Text

Seismic & Structural Analysis of Genoa 3 Stack Using NRC Site-Specific Ground Response Spectra
	ML20062K294
Person / Time
Site:	La Crosse File:Dairyland Power Cooperative icon.png
Issue date:	11/25/1980
From:	Rumpf R, Strnad T; NUCLEAR ENERGY SERVICES, INC.
To:	;
Shared Package
ML20062K293	List: ML20062K284; ML20062K294;
References
	TASK-02-04, TASK-03-06, TASK-2-4, TASK-3-6, TASK-RR 81A0040, 81A40, NUDOCS 8012080495
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PAGE nF 9

SEISMIC AND STRUCTURAL ANALYSIS OF THE GENOA 3 STACK USING THE NRC SITE-SPECIFIC GROUND RESPONSE SPECTRA PREPARED FOR DAIRYLAND POWER COOPERATIVE 1

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TABLE OF CONTENTS Page 1.

SUMMARY

4 2.

B ACKGROUND INFCRMATION 4

3.

DESCRIPTION OF STACK 4

4.

APPLICABLE CODES, STANDARDS AND SPECIFICATIONS 7

5.

LOADS AND LCADING COMBINATIONS 3

6.

ANALYTICAL PROCEDURES 10 6.1 Seismic Analysis 10 6.1.1 Mathematical Model 10 6.1.2 Foundation Spring Stiffness 10 6.1.3 Eigenvalue Analysis 16 6.1.4 Dynamic (Seismic) Load Analysis 16 6.z Structural Analysis 19 7.

ACCEPTANCE CRITERIA 21 s

3.

RESULTS OF ANALYSIS AND CONCLUSIONS 22 9.

REFERENCES 27 9.1 Cited References 27 9.2 General Ref erences 23 APPENDICES 29 A

Stack Analysis Calculations B

Foundation Analysis Calculations L5T OF FIGURES 3.1 Schematic Sketch of Genoa 3 Stack 6

5.1 LACBWR Site-Specific Response Spectra 9

6.1 Mathematical Model of Genoa 3 Stack 11 6.2 Effect of Variation of Soil Properties on Structural Response 13 6.3 Soil Spring Constants 15 6.4 Cannon's Solutions 20 3.1 Summary of Seismic / Structural Evaluation (Moment) 24 LIST OF TABLES 6.1 Natural Frequencies of Vibration 12 6.2 Genoa 3 Stack Properties 14 3.1 Summary of Seismic / Structural Evaluation (Moment) 25 3.2 Summary of Seismic / Structural Evaluation (Shear) 26

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1.

SUMMARY

This report, prepared for Dairyland Power Cooperative (DPC), presents the results of the seismic / structural analysis of the GENOA 3 stack using the NRC site-specific l

ground response spectra for the Safe Shutdown Earthquake Event (SSE).

Linear seismic analysis, tsing the site specific spectra and modal superposition, was used to determine the response of the GENOA 3 stack for the SSE Event.

Soil structure interaction eff ects were included using the information provided by Dames &

M oo re.2 The foundation springs reflect the updated information of the most recent boring program. The seismic response of the stack is compared to the load carrying capacities of the stack at corresponding elevations. From the results of the analysis, it has been concluded that under an SSE seismic event, the GENOA 3 stack will experience a failure 150 to 200 feet from its top. The surviving 300 to 350 feet of the stack will remain upright and attached to its f oundation mat. Since the GENOA 3 d

stack is located approximately 400 feet from the LACBWR Reactor Containment Building and other safety related structures, the failed section of the stack should not impact on these structures.

2. BACKGROUND INFORMATION in response to recent NRC questions Dairyland Power Cooperative (DPC) requested Nuclear Energy Services (NES) to analyze the GENOA 3 stack. This analysis was made using the most recent soils data from Dames & Moore, most recent design codes, current NRC Regulatory Guides and Standard Review Plans, and the recently established site specific ground spectra. Investigation of the following variables was made: soil properties, cracked, and uncracked section properties of the concrete. The results'are presented within.

3. DESCRIPTION OF STACK The GENOA 3 stack is a 500 foot high, tapered, reinforced concrete chimney with an independent steel liner. The outside diameter at the base is 38.198 feet with a wall thickness of 24 inches; the stack tapers to the top diameter of 17.42 feet with a wall thickness of 7 inches. The independent steel liner has an inside diameter of 15.25 feet

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f or most of its height, bells out at its base and is supported on a concrete pedestal.

