ML18102B025

Structural Analysis of Containment Vessel (Conrad Rept).

ML18102B025
Person / Time
Site:	Salem, Oconee
Issue date:	04/28/1997
From:	Public Service Enterprise Group
To:
Shared Package
ML18102B015	List: ML18102B014 ML18102B019 ML18102B020 ML18102B025 ML18102B027
References
6S-791, 6S0-0791, NUDOCS 9705050073
Download: ML18102B025 (33)

Text

ATTACHMENT 4 PSE&G CALCULATION SS0-0791 STRUCTURAL ANALYSIS OF CONTAINMENT VESSEL (CONRAD REPORT)

PAGES 225, 241, AND 243 THRU 270

6S0*079

,. CIR CU MF ERE PITIA !,, Ill 0 lllE~t ~...__.111:.:.!::!!R_,,IO'-'l'=;O!!N_,,A,,L~Y,,_,O<!M:.;E:;H~T'-- RA 0 IA b SHE AR *-+--"TA"-'N"':;,,,E:.;N~T.._lc:A,_,,___S:.H=E:::A-"R---

MOOP FORCE (l(Jr I FTl (KIP /FT l (KIP/ FT) ( Kl P FT/FT)  ! (KIP FT/FT)

~i I

40.9 IZC t

102..Z

-lS.I

• 0 200 400 0 100 zoo ELEV 76' EJ..[V K/>"T E.t..EV. 71° K.FT/ FT NAOIA.t. STll[S!i IJt.Sr) VERTICAL STF?E!S (K!!"'l SHE.AA sTi.!'95 IK!F1 TANO[NTIAL STRESS (KSF) 910S06CD72 01

...... Fi9uro 3 - 8 FORCES JN CONTAINMENT

VESSEL DUE TO INTERNAL PRESSURE LOADING

~

...:. (*. 241 6S0*0791

... HO.JP STRESSES (KSI)

MER DIONAL STRESSES (KSll._. HOOP STRESSES (~~!_)_ MERIDIONAL STRESSES (KS!) __t!QOP STRESSES (KSI! MERIDIONAL STRESSES (KS!)

/

-Z9.I

( ---1 f

14.7 II I 14./ -+-

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11.2 8.4 10.7 8.1 7.S 9.8 7.1 9.7 z

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01

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LINER l l~il~ER REBAR OUTER REBAR Figure 3-15 STRESSES IN LINER PLATE AND REINFORCING STEEL DUE TO THERMAL LOADING UNDER ACCIDENT CONDITION

... ...... . .. CONRAD .ASSOCIATES

.~ - ......

6S0-0791 Section ll REVIEW OF STRUCTURAL DESIGN OF THE CONTAIN~ENT VESSEL 4-1 Introduction The data presented on the following pages is a culmination of the work documented in the previous sections of this report.

Sections 2 ~nd 3 pertained ~~ecif1cally to the er.alysis of the containment vessel for individual static and dyn~~ic load cases. These load combinations were formulated to safeguard the containment vess~l a~ainst the most critical conditions of earthquake or tornado acting simultaneously with accident pr~ssure, thermal loading, buoyancy and dead load. The major criteria used in the review of the reinf~rcing steel 1es1gn was that stresses in the steel be limited to the minimum guaranteed yield. In addition maximum strains in the rein-forcing steel were limited to insure the integrity of the liner.

This was accomplished by limiting all stress combir.ations 1 in the liner to its minimum guaranteed yield.

In examining the behavior of the containment vessel

~ under the applied load combinations, the containment shell

• t and the foundation mat were reviewed sepa~~tely. In the

.~

case of the containment shell, the maximum forces and moments

~

~ 1n the containment wall resulting from the different lc1ad co~binations were determined and applied directly to the

~

... rei_n_f_~rcing scheme. The resultant stresses in the reinforcing

.!!. bars were tabulated and reviewed accordingly .

650-0791 In reviewing the design of the foundation rnat, the ~ax!~u.~

forces incurred at critical sections of the slab were evaluated r~r each load com~inatlon. The ability of the steel reinforcement to resist these forces was checked !n order to ensure that the base mat would function satisfactorily I

t under any of the load coMbinations considered.

The final item pr~sented 1n this section is the r.ax1~u~

relative displacements due to earthquake between the contain-ment vessel and the auxiliary and fuel handling buildings.

The displacements 1r.curred by the containment vessel due to internal pressu~e and thelT.lal loading have ~lso been tab-ulated.

U-?. Ultimate Load Combinations The design of t~e containment vessel was c::. cked ror 0

various factored load co~t1nat1ons 1~ order to er.sure t~e structure's ~ntegrity under the most critical load co~d1t1ons conceivable. ~he details and s1gn1ricance or the five load cor.ibinations rormulate<.l for l.. onsideration in the analysis ar.:i deslgn er the Sal.?m containment vessel have beer. described 1 n Sect1.on 1-4. ll. The five .:ombinati,:ms are sum~arized below:

(a) C = l.OD + 0.05D + 1.5P + l.OT + I.OB (~-1~)

(b) C = l.OD + 0.05D + l.25P + l.OT' + l.25E + l.OB (4-lb)

(c) C = 1.0~ + O.O~D + l.OP + l JT" + l.OE' + l.OB (4-lc)

(d) C = l.OD + 0.05D + l.lO~t + l.OPb + l.OB (e) C = l.OD + 0.~5D + l.OTm + 1.0E' + l.OB (~-le)

CONRAD ASSOCIATES

Symbols used in tnese formulas are defined as follows:

6S0-0791 c = Required load capacity of section.

D = Dead load of structure and equipment loads.

p = Accident pressure load as shown on pressure-temperature transient curves. (See Figure 3-4, 3-5, 3-6).

T  ::s Load due to maximum temperature gradient through the steel liner, concrete shell and mat, based upon temperatures associated with 1.5 times acci-dent pressure.

T' = Load due to maximum temperature gradient through **~

the steel liner, concrete shell and mat, based ,.,.

upon temperatures associated with 1.25 times accident pressure.

