ML19329E162
| ML19329E162 | |
| Person / Time | |
|---|---|
| Site: | Arkansas Nuclear  |
| Issue date: | 11/24/1967 |
| From: | ARKANSAS POWER & LIGHT CO. |
| To: | |
| References | |
| NUDOCS 8005300776 | |
| Download: ML19329E162 (40) | |
Text
{{#Wiki_filter:. APPENDIX 5-F TABIS OF CONTENTS Section Title Pam I . DESCRIPTION OF THE FINITE ELEMEIE TECHNIQUE TO BE USED IN CONTADDENT STRUCTURAL ANALYSIS 5-F-1 II ShPPIEMEICARY INFORMATION ON CONTADBSNT EASE MAT (SUEMITTED WITH SUPPLEMENT NO.12) 5-F-3 III REVIEW OF ANCHOR ZONE REINFORCING AND STRESSES IN BASE SIAB - BY T. Y. Lin (SUEMITTED WITH SUPPIEMENT NO. 12) 5-F-4 .g. IV ANCHORAGE ZONE REINFORCEMENT 5-F-5 V INVESTIGATION OF COLD WEATHER STARTUP AND ShVfDOWN CONDITION ON COETADBENT WALL-DESIGN 5-F-6 VI RING GIRDER DESIGN 5-F-14 18 i
/ '
18005300 gQ k + 7-13 -70 g GUPPIEMENT NO. 18 O,.; q_ G
r ; APPEUDIX 5-F DESCRIPTION OF THE FINITE ELEMENT TECHNIQUE TO BE USED IN COIITAIUMENT STRUCTURAL ANALYSIS 1.0 ANALYTICAL METHOD The finite element technique is a general method of structural analysis in which the continuous structure is replaced by a system of elements (members) connected at a finite number of nodal points (joints). Conventional analyses of frames and trusses can be considered to be examples of the finite element method. In the application of the method to an axisy= metric solid (e.g., a concrete containment vessel), the continuous structure is replaced by a system of rings of triangular cross-sections which are interconnected along circum-ferential joints. Based on energy principles, force equilibrium equations are formed in which the radial and axial displacements at the circumferential joints are the unknowns of the system. A solution of this set of equations is inherent in the solution to the finite element system. There are many advantages to the finite element method, when compared to other numerical approaches. The method is completely genbral with respect to geo-metry and material properties. Complex bodies composed of many different materials are easily represented; therefore, in the analysis of the contain-ment, concrete, and foundation material can be realistically considered. Also, arbitrary thermal, mechanical and gravity loading can be analyzed. It can be shown mathematically that the dethod converges to the exact solution as the number of elements is increased; therefore, any desired degree of accuracy may be obtained. 2.0 COMPUTER PROGRAM The initial development of the computer program used in the analysis of the containment vessel was conducted at the University of California at Berkeley, in 1902, under a National Science Foundation Grant. Since that time, the program has been further modified and refined by Dr. Edward L. Wilson. The validity of the specific program to be used in the containment vessel analysis has been established by the analysis of axisy==etric solids with known exact linear solutions. It is noted that the results of a finite element analysis always satisfy statics, since the equations solved within the computer program are based on force equilibrium requirements. 3.0 COMPAP.ISION WITH ICiCWN SOLUTIONS An exact analysis of the containment structure under consideration is impos-sible by classic methods. A preliminary approximate analysis of the structure will be conducted, based on classical shell theory. In addition to the dif-ficulty in representing the steel liner, reinforcing rings and foundation material, shell theory neglects thickness and shear deformations. Since the finite element approach -includes thickness and shear deformation, an exact com-parison with shell theory cannot be expected. However, cross section forces obtained from the finite element methed at sections not near rings or the foundation should agree with the results based on shell theory. 5-F-1 m
The attached Figure 5-F-1 illustrates a comparison of the results of a finite element analysis with an exact elastic theory solution of an infinite cylinder . subjected to an internal pressure. Three different finite element analyses k:: a were performed. Except for the very coarse mesh, agreement of the radial and hoop stresses with the exact solution is excellent. An analysis of the containment structure will be done according to general shell theory for homogeneous surfaces of revolution. The matrix of influence coefficients (the unknown forces -- deflections, moments and rotations for the _.~ dome, ring, and cylinder) will be solved for the condition of equal deflection and rotations. Similar analysis methods will be used for the intersection of the base slab and the cylinder wall. The base slab will be. analyzed as an
=
elastic plate on a rigid foundation. The results thus obtained are expected to be within five per cent of those obtained by a more rigorous finite element program for ring girder, dome and cylinder wall of a similar containment structure. For the base slab analysis, using the finite element program, the matrix will be extended into the ground approximately 160 feet below the base slab and modulus of elasticity of the rock will be considered in the analysis. For determining the anchorage zone stresses as well as the stresses in the nearby region of anchorage caused by hoop prestressing forces, plane strain analysis will be carried cut using finite element methods for the buttress. As the problem is three dimensional, plane strain analysis is a better approx-ination than plane stress analysis. However, as the program is prepared for e plane stress analysis, modulus of elasticity, E, will be changed t 2 and Poisson's ratio,h , to in order to have plane strain effect. For the 1'O analysis, a cylindrical quadrant with unit thickness and with one buttress at the center of this quadrant will be considered. Since the anchorage areas are quite close, and one above the other, they can be approximated by a vertical line load. The effects of a prestress will be applied as concentrated forces at the anchorages and the loads will be unifomly distributed acecrding to the curvature of the tendons. Guyon's method, or the " standard" treatment, is relatively much mere approx-imate and empirical than the above method used in our design. Eorever, it will be used as a check method in confirming the design. 5-F-2
~ 0348 4-..
. ._ m.._._ ._ , , ~ - _ . _ ._. T'. i
- " ,
4 '! CI 7 ~. LII. . SUPPLEMENTARY INFOR1% TION ON CONTAIlOENT BASE MAT j -(Supplement No.~12). li < 1
- 4. a 1
i
)
1 4 f T i i 't i i. t-i 1 3-4 i i > r i 1 J f i
?
4 l i i i k a l 4 i f i e i 1. 4.- i. j . i. I b. e i. 3, , k 1 i 1 , ;
--5-F-3 ~
i 10-31-69 e-rw . Supplement No. 13 i I 2- , [.'C 4 . -- , '0349 : I e I
'- l
. ., , .: s e
a'- . . - - . , , . - . . . . . _ _ . . _ _ _ _ . _ _ . . . . . _ _ _ _ _ , _ . . _ . - _ , _ _ . . _ . . , . . _ . . . . . . _ _ . _ - . ~ _ , .
._. _,..~ ....- ,- ._ ,.
I L f',, 4 ' l .A f-l
.III- REVIW OF ANCHORAGE ZONE REINFORCING AND STRESSES IN BASE j -- -SLAB - BY T. Y. Lin (Supplement No. 12) 4 I.
T:
- s i
i
- t. t e
i . 4- ! ! t I ! I 1 +
- t. l 5-i i :
I' i i i ! ^. 1 i i
./ -
- > t 1; '
i 1 1 i. ]- ., t I ! i. 1' 4 l 1 a .i . 1 4-t i.
;
i-1: i 4-1 1-i- 3-F-4 { ~. -
- 10-31 :.
- ~
Supplement No.13 , 4 : i a' d j L (.! 11 o ~ M 0 3 5, 0 - F i-I ^ ?- I ,_. ___ : : _; ; __ . _ _ =_ _ ,_; u a . :-__ _,,, ,_. _,.a _, . __ _ _ _ _ , - ..,,.+,.. - - ,,ve- n - n.e.-~ ,
. , -v ,
ANCHORAGE ZONE REINFORCING IN THE BUTTRESS This supplement contains the revised buttress reinforcing-steel details. ,
- 'The' original design approach was in agreement with past
-- buttress designs for the 90 wire tendon systems. The reinforcement based on the original design resists all
. -- loads expected during the lifetime of the structure. - -
However, due to lack of extensive test data, and the _ relatively new application of the 186 wire system, this- -_- revision is based on a more conservative approach for predicting the stresses in-the-reinforcing steel. With
- the latter approach, an additional 6 #11's vertical and 3 #8's radial (ties) reinforcing bars were added at each end anchorage, giving a total of 8 #11's vertical and 7
#8's radial reinforcing bars. See Figure 15-1, 15-2 and 15-3. All reinforcing has a 60,000 psi yield stress.
Under the most critical factored load combination -
-(1. 05 D + Ta + F A- 1. 5P ) the major stress and strain in
- -the rebar is due to the bursting force and the thermal gradient.
After an extensive review of all applicable information -- ~ pertaining to the bursting forces in the anchorage zone, the upper bound of the bursting force for the buttress . should certainly not exceed 17.5% of the applied load at .7 f's (.7 ultimate strength of pres '- -- -~
. This results in a bursting force of 270gressing steel)~.