Both the stack and its liner are founded on a 75 foot reinforced concrete octagonal mat. The foundation mat varies f rom 7 feet to 3'6" in depth and is directly supported by the soil (see Figure 3.1).3

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500 FEET TALL y

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4. APPLICABLE CODES, STANDARDS AND SPECIFICATIONS The following codes of practice and regulatory guides have been used in the analysis of the GENOA 3 Stack Analysis.

1.

Specification For the Design and Construction of Reinforced Concrete Chimneys (ACI-307-79), American Concrete Institute, Detroit, Michigan, 1979.

2.

Building Code Requirements for Reinforced Concrete (ACI 313-77),

American Concrete Institute, Detroit, Michigan.1977.

3.

USNRC Regulatory Guide 1.61, " Damping Values for Seismic Design of Nuclear Power Plants", October,1973.

4.

USNRC Regulatory Guide 1.92, " Combination of Modes and Spatial Components in Seismic Response Analysis", Rev.1, February,1976.

5.

USNRC Regulatory Guide 1.60, ' Design Response Spectra f or Seismic Design of Nuclear Power Plants", Rev.1, December,1973.

6.

Unif orm Building Code,1979 Edition.

DOCUMENT NO.

11 mur PAGE Oh9 NUCLEAR ENERGY SERVICES. INC.

5. LOADS AND LOADING COMBINATIONS The seismic lateral inertia loading on the coupled model of the stack and its foundations is in the ferm of the ground acceleration response spectra given in Ref erence 1.

The f ree field ground response spectrum (Figure 5.1) f or the Safe Shutdown Earthquake for 5 percent structural damping was modified to 7 percent and used in the seismic analysis. (See USNRC Reg. Guide 1.61).

In addition to the seismic inertia loading, the dead loads and their resulting moments have also been included in the analysis. The following load combination equation was used in evaluating the adequacy of the stacks to withstand a seismic event.

I U = D + 1.0 E Where:

D=

Dead loads and their resulting moments E' = Loads and moments generated by the Safe Shutdown Earthquake U=

Section strength required to resist design loads and based on ultimate strength design methods described in ACI 318-77 Code.

The design loads f rom this load case were assumed to be resisted by the ultimate section capacities of the stack and its mat foundation.

81A0040 DOCUMENT NO.

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6. ANALYTICAL PROCEDURES 6.1 SEISMIC AN ALYSIS 6.1.1 Mathematical Model in order to perform the seismic analysis, the stack is mathematically modeled as an assembly of elastic-structural elements interconnected at discrete nodal points.

The three dimensional, multidegree of f reedom model of the stack is attached to the ground by means of foundation springs, representing the def orm ations of the soil under the stack foundation. Lateral, as well as rocking springs, have been provided ur. der the GENOA 3 stack mathematical model (Figure 6.1) to account fcr the shear and vertical def ormation of the soil under the GENOA 3 stack foundation. To account for the variation in the soil properties and to evaluate the eff ect of changing the foundation spring constants on the seismic response of the stacks, the foundation springs were varied using information supplied by Dames and Mocre. The f requencies found using this data is shown in Table 6.1. The eff ect of the variation can be seen in Figure 6.2.

The distributed mass of the stack is lumped at the system nodal points.

Each mass represents the tributory weight of the stack walls above and below the nodal point.

Masses are lumped so that the lumped mass, multidegree of f reedom model represents the dynamic characteristics of the stack. In order to reduce the number of dynamic degrees of f reedom, only translational degrees-of-f reedom are considered at each mass point.

(The masses associated with the rotational degrees-of-f reedom are set to zero). The physical properties used in the model are given in Table 6.2.

6.1.2 Foundation Spring Stiffness The stiffness of the lateral and rocking springs representing the shear and vertical def ormation of the soil beneath the foundation mat are obtained using the equations shown in Figure 6.3.

These equations are taken f rom Ref erence 4

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TABLE 6.1 NATURAL FREQUENCIES OF VIBRATION - GENOA 3 STACK Model 1 Model 2 G = 1000 ksi G = 3000 ksi Softer Stiffer Mode No.

