ML20024E301
| ML20024E301 | |
| Person / Time | |
|---|---|
| Site: | Big Rock Point File:Consumers Energy icon.png |
| Issue date: | 08/03/1983 |
| From: | NUS CORP. |
| To: | |
| Shared Package | |
| ML20024E297 | List: |
| References | |
| NUDOCS 8308100211 | |
| Download: ML20024E301 (14) | |
Text
_
J Consumers Power Company Big Rock Point Plant i
Docket 50-155 ENCLOSURE 1 y
l 4
i ORTH 0 TROPIC PLATE' ASSUMPTIONS I
August 3, 1983 l
l l
l 13 pages ic0783-0238bl42 8308100211 830803 i-PDR ADOCK 05000155
(
p PDR t
)
p ge 1 of _ @
ENCLOSURE 1 C5/ 12,/63 CORPORATION DATE CLIENT GCo - ERP FILE NO. 5t 4 8 -FA-o6 sy MKP SUBJECT NRC-I4 ems.
M' Checked ey f,
Or4hoko)ic Pla4e AssuMplions:
'Ibe 44 tain - af fess relakons fot on ov-tholtopic plAc can be w riWen es: _Ref: 3. E. A slan and 3.M. Whitec1 "Tocoff of
~
3 Larni noled Plates," Tec.hn omic Nbliswng Co.,1976 and R.M. Jane 5," Mechanics of composite Mohetials" McGraw Ml> (9153 g
r e
o e,
e, gyeY Z
E x. =
{ Ex E
y E%
Ey Ey J.
o c.
e.O+TL 9?
E',
E y
7 Ex Ey f '/.,
i o
o c
y Ta.y G,7
.t
- 1,
- cy-G27
_ g.c o
- wherc, E
e.7, C aw 4be strain cornpo n ents, 2,
r, b ate 4hc 3}ress cornpone nts r3,
y y
l Ez is 4he elaskc roedslus in x - di reckon l
E is
+he e.loskc modulus in 4he Y-c\\ireck n y
- g is 4he Poisson 's
-mko
-vciakng 4hc stro:n 6 g With h 54ress cy 1
is +he Poisson's
-vaka
-rclakro, -the 54ro n i
o l
l e
wi4h 4be stress ax y
G is A 6 hec.r recclu.lus for x-T diveckens.
27
.. ~.. -.
Paga of G
2 CORPORATION DATE o5/I2/B3 CLIENT C PCo - BRP FILE NO. 5(48 - FA-oG BY MEP SUBJECT hlR C-14e vns.
Checked By ML The telakon be,hween given by 9
and 9y is x
9x Vy
=
Em E y Thetejote, 4hc velakens ex)te ssed in Eg.0) con also bc Wti ne n as
~
F i
_9y o
g 1
E E
3 y
S l
o T
1
=
1 y
E, E g. (t O b
/_
xyl-o o
L i
g,y l
Which is ihe. -joym used in AW s YS.
l
%c shear rned u(us Gxy Joy iso f vokic.
Con i
is yven by E.
G *Y E. (z)
= -
b E Ct+D Uncvacked Tor ov4ho4vobic mcdevials Auch velolich exis ts. S c e c no l
for rn of ennpi tica)
Yelakon be t ween Gxy, E E
4 2,
7 ad g has 4e be used for4he com pudolion hv rbz s-Bosed on an analog y wi+h 4hc Eg- (2),
ANsYs uses embitical
-relaken cp h fe w cn
- Pig, of f3 CORPORATION DATE C5)t2/So CLIENT C PCO - BR P FILE NO_ 514 FA -o 6 gy MRP SUBJECT NRC-IIeans Checked By Ex Ey Gxy =
y x. + 4 E Ex+Ey+V E
3 y How evet, ANSYS also hos 4he o)} ion cf a voluc of Gsy lin>d dive c+ly.
%e ov&olyoby in he present cosc is d u c.
4o concve}c c-vacktrg. Once 4he'concvde evacks &cyc is a considevable teduchion in &c vobe of Gcy A Vo\\uc ch Gctacked =
.2s G m emended by s chnobn'ch unct ciud (AscE sfafe - of -%e-Art Repod on Finik Elcment Anoiysis :i Rcinfovced conctele, A B2.,
P. 2.95) is used. Tn c valv.c s.ai-t, E, Czy. a nd N c(yc inpv}
into ANSY6.