-In the vertical direction, 'the 8 #11's will resist the bursting force with a stress of 22,500 psi.
The 22,500 psi was calculated assuming that the End Anchor Zone was similar to the end of a prestressed beam. In the actual continuous buttress, the stress
-level is expected to be much lower than the level cal- " --
culated by this method, especially at locations between - the end anchors. - The stress in the vertical #11's due to the thermal
.= gradient is calculated to be 16,300 psi by using an -
analysis similar to ACI 505-54 (Specification for the.- Design and Construction of Reinforced Concrete Chimneys).. .. ~- Combining the two stres'ses', the maximum stress'of the: vertical rebar will be-38,800 psi. 1-6 Supplement No. 15 5-F-3 Ql3
L . 1 s
-The combined stresses do.not_truly represent the_act'ual
, structural condition. . Temperature reinforcement is provided to control cracks and not.to' eliminate-cracking. +
.The-forces:from the thermal gradients which cause cracking, diminish as the cracking increases. The bursting .
force' reinforcement.will inherently control cracking ---r __ . . and--when a thermal gradient is superimposed, the crack - width will increase in some locations and decrease in . . - others. The vertical bars are continuous, even=though - concrete may be cracked. Accordingly, the average -- -
' strain along - the length of the rebar cannot be- greater -~ -- - -
than. the - thermal. strain since continuity of the bars ' -- - result in.a' decrease at one elevation when-there is an --
-increase at another.-
j ,In the radial-direction, the 7 #8 radial ties resist _ . - - i the effect of the bursting force with a stress of 24,600 . psi.
- In the hoop direction, the tensile stresses in the rein-forcement will'be approximately equal to or less than _.
.the hoop-reinforcement in the reactor building wall. ,.g Additional light' reinforcement is added to the narrow b i strip of_ concrete-outside the anchorage plate to prevent
- _spalling..
4 ~ Additional. hoop reinforcement-(#10 @ 12") is provided at the' corner between the inside of the' anchorage plate r
- -and the shell-to more effectively control cracks.
z
- .
The average concrete bearing stress under the bearing plate is 3,330 psi, calculated from P/Ab where P is
.7 fs. This is about .85% of the allowable bearing stress fcp = 3,960 psi. - as defined in ACI 318-63 (fcp = 0.6fci .[Ab'/Ab)
- g. 0352 .
1-6-70 ' J ~ Supplement No. 15 F-5A;
, _ . _-_ _ ~.-.._a_..-.__ , _ - _ _ _.a
V. INVESTIGATION OF COLD WEATHER STARTUP AND SHUTDOWN CONDITION In order to investigate the effect of cold weather startup and shutdown con-ditions on the containment wall design, new ther=al gradients have been de-veloped. The inside temperature of the containment will never drop below 60 0 F during the lifetime of the plant. Figure V-1 shows the transient thermal gradients during containment heat-up. The outside te=perature is maintained at 00 F while the containment ambient 13 temperature rises from 60 F to 1100F. Figure V-2 shows the transient ther=al gradient during containment cooldown. The outside temperature is maintained at 00F while the containment ambient temperature drops from 1100F to 600F. It is apparent that the newly developed thermal gradients represent less severe design conditions than the gradients used in the design. l l 0353 l l l 5-F-6 10-31-69 s Supplement No. 13 - J' \ L'- 23 -b D cpyn WPM (We dy' & gggba.,f, ?Lw.:e han a ,28tce - l
- 0. ( l } ' -h _M!
. . ie .
T.Y. LIN, KULKA, YANG & ASSOCIATE STRUCTURAL ENGINEERiNC October 23, 1969 Mr. D. ??. IMTV; c/o Rota : l'u:2.* Bechtel Corpora h 301 Miscion Strec , u.- i.% San Francisco, California
Subject:
. Proicot No. 6600--Arkansas lluclear Power Plant
Dear Sir:
In response to your letter by Eotand Marsh dated October 22, 1969, I have checked over the buttress details shown on your drauing C-127, as revised. Tre are satisfied with ti2e rainforcing details uh *ch have been revised in accordance with our letter to you of April 29, 1969. The one question. remaining was the predicted stresses for the anchor-age zone in the buttreco along the vertical direction. Your calcula-tions shou a total of 31,300 psi total tension in stect. This occurs under the extreme accident condition uith thermal gradient plus 1.5 times design pressure. Under this condition ve could attou a stress up to .9 yield point, uhich vould bc 54,000 psi. The calculated amount of 31,300 pai is vett belou that value hence the design is considered safe. It is further noted that the active stress due to internal pressure is practically balanecd by the design prestress hence the above tension of 31,300 psi results mostly frcm themat gradient and anchorage burst-ing force, both of uhici vitt be reduced as soon as cracking occurs. This adds another factor to the safety of the design. Sincerely yours, T. Y., LIN, XULXA, YA(!G a ASSOCIATB
>---( , L(.w T. Z. Ein TXL:sc r 8 - 2.7 ') 0 035A- 0 ghw22 W Y fr E Y & oy '
E q A A. h A A
/*e*= s da
.-nnum..sw remasco.cmrmenma .emo x. / m - ,,
ADDITIONAL INFORMATION FOR THE ANCHORAGE ZONE REINFORCING IN THE BUTTRESS ANALYSIS I 1 A. General l The following information should be considered in conjunction with the information previously supplied in Arkansas Nuclear One. Supplement No. 15 to the PSAR. The design of the Anchorage Zone reinforcing steel was based on the most conservative data on bursting forces. This data was obtained from the Group H paper by S.J. Taylor (Ref. 1) who included many theoretical and experi-mental results in his paper. B. Analytical Approach Based on Taylor's Paper (Ref. 1). In post-tensioned beams, some theories assume that the bursting force is distributed along the length of the tendon, between the face of the beam and a point that is approximately the depth of the beam away from the face. Using this assumption, the bursting was considered to be distributed from the face of the buttress to a distance from the face that is approximately equal to the depth of the buttress. The tensile stress distribution resulting from the bursting force may be approximated by triangles as shown on Fig. 1. Refering to Reference 1, Page 567, Table 1, the work by Zielinski & Rowe indicates that the peak
=.7 ( As shown in Fig. 1) is .30 f where burstingstressfora[9essivestressinthesectionund f is the average cok er c6nsideration. These experiments by Zielinski & Rowe gave higher predicted bursting stresses compared to the other analytical and experimental results shown in Table 1 of Ref. 1.
ratio of.7 is based on 1/2 the width of the bearing plateThe a1 /8 relative to the distance from the tendon centerline to the outside of the buttress for the radial direction. For the vertical direction, half the distance between the tendons was used. A value of .35f ewas arbitrarily used for the maximum bursting stress to reduce any concern about the conservatism of the reinforcing specified by design. The following equations were used to obtain the bursting force: F f = .35f u .35 4ab f y = Max. bursting stress y F = Applied prestress force R ss.35 4ab ( ) (4 ab) s8 .175 F R = Bursting force .(' Note: This force calculation assumes that the center-line stress distribution is constant throughout the section. Q 0355 5-F-s 3-5-70 Supplement Nan RM
D'
, h
.3a ~ASSUMEO $7tdS$
ri 9 " DISTR /80r/0Al l -. x 's ~crua sresss
>, n -
Cq t
%. fic -
O/STRIBUT/CA/
%. % g% i e ._s N Sg = l2 "
" a = rt "
ge
- 2b ~- *
- ivinh = =
E AID V/5W SECT /CN A -A F/4. 1 C. Cracked Buttress Analysis To verify the adequacy of the anchorage zone, a cracked buttress was assumed, and a separate analysis was made assuming a wedge shaped failure mechanism such as have been observed in concrete cylinder tests by Taylor (Ref. 1). Figures 2 and 3 show some postulated crack patterns on the outside face of the buttress.