Modal Direction Foundation Spring Foundation Spring i

X 0.363 CPS 0.333 CPS 2

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1.349 1.437 y

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2.976 3.235 2

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3.497 4.710 3

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4.67 5.561 2

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6.124 S.133 2

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TABLE 6.2 GENOA 3 STACK PROPERTIES Outside Concrete Area Area Steel Dead Node Diameter WalJ Concrete Steel Ratio Weight 2

2 No.

(in)

Thickness (in)

(in )

(kips) 1 7.0 11.60 14.325 2

211.0 7.0 4486.19 11.80 0.00259 60.810 3

217.0 7.0 4618.14 12.00 0.00260 132.965 4

223.0 7.0 4650.09 12.40 0.00261 207.130 5

229.0 7.0 4S82.03 12.60 0.00258 233.457 6

235.0 7.0 5013.93 12.60 0.00251 361.795 7

241.0 7.0 5145.93 12.30 0.00249 442.195 3

247.0 7.0 5277.88 13.20 0.00250 524.657 9

253.0 7.0 5409.37 13.40 0.00243 609.180

_10 259.0 7.0 5541.77 13.30 0.00249 695.765

+

11 265.0 7.0 5673.72 14.00 0.00247 786.410 12 271.0 7.0 5805.67 14.40 0.00248 877.119 13 277.0 7.0 5937.61 14.30 0.00249 970.017 14 284.5 7.0 6102.54 19.60 0.00321 1065.367 15 292.0 7.0 6267.48 24.00 0.00383 1163.237 16 299.5 7.0 6432.41 29.14 0.00453 1263.787 17 307.0 7.0 6597.34 34.72 0.00526 1366.367 IS 314.5 7.0 6762.23 44.00 0.00651 1474.517 19 322.0 7.5 7410.23 54.56 0.00736 1590.377 20 329.5 S.0 8080.13 64.30 0.00300 1716.417 21 337.0 3.0 8268.67 74.26 0.00898 1347.797 22 344.5 8.5 3972.39 85.32 0.00950 1990.057 23 352.0 9.25 9960.22 96.00 0.00964 2145.717 24 359.375 10.0 10975.93 104.00 0.00948 2315.397 25 368.375 10.5 11805.12 108.00 0.00920 2499.897 26 377.375 11.0 12661.00 112.00 0.00884 2697.767 27 386.375 11.5 13543.60 116.00 0.00356 2911.427 28 395.375 12.0 14452.90 118.00 0.00S16 3144.187 29 404.375 14.0 17169.58 124.00 0.00720 3412.617 30 413.375 16.0 19992.47 130.00 0.00650 3738.947 31 422.375 21.0 26430.09 134.00 0.00506 4179.777 32 431.375 24.0 30715.35 134.00 0.00436 4698.777 33 440.375 24.0 31393.94 134.00 0.00427 5206.177 34 449.375 24.0 32072.52 133.00 0.00415 5707.277 35 458.375 24.0 32751.10 133.00 0.00406 11580.127

DOCUMENT NO.

11 mur PAGE OF NUCLEAR ENERGY SERVICES. INC.

Spring Constants for Rfgid Circular Footing Resting on Elastic Half Space Motion l Spring Constant Reference 4C".

Timmhenke and Goodict (195 t)

Verticai 4,. 1-r k, ~ MI - v)Cr.

Dycroft (1956) licrirental 7sr Rocking S C,*

Dorowicka (190)

Reissner and Sagoci (1944)

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6.1.3 Eigenvalue Analysis The eigenvalues (natural f requencies) and the eigenvectors (mode shapes) f or each of the natural modes of vibration are calculated by solving the Iollowing f requency equation:

(K-v]A1) {c 0}

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th Natural angular f requency f or the n mode w =

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The eigenvalue/ eigenvector extraction is performed using the Householder QR Atodal Extraction Niethods.

6.1.4 Dynamic (Seismic) Load Analysis Considering only translational degrees of f reedom and assuming viscous (velocity proportional) form of damping, the equation of motion in matrix form can be expressed as follows:

11 (Ut+Ugt) + CU +KU 0

(2)

=

t t

Where:

U

= Relative acceleration time history vector t

b

= Gr und acceleration time history vector gt L

81A0040 DOCUMENT NO.