T" = Load due to maximum temperature gradient through the steel liner, concrete shell and mat, based upon temperatures associated with tr.e accident pres~ure.

T"' = L0ad due to operating temperature gradient through the ste~l liner, concrete shell and mat.

E = Load resulting from Oper~ting Basis Earthquake or wind, whichever is the greater.

E' = Load resulting from Design Basis Eart~quake.

wt = Wind load due to tornado.

Pb = Bursting pressure associated with a tornado.

B = Load resulting from bu~yancy affect of ground water.

The numerical values of the m.iximum temperature gradients associated with thermal load cases T", T' and Tare shown in the transient pressure-temperature plots of Figures 3-4, 3-5 and 3-6. The peak liner temperature associated with each of these load cases 1s""246°F, ~84°F, and 306°F respectively .

CONRAD ASSOC:CA.TES f

~~7-~~Z*;;;;~~~~**~."?;::y,~.iiJJ-r,.w.,.,.~~~~~.r~.'.'\.""l~-:~~~~">r.~~~~~*!'>": ....;.v,~~:-.:-.Qi~';.\C""'~~~~Y*"~*if~;t:S;~~.

" f' 2 ti 6 In addition to the above lead combinations> the liner plate was checked for the condition of test pressure (1.15P) acting simultaneously with dead load. It was apparent that under this load condition the liner would be subjected to the most severe tensile stresses.

6S0*0791 4-3 Review of Containment Shell Design 4-3.1 Reinforcing Pattern in Containment Shell The main load-carrying reinforcement in the containment wall consists of continuous meridional and hoop reinforcing bars that Extend the height and circumference of the dome-roofed structure.

In addition, the containment shell is characterized by two-directional diagonal reinforcing bars that extend throughout thf cylindrical section and into the lower third of the hemispherical dome. These bars serve to resist the membrane shear induced in the containment wall by wind or s~ismic loadings. As shown sche-matically in Figure 4-1> five sets of reinforcement contribute to the capacity of the containment wall in the hoop and meridional directions. These* .consist of two inner reinforcement cages, two outer reinforcement cages &.nd the diagonal shear reinforcement which has components in both the hoop and mericio~al directions.

For the purpo~es of this presentation, the two inner reinfor~ing r!ngs are referred to as Rebar #1 and #2, the diagonal reinforce-

~ent as Rebar #3 and the two _outer reinforcing riPgs as Rebar #4

~

.~ and 115.

';"'lti:

1~

t

' The :ner.1.dional and hoop reinforcing patterns shown in Figures L:.-2 and 4-3 were checked for adequacy in res1stir.g the five load

~-

• z; combinations. As indicated by these two figures, the main

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t"

~ ~

~-

~

CONRAD ASSOCIATES 'Sr*

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• 6S0*0791

(

MERIDIONAL ANO HOOP RE!!AR f# 3 MRICIONAL REBAR fl Z MER1DIONAL REBAR fl I r--MERICIONAL REBAR If !!

MERIDIONAL REBAR fl I

~*"~" "~ ~ Ht'OP REBAR fl I HOOP REBAR fl 2 HOOP RE8AR ti 5 HOOP REBAR ti 4 MERIDIONAL (~~!~~~er 3 \

MEftlOIONAL R[!!AR ti !!

LINm PLATE **

TYPICAL QUADRANT I I

_/

R

• 7r/-O" HOOP REBAR ' $ _/ R

• 10'-5',f I R

• 70'-T~z" HOOP REBAR f# 4 __/

HOOP REBAR ' 3

!SEISMIC!

HOOP llEBAll # 2 -

HOOP REBAR I I --; / R

• 73'-9" LINER PLATE--~ ' . 4.~*

~R-*_7~~::._-~ll~'t..L"--~~~~~~~.-,.

~R-*_7~~~'-....:...l~~t~*~~~~~~~~-i*

figUrl 4 -1 DESIGNATION OF MAIN REINFORCEIAENT PATTE:RN FOR CONTAINM!::NT VESSEL PLAN VIEW SECTION A-A CCJNR..A.0 Agsoc:A.TI:"B

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LINER !'LATE REBAR 111 I REBAR 1111 2 REBAR tlJ 3 i!EBAP. tlJ 4 REBAR tlJ e (SEISt.llCJ Fiqure 4. 2 LINER PLATE AND HOOP REINFORCEMENT FOR CONTAINMENT VESSEL CONRAD ..A.990C!J"TE9

• :1r2 5 o 6S0*0791 I

1 EL. 2*9 EL. 218 I ..

5

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!c; II.  : '

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EL. 110 fL. 99

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EL. TS EL. 76 EL. 7il ~~~~~E~L._T_e_.~"-~'f f.!E:f,R () 3 F.ESAR II 4 RE!IAR fl !I LlllER PLATE REBAR II I REBAR ;,I 2 (SEISl!.IC)

Flqure 4- 3 1.11\!ER PLATE Mm l.CERIOlOt..:AL REl~\Fo;:;::Er!.ENT F'OR CONTAl~!W.!WT VESSEL CO!""R.A:O AS~c:::.1..."':"'=.S:

-~-------------------*--*-----------.~==-----_-**----~-~, 2~-;--*

• L I

650:0791 I j

meridional reinforcement and the hoop reinforcement are comprised of #18s bars that range in spacing from 13 to 16-5/8 inches.

should be noted that Meridional Rebar #4 was not included in the It f

] reinforcing scheme adopted for the final review. This was due to results from the static and dynamic load analyses which indi-1.

..ll cated that this ring of meridional reinforcement was not required fo1* the design of the containment shell.

] The diagonal reinforcing bars, though continuous throughout l the structure, change in size at several locations along the

.J height or the containment vessel. Changes in bar diameter occur at Elevations 96, 188 and 218, with the final termination of the diagonal reinforcement at a point one third or the way in-

] to the dome. In the upper portion of the dome where the diagonal bars do not extend, the steel liner plate is relied upon to resist membrane shear. A l/2 inch steel plate lines the interior j of the dome and the lower portion of the cylindrical section. The thickness of the plate is reduced to 3/8 inch in all other regions 1

.. of the containment shell.