- SurreESS -9 __
+ I/ /
W -
// /
~X
}: u /{
r ,y
-h',/ &
~
/ A , ,
1 1 ---> t
; 2-f SEAT /N4 f Qf F/6, 2 l
FIG. 3 ( 5-F-7 3-5-70 h GE supplement no. 16 1 l
Figura 4 chowa tha postulat d crack patterns insido the buttress based on Figure 3. As the force F is applied on the central wedge, it will have the tendency to create forces perpendicular to the applied force. The forces may be considered as the bursting forces. The reinforcing steel confines all the outer blocks. Section A, as shown below, provides one view of the simple system formed by the postulated cracks. R
,/' -- &- ---. ..- y n
s
}{, ' I 3
,- t
/ ,-r D l, 2
. , i l h,#
Nh9
~
- ',/^, /,,,o'* _,i '~, ' A '
g
---} e
~
m a ;
/
1 o o o n a
, l , l'I$'III/Il/lll/ll$///// ll] Ylf/lk!$
" ; 5
.. + - 4 k.- F/G. 4 SECT /CA/ W-W R = Bursting force F/4 = Applied prestress force on quarter section f = p N = is the frictional force N = normal force exerted by the wedge p = coefficient of friction o = Included angle of the postulated failure plane For Equilibrium of the System: i fF =0
.25F = N sin G + f cos e l
.25F = N(sin G +p cos G) Equation 1 (F y
=0 R = N cos G - f sin G R = N (cos G -j.4 sin G ) Equation 2 Solving for N in Equ. 1 and substituting into Equ. 2 cos G -p sin G )
R= .25F Equation 3 (sin G +p cos s ) The same solution will result if a similar solution is per-formed for Fig. 2. h 5-F-8 3-5-70 Supplement No. 16
Equation 3 shows that the bursting force (R) is a function of the coefficient of friction ( /J ) , the inclined angle (G) of the postulated failure and the applied grestress force. The expected values of/l= . 7 5 and 6 = 4 5 will re-sult in a calculated bursting force of .0358F (55 Kips). It is expected that the actual value would be less than 55 Kips, since the friction and shear on the plane is likely to be larger than .75 for the rough failure sur-faces observed in the tests mentioned. As a very con-servative limit, however, values of /> = .50 and 6 = 30 were assumed. This yields a bursting force of .165F (252 Kips). The upper limit value of 252 Kips is very close to that calculated for p l75F in the previous section where the formula was R W.35g( ) (4ab) . D. Results and Conclusions The previous solution is assumed to be applicable to both the radial and the vertical directions. In the real buttress, the amount of vertical reinforcement is questionable, since the buttress is continuous and the assumed bursting forces are really not applicable. However, to assure substantial conservatism,. additional vertical reinforcement relative to Supplement 13 was provided. The stresses in the reinforcing steel due to the thermal gradient and the bursting forces for three locations are listed in Table 1. The stresses in the vertical rebars from temperature effects are calculated by using an analy-sis similar to the ACl-505-54 (Specification for the De-sign and Construction of Reinforced Concrete-Chimneys). The following table assumes that the prestress force and 1 pressure force cancel each other. TA8! E I STEESS REINE MS/6N 1 DES /SN 2 STRESS WC* YPE STEEL BURSTlWS BugST/NG DUE 70 llTTRES O/ REC M N STEESS STRESS $jp",f7 VERT
- 22,500 20,200 5,000 TOP OF HOE /E. /2,000 84fE MAT 240ML 24,600 23,0 %
TYR VERT 22,500 20,200 /S,300 BUTTRESS HOE /Z. /9, 70 0 CQVT Wall- geotAL 24,600 29,000 BOTTOM VERT
- 22,5CO 20,200 2/,500 W RING H0g/Z. 17,000 6IEDER g:4of,4L g4, g90 g3,000 w
O' a 8- 3-5-70 5-F-9 Supplement No. 16
'cFirst horizontc1 trndon niiarts at El 341'-6" (6'-6" above the mat).
Last horizontal tendon ends at EL 511'-6~ (3'-6" below ring girder). Design 1 - Design based on data from paper by Taylor
- Design 2 - Design based on the wedge shaped failure mechanism of the buttress.
From Section B, considering the radial distance (a) as measured frem
'the tendon centerline toward the center of the reactor' building the l
ratio of al/a will decrease. However, using the expression developed ' by Leonhardt R = .3F (1 - al/a) and letting al 0 an extreme upper limit of R = .3F will result. The use of the p/a--*ious rev logic is really not valid for a buttress, but this approach will only lead to calculated , bursting stresses in the radial rebar under worst conditions of approx- j imately 2/3 yield. l It may be concluded that the design of the reinforcing steel in the 4
-buttresses is sufficient to withstand the major predicted loads from t the temperature gradient and the bursting forces, under both operating cnd accident conditions.
The Arkansas Nuclear One buttress reinforcement design has also been analyzed on an alternative,more conservative basis illustrated and explained in sections below. Radial Direction _ f ... sorrms .;.'.:'* - ::' : *:: :. c....:*
. . . . S, . .,. .. ., -..'..:.. ~ M T&VDON 4
t .......
, , , , . , ..,* . , 17
~~BF.KRING:K~ ',*'..'.,'.',*,'l-
- .;; ;. tg:.;.:h.
46 4 ..
. *o. .:. ?.b. A
. ... . . .*,. . ,., .* v. . ::-
- .. ;;* ..o
'; '
o
*l : ..,,,.. ;* . o;..:ll; =* ,'. ......,. *,. -
,........a..
t . s. : ,.;
..~:
.- ;
;. .
i 1 I 8 ~FfGURE7VO.~5 ' ~ i t . 035D -
~ 1 5-4-70 l 5-F-10 Supplement Rh 17
k 8+%> + f9M)
%4 \ IMAGE EVALUATION NNNN TEST TARGET (MT-3) 1.0 lf EE EM g m g=n a su l,l D bb I.8 1.25 1.4 1.6 l
6" MICROCOPY RESOLUTION TEST CHART l 4lI//%# %p
//
1
- $$,'N/ k+A,4 k
7 1 iI_ -- - . _u _ u...-__, 4
A.
% V iMieEEvitu 1,Os TEST TARGET (MT-3)
A.'s 1.0 EDEBM i g m gg m ia l,l pf
- hN 2
1.25 1.4 1.6
= e =
MICROCOPY RESOLUTION TEST CHART 4*////%
- %f >///;/
5,,,,, y
$++4WO 9
L..,- _. ... .=. ....:.a _ ___ .-
r
+.
k IMAGE EVALUATION
.o NNN\
TEST TARGET (MT-3) 1.0 'dBaa un y lE IlE l,l [" O!!$3
.8 1.25 l.4 1.6 l ,
4 6" > l MICROCOPY RESOLUTION TEST CHART I l 4% '
++4 Wb,h/ %+:%
i 7
;
7 4 .
.. - .= . = .
p: j M<>W+ 4
$,,N,.
IMAGE EVALUATION TEST TARGET (MT-3) 1.0 En EM
!l"!$HE I u i." ILE I a 1.25 IA 1.6 MICROCOPY RESOLUTION TEST CHART &% + //p kh' ' // _ _,, #ks ?*;>.
9 3,pp
;
.: . .; + = . . --.
6 k! IMAGE EVALUATION TEST TARGET (MT-3) NNN\ 1.0 'dHM BM i[$ El u l'"llE
.f j l.25 IA 1.6 l l
4 6"
- MICROCOPY RESOLUTION TEST CHART l
#*r4 +4%
- 5$>k'I b+dy?
c e :
!,_.._=.._._
8 . l
Referring to Fig. 5 and assuming that the Leonhardt formu.la is applicable, then the bursting force is: - Rr = .3F(1 "l /a) F = Applied prestress force
= .3F (1 - 1/5) Rr = Bursting force in the radial direction .
= .24F f's '= Ultimate strength of F = .7f's = .7(2192k) prestressing steel
= 1540 k Therefore, Rr = .24(1540) = 370 k This fo3ce is resisted by 7 - #8 radial ties with an area _of 11.0 in. The stress in the reinforcement is 370 k /11.0 in" =
33.7 k.s.i. m 0.56 x yield stress. Vertical Direction . AN/T M ESS. ~1 '
~
; ". ' *
- 17
. l ; . , . . .' to. .. .'of.....
.. . . . ,' ,', ....c o'. *o *o *.'., . ,'
.,*~
. e . . o a..;. '.a <: : ' * ; .'.,. , . . .
** ....e..;*e' i l
*** e **
.. c [ . ? .' .* * *e
- ....'...+
'.a ..
t y . o .:. , ~f l s ~s.
)
.> 0 Af
..' MSSUMED : / .lli
~ 2DGE OFA. l6
~jTENDON-kf l'
/
\
.o, i
/ .-
* - , 4 CON 77NUOUS ~ :
{, ~_ BEAR /NG A.
;
f7GURE NO.' S~
~...
0001 54-7o-i j - Supplement No. 17 5-F-ll l
4 Using the approach used in the radial direction: -
. i Rv = .3F(1 - 1/6) = .25F Rv = Bursting force in the Rv = .25(1540) = 385 17 .
This force is resisted by 8 -#11 vertical bars with'an area of 12.5 in 2. The stress in the reinforcement is 385k /12.5 in2 mi 30.8 k.s.i. 98 0.52 x yield stress. E. Test In order to investigate the behavior and verify the adequacy of the original and present anchorage ?.one reinforcing in the buttrass, the applicant will participate in a full scale buttress test program. The specific objectives of this test program will be:
- 1. To provide' experimental evidence of the structural adequacy of the rainforced buttresses for concrete containments which utilize large. force capacity prestressing tendons.
- 2. To verify the capability of the buttress to withstand, during prestressing, an imbalance of end anchor loads.