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C

= Damping matrix b = Velocity time history vector U

= Relative displacement time history vector Rearranging equation (2):

11Ut + CU +KU

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=

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gt eff To uncouple equation (3), assume:

U cY

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Where:

= Characteristic f ree vibration mode shapes matrix Y

= Generalized coordinate displacement time history vector Pre-and post-multiplying equation (3) by the transpose of $ and $

respectively and using orthogonality conditions, the following unCoJpled equations of motion are obtained:

E

'h n nt + f Ynt = (R (4) nt n gt Where:

Ynt =

Generalized displacement coordinate time history th f or n mode.

th A

Damping ratio for the n mode expressed as

=

n percent of critical damping.

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th M* = Generalized mass f or the n mode

= & M&n "

i Din The mode shape c is normalized such that M * = 1 n

th Participation f actor for the n mode.

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The solution for the differential equation (I) is given by the Duhamel 4

Integral:

- n *n(t-T)

Y nt M3 fT U e Sine (t-T) dr n

Using the response spectrum method of analysis, the maximum values of the generalized response for each mode is given by:

Rb n an n max M*

(5)

Where:

M ximum g ner lized coordinate acceleration Y

=

n max th response f or the n mode.

th Spectral acceleration value for the n rnode (f rom S

=

an the applicable response spectrum curve)

DOCUMENT NO. 81A0040 19 29 PAGE OF NUCLEAR ENERGY SERVICES, INC.

From the maximum generalized coordinate response the maximum acceleration (bn max) and maximum int rtia forces (Fn max) t e 6 m ss point are given by:

=Y iin n max n max F

n max n n max The inertia forces (Fn max) f r each of the systems' natural modes are applied as external static forces, and system response (displacements, member internal forces and stresses) are calculated.

Total system response is than obtained by combining the individual modal response values by the square root of the sum of the squares method; lower modes having large contribution to the response (all modes having natural frequency under 30 cycles per second) are considered and higher modes with negligible participation are neglected.

6.2 STRUCTURAL ANALYSIS The Genoa 3 Stack was analyzed using the ultimate strength design method 5

presented by Cannon. The graphical solutions derived by Cannon are shown in Figure 6.4.

The basic assumptions used in this method are given in Appendix A of this report. Tests performed at University of Michigan verif y that Cannon's method predicts f ailure well.7&S The tests show that actual failure occurs at approximately 10 to 15% over the predicted. This is assumed to be due to the eff ect of strain hardening, which is not accounted f or in the analysis method.

The octagonal mat foundation was evaluated using methods presented in Reference 6 and in accordance with ACI 313-77 Ultimate Strength Design Methods. The method used appears to be quite conservative.

Appendix B contains the f oundation analysis calculations.

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7. ACCEPTANCE CRITERIA The ultimate moment and shear load-carrying capacities of the stack cross-sections have been calculated using the acceptable ultimate stress values as given in the ACI 313-77 Design Code and References.

The specific acceptable stress values used in this analysis are given below:

Maximum concrete compressive stress

= 0.35 f'c (ACI 318-77)

Maximum concrete shear stress

= 4$3 f c (ACI 313-77)

Maximum stress in reinforcing steel

= fy (Ref erence 5)

Where:

Ic

= compressive strength of concrete at 23 days

= 4,000 psi for Genoa 3 Stack 3,000 psi f or Genoa 3 stack foundation mat

,)

= 0.75 for Genoa 3 stack (Reference 5) fy

= Yield stress value for reinforcing steel

= 40.0 ksi f or Genoa 3 stack 60.0 ksi f or Genoa 3 stack f oundation mac L

81A0040 DOCUMENT NO.

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8. RESULTS OF ANALYSIS AND CONCLUSIONS The results of the seismic analysis of the Genoa 3 stack performed with Stardyne computer code are contained in Reference 9.

Appendix A contains the assumptions used in the analysis, and the detail structural evaluation of Genoa 3 stack. Appendix B contains the detail calculations for the structural evaluation of concrete mat f oundation.

The natural f requencies of vibration of the Genoa 3 stack are given in Table 6.1. From Table 6.1 it can be seen that the stack is a low frequency system (fundamental f requency of 0.363 and 0.388 Hz) and the variation in the fundamental f requencies is small (0.363 Hz to 0.383 Hz) as compared to the variation in the foundation soil constants (G = 1000 ksf to 3000 ksf). The results of the seismic and structural analysis are summarized in Table 8.1 and 3.2 and shown in Figure 3.1. Table 3.1 summarizes the moments due to the SSE seismic event and compares them to the allowable ultimate moment capacities of the stack. From Table 3.1 it can be seen that the moments due to SSE event at Nodes 15 through 4 (height: 300 f t. to 465 f t.) exceed the allowable moment capacities (ultimate moment capacities).