In addition to the principal reinforcement patterns described J above, radial shear reinforcement is provided in the lower cylin- I_*-

1 drical portion of the ~ontainment wall. (See Figure 1-17). These diagonal bars are designed to resist radial shear forces produced

] by secondary bending moments induced in the shell at its juncturd with the foundation mat. t J ~-3.2 Criteria tor Stress Review r. ..

i

• J Evaluation of the maximum stresses induced in the steel

~

t .

r. .

r<--

CONRAD ASSOCIATES

.--.w~.

,........._ _ _ _ _ _. . __ _ _ _ _..,<M_ _.__.* - - - - *_ _...,,;,.,,- *...

• --_,__...,.._~~~-~~* .. _., ...

rr2s2 6S0*0791 reinforcement and liner plate by the five specified load combi-nations was based on the following criteria: -

I

->-~**

• - I

1. The concrete was assumed to be completely cracked and incapable or resisting tension, compression, or shear when subjected to the rour load combinations (a), (b),  ;-*

~,-~

(c), ar.d (d), in which pres3ure loading was a factor. *'.,;

Although uncracked sections produced the most severe r I

I stress conditions in the finite element model, no credit was given to the load carrying capacity or the F I.

concrete when computing reinforcing bar stresses. For load combination (e) the concrete was assumed to be un-cracked, since this combination induces a state or com- I  ;--:

f pression in the containment wall and the liner plate.

In computing the trar.~formed area for the uncracked ,,.____.

,/

section in load combination (e), modular ratios of 8.0 2.

and 8.5 were assigned to the liner plate and the rein-forcing bars reepectively.

The axial ~orce capacity of the liner plate was counted t

-- l

• upon along wtth t,:e main reinforcement to res1st all hoop anj meridional forces.  ;---*... *

3. In regions where diagonal reinforcement was present, only these bars were counted upon to resist membrane shear. No credit was taken for the shear resistance or the l~ner pl~te except in the upper regions or the dome where diagonal reinforcing bars did not extend.

Nevertheless, the presence of shear stresses in the CONR.A::O .ASSOC%.A.TEB

""""~"""""~~~~~;,;;:;;;~;::;;:;;;;;:s:;;:;:;;;~:=:;:::;;;;~;;;;;~~~~;;:,;;;;;::;:;;:~~;;;:;;:~

~---~.....~-----...*---*------~:~:~-i-

__;ex::=

6S0-0791 lo*d Coab1n1t10" Crttfc1l Elev. A II c D E C1111 289.71 288.U 285.42 zsn. u 272.96 Z64, 12 253.87 242,54

- 2:10.46 227.38 Z24,Z8 221.15 218.00 Sl. 75 46.36 38.80 4.48 -5.06 A 215,00 55.45 49.58 41.41 4.54 -5.21 A ZlO .DO 56.46 50.60 42.35 4.13 -5.35 P. '\

200.00 55.27 49.69 41.~2 3.26 -S.48 A 190.00 56.07 S0.72 42.63 4.24 -5 .62 A 180.00 56.19 51. 29 43.42 4.27 -5.74 A 170. 00 55.87 51. 56 43.94 J.30 -5.83 A

- 160.01) 150.00 55.54 55.38 s 1. 87 52.34 44.55 45,21 3.57

• J.82

-5.96

-6.12 A

A 140,00 58.50 56.00 48.51 4.36 -6.42 A 130.00 57.35 55.65 48.27 4.45 -6.91 A 120.00 54.42 53.80 46.99 4.47 *7.80 A 110.00 48.15 49.17 44.28 4.72 -7.03 6 100.00 37.46 40.20 3C.44 3.44 -3.16 il*

92.00 24.04 28.78 24.78 -3.12 -1. 93 8 84.DD 12.58 20. 30. 20.91 -4.62 -3. 77 c l -.

76,00 4.59 10.83 6.05 -3.45 -2.06 I ~- ..

~-* .

t ~

r*

i' ..

TABLE 4-1 STRESSES IN HOOP REINFORCING BAR fl

( ICIPS/ 1111 1 )

i~~ ~

~

CONS.AD A.SSOCI.ATES it' . **

r f':.-

~,,,.~ .... ...... d **-* -. . . . h " . . .- * **~~-...---..------,;.-.-......l:>Al~..........i:i~~~-*

• r.r 254 6S0-0791 Lo1d Co11b1nlfion EhY. A a c D E Crit1c1l I Cue 1 28tl. 71 54. 12 47.53 38.58 -1. 77 -4.27 A I 28R.66 56.63 49.10 39.69 -2.67 -4.28 A 43.25 35 .13 -2.Sl -4.24 28!..42 zarr.14 49.56 55.96 48.80 39.65 -3.37 -4.59 A

272.96 so. Ui 44.15 36.02 -2.80 -4.96 A 264.12 52.09 45,89 37 .48 -3.28 -4.98 A 25j.87 52.12 46.02 37 .66 -J. 77 -4.56 A 242.54 52.25 46.35 38.05 -4.34 -4.42 A 230.46 52.53" 46.83 38.56 -4.88 -4.55 A 221.38 52.29 . 46.80 38.62 -s.21 -4.65 A 224.28 52.39. 47.02 38.86 -5.42 -4.61 A 221.15 48.97 44.02 36.44 -5.65 -4.24 A 218.00 42.67 38.40 31.87 -5.89 -3.47 A 2H.OO 43.69 39.47 32.87 -7.02 -3.14 A 21(1.00 43.02 39.26 32.87 -7 .49 -3.33 A 200.00 42.28 39.24 33.15 -8.19 -3.58 A 190.00 41. 39 39.24 33.51 -9.08 -3.83 A 180.00 40.59 39.41 34.03 -10.09 -4.10 A 17tl.OO 39.79 39.63 34.63 -11.19 -4.39 A 16J.OO 38.96 39.89 35.29 -12*: 46 -4.69 B 15il.OO 38.61 40.U 36.37 -13. 72 -5.14 B 140. 00 38.Sl 41. 67 37.70 -14.96 -5.60 B 130. 00 37.97 42.34 38.76 -16.19 -s. 91 8 120.00 37. 79 43. 39 40.13 -17.40 -6 .13 B llC1.00 34.68 41. 78 39.32 -18.60 -5.90 B 100.00 26.86 35.52 34.84 -20.03 *5.53 B gz.oo 84.00 14.23 18.79 19.96 15.11

18. 76 2$.82

-13.83

-15.56

-3.86

-4.65 B

c

, ** 00 19.U 19.49 lS.69 -11.99 -3.21 a TABLE 4-*2 STRESSES IN l'lERIDlONAL REINFORCING BAR #1 (KI PS/IH 1 )

• "' .... -J~". -* *. .., ........... ..&.. . . . . . . . . . i..- **i.: .:.:**** --** - -*..i.