- 3. To achieve a limited failure of a portion of the structure when the feo as defined by ACI-318-63 is larger than the value for which the buttress is designed.
The test structure will be constructed to include the physical features of Arkansas Nuclear One, as well as alternate buttress designs to demonstrate the validity and margin in the design. The test structure will simulate, within practical limits, the butt-resses-used on the actual containment structure except where devia-tions are required to obtain representative stress levels or to incorporate more conservatism. The test structure will have a concrete strength at the lower end of the strength range, which is typical for actual containment structures, and the reinforcing steel will be ASTM-615-68 GR60. The tendons and end anchors ~will be supplied with a force capability equal to or greater than those supplied for the Arkansas Nuclear One containment. Of the ' twenty tendons supplied, sixteen will have an ultimate strength of approximately 2.2 million pounds and the other four will be used to apply a load of approximately 2.4 million pounds from each of the eight end anchors to the test structure. 0002 ' t 5-4-70 ' Supplement No. 17 l I 5-F- 12 l l_ '
Heat will be supplied to the test, structure from fluid flowing , through pipes placed on each side of the longitudinal axis of.the test structure. The outside faces of the test structure will be 1 cooled. This combined technique will be used to simulate the temperature gradients for winter operational and design accident conditions. The details of.the test procedure are presently under preparation - by the Bechtel Corporation and it will be reviewed by their consultants. The test procedure sequence of. applying heat and stressing loads on the test structure will be similar to that for stressing an actual containment structure during the winter and will also simulate the stress loading of the containment structure during an accident condition. At approximately three-month intervals after the initial short-term test, the test structure will be reheated to simulate the winter operating gradient at which time additional readings will be taken. It is anticipated that some test results will be avail-able during April 1970. The buttress reinforcement will remain as shown in Supplement No. 15 until justification is provided for reduced reinforcement. References
- 1. Anchorage Bearing Stress, Group H. Paper 49.
S. Taylor, Pages 563-576.,
- 2. Prestressed Concrete Design and Construction.
F. Leonhardt, Page 271.
& 0003 /
5 4 -70 5-F-13 _ Supplement TR%_R7/
ARKANSAS NUCLEAR ONE RING GIRDER DESIGN I. Summary The concrete and reinforcing steel stresses in the ring girder were examined for all the loading conditions specified in the PSAR by the use of the f.I. nite element program for an uncracked concrete section. The concrete and reinforcement stresses were calculated by conventional methods from the moment caused by loadings other than thermal. To derive the thermal stresses in the reinforcin'g steel, the effect of cracking in concrete was simulated by an analysis similar to the example shown below. This example considers the equilibrium of forces in a homogeneous section due to.a 1000F_. thermal. gradient. . NT
-c } , P POISSON'S RATIO -
i J_Q= MODULUS OF ELASTICITY OF C0tlCRETE
-- J BG O % d = COEFFICIENT OF EXPANSION OF CONC.
_ b , _ _ (T -% nT= THERMAL GRADIENT . joRIGINAL NEUTRAL O U
-- m3 .'A . .
.T_=.. TENSION FORCE DUETO SHIFTED N. A.
E. Cne+= NET compression roncE ou secnon TAs=l*27fF'G g YC =~' MODULAR RATIO I y .Sl y ~~ C =~ THERMAL STRESS oi: UNCRAOKED CONC.SECTION
~ ~ ~f 7' = TENSILE _ STRESS.lN REINF.
g
- r
,, ', = C nc+
,DACc /1 .-19.5 ON=~5(.Eeat_ @ ( 2. 3C (l2)-Yl. As 22.5 c~+sce -
=o ,
~
~2(l-:~1T) -c ' a - -.
= G.5 x 10 x 4 8 x)ox loo c 18GO-Acr 2 (18GO-40'c)225x12 18GO
-78f 27 IGIOfoG =0 2( l ~-7 P_5 ) - - _
= 18GO PSI 251,000-270ar +c 072G AG -8 f4,300-8.9 AG = 0 US!?G SIMILAR TRIANGLES cN #
.THEicoMPRESSION SIDE __.
SOi .072G AG -2794 6 + 23G,7CO =,o l8GO _ _l 8GO - arc /. scc = +273 $ $7S -4x.072G x 25G700]*
- 22. 5 ~ X 2 X . 072G 2 g q = ,g X = (l8GO - A Oc) ,*g = 2 GOO > 18 60 N.G.
C -T = C net @ Ac c= _182 = iggo ps; o,g, (EQUArtoN OF EQutLIBRUM) ,(452 SO ' ' fT P _O_ x 18GO+1250 7 LM.b _] q R.. : gg.4 =- 20,000 PS j _, ,
., 5 -F-l?+ 7-13-70 ,
, SUPPLEENT no.18
The thermal stresses in the reinforcing steel were also calculated by using the Chimney Code ACI-505-54. Local stresses in the reinforcing s,ceel due to bursting forces of the dome and vertical tendon anchorages ""#* analyzed by using Leonhardt's formula R = .3F (1 a1 /a). These stresses were added to the reinforcing steel stresses derived from the governing loading combination where the latter reinforcing steel were used to resist the bursting force. To verify the adequacy of the anchorage zones, separate analyses were made by postulating crack patterns in the - ring girder. It was found that the stresses in the reinforcing steel of the ring girder were below the allowable stress of 54000 psi (.9 times yield stress) for all loading conditions. II. Reinforcement Stresses at Dome Tendon Anchorages Bursting Stresses Due to the dimensions and orientations of the dome pockets, Fig. 5, the main vertical and hoop reinforcing steel was placed 1 foot inside the face of the ring girder. To trans-fer the bursting force from the bearing plate to the main reinforcing steel, the #5 spirals were used. The bursting stresses in the reinforcing steel were calculated as shown below.
' ~T00METENDOiv L'.: .- . .
/ .4 .. .
g ,. %__ __ __. .- . . . ,. . m."E
~t
/ 4, my 4y . "s s
e f' u A* ph TOP AN W0i? AGE s
. ~. N, f q Y- -:- 'V '
..[ fp db, eorr.gaones e_
, c. ; 0.'
'g
. ; ,.. ,- ,: N- i
,:: 6. ': b$
.:2
., d 0 -
ABEAA%VGM, '.
.d g
I 4 .. fi'/NG~G/ffDDT ErEV mayu y - S:.27'*/0.^:/. .
, g 0005 5-F-15 7-13-70 l SUPPLEMENT NO.18 l
I
- a. Vertical Direction Rv = .3F (1 al/a) ^1 = 12" a = 72"
= .3 x 1540 x .83 al /a = 12/72 = .17
= 383 k F= .7f's = .7 x 2192 = 1540 k
The bursting force of 383 kips is resisted by 6 - #11 (2 - #11 @ 12) vertical and one half of 9 diagonal re-inforcing steel (A = 14.31c") yielding a predicted s bursting stress of 26,800 psi.
- b. Hoop Direction Rh = .3F (1 "l/d) 1 = 12" a'= 42"
=
.3 x 1540 x .71 al/a' = 12/4 2 = . 29
= 328 k F = 1540 The bursting force of 328 kips is resisted by 10 - #11 hoop reinforcing steel (A = 15.60") yielding a pre-dicted bursting stress of s21,000 psi.
The #5 spirals were designed to distribute the load into the main reinforcing steel and act to confine the burst-ing force. The analysis used for the design of the an-chorage zone reinforcing was used to determine the burst-ing stress of the #5 spirals. The predicted stress in this reinforcing steel is 13,200 psi. Combined Stresses The 2 - #11 @ 12 vertical reinforcing steel resists the critical factored load combination (D + F + 1.5 P + Ta) with a predicted stress of 15,600 psi. Combined with the bursting stress, the total stress in the #11 vertical rein-forcing steel is 42,400 psi. The #11 hoop reinforcing steel resists the same critical l factored load ccmbination with a predicted stress of 11, 000 psi. Combined with the bursting s tress , a total s. tress of 32,000 psi is predicted. III. Reinforcement Stresses at Vertical Tendon Anchorages Bursting Stresses S 0006 ' ( 5-F-16 7-13-70 SUPPLEMENT NO.__18 .
?
, , ~
v4 /0 ! "
\ TG.7&TE TENDON - = - \[ x di =l# -
F s -
=.
s *-
.b, f.
..-. * =
w .
. .. a:.
-f . . . . .
_. .\ ..- . TSW75C72 '
*A',*: \ ' L;
\ g-y \gQ -
.s -
\g ,
\
Q :-
.\
\ ,
. . I .o .
b
}.~-
\ ...
1 I l'
.s . .