The maximum ratio of SSE seismic moment to the ultimate moment capacity is 1.6.

This 60% overstress ouring the SSE event is considerably greater than the 10 to 15%

variation between the test results 7&8, and the calculated ultimate moment capacity.

Figure 6.2 shows the continuous variation of the seismic moment through the height of the stack and the insensitivity of the seismic moment response to the foundation soil properties.

Table 8.2 compares the ultimate shear capacity of the stack to the SSE shear values.

It can be seen that the ultimate shear capacity of the stack is considerably greater than the SSE seismic shear.

0040 DOCUMENT NO.

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The octagonal mat foundation has been evaluated for the foundation pressure distribution resulting f rom the seismic moment and dead weight loadings. Results of the analysis shows that the foundation will be slightly overstressed. However, the method of analysis are quite conservative. A detailed finite element model is now being developed for further evaluation of the mat foundation.

It can be concluded f rom the above that under an SSE seismic event, the 500-foot GENOA 3 stack will experience a f ailure 150 to 200 f eet from its top. TSe surviving 300 to 350 feet of the stack will remain upright and attached to its foundation mat.

Since the GENOA 3 stack is located approximately 400 feet from the LACBWR Reactor Containment Building and other safety related structures, the f ailed section of the stack should not impact on these structures.

The seismic and dead weight loadings and the soil bearing pressure distributions have been supplied to Dames & Moore f or their evaluation. Dames & Moore will confirm the soil's capability to withstand these loads.

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TABLE 3.1

SUMMARY

OF SEISMIC / STRUCTURAL EVALUATION (MOMENT)

Distance from Ultimate Moment Moment due to 5

3 Node Top (f t)

Capacity (K-in) x 10 SSE Event (K-in) x 10 2

5 0.061 0.0069 3

20 0.13C 0.095 4

35 0.220 0.252 NG 5

50 0.307 0.447 NG 6

65 0.387 0.656 NG 7

SO 0.485 0.862 NG S

95 0.590 l.055 NG 9

110 0.703 l.234 NG 10 125 0.322 l.401 NG 11 140 0.9511 l.559 NG 12 155 1.0854 l.713 NG 13 170 1.2270 l.861 NG 14 135 1.5500 2.001 NG 15 200 1.9270 2.130 NG 16 215 2.4260 2.250 17 230 3.1520 3.368 13 245 3.7405 2.482 19 260 4.5020 2.602 20 275 5.1730 2.731 21 290 5.310 2.873 22 305 6.640 3.032 23 320 7.450 3.210 24 335 8.340 3.410 25 350 9.059 3.635 26 365 9.640 3.322 27 380 10.440 4.189 23 395 11.070 4.530 29 410 11.490 4.918 30 425 13.094 5.358 31 440 12.270 5.853 32 455 12.560 6.411 33 470 13.660 7.039 34 485 15.020 7.732 35 500 17.742 3.491 Results f rom Computer Program 5532 E82

.. ~..... -..

.--- +

DOCUMENT NO.

PAGE OF NUCLEAR ENERGY SERVICES. INC.

TABLE 8.2

SUMMARY

OF SEISMIC / STRUCTURAL EVALUATION (SHEAR)

Distance from Ultimate Capacity SSE Shear

Node Top (f t)

(kips)

(kips) 2 5

964.69 11.65 3

20 993.06 49.92 4

35 999.93 86.97 5

50 1049.81 103.05 6

65 1078.18 116.71 7

30 1106.55 118.95 8

95 1134.93 120.94 9

110 1163.31 125.99 10 125 1191.67 133.01 11 140 1220.05 138.94 12 155 1248.42 141.28 13 170 1276.79 140.39 14 185 1312.26 139.00 15 200 1347.73 140.39 16 215 1383.19 147.74 17 230 1418.66 158.99 18 245 1454.13 171.66 19 260 1593.46 183.38 20 275 1737.52 193.38 21 290 1778.05 202.54 22 305 1929.38 212.23 23 320 2141.79 224.90 24 335 2360.21 242.03 25 350 2538.51 263.30 26 365 2722.56 287.09 27 380 2912.35 311.24 28 395 3107.88 334.62 29 410 3692.06 357.29 30 425 4299.08 382.19 31 440 5694.14 414.03 32 455 6604.87 463.24 l

33 470 6750.79 508.74 1

34 485 6896.71 543.41 l

35

.' 90 7042.63 583.08 l

Results from Computer Program 5532 E32

1A0040 DOCUMENT NO.