CONRAD ASSOCXATES

. .. ... ~ .... -............

toad Co11binatton tr1t1c1l Elev. A B c D [

Cue 289.71 54. 76 47.56 38.41 -2.25 -4.36 A 288.66 S3.77 46.83 37.94 -2.ll ., -4.35 A 285.CZ 53.24 46.52 37.85 -2.47 -4.33 A 280.1' 53.59 47.0D 38.38 Z.31 -4.29 A 27Z.96 53.89 47.46 38.92 2.81 -4.22 A 264. lZ 53.95 47.74 39.37 J.43 -4.11 A 253.e7 53.89 47.98 39.83 4.25 -3.99 A 2'2.54 47.61 42.75 35.69 4.00 -3.93 A -*.

230.'6 49.54 44.51 37.26 4.54 -4.0l A 227.38 S0.42 45.32 37.H 4.72 -4.04 A 224.28 52.06 46.73 39.16 4.88 -4.48 A 221. J 5 53.91 48.32 40.49 4.99 -4.78 A 218.00 51.75 46. 36 38 * .-10 4.48 -5.06 A 215.00 SS.SO 49.64 41. ,Jg 4.60 -5.22 A 210.00 56.54 50.67 42 * .CZ 4.24 -5.36 A

.i 200.00 55.34 49.75 41.cil 3.40 -5.50 A 190.00 56.12 50.76 42.68 4.07 -S.63 A IBO.DO 56.21 51.31 43.44 4.11 -5.75 A 170.00 55.87 51. 56 43.95 3.44 -5.83 A .. )

] 160.00

~

55.53 51 .87 44.55 3.71 -5.96 A 150.00 55.37 52.34 45. C'Z 3.97 -6.13 A 140. 00 58.49 56.01 48.f.l 4.55 -6.44 A 130.00 57.39 55.70 48.50 4.69 -6.97 A 120.00 54.S4 53.93 47.33 4.76 -7.86 A 110 .oo 48.38 49.38 44.49 4.92 -7.04 s 100.00 37.71 40.53 35.59 3.81 -3.42 B 92.00 24.17 29.01 26.11 -3.49 -2.31 8 84.00 12 .46 20.27 21.30 -4.87 -3.93 c 76.00 3.82 lD.52 8.07 -3.70 -2.35 B TABLE lf-3 STRESSES IN HOOP REINFORCING W 112 (KI PS/ lH')

CONRAD .ASSOCIATES

}'~.

i:*.

.1 *

'th i , ; "}' ., ... [ ..

-- (:"256 E 6S0-0791

• ' "-' lo1d Co11btn1tfon c E Critf c1l

'..... I E1 ev.

289. 71 A II D Cue

~

.... i

~

~

Z88.tifi *--

I.' 285.42

~

,._ 280.14

-I'

'I I

§ 272. 96 264.12 a

'./

~ 253.87 i

242. 54 **

~ -

~

i f

{

I 230.46 227.38

> 224.211 g

P. 221.15

"*. 218.00

.~ 215.00

~

210.00 200.00

~

~

190.00

• ~ 180.00

] 71). (l0 160.00 m 150.00

• 140.00 m 130.00 120.00 m 110.00 100.00

- 15.70

~ 22.42 22.37 .4;55

' 92.0D -15.05 B 84.00 17 .44 25.36 25.84 -16.61 -4.99 c 10.97 c

~

76,00 16 .11 16.15 -10.89 -2.31

' p TABLE 11~4 STRESSES IN P!ERlDIONAL REINFORCING BAR 112

}

( ICJ PS/ 111 1 )

-- ......**.*.~ ........... ~.~-**'"'*~~

~*

('. :* 2 5 7 6S0-0791 l

~-

).

., I Elev. A a Lo11I Co11bfnatton c D [

Cr1tfc1l CllS e I

~ 289. 71

 ; 288.66 --.

)

J 285.42 I 280. 14 I 272.96 264.12 253.87 242.54 46.98 42.17 35.21 4.00 4.64 A 230. 46 48.93 43.95 36.80 4.54 4.79 A 227.38 49 .78 44.73 37.50 4.72 4,83 A 224. 211 SL 36 46.09 38.64 4.88 4.86 A 221.15 53.15 47.62 J!J, 91 4.99 4.79 A 218.00  !:0.93 45.61 38 .19 4.48 4.63 A 215.00 55.09 49.37 41. 51 5. 14 4.65 A 210.00 56. 41 50.!iJ 42.39 5.11 4.60 A 200.00 55.21 49.!18 41. 79 4.54 4.67 A 190.00 55.83 50.49 4l.63 2.74 4.79 A 180.00 170.00 55.70 50.87 51.04

43. iz 43.58 2.87 4.60 4.96 5.18 A

1 SS.24 A 160.00 54.84 Sl.29 44,09 4.83 5.37 A 150.00 54.65 51.74 44.88 5.12 5.S:i A 140.00 57.87 55.53 48.93 6.01 s. 71 A 130.00 57. 15 55.63 45.90 6.59 5.65 ,,