AA l -
- L
~BIRG~S/RDMRAN :~SECMV-gra 2 -
- a. Radial Direction Rp = .3F (1 "l/a) #
1 = 12" a = 58"
= .3 x 1540 x .79 "l/a = 12/58 = .21
= 365 1
4 The bursting force of 365 kips is resisted by 4- #11 radial and one half of nine diagonal #11 reinforcing steel (A = 11.90") yielding a predicted bursting l stress o5 3 0,700 psi. I
- b. Hoop Direction R
H
=. ( -
/a) =1" a' = 4 2 "
= .3 x 1540 x .71 1/a'= 12/42 = .29 k -
= 328 8 0007 5-F-17 7-13-70 l SUPPLEMENT ESO J
. l.
The bursting force of 328 kips is resisted by 8 - #11 hoop reinforcing steel (A = J2.48a") yielding a pre-s dicted bursting stress of 26,.'JO psi. : Combined Stresses The #11 radial reinforcing steel resists the critical. I factored load (D + F + 1.5P + Ta) with a predicted stress , of 11,700 psi. Combined with the bursting stress, the I total stress in the radial reinforcing steel is 42,400 psi. The #11 hoop reinforcing steel resists the same critical factored load combination with a predicted stress of 13,100 - psi. Combining it with the bursting stress, a total stress of 39,400 psi is predicted. IV. Cracked Section Analysis The ring girder was checked for equilibrium by postulating some crack patterns as shown in Figures 3 and ... F VERE TENDON h BEAR /NC 8, _. _y \ i
;I
~
.'..' . . , . M'
*... m fctsHoo?-
s
'.y* N*n ' g*;
BARS sI p Jophycnosas
,; N is .
I . ., x
/* ,y .
./_ E077: A! TOR 4GE ., .. , j
% \
Q- _{c u :
.s ?.'
s.
. .; . . '
\ \
BEAR /NG A Pure :.; '. 'f .
.'- ~
R/NG G/rTDER BLEV
- SECTf0WL .
FIS. 8 ~ q / ~ .- g 5-F-18 0008 g3_, SUPPLEMENT NO.18
In Figure 3, a diagonal crack, extending from the inside edge of the vertical tendon bearing plate to the top of the dome anchorages, was assumed. The shear friction theoryl was used to analyze the adequacy of the reinforcing steel in the ring girder. The vertical prestr ess force is resisted by 16-#32L hoop, 6-#11 diagonal and 2-#11 radial reinforcing steel. k 9_ APPLIE'D'PRESTREF.Ji FORCE-- ._ V = .7fs = .7x 2192 =k 1540 NFS
. Vp.= FACTORED. LOAD OF PRESTRESS YORCE \lg= l 5 x !540 = 23IO MIPS b3 WIDTH OFCkAck =24"L- -. .. Q=$ , 2310 , ygo K pgg dN DEPTH OF CRACK = 1.92" ' _
EW32 Yic,= NOMINAL DEstSN SHEAR STRESS
~730 PSI < .2[c = l100 PSI fh~.=.XIELD STRENGTH OF TENDON730PSl <;
~
BOO PSl fdxcome. sTaeneTwrconc. = ssco est' gen s = 24 x l.5G ""= 97 4" " [s.5; REINFORCEMENT STRESS -
= W, _
y, = COEFFICIENT OF FRICTION ~ 23 LOK
,pjzAg~ , ggx g.4 x 374 p.._ .C.'.cW REDUCTION FACTOR .
= 52,000 PS) i CHAPTER 11, REV.OF ACI .OIO-GS ,SU!LOING CODE R!EQUIREMENTS FOP. ~
7 REINFORCED CONCRETE # JOURNAL O.= THE ACI. FEB.1970 . The 24-#11 reinforcing bars kips with a predicted stress ofresist S 4 000 the factored psi. load of 2 310 TEdl. /W/OON \. as4n/us n,I , . . F .. .
.t u r t
i 1 a.. uy;
/ 'a .! '. .. . - g-sul
\ '\ r .
' ji ,
( J rob, umomes: 1'E% .
.'l
<:/
N l y h serij m w w u
/_ ~
Q \ f . I
, .- l
..a.. K F 4 .* .- L gg,winag) ..' .
. i-e ., .
;
..R,WS~GI/i'DE9 ~EEEV cocs -
SECT /0N_ N 5-F-19 ~ FIG, 4
)
In Figure 4, the simulated cracks extend from the bottom edges of the dome tendon bearing plates to the vertical tendon anchor-ages. This postulated condition assunas the top of ring girder corner to be displaced by the wedging action of the dome anchor-ages. Assuming that this wedging force is equivalent to the bursting force, (See 5-F-7, 5-F- 8, and 5-F-9), an upper limit of 383 kips is predicted. The wedging force is resisted by 5-#11 hoop and 3-#11 diagonal reinforcing steel (A s = 12.48c") with a predicted stress of 30,700 psi. The end anchorage reinforcing in the ring girder was reviewed by T. Y. Lin, Kulka, Yang & Associate. The reinforcement was found to be ddequate. i l l 1 i J g 00iO' , , S-F-20 743-70 SUPPLEMENT NO. 18
- , -
-g an fop _ '9 "
' A3./ //. * ,
D I/O' kom -
=
4:o* .. d 8, I_2 ,, 6-fa w -- sadia(~$ \ \ /pagigaIs'Lo.. ys, ~ fon s"""#ON V N 'nsvis'
- N - > - G .s
~
- . J .&
xx ,- _ N4%' % ,'.,4 5 .
.m. -
*.i
{ .} . C,, , , ,-( ! '
\ ,N: ;.
~
~
+, 'Cf - '. ;,l)f,$
i. W ;f'l$'k . p' Tf,',l$Ti c u l eawr revoa/r'- TCPANMMME
- n snaa ~.
'%. p [J ~d # M c sn N _ .t ' . - .
s
- j. s k
;
I'
, ,,-tme rocavs
~
_ s.ea iG/J#c J ' BOXA//CWe%AM xmuseoarn ado. N
.?
([-L j$C,'/AL; BAP.3) - . 3-f N' Gj ~ 4 .
,7mn:o
- xcu h -\
L ;
-.x
-d i o
i -y . l.t. s. y.. (C).fl.5/SI o'
,g
[~~
~
'st
- r.
ones . ,
% f 8 G l3 %
,a
' Q '
1ns w 4%
.*Y o
'4 -
OJ b
-///ce
, .spart G LINF
~
~EL..S$ 5 6 ' y ,.
, xk ggpgl- [$
(,,, g3,gg
. .* g*o* N i o
.}.
T 'f - y 5 s 1 _Q I u
- t
--Q en m
.gre s en m t t aw st u.
'm I,
t Y-roas c *n.
- p ,/ -. s qc.s.rt qeslo* - .
.m ,___r -
- pgg, 5 .-
~
S-F-21 7' n ^" -70 ' SUPPLEMENT NO. 18 0031.
n w ... .
~
L nmu.
, ~l J
+p__. h h r -
31 r- t r:
~ -
'I
(- .--r I$ -.: .: ~r --
~
'L1 I
q ,l l,# { 'l
.kiI[Ti ry 7
. ', , ', , , , , ,f ,j, j 1 1 -r--
l *1 *'lIII II ~
' I
*iiiiit I / ! / ,'
u.l- J I is
\. J l3 j ! j%:: !. '
lll
* * " ' . __ t /!/t/ / / /
!/////
[+
//>'E
,'// )I
' N -~..,Jl/?+//
/,
! / /* / / / .
/ V '/ i/ /
e ll$.l
-i ~
iA/. s. ' l*,' M/._ %,'. , / '
' //
\ ._
'} ..
/ ,/
'sp$ k .
v 0, y / // -
, /,l,1 l 4 ";:s
. '/ /
l .. m, '/ W
\
\/ -
s .\ 3 s'
* ' ,/
\/ s \ \ fk C s '
km pY\ i\1 \, ! . . . _
/\ E
, ~ ~
( ,
\
' N' e, \ ,\ ! m ,,, _ \
- u-
_\.
\
/ s i
.- )/. - )?'\
/
' ' ' G $* .
'. 'hry, s, g . ,
eta /v l/ y / 2' Qq;'n OR p9: n&h t 1 n' _ RIG EG D 5-F-22
~. 'P-13 -70 SUPPLEMENT'NO. 18 1 i g ' '
00 ir. ? ;
- s. . .,-
Additional Information for the Arkansas Nuclear One Ring Girder " Desicn g
?
- 1. The concrete and reinforcing steel stresses in the ring girder were analyzed for all loading combinations specified in the PSAR (Refer PSAR sections 5.1.4.5 and 5.1.4.6) .