E y
L
'velakons between stressu a nd siro t ns, l
bn inverHng
- g. t,
con be w w#en as r
p c x. '
E.
9 E x.
o q
x y
l 9
93E E
6e Y
7
()- 9 9y) 3 O - W G x.7 L t d _.
Ex4ending hese eg vakons to flo.tc % cory, 4he telo tien
of 3 A
Paga CORPORATION DATE 05 /12/83 CLIENT cPco - BRP FILE NO. 5148-FA- 04 BY MKP 14RC-I4eM$
Checked By NU SUBJECT bed Wecn rnorn enkS, CLAYVMMTt6 and YWISk Con be WTib'n 05 q
6N/V MS 3
E N E 0
t y
x, My vE E
0
-~3
/*1 g _g g 3
7 y
(I-M y) GxyJ. z 8W My-i e
a e xay a
subs 4iMing.
Mx, M ana Mxy into h
Hale.
eguiUbevm y
" I "
fMx a*Mx a*Myy 2
-=-9
- +
d x' by 8867 E
B*W bb
_e p
.p 3,3,z (g x
.)* 3 + 4 D )
p y
ax4 y ay y
n 4
t-
=
wheve Dxy =
JY n, =
t=-
-~
s y
12.
12 (\\ V 9 )
Il h"' s Y
7 Consiclesng 4hol V3f=97 D c, 4he ovkofvobic p!ak x
eguakon con be W3iHen 05
-4 4
(
+
- D
+
y 8
x1 2
Y
-'I g4
Pag' b of CORPORATION DATE 07 Ed/63 1
CLIENT cPea-RRP FILE NO. 5fA8-FA-o 6 sy MKP SUBJECT NRC-Items Checked By ML Fev applicoken 4o 4he present cose, JCY Q SecNOn l
4 hat is not crac ked in
+h e x
and y direckens,
E a -J x
Ey ove egual fc.
E and 9e = c.17 Fe t o sechen c
cracked only in 4hc X direction, (=EIc cy /q, E = Ec y
ud i
and 97 = 9c..
In 4his cose W ill be very sen2114 "d VCA-i by 9x = OcEx / a.c.
Fet a
.sechon eracked only in 4he 1
y ckveeken, E, = Ec,
Ey =. Ee Ic.r / g and 9x = 9 x
e,
l E9y c/gc is a very srwou nuber-l FoY dhi5 Case
~) y =
l and Y divcch, Fev a se ckon cracked bo4h in 4hc x
l Ee.I y x /I,
E=
F.I.yy /
and 9
and 97 att Ex=
c g
y e c x
Aw;cw my -
bd and 4he valucshab>r>6eNY iven by v, = E 9c/ge very smoli n urnbets 3
1 9c/e can bc uscel.
Tne velo 4icnsWb %E =V Ey3 and 97=Ey c
y 1
l will sWil be. mai ntained-(Ee rnanner in which 4be vncdetial L
kveviously,
btoberbs weve. input into AN5YsgevetcShmafed 9 (and hence
'4 py+zwy' 4erm) k elevnents ctocked in Y-direcken).
new analysis and b
vatlows Ao.fely margins Swm 4he.
- c. discus ston of 4hese teso.lls ate byesented In +he fonowing pqes.
E2 k$
T
~ m o
Leoc4 Mave'n lov b koo) slabs =
- 7. zo g
20 a o
i g
i sending Bencling Local Aveyagc Avc q e Develop-i 3
Moment Moment Sbcat Sbcat 6 heat
-ment
$ sd Mx My Tovce vx Vy lenq%
Wesk Wall
(.46 2 2.7 3 4Z 4 3 2.
3 35 Is 14 Nlorth Wall i.76 1 27
- 2. 9 4 2 59
- 2. 12
\\M k
6 Eosk Wa\\l 1 32.
2 19 4 00 Z 82 3.Z6
- 1. t O g
h souAh Wall o-z3
( iz 3 57 3.t4 2 22 1.06 Voci Floor I 4 2.
- 2. 43 3 32.
3.zo z.47 1.01 g
DN 9R Z'
$9*
x o
$-1 e.,
s (Ag c
.x I
r 1
-tNUS DATE ~ 07/2d /S?