120.00 55.09 54.55 49.63 7 .03 5.21 A 110.00 49.88 50.75 45.91 6.44 4.45 c 100.00 39.52 42.91 44.42 6.78 S.43 c 92.00 25 .09 30.73 35.48 .5,37 5.27 c 84.00 11.48 20.02 24.32 -6.M -3.65 B 76.00 *2.36 -11. 62 *26.43 6.76 6-.26 c TABLE 4-5 STRESSES IN HOO? REINFORCING BAR #4

{KIPS/Hi 2 )

- . ****- ...... *--*- *- ........ *-;******-~- *----'" -** .. :~-*=-*"'-"""'---'*~---=--__..:.;**...:..*.:_*~

>\ 'Ch

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~

f::C258

~

re 6S0-0791 I Lo1d Co111b1nat1on c 0 E Crttic1l

. I Elev. A B C1Je m 289.71 288.66 48.60 s 1. 25

41. 93 44.52 33.75 Jt:.03

-2.25

-2.31 3.68 3.73 A

A

. 285.42 51.85 45.25 36.80 -2.47 3.80 A m 280. H 52.57 46.07 37.62 2.31 J.90 A

. 272.96 53.04 46.68 38.28 2.81 ".oz A m 264.12 53.19 47, OS 38.79 3.43 4.21 A 253.87 53.19 47.JS 39.30 4.25 4.45 A

~ 242.54 46.98 42 .17 35.21 4.00 *.64 A 230.46 48.!ll 43.95 36.80 4.54 4.79 A

~ 227.38 49.78 51.36

44. 73 46.09 Ji'.50 38.64 4.72 4.88 4.83 4.86 A

A 224.28 53.15 47 .62 39.91 4.99 4.79 A m 221. 15 218.00 50.93 45.61 Jo. l!l 4.48 4.63 A 215.00 55 .14 49.42 41. 59 5.21 4.66 A 210.00 56.48 50.60 42.46 5.22 4.6(\ A 200.00 55.28 49.. 64 41.88 4.68 4.68 A l!)0.00 SS.68 SO.SJ 42.69 2.57 4.79 A 180.00 SS. 72 50.89 43.14 Z.71 4.96 A

~~ 170.00 55.24 Sl.05 43. 59 4.75 5.18 A 54.83 51.29 44.011 5.37

. l6().00 4.97 A

~

150.00 54.64 51. 74 44.110 5.Z7 5.56 A 140.00 57.86 55.54 49.02 6.20 s. 74 A 130.00 57.19 55.68 S0.13 6.83 5.71 A

~~ 120.00 55.21 54.68 49.97 7.Jl 5.28 A 110.00 50.12 50.96 46.12 6.64 4.47 B

m 100.00 39. 77 43.24 45.57 7.16 5.70 c 92.00 25.ZZ 30.96 37.81 -6. 74 s.n . c

~ u.oo 11.36 19.99 24.72 -7.09 -3.80 c 76.00 -3.13 -12.sz -29.32 7.37 7.03 c

~?

~

\

I TABLE lf-6 STRESSES JN HOOP REINFORCING BAR IS

{

(KIVS/IN 1 )

" I 1Cr1tlcil riev. a c 0 j E I CBe H89. 71 I' .4 7. IS 41.15 33. 31

• l. 77 4. 77 A RR.66 56. 19 48.70 39.36 -2.67 3.60 A 285.42 49.27 42.99 34.91 -2.51 J.57 A 280. 14 55.62 '48.48 39.39 -3.37 3.88 A 272.96 49.83 43.84 35.76 -2.80 4.24 A 264.12 52.08 45.aa 37.48 -3 .28 4.18 A 253.87 52.32 46.20 37.80 -3. 77 J.67 A 242.5.C 52.36 46.45 38. lj -4.34 3.44 >.

230.1\6 53.19 47.43 39.06 -'4.88 3.50 A 227.38 52.88 47.34 39.07 -5.21 3.52 A 224.28 51. 51 46.21 38.19 -5.42 3.31 A 2 21. 15 46.82 42.05 34.81 *5.65 2.75 A 218.00 40. 54 36 .'46 30.25 -5.89 l. 84 A 215.00 42.17 38.08 31. 7 l -7.02 l. 43 A 210.00 41. 96 38.29 32. 07 -7.49 1.52 A 21)0. 00 41. 49 38.52 32.5!: -8.19 1. 59 A l*lO .00 40.63 38.55 32 .93 -9.08 l. 65 A

};JO.DO 39.96 38.83 33.55 -10.09 1. 71 A l *.H). 00 39.33 39. 21 34.28 -ll.19 1. 79 A 160.00 38.74 39.69 35. 12 -12. 46 l. 90 B 150.00 38.52 40.56 36.30 -13.72 2.12 B 1,0.00 38. 54 41. 70 37. 72 - u. 96 2.39 B 130.00 38.12 42 .48 38.87 -16.19 2.57 B

• ---j 120.00 110. on 37.69

34. 39 43.29

41. 52 40.1)5 39.10

-17.40

-18.60 2.73

-2.47 B

B r-lJ0.00

i2.00 26.80

15. 15 35.-47 22.35 34.80 22.93

-20.03

-15.52 2.65

-3.41 B

c

(*= .

J4. OD 76.00 lJ.9a 5.90 22.53

12. 2 7 23:62 13.60

• 17.02

-10.68

-4.99

-3.71 c

c t.>-......

[ _.....

~;~

~

TABLE 4-7 STRESSES IN MERIDIONAL REINFORCING BAR #5

{KIPS/IN 2 )

~j

~'*.

~ .. ~

~

l W:'.

\i*'

• • • • ,.._._,.,..__~A .........

tt2r-O

. " 0 650-0791 liner plate even where diagonal bars were present, could not be overlooked. Since the liner plate is mechanically fastened to the ~ontainment wall, it._w111 be subjected to the same shear and axial deformations as the contain-ment vessel. Thus> the integrity of the liner plate had to be checked for the condition of bi-axial stress and in-plane shear for load combinations (b), (c), (d), and (e).

This was achieved by means of an interaction formula when the liner was in a state of compression, and by means of the Tresca Theory when the liner was subjected to tension.