The loadings considered in the ring girder design include earthquake (design.and maximum), tornado, thermal (normal operation and LOCA) , dead and live loads, pressure and applied prestress loads. The thermal gradient caused by the normal operation condition has been found to be more adverse than the gradient caused by the startup and shutdown conditions (refer to supplement 13) . The thermal gradient immediately after prestressing is also less critical than the thermal gradient caused by the normal operation condition, because the te'mperature within the contain-ment is not expected to approach the 1.100F that analyses established as the highest average air temperature during normal operation. Thermal transients have been predicted for time periods from 130 seconds to 10,000 seconds after the LOCA (refer to the PSAR Fig. 5-4) . During this tire the pressure is predicted to drop from 59 psig to approximately 20 psig. In the analysis, the factored pressure was combined i. with the gradient at 1000 seconds (this condition yields the largest predicted tensile stress in the reinforcing steel) . For this reason, the post-LOCA condition, with the lower
'than assumed pressure, does not control the design.
Creep and shrinkage were not considered as a loading case. However, sustained modulus of elasticity of concrete was used to account for the effect of creep and shrinkage (refer supplement No. 4, page 11.2.3-1). The effect of creep and shrinkage was also considered when evaluating the effective prestress forces. Discontinuity stresses at the ring girder were predicted by the axisymmetric finite element analysic for the axisymmetric loadings. 2.a The finite element computer program used in the design of the - ring girder requires the assumption of the elastic behavior of the concrete. To simulate cracking of the concrete in ten-sion, the concrete and steel stresses due to the thermal grad-ient were calculated by the method shown on page 5-F-14. The concrete and steel stresses due to flexure for loadings other than thermal were calculated by the conventional Working Stress Method in accordance with the ACI Code 318-63.
~0013 ' ~ ~.
9-30-70 5-F-23 ,. . Supplement No. 19 V ' u :r ' i
; .Examplo ,
~
w
'.g lE" -
.i
-_i 4
IU I 3 /4 -" - u "Lm h1= MOMENT CUE TO LMADING e4 v / i
.:1 d COMBINATION G
N - a
* -l = TENstoN FORCE IN RElblF.' ?
2 'a 11
" g' ._
7 "S STEEL
, C =. COMPRESSION FORCE' 29U
' IN'COMR BLOCK
[-n As =G x3.lG %= STEEL STRESS -
" l 8.9 G K=FCONCRm = ' COMPRESSIVE (12 Kd)(b) 2 =l8,9G(72-Kd) gTRE s.m_ _ _ _ _ .. .
G Kd*+ ie. 9G Kc! - 13 G3 = 0 .h = MODULc.R ratio
. Kd =. - 19.9G gh8.9G d x G x- 13G3 ' '
12. Kd o lS.G
'*I TS = =. Il 2 HSI 3 .l G x G 7: 5 _ __
S
, 11. 2. I S.G Yd -c = 0 x =
435 KSi \ g3/M d-Kd d
#8'4 <, I The method shown previously considers the distribution of stress on a cracked cross section, but does not consider -
the possible redistribution of forces and moments due to cracking. Since the structure will be fully prestressed during its lifetime (with the exception of some losses) and pressure tested to 1.15P, the conceivable loading l conditions will be banded by actual tests. The 1.5P pres- ' sure case essentially cancels the applied pres tress , this accident conditicn is very similar to the loading Osndicion prior to prostrecsing. Tha thermal effect, which wen: m considered in the previous statement only Icad to self- , limiting forces and moments, which will not affect the overall stability of the structure. In the ring girder design, the predicted stresses in the reinforcing steel for the governing loading combination (1.05D + 1.5P + 1.0T
+ 1.0F) is 15,600 psi which provides an additional factor g of safety in our design.
Stress limitations, as mentioned under " Design Loads" and
" Loads Necessary to Cause St-" ' $ral Yielding" in the criteria discussed in PSAR L. .section 5.1.4 were used in _the design. _
, / , The allowable concrete stresses, of 0.3') f'c for membrane compression and 0.60 f'c for' flexural '.:ompression combined with membrane compression, as mentioned above, were es-00M
, tablished on the basis of what seemed reasonable for a 9-30-70
4
- s . s ., ,
structure of this type which is subjected to a detailed taalysic that also includes thermal leads. In the design, the practress is primarily used to induce =cmbrane ccmpres-sive stresses and it was necessary to place a 1cw limit on predicted concrote compressive stress to reduce creep effectc. The value of 0.30 f'c is considered a conservative limit for concrete membrane compressive stress and was ,impoced to ensure that the membrane creep losses wi31 be generally small and
~
linear. The limit 0.60 f'c applies to combinations of pre-dicted membrane and flexural compression due to factored loading conditions. These limits are considered to be con-servative. ,, 2.b In the design of the ring girder, the concrete was assumed to carry no tensile stress. 2.c The Working Stress Method assumes a straight-line stress dis-sciburion. It is the basic working stress design in acccrdance with the ACI 318-63 except with a reinforcing steel strecc allcwable of .5 R7 (.5 x yield stress) . The Ultimate 3:_wngth Method for centainment design is a modified Working Strecs he tnod. It also assumes a straight-line stress distribution but with maximum allowable concrete stress of .60 f'c (.6 x compressive strength of concrete) and the maximum allowable reinforcing steel stress of .9 fy under. factored loading combinations. To arrive at the resultant stresses in concrete and reinforcing steel due to the critical load combination, the thermal stresses independently calculated (as shown en page 5-F-14) , were superimposed on the stresses caused by loads other than thermal.
- 3. The finite element program essentially divides the entire ring girder into a series of ring-shaped elements which for mesh-preparation vary from square to rectangular to triangular in cross section. The program develops ~ the force-displacement rea'tionships (element stiffness matrix) for each individual elene. t from its geometry and material properties. The element relat:anships are then assembled into an overall structure force-displacerent relationship (structure stiffncss nat: 1:n .
Equilibrium equationc are developed for eacn degree of 'r+>- dom at each nodal point in terms of a) the sturcture forc2-displacement' relationship, b) the unknown nodal point dis- ' placements and c) the externally applied nodal point forces. Finally these equations are solved simultaneously for nodal point displacements, and element stresses. Moments , shears and axial forces are also predicted for some selected sections. In the Ultimate S trength Method for containment design, the i moments , forces, and shears for each loading case are fac-l tored and combined appropriately in accordance with the equa- 1 tions sp'ecified in the PSAR. The reinforcing steel is then proportioned where necessary to resist the critical factored 0015
, g 5-F-25 9-30-70 Supplement No. 19
7 l' leading combinntion. The approach. to the verking stresc rcthod la similar except unfactored loads / are introduced in the load-ing equations.
- 4. The allowable and ultimate bond and anchorage stresses are in accordance with the ACI 318-6 3 code. For some loading combin-ations a state of uniaxial tension in the reinforcing steel and biaxial tension in the concrete is predicted for the cur-side face of a t'.rpical wall section. (This situation is con-sidered in the e CI 318-63 code in the two way slab and wall designs). The predicted maximum tensile stress in the rein-forcing steel is approximately 40,000 psi for Ultimate Strength Design. Converting this stress into elongation of the rebar, a very ccccervarive concrete crack width may be determined.
22 ample: Gg
- g-g -
. . e . g 2. e, mo m SQ x 100
= ,OlG "
g = STRAIN IN REINFORCING STEEL (in/in) 0 = STRESS IN REINFORCING STEEL (PSI) =40,000 psi E = MODULUS OF ELASTICITY OF STEEL = - Sox 10' psi
- 6.
- ELONGATION OF STEEL (EGUlVALENT To CONCRETiE CRACK W L = LENGTH OF REINFORCING UNDER CONSIDERATION = 12.*
e From the above calculations, crack width of .016" is pre-
.dicted occuring on 12" centers. -
001G
/ ~ ,
3 9-30-70 5-F-26 Supplement No. 19
, m. .
-T . .
A
- i A
g D?Y.b:. o
.wFORCING
. STEEL i
. . . . . ,. ._ - 4_ h .
i, ,. '
.,4;..
3,-. o -- %
-.,. li .
L ,>
.o ,y.- '
[~-;.[.[,-ltjf. i l j t' O -;FECE OF:BING _s~~- =GIROE8'
==
- d. l l i 4%
. .- gi
=4 p
w
-< i M ~P .
"..U m2 _T-
, ,-: W .i, ku -
~
.. -Y' gl&'CONORETiE -.
y .-
- CRACK ~. WIDTH .