11 mur

=

NUCLEAR ENERGY SERVICES. INC.

9. REFERENCES 9.1 CITED REFERENCES 1.

NRC Letter to Dairyland Power Cooperative, Docket No. 50-409 (August 4, 1930) 2.

Dames & Moore: Liquef action Potential under Genoa-3 Stack Adjacent to Lacrosse Boiling Water Reactor, Genoa, Wisconsin (October,1980) 3.

Genoa 3 Stack Drawings, The M.W. Kellogg Company, Genoa 3 Drawing Nos. 6152-1, 2, 3, 4, 5, 6,13, and 16 ED.

.4 Richart, F. E.,

Hall, J. R., and Woods, R.D.: Vibrations of Soils and

'>oundations, Prentice-Hall, Inc., Englewood Cliffs, N.J. (1970) 5.

Cannon, R.W. and Boop, W.C.: Ultimate Strength Design Charts for Design of Reinforced Concrete Chimneys, Civil Engineering Design Research Report, p 14, Tennessee Valley Authority, Knoxville, TN (1971) 6.

Marshall, V.O.: Foundation Design for Stacks and Towers, Foundation Design Handbook, reprinted from Hydrocarbon Processing, Gulf Publishing Company, Houston, Texas (1968) 7.

Mokrin, Z. A.: Reinf orced Concrete Members of Hollow Circular Section under Monotonic and Cyclic Bending, unpublished Doctoral dissertation, Department of Engineering, University of Michigan (1973) 3.

Rumman, W.S. and Ru-Tsung: Ultimate Strength Design of Reinf orced l

Concrete Chimneys, A.C.I. Journal Proceedings, pp 179 - 183 (1977) 9.

Genoa 3 Stack, Stardyne Structural Analysis Project $101, Task 051, NES Computer Output Binder No. 5-53, Oct.-Nov.,1980.

81A0040 DOCUMENT NO.

11 au PAGE OF NUCLEAR ENERGY SERVICES, INC.

9.2 GENERAL REFERENCES LACBWR Application fqr full term operating authorization, LAC-2783,(October, 9, 1974)

George Winter et. al.: Design of Concrete Structures, McGraw-Hill Book Company, New York (1972)

Fintel, M. (ed): Handbook of Concrete Engineering, pp 477 - 490, Van Nostrand Reinhold Company, New York (1974)

Rumman, W.S.: Basic Structural Design of Concrete Chimneys, Journal of the Power Division, pp 309 - 317 (June,1970)

Run. man, W.S. and Mauch, L.C.: Earthquake Forces Acting on Tall Concrete Chimneys, International Association for Bridge and Structural Engineering (September,1968)

Rumman, W.S. and Ru-Tsung Sun: Ultimate Strength of Reinf orced Concrete Chimneys, Journal of ACI Proceedings, pp 179 - 134 (April,1977)

Rumman, W.S.: Vibrations of Steel-Lined Concrete Chimneys, Jc'irnal of the Structural Division, ASCE, pp 35 - 63 (October,1963)

Rumman, W.S.: Earthquake Forces in Reinforced Concrete Chimneys, Journal of the Structural Division, ASCE, pp 55 - 70, (December,1964)

Maugh, L.C. and Rumman, W.S.: Dynamic Design of Reinforced Concrete Chimneys, ACI Journal Proceedings, pp 558 - 567 (September,1967) 1

81A0040 DOCUMENT NO.

PAGE OF NUCLEAR ENERGY SERVICES, INC.

APPENDIX A STACK ANALYSIS Assumptions:

1.

The assumptions used for ultimate strength design and compatibility of strains are the same as those given in ACI Building Code (313-77).

s 2.

Maximum steel stress at ultimate capacity is assumed as "fy".

3.

The ultimate moment occurs when the strain in the concrete reaches 0.003 inch per inch.

4.

A uniform compressive stress block is assumed with (a = 0.85 K ).

3 5.

Compressive reinforcement is not considered.

6.

Reinforcement is unif orm throughout the section.

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NUCLEAR ENERGY SERVICES INC.

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CHKO. 7~5' DATE///N/N PAGE M OF M M b%BA NUCLEAR ENERGY SERVICES dtenoA 3

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ML20062K294

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