l, .. . ' .
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*.s..
. >. s
~
U \ ._ N __ h 2 ) _ e :- --: g-t off = 3 = x _ t g= 4 a4 Of l Relative Dimension of Typical Composite Wall 0 1 i 4 *" 1 tr' l ., g *
'II WO92
- I*M N05 9 'y e-- +w ,+ =
- s.__. __ . __
4 , J
- o j
. s* *
- t o v
FIGURE C-5 l i i Shear g
- Stress O (psi) cr G 1 0
/
- 1 /
/
V cr f
+11%
v- --
/ Y '
' ' i-l . .
l l I L l . .; l r Shear Strain (in/in)
- Y I c,.
Variation of Shear Stress - Shear Strain Envelope I (below the Cracking Shear Stress) i I l 1 1 1 i s l l l 1 l
# o
* **=* 4 f,. y 1
1 C-14 l 1 l l t l}}