CORPORATON CLIENT C Pro - B R P pite no 51M - F A - o lo MN sy NRC MeM5 checked ey-SUBJECT Sh e o.y Mow 9 ins duMnq h. hansied i
Wes4 Wall l
l l
l T me ss go too tzo (so
<ss l
(Houw) local shes.t 2 40 a. s2.
3.t3 a.z6 3 33 s.42 Force l
Avg.
l shear
- 3. o 2.
4 12.
4 11 4.Zi 4.E6 4 32.
I vs Avg.
z.9 z. fo 6 3,03 3,i7 3 24.
I g,33 sheo.e vy bloRTH WAL's T me 33 go.
too tzo
<so
<ss (Mout) 1 1
Loca\\
26 sh eo.t 3 42.
2 20 2 16 32.3 3 13 Force Avg.
shear 7_. q z.
2_.05 2 13 2 74 2 66 a.59 vs Avg.
shco.t l' T5 P.oi
- 2. o 2.
- 2. o g 2.OS 2 12.
VY l
tNUS
"* al25 6 7l 2.6 orig mm CUENTfPIM BRP p;te no 5/M-FA- 06 MW sy
/A L NRC-IbMS Checked By_ _.. _ _ _ ' _. _.. _ _ _,
SUBJECT Ead wall Time gg go too tto zgo
<sg (Hou.t)
Lo co.1 shear 3.t6 2 5 f,
- 4. 14 4 07 4.00 4 00 Force Avg-shear z.16
- 2.. o 9
- 2. 90 2.. M
- z. er, '
2 82.
Vx Avg.
shme g,5(,
- 3. g f 3 46 3 33 3.St 3,26 vy i
hu Wol]_
Time ss so too 12.o (so
<ss (Hov.w)
Local sheo.r 1 82.
3'91 3 17 3 Io n 3 IoD 3 57 Force Avg.
I shear z.84
- 3. zz 3 21
- 3. t t 3.og 3.g4 Vx Avg.
shur z' 3/o 2 25 2 23 2 21
- 2. 20 2 22.
I vy
r Paga q cf
/g.
_(
07!2b/85 DATE mg blM"bA ~Od BY MP
(
C PCO -ENP FILE NO l
CLIENT NEC ibm 8 Checked By
_... ' L_.
O SUBJECT Pool Floor I
I *
- 55 8o too
( 2.0 Wo 4S5 (Mout) l Lotal sheo.t 3 31 3 56 3 49 S.63 3 37_
3 32 l
Force.
f Avg.
Shear 419 3 29 3 20 3.I6 3 18 3 20 W
Avg.
56y E'. 3 4 z'.6g 2 4q 2 46
- 2. 4 5 2 47 Vy h
ron gMS for local and svevage Ahear f yces ao hou-vs info Ec fvansienk o.ve. given In -Ehe Table bekw.
West N ot+h Eas+
Scum Pool W all Wall Woil w a))
pgooy l
Loco.1 I
shear 2..So 2 44 3 40 2 4G 3 53 Fcrece.
Avg.
shear 3 38
- 3. (6 2 67 B 28 3 30 Avg.
sheo.v 3 28 2 75 z.81 2 23 2 56 vy
b P:g' of 07/ 2B/ S3 OATE CORPORATION CLIENT CPCO - BRP FILE NO.
514 8 - F A - o 6 sy MM SUBJECT N8C 148F/S Checked By b
Abeat mavgins both fot Iocal oncI Avevege jveder 4 hen 40 indico.kng acieguede 4heo.y dovces are l
beideh og aMsl 4 bear. %e momenf vnavgins ocre peder
%n bo exceld for 4be south wali elemerd
\\7 The Akefch bc)ow.shows
% d 4he e.Iem ents
,6wytcundMg 4 bis elerned have large vnavyns of 4deh o.te e'4het uncyocked et j
l l
d 4kAy 0-vc C-rackec\\.
If is obseYved 4hal 4he neighboving r sotaw well EoA well
-e Top l
El. T EL. S l
EL.\\
E L. 2 l
Uncy.
Uncy.
Uncr.
uncy.
El.15 E 1. IG E9 9 E2.10 Uncv.
Uncr.
4 47' U ncr.
El.23 El.24 Ed.17 El. (8 EL.l9 02.3*
9 88*
Uncy.
llnct.