4-3.3 Results Reinforcing Steel The maximum stresses indu~~d in the meridional and hoop ri. inforcing bars by the r.1 ve factored load combinations are presented in Tables 4-l through 4-7.

These stresses were obtained by combining the stresses re~ulting from the individual load cases in the manner speci-fied in Sect!on 4-2. The stress induced in any meridional or hoop rein.forcing bar, "i", by an individual load case was c.s.lculateG. using the standard axial and bending stress

.formula:

Nl M2 Y.i.h f .lh --+

II!!

• a."'h *bzh (4-2a)

N2 Mi!I .lm f .(.m

• * +

9bZm

• a.Am (4-2b)

CON'::R.AD A.SSOCJ:.ATES

6S0*0791

. "'-" where:

f,;,.m > f.i..h = stress in meridional or hoop rebar due to the individual load case

= meridional and hoop forces induced in section by the load case*~n question lJ (kip/ft) (See Figure 1-21) meriuional and circumferential moments induced in section by the load case in question (kip/ft/ft) (See Figure 1-21) a areas effective in resisting axial forces, N2 ~~d N1, compu~~d per foot of contain-ment wall and neglecting diagonal 1ein-forcement.

= moments of inertia per foot of containment ...

wall and associated with M1 and M2 3...

Y.im, Yi..h

• distance rrom bar 11 ..l" to neutral axis of the section in meridional and hoop direc-tions (positive y extending radially outwards)

~~ a axial capacJty reJuction factor: 0.95

~b = bending capacity r~duction factor: 0.90 . '

Once the stresses induced in the rein!'orcing bars by the individual load cases were evaluated, they were factored and combined as specified by the various load combinations, The general expression for the calculation or the resultant stress in any meridional or hoop reinforcement bar, ".i", due to any load combination is given as follows:

Ifi)tot = k1f v + k2fp + k3f5 + k4fr  : ..

(4-3)

+ ksfE + k6f f' + R1fw 3

o;>N.R.A.D ASSOCXA.TES

6S0-0791 where:

stress in reinforcing bar due to dead load stress in reinforcing bar due to interilal pressure stress in reinforcing bar du~ to buoyancy stress in re1nrorc1ng bar due to thermal load peak stress in reinforcing bar ~ue to Operating qasis Earthquake f E' peak stress in reinforcing ba~ due to Design Basis Earthquake peak stress in reinforcing bar due to tornado zero or non-zero load factors 1 as n1ctated by the load combination in question The systematic application of Equations 4-2 and 4-3 for each factored load combination resulted in the stresses presented in Tables 4-1 through 4-7.

The peak stresses induced in the diagonal reinforcement as a result of each lnad combination are presented in Table I 4-8. No values are shown for load combination (a) since none of the loads in the combination produced membrane shear.

The stress in a diagonal reinforcing bar at any section or the containment vessel was evaluated as follows:

ti v8 f ., n ( 4-lJ) v ~VAV where:

= stress in diagonal reinforcing bar due to seismic or wind shear evaluated for a particular load combination (ks1)

~ f~:

~ ..

CONR.A.:O ASBOCJ:ATES ~

.Pi**Jf*\;"+*. ...

. . . . . . (-.'\I'..... , . . . . . - * . , , . . ....,.-..~_......vw;~.-~~7'"7*,_,,. :"'->0""~""'.>-

• ~

Lo1d Corab1niit1on 6S0*0791 I

ICritft1l E1e v. A B c D E 1 cu~

289.71  !

2RR.66 I 285.42 - I I I

ZBCJ.14

) I i I 272. 96 I I

264. l z I r 253.87  !

24 2. 54 29.70 38.30 *Z 1. 94 38.30 1c* E 230.46 35.58 45 .85 -24.89 45.BS

! CI E 227.38 38.83 so.01 -26.03 50.01 *I c' E 41.03 52.83 *26.95 52.83 224.Z.8 c' E 221.15 43.43 55.89 -27 .90 55.89 CI E 218.00 4!i.~7 59.14 -28.85 59.14 I c Ir E 215.00 31. 16 40.06 -18.94 40.06 l CI E 210.0ll 33.87 43.49 -19.44 43.49 I c I E 200.00 38.08 48. 79 -20.24 48.79 cI E 190.00 42.00 53.67 -21.20 53.67 cI E 180.00 31. 71 40.40 -16.04 40.40 C Ir E 171).00 34.01 4 3. 17 -17.29 43 .17 c £ 160.00 36.16 45. 7Z -20.43 45.72 c 'I E 150.00 38.19 48.07 -23.69 48.07 c l E 140.00 40.10 50.23 -26.98 50.23 CI E 130.00 41. 84 52.25 -30.16 52.25 t E

- c 'I E 120.00 '3.36 54.20 -32.78 54.20 110.00 44.50 56 .15 -34 .11 56 .15 cl [

100.00 36.82 46.63 -27.02 46.63 c a. E 92.00 39.96 5 l. 33 -27.02 51. 33 E c'

t 84.00 44.26 60.79 -27.02 60.79 E c'

76.00 Jl. 59 44.44 -27.0Z 44.44 cI E

~

I

-~

- TABLE 4-8 STRESSES IN DIAGONAL SEISMIC REINFORCING BAR #3 tt f,

f

~-

.r CONRAD .ASSOCLA.TES l

-~~~!C_.;..,'V~~~~~ 1~.*'.:~--~-~-P.P.Pkt,.""'P\i+V'+'O.Pltj(~~~t'f.~~'"~"""_.,__-~_-.*--.*-~-p-.w-~~~~-:-~,.*~~. .-~_..,....,"r"".:.J,..

---

~----------* ..

r.