T ut- t-vMMATIONS-ON.REINF. STEEEL Figure 7 In Figure 7, a crack was postulated directly at the rein-forcing steel. The crack in concrete essentially acts :: shear key with :.he deformations on the reinforcing steel re-sisting pull-out by bearing against concrete.-
- 5. The Ultimate Strength Design of the ring girder is essentially a modified Working Stress Design based on a straight line tri-angular stress distribution. Under factored loading combina-tions, the calculated stresses of the concrete and steel are
~
allowed to approach yield. (Refer to section 2 for maximum allowable stresses in concrete and steel') . The ductility of the ring girder, expressed as steel percentage of the gross cross' sectional area was investigated. The maximum allowable { steel ratio for 5500 psi cylinder strength and 60,000 psi yield strength of reinforcing steel, .specified by the ACI ' code for Ultimate Strength Design is 2.'5%. The maximum steel 0017 g .p 9-30-70
]
5-F-27. SS relement No. 19
. m H ;
l I ratio provided in the ring girder is .38%. l l 6.a Due to the end anchor force applied in the direction perpen-dicular t3 the prestressing tendon, tension cracks in con-l crete, parallel .to the periphery of the bearing plate may develop. This results in the formation of what may be con-sidered as individual beams for each tendon anchorage. Leonhardt's formula for the computation of the bursting stress is therefore as applicable for this. condition as for beams. 6.b Due to the large dimensions and orientations of the dome pockets, it is impossible to place continuous vertical o' r' hoop reinforcing steel under the bearing plate to resist the bursting force. To transfer the bursting force from the bearing plate to the main reinforcing steel, placed approximately (l'-0") into the ring girder, the spiral rein-forcing steel was used.- The spiral diameter was sized to essentially match the bearing plate dimensions, and the length of the spiral was made equal to length from the bearing plate to the main reinforcing steel.
- 1) The design of the spiral reinforcing steel for both Working Stress and Ultimate strength Methods were identi-cal since prestress is not factored. The. spiral rein-forcing steel was analyzed both as a column tie and as anchorage zone reinforcing steel. The la. uter condition governed, as the largest predicted bursting force of
.3V (.3 x applierl prestress force) derived from Leon-hardt's formula (F = .3V (1 a/ d) with a/g approaching 0) is greater than a calculated force due to the . Poisson's strain effect of concrete caused by a perpendicular load.
In the design, the spiral reinforcing steel was trans-formed into an equivalent cylinder and resists the bursting force which is converted into a lateral pressure.
- 2) The concrete compressive stresses- under the bearing plate were calculated by dividing the applied force by the resisting concrete area.
- 3) The influence of cracks in concrete parallel and
~ through the center of the trumpet will increase the -
predicted stresses in the spiral reinforceing steel. In the design of the spiral reinforcing steel, the largest lateral force caused by .the bursting force was considered. Therefore, the most conservative ap-proach was used in arriving at the predicted stress. 6.c The allowable stresses and the ultimate strength of the concrete blocks were derived from tl e shear friction .sec-tion of chapter 11, Rev. of ACI 318-63 Building Code Re-quirements for Reinforced Concrete published in the Journal i of the ACI, Feb. 1970. The new section in the proposed - ,- t 0018 9-30-70 5-F-28 Supplement No. 19
, e code came as a result of some extensive tests by Hofbeck, Ibrahim and Mattock who were more interested in the direct shear failure as opposed to diagonal tension. (Refer to
" Shear Transfer in Reinforced Concrete," ACI Journal, Pro-ceedings V.66, Mo. 2, Feb. 1969, pp. 119-128.)
6.d In Fig.'s 3 and 4 pages 5-F-18 and 5-F-19, a series of postulatrd cracks were assumed in the ring girder. The , shear stresses caused by the applied prestress force will be resisted by friction of the two concrete surfaces. To develop a frictional force a normal force must exist. This normal force is supplied by the vertical and hoop reinforcing steel which is essentially perpendicular to the assumed cracks. Groups of rebars, which act to resist the bursting forces due to the Dome and Vertical Tendon Anchor-ages, are identified below: (Refer to FIG 5 and FIG 6, pages 5-F-21 and 5-F-22.)
- 1) Dome tendons, vertical direction Two groups of reinforcing steel were used to resist the bursting force due to the dome anchorage in the vertical direction. The first group includes 6-#11 vertical bars (2-#11 @ 12") placed between each adjacent dome tendon trumpet which are approximately on 3'-0" centers. The second group consists of one half of 9-#11 diagonal bars
, (3-#11 @ 12") placed between each adjacent trumpet.
- 2) Dome tendons, hoop direction A total of 20-#11 hoop rebars, arranged in two layers parallel and near the vertical face of the ring girder (10-#11 hoops in the outside layer, and 10-#11 hoops in the inside layer), resist the bursting forces due to the top and bottom dome end anchorages. The 10-#11 hoops in the outside layer include 4-#11 hoops above the. top an-chorage, 2-#11 hoops between the top and bottom anchorag-es and 4-#11 hoops below the bottom anchorage. The 10-#11 hoops in the inner layer include 3-#11 hoops above the top anchorage, 4-#11 hoops between the top and bottom an-chorages and 3-#11 hoops below the bottom anchorage.
- 3) Vertical tendon, radial direction To resist the bursting force due to the vertical anchorage in the radial direction, two groups of rebars were used.
The first group consists of 4 ^11 radial bars spaced eodal-Ly between two adjacent vertical trumpets. The second group consists of one half of 9-#11 diagonal bars (3-#11
@l2"),also placed between each adjacent trumpet.
- 4) Vertical tendon, hooo direction u' ~0019 A total of 8-#11 hoop rebars, 4 on each side of the ver-tical tendon trumpet, were used to resist the bursting )'
5-7-_2_@ a- w
force due to the vertical anchorage in the hoop direction. Based on the assumption as stated for the reinforcing steel, the magnitude of bursting forces and corresponding rebar stresses are as follows:
- 1. Dome tendon, vertical direction Based on Leonhardt's formula, the predicted bursting force
~
is calculated as shown below: Rv = . 3F (1 al/a) Rv = Bursting force in the vertical direction
= . 3x154 0x (1 12/72) F = Applied prestress force
= 1540k
= 383k al= Half the width of the bearing plate = 12" a = Max. distance between ad-jacent tendon center line
= 72" The predicted bursting force of 383k is resisted by 6-#11 (2-#11 @ 123 verticals and one half of a 9 diagonal reinforc-ing steel (iAs = 14.31"") resulting in a predicted rein-forcing steel stress, due to the bursting force, of 26,800 psi.
- 2. D6me tendon, hoop direction Using the approach as for the vertical direction, Rh = . 3F (1 al/a) a1 = 12"
= .3x1540x(1 12/42) a = 42"
= 328k Rh = Bursting force in the hoop direction Since top and bottom dome anchorages are located close together, the combined prediction of bursting forces of 328k x 2 = 656k may be assu This predicted force of 656ged is to act simultaneously.
resisted by 20-#11 hoop bars (iAs = 31. 2" ) resulting in a predicted reinforcing steel stressf due to the bursting forcef of 21,000 psi.
- 3. Vertical tendon, radial direction _
Rr = . 3F (1-al/a) a1 = 12" a = 58
=
.3x1540x(1 12/58) Rr = Bursting force in the
= 365k radial direction The predicted bursting force of 365 kips is resisted by 4-#11 radial and one, half of 9 diagonal #11 reinforcing steel (i A = 11. 9 0" ) resulting in a predicted reinforcing steel stress fdue to the bursting forcefof 30,700 psi.
( ~
- 4. Vertical tendon, hoop direction 00?J3
$lf 5-F-30 10-12-70 .. . .
s R a1 = 12" a=42" h == .. 3x154 3F (1 0x al/a)12 (1- /42)
= 328k ,
The predicted bursting force of 328 kips is resisted by 8-#11 hoop reinforcing steel (dA = 12.4 8"* ) .resul ing in a predicted reinforcing steel stress,due to the bursting , forcefof 26,300 psi. It should be noted that no credit was taken for:
- a. reduction of the bursting force in the vertical direction due to the dome tendon anchorage, because of the applied vertical compressive force exerted by the vertical tendons
- b. reduction of the bursting force in the radial direction due to the vertical tendon anchorage,because of the applied compressive force exerted by the dome tendons.
- 7. For resisting membrane shear, refer to the criteria described under section 5.1.4.6 of PSAR Vol. I. The effect of membrane shear will contribute to the principal membrane tension stress and cracking will occur when the principal membrane tension stress exceeds the tensile stress capacity of the concrete.
Reinforcing steel was provided in each direction at the out-side face of the ring girder so that the resistance across the crack intersecting the reinforcing steel mesh will be indepen-( dent of the angle at which the crack intersects the mesh. (Refer to Question 11.2.12 of supplement No. 4 for the transfer of radial shear in the ring girder.)
+
.. 0021 6 '
5-F-31 10-12-70 Supplement No. 19
..m *
- - ~ ~ . . .
//Od12 s8 O'LON4
~
TYPICAL WALL *o* Atg/MFOCC#N6 7 *H VetricAL (STA.tTS fccM c0MittuCTt0AJ
- Ah JotUf CETH !Al WALL ().l-
=
' . k AMO 3ASE SL A *ff f2 'q %
?e s
CU GPPCJir3 S44) \l .<
% esActud M. 1 K ,* .u4 L
. , w:f x 9
t! . C p .I I e f I . fl fD 4W *f JM .I /' i k
}lhhg"'"'
~
h W; .j . Qf 'i ll?,b Ul% e % ., , t %b
~.y..\. >, d . o .Y
~ e ~~A_- \ t' f.*
~
4-s eg 7,gg b (kwk{k '
*2*cI..ll!' / ! F/>J %*)
0 bR . { ,' *cl
$--) isk
, .-i >! - w -lz, oh =_
M"+,,7 7, Zr
]j_
=
f_/ t, y $ D g/gM
=./t
# +
./['
q % ,. - - eo rat 3 eluu a =>1 b, ,j .. ? "< vr1 4; Wh* g r,4 4h f. soy =w 1 +. <s t,,, U kwQ ..
),l- 1 MWE ~X*)
f V?N?c"' s. D
~
- f. 53 ft%rtCAL g.24
- - -t h sY. .
h $7pcis rc,ye cpy. ~3 Q J) .
),* ,_ , {'.
\,
q., s 22 wg U wp L d ',^ v2s s:.n) cers) ,_- 4D0/7/00Al. NCCEO4rdL Se t$. "(' L*/O G /2 x 8 o* ?ONG 70 d2 L
' peO/sCZ3 Af guowst re f.12 A:OI Tt0AJA:. LL 145 C4.4 (C2 #20/QEO AS SuAJXf f C*
TWO 81%S= Ov! ACO o TIONA L BAA PL L/1 0%15 TfDICAL &l?.* TO RSOUCS COMs/ds TiO V) 8UTTRESS P l. A AJ i ARMNSAS POMD & L!SDT CDr.IPANY 4 AR!(AMSAS MUC!EA!10.5 L _._ , 00.?2 ' . O SUPPL.EMENT (M f5 \
jeurr<ess . , 2-- 3 .; v=} [i}l[ilF. .,l , anaara
,,r.,.,"
, ..o.
3.
- . . . .. . .. .. .. t RKo AJ* Stt # eo O NN}N l ! !- ! _
=-
l i hh S. 7/C/43 /8-J [ O .f*.' ' Y t - l 4 l . . @--. llll . ?{- y 'g , t a [9 ';
- 9' .
. .=e- - 1 wweuu.)
hi
,. o'ii :9 - ;
'6N ,, 7,,,
e *
-5HI
' ~ .
b l -'- ! i c- i l a ,1 - li O. ;-G- ~- i -- i i hi-- [.-['*gpI 3! t w
.o-1 _ " .- l_. .-
{ j l 7,,,,
.l 1 , :c WN g yfy 4 lll-! ! y- i l-- . jk C!
. - - _ , ?-,-t : -- -)-QJg ...fr._ j b rres yrespy j . , ,. o , ,
- . 'l f ---i-l- 1
< --r-
- ,; $ l O
> -4j[ll >
-- l ll ,
( -d- - - -
.u R ll 0.._.< ],-
.- ,g 4, ,
,+- -
3--- p: --p-- p c..,, }y (3 q . r c , # .. a #q e .. o ji a
..o-
~~~
_ _ _ _ - * -. { [--[ $ ~& m-u -~ ~~ ,- Q. -f ll
*o
- 3 '*",
-illtf1MH -- : H-* -v ' I h m, v r.<,%' -
,O p-y 110_ __<_ --
i L-
. o-s_ , J- i = -1 - Mt. .o I .943 ; Ich
-L y- h L-- 'cr*resrers .)
y _ h-{-! - -{+- - l l
< n p _3.He' N 6 0- < d-
~
-!H!lF-t-4 i i 4 <
i - . . q . 8 'L i. hq L O. . 1
}- ,
. .'j {--l.4441Q b . -
&- i -
p ., .o. . f- H, - - toh ___-.-- . t --4 i_g- l - o<
-fill 0l f - I t --
; gFHth-Af ... 1 ut - 1.
E l l . , . s . lil O'.'o- .
<-,m e, ,, c,,,,
<anur u m ,
i l j $~ _._.o..5
.0
$3h. 6
<. .. l-a .
/ i 8 i . ' 93 '}.-aR .7 .
/ l f , [ . - .
.I
~
l lm'~e'" X ;ol kf kl m i yt.! .U ; i i n . esn e I I % ni N _t-.
.i
] .\
(,c.mv f I ' 44-) ' .1 ' - .. .-] l
, , . s+
79/ CAL. HORIZOA)TA L er RADIA! 6AES .S E' C 7 / O K1 Q
. OUTS rOS fACQ .
W ' I 1 1 4 1 AQXAN5AS FOMR & UCG CO.~,JPANY
^
ACKAMSAS NL! CLEAR ONE
~. -
0023 1 l
. SUPPL EMSNT NO. /5
_ -- w
m . . . ,-
, r , ...... w .
c - - ,.
., ;
~ 7 3' .i ;
t 4 ve :ric a we aruiva - y .' 'o
~; 1 .' - - -
i,
) .
a.s , i l i 1 e.) emp'o* l i 3
., < l 4,
l1
- ...- i l l j i
.'- l l '
l ll I-l I
- a ,
I I l l l ll l[ i
. . I I I
- i
- 9 l
, . 2 i l l, l l i
c.s ,c. .,4po , ___ i i
! ! I l .1 .
f i
. , i
; -
, _r,, n l 1 I ,i ! ,,...,
=
lI
- =
" T '
1 l l 1
? l l ll l l I
;
'
- i I
I I i ]
; )
,1 3 #7 c.J zt. .sps!o*
r--
- I f
g i ;
# // g .
l l l l I fe i t l li i l l t l
.. . ---f roa n u 2Ans s.gmseneur , li.s, I i 4
- ' . sse surmass m I,
\ \ l '
I li l lI
- l
! I a I*;
i
~
i ._. e J ec .refoL_,~_ _;g ,d I f1,1 __ 1 i i l l
.' r. 1 i l i i i I
i i i i I i
.! 'i 1 _
_t A ! "<a i J/a .. l 3 l
*- I I l l
- - .. a _
l - l
;
l 4 l f a
,= n s - T ! ! ! ll l
. .asr ..ir e
. ;
. .- riewwriou- p;
- v .. ; - . I :, .
. . . , .. . c
.. a . .
.' f .' , ' -
;I ,~ , A 6 1 1
.; e TYP/CA/-. SEC770N TYP/ CAL VE27/ CAL 2E/MFC20/MS ourgiog ,=xc5 T Y PIC A L f5 U T T R E S S 2 E /M FO R C /UG
- t. . A2XAGES FO'!E2 a l!%T C07.lPANY 00,,, w Aa, l A,u,m, , S nu n:.,A3 G,.a.
,,,,C,
$UPPLEMENY NO /.5
,3 L) - /2S ,
h, -LIN5E PLATE
$ ?>
/ n d M 3 d,
. ,9 .
M /oo-; > b1 h v A IA $ l -T . R, s \ :;s o dg g
, , sn e.,
.s 75 _ ? N ' nW s N ga s i;; c: o s d ca g a :j po- s' m- -
\ bm 8. .,
h % : E$ t .
.,N R s .. 4
N ..
25 ,-
~
'~- ~
Ti e o.2 l-IRS a 72 e o.8 HRS. . -
~~
_ ' '~~~ Q 73 e 3.0 HRS. ~ s 77e $TEADY STATE -
~-
,0 .9 IO /5 20 29 .50 35 40 45 e
DISTAMCE /MTO COAIC2E TE, in. (/-in. = 5-in.) THE2 MAL TRAA/S/EA/ TS DU2/NG REACTOR BUlLD/NG COOL -DOWAl "";fb??CZ"i"
' ~'
f-t)
\V
~
r
. /25 -
l /LINEe PLA TE Tj e 0. 2 H 2 S. p j Tc 2 /. 2 H 2 5. y Q $ T0 3 4 0 H K S. (q tQ t
/oo-?N f
! ! Ype . STEADY STATE Q
?>
'N j \' U.SM t
ea
- k. 7, _
6 e x ,
/
's aM a m n
hs f N \ . \ .E} "
- c. --
l .
's ,
s $ I I> \ 'N ( . So-g N ,, Q @,
- f su .,
N f ' N N., N N ' N N t; kJ N
- N - ,
r 25 - ~
\ ~
ha
- h. o x 8
G '%:s% o
'.O 5 /0 /5 20 25 30 35 40 45 D/.5 TA A/ CE /A/TO COA /CEETE , in. (1-in =5-in)
THERMAL 7~24A/SIEAITS D Ul?lh/G RE4CTOR. BUILDikl6 HEA T - UP ""X%t%f";,L"L'
CASE I CASE 11 XXXXXXXXXX CT FINITE ELEMENT IDEALIZATION LEGE ND EXACT S CASEI E CASE 11
$ A CASE Ill e 4 M
N Z b 3 s< 4 Q k _
,/ I t i i
- O I
.5 .6 .7 .8 .9 ID RADIUS g STRESS DISTRIBUTION 0027 Figure 5-F-l
.. .}}