6S0*0791 v ~ peak membrane shear force induced at the section by wind or earthquake (kip/ft)

~ Load factor applied to the shear force in accordance with the load combination in question 8 = spacing of diagonal reinforcement measured perpendicular to the direction of placement A = cross sectional area of an individual v diagonal bar

~v a shear capacity reduction fac~or o.85 The same procedure as outlined above was applied in the review of the radial shear reinforcement, utilizing _1 Equat5-:in 4-4. Results from this review indicated that the reinforcement was adequate for each of the load combinations *

. Liner In the general case, the steel liner plate is in a state of combined bi-axial stress and shear under the effects or the applied load combinations. Only when the containment vessel is subjected to test press11re or to load combination (a) does the condition or the liner degenerate to one or bi-axial ~tress only. The criteria U8ed to review the liner plate design depended upon the nature of stress under 1nves-tigat~on. In regions where the liner was subjected to bi-axial compression and shear, its performance was evaluated by means or an interaction relationship. In regions where the liner was in a state or combined tension and shear~

its integrity was checked by mea~s ot the Tresca Maximum Shear Theory.

..4-21

"""1"_+'-,___,_

4

• ..,.,.....,,..,,,.,..,...-.,........, .. ,..._4""'_.

...-.---~:pl-'"'!", u .,.*t...,H"W':oll. _ _,,,..___,,_.,.., ** ,.,poq. .U:'h.P #'

• 4 ~

?. CC265 L

ti The following interaction formula (l) was used to examine the behavior of the liner plate under combined bi-6S0*0791 Ir axial compression and shear:

~

t~.r ax + az "< 1.0 (4-5)

+

I \a xo + azo

,~~* f ,

B where:

/' . . . JI ~>fl'" ,ti,... .,.::/

(.

§ ax

• a z = hoop and meridional stress in the liner plate a a = maximum allowable stress in hoop and

~ xo, zo meridional directions T = shear stress in the liner plate m T 0

• maximum allowable shear stress  ; z.11 ~ JIS-:l.c.'

The hoop and meridional stresses generated in the liner plate by the various load combinations were evaluated by

~ applying Equations 4-2 and 4-3. The shear stress, T* was I

. I determined by dividir*.g the liner plate shear force, associated *!

m with each load coml:'lnation, by the liner's cross-sectional m area. In regions where diagonal reinforcement was present, the portion of the membrane shear resisted by the liner

~ plate was determined assuming that the liner and the diagonal

~

bars were strained equally. As a result, the distribution of the shear between the reinforcing bars and the liner

_...... --~- .... --.~-------------_.... ...... ______________ .

m --'"...*** ........... -..... _..... ___

plate was a function of their respective areas per unit length of containment wall.

~ - - - - - - * **. **- *-**""*r-**--.-..... . ,. ..., ___ ,_,.,,,___,,._**

L

?-:

~

.. r" i

N

,...,. .._.._.,.,.,, P,P:9.Jv+t,* aq .... . . ,. . ,._ , ,.. . . . -.....,~~~~~e~~~::J

0 so - c::r1cn ~4'1

'Pb. 2(o s , ,. .

• The maximum allowable stresses in the hoop and meridional directions were selected from the critical buckling stress and the yield stress of the liner, whichever of the two was smaller. The critical buckling stress in the liner was determined from the following equation for simply-supported 2

plates subjected to uniaxial loading:( )

(4-6) where:

a c.r

a critical buckling stress fz. .. plate coefficient E* = elastic modulus t

• plate thickness b = plate width between supports

µ = Poisson's ratio Although the assumption of simply supported boundary conditions was conservative, the maximum allowable stress as controlled by buckling was still larger than the minimum guaranteed yield s.tress of the material which is 32 ksi.

Thus,the minimum yield stress of the liner plate was sub-stituted for the allowable stress terms, axo and azo' in Equation 4-5.

The critical buckling stress in shear was computed by the same formula as Equation 4-6 with a different plate coefficient assigned, The resulting buckling stress exceeded the minimum yield stress or the plate in shear. Thus, the allowable shear 4-23 CONRAD ASSOCIATES

6S0*0791 stress, Txo' in Equation 4-5 was assigned the minimum

...,,.... -- r-- ... .... _ ..c : -_ _ _ __

yield stress value of 24 ksi. The final results or the I liner plate review,using Equation Q-5,are presented in

-.~

I Table 4-9. It should be noted that values have been enter-ed for the different load combinations only where the liner was in compression.

The integrity of the liner under combined tension and shear was checked by means of a procedure based on the Tresca Maximum Shear Theory( 3 ). The Tresca yield condition assumes that yielding occurs when the algebraic difference between the maximum and minimum principal stresses reaches the uni-axial yield strength of the material in question.

Thus, a' ., 0 mttx - am.c..n. {<a )

- tJ (4-7) or c' *J(o ~

-er ) 2 + 4T2 z I<- o y l (4-8) where:

a

• maximum equivalent uniax1al stress (j

mdX

"" maximum principal stress C1

• minimum principal a tress m.i..n C1 IJ

= yield strength of the material In checking the performance of the liner under combined tension and shear, the equivalent un1axial stress, o', was evaluated and compared to the maximum principal stress

~:

0

" max.

r The larger or these two values was aelected as the critical tensile stress in the liner plate. The integrity of the

• ~---~--..,...~--~~~----------------------~-----------~_:-:--:::=:--:-:--:::--:~~~~-:--co~-~-~~--D~A..~S~B-OC~-z-.A:._~~*:s:_s ~:

--4--24

~~

CC-267 6S0*0791 Laid Co111btn1t1on Cr1tic1l Elev. A 8 c 0 E Cue 289. 7l . 163 .225 .213 .026 .282 E 2RR.66 .019 . 108 .12 3 .029 *-. .283 [

285.42 .128 .194 . l 90 .023 .284 E 280.14 .063 .143 .151 .018 .285 E 27Z. 9fi .191 .25] .237 .010 .287 E 26'. 12 . 153 .223 .216 .005 .290 E 253.87 .093 .175 .181 .000 .297 E

?~2.54 . 144

• 227 .230 .009 ."311 E 230.46

• l z7 .223 .237 .015 .333 £ 227.38 .116 .223

• 243 .023 .346 [

Z24.28 I .048 .177 .210 .025 .345 £ 221.15 .038 .170 .ZlO .027 .349 £ 218.00 .106 .ZJS .269 .035 .358 [

215.00 .029 .204 .272

- .048 .409 [

210.00 .055 .245 .JIB .054 .435 E 200.00 . 107 . 317 .400 .074 .475 E l !JO. 00 .103 .345 .447 .095 .516 E 180.00 . 10 l .372 .492 .117 .556 E 171) ,(10 .]13 *4 I2 .545 .139 .595 E 160. 00 .131 .455 .601 .172 .634 E 150.00 .158 .507 .662* .208 .673 E 140.00 .135 .516 .688 .247 .715 £ uo .on .180 .582 .759 .292 .759 E 120.00 .325 .732 r.~02"\ .339 .814 c 110.00 . 136 .5f9 --

.791 .381 .787 c 100.00 * .059 .419 .415 .683 £ 92.00 * * .186 .276 .517 I.

84.00 * .051 .473 .2" .723 E 76.00

• * .157 .344 .454 E

• LINER JS IN TENSION TABLE 4-9 INTERACTION COErFICIENT RlR llNER PLATE IN COMPRESSION CONRAD ASSOCl:ATES

('"268 E 6S0*0791

• • a '-""

liner was assured only if the critical tensile below the specified yield strength uf 32 ks1.

str~ss The review of the liner plate under combined tension and was

=--*

• A

~ shear was performed for the !'our most cr1t,1cal loc....:ing ., '

conditions considered: test pressure (l.15P), load combin-

~ ation~ (a), (b), and Cc). The critical stress induced in

~ the liner by these four loading cond1t1ons are tabulated in Table 4-10. Values have bedn shown only at those elevations

~ of the containment vessel where the criti~al stress is tension.

~ 4-3.4 Conclusions

~ Based on the results shown on the previous pages, the

.following comments can be made with regard to the design or the containment shell:

1. The main hoop and meridional reinforcing pattern shown in Figures 4-2 and 4-3 satisfy I

the ultimate capacity requirements est~blished r*

for the containment vessel design.

2. The diagonal reinforceffient scheme shown in Figures 4-2 and 4-3 will perform satisfactorily in resisting wind and seismic shear. T~e only location where the diagonal bars are critically stressed is at Elevation 84, under load cor:ibin-ation (c). The computed va!ue of the seismic t...

i... '

shear stress in the reinforcing bars at this ~ .

~

I,_ elevation is 60.79 ksi, compared to an allowable iJi or 60 ksi. It must be noted, however, that this

~

(*

\"

~*

t~

, _________________r:,.

CONRAD .A.SB_OCJ:ATEB

• U&&Ailll"Kfll0 6 &~\

• 259 6S0*0791 Load Co11binat1on lest Crltlcal Elev. A B r. Pressure Case Tut 289.71 .22.8 F'r11ssure 7.88.66 24.6

• 285.42 20.5 .

280. i4 23.Z .

272. 96 21.0 .

264.12 21.6 .

253.87 22'.3

• 242.54 20.J .

230. 46 20.l

• 227.38 21.6 .

'24.28 23.3

• 22 l. 1s 25.2 *

~

218.00 24.2 215.00 26.4

• 210.00 27.6 .

200.00 27.6

• 190.00 28.8

• 180.00 28.J

• 170.00 28.3 w 160.00 28.2

• 150.00 28.4 .

140.00 30.8 .

130.00 30.9 .

• .20 .00 30.1 ..

1l o.oo 27.3 *

~00.00 22.6 26.4 25.6 20.7 B 92.00 22.4 27.5 27.3 13.4 8 84.00 76.00

17. 2 26.0 24.8

24. 1 26.9 22.6

10. !I 21.6 c

A r*

(.

i:.

~

TABLE 4~10 MAXIMUM TENSILE STRESSES IN LINER PLATE

~

~

(KIPS/IN 2 )

[ .

CONRAD A.SSOCI:ATES

---

=------=----,...-..*--~-----*~*-**** ~- . *---"--'**-*. -....

~

L 6S0*0791 value was obtained neglecting all contri-I bution of the main meridional and hoop reinforcemer.t to the shear-resisting

§ capacity of the containment wall_. An insp-

• • • ection of the stresses incurred by the main

'§ reinforcement as a result of forces other

~

t~ t1,an shear indicates that these bars are markedly understressed in this zone of the

~~ containment shell. Thus the stress value r 0£ 60.79 ksi in the diagonal reinforcing

.~~

bars resulting .from seismic shear is over-estimated. With two th1rd3 of the strength tm L.

capacity of the main reinforcement unaccount-ed for at Elevation 84, the containment wall will have no difficulty in resisting the seismic shear force present at that ~ection.

5. The integrity of the steel liner plate shown in Figure 4-2 is assured under all load combinations considered, including test pressure.

4-4 Review of Foundation Mat Design 4-4.1 Reinforcement Pattern The main reinforcement in the base mat consists of heavy #l~s and 114s bars that run* radially or tangentially

~

with respect to the center of the circular concrete slab.

~r

...... These bars are distributed to the top and botto~ of the

'* 1'5-root slab in the manner shown in Figure 1-19 and 1-20.

CONRAD .ASSOC.:CATES

j' 6S0*0791 value was obtained neglecting all contri-bution of the main meridional and hoop reinforcemer.t to the shear-resisting capacity of the containment wall. An insp-ection of the stresses incurred by the main reinforcement as a result of forces other tl1an shear indicates that these bars are markedly understressed in this zone or the containment shell. Thus the stress value of 60.79 ksi in the diagonal reinforcing bars resulting f'rom seismic shear is over-estimated. With two thirdB of the strength capacity of the main reinforcement unaccount-ed for at Elevation 84, the containment wall will have no difficulty in resisting the seismic shear force present at that section.

5. The integrity of the steel liner plate tm I

( shown in Figure 4-2 is assured under all load combinations considered, including test m

pressure.

~ 4-4 Review of Foundation Mat Design 4-4.1 Reinforcement Pattern

~

The main reinforcement in the base mat consists of

~I heavy #18s and #14s bars that run radially or tangentially with respect to the center of the circular concrete slab.

These bars are distributed to the top and bottom of the 16-root slab in the manner shown in Figure 1-19 and 1-20.

CONRA.:O ASSOCJ:ATES