25 47 El. 31 El.32 El.25 El. 2G El. 27 5
Unct.
U ncy.
(.og Uncr.
U n cr.
El. 4o El. 33 Ef 34 U ncr.
2..(6' Un cr.
El. 34
- 2. 14
- cale.u.lo. led enoment enovgins fot cracked elemenI5.
'" " L,63 DATE 07 QRPORATION CLIENT CPCo - B R 9 FILE NO.
5f AB -FA-06 BY MKP NRC - I+e M6 Checked By SUBJECT TcStY VC CohGCNy ko E 5cYb d.lem enhs have adepake addikono.)
Lending moments redis4ribu. led
+o -Poem by 4he elemen) 17-l l
l l
t l
l l
4
+, gy
,j s'
.A &
- D 29()
REINFORCED CONCRETE 291 4;
- l
[
%h In the current practice, however, only the second method ha s been O-anS the stif fnees Ky may represent both aggregate interlock and dowel
~!
gen 1 rally adopted, and the occurrence of cracking ha s been estimated i
aetton. Examples of the derivation of Ky from ehear ally and acasel
(
l by comparing the strees esisting in the e13eent with the
,.1 action models may be found in Ref.
5.3.
4 ten!!!e strength.
In this way, huge sones of finite elemente become a(
cricked at one time (Fig.
5 30c), thus violating the phyelcal De same approach ha s been used in connection with a ameared crack repre senta tion.
In this came one can consider the average 49 reality.
%e same situation would be obta ined, however, with a
- ]g discrete representation of cracking, in which the stif fness g of link C
engular distortion due to slippage along the cracks (Fig. 5 31a) and a
u se, in the material matris, e r ed*** S shear modulus f. which t
- [l1l.
represente the effect of aggregate interlocking.
schnobrich.
(5. 2 31
- /'
clements to reduced to sero on the basis of the existing stress at evity node.
In this case several discrete cracks would run parallel f
who first proposed this solution mainly for p snerical rea sone, used a to each other, determining a cracked zone.
Q
[
constant value for C.
Later, Cedolin (5.12] observed that a value of C linearly decrea sing with the fictitious otrain normal to the crack g
g If the element else is not large, both methods are practically t]
i (which represents the crack width) would give better predictions for equivalent in r epre senting the crack propagation, but the masared j
beams failing in ahear.
?
crtch concept le much more ea sily implemented. What is really lacking N
i is a criterion for crack propagation of a single crack, independently
., p '
{ l J
e t its sharp or blunt repcomentation. De tonelle strength criterion p.i al.Mahaldi (5.3] ouggested the following hyperbotto empreselon
(
ha s a fundamental drawbacks the fact that the stress which t o j^.
for the reduced shear stiffnese 4 to be employed in the constitutive
(
N compared with the tonelle strength depends on the else choenn for the relation of cracked concrete i
flatte etenent grid. A recent work (5.7) steggeste practical methods 6
far avoiding such spurious dependence, ba sed on f rac ture mechanice 6 = 0, for c E
concepts.
g g$ y,y 1 to s<
t e
5.C.2 constitutive Relatione M shear Transfer 1
l1 ;
4-C for
<r (5.36b)
.I i
Constitutive relations of concrete for ahear tran sfer are d
l effected by many parameters.
The following la a stannary of some d
important a spects of shear transfer due to interlocking of oppo site Cg to the sidae of a concrete crack which should be reproduced by a finite
(
t; we,ere C le the elastic sheet modulus of uncracked concreta e
sleeent models
.]
principal tensile strain normal to the crack, and E to the cracking tensile strain.
11 la) he shear stiffe.eas depende on the inverse of the crack i
P s{
opening.
Fig.
5.11b shows a comparieun of various empreselone propo sed
{
A for the reduced ahear stiffness of concrete.
b (b) We ahear force ha s a frictional nature, and consequently 3
r Representation of aggregate interlock by the use of the above a normal force must be present*
7 mentioned model can yield rea sonably accura te analysis re sult s.
l However, the dowel action mechant ee of shear transfer is usually (c) Wie normal force in reinforced concrete to generally pro"
},,
wided by additional tensile force in the reinforcement.
Imrly reproduced because of its dependence on the bending stif fnese (if reproduced in the finite element modell of the reinforcement crossing the crack, which to related *e the finite element mesh used.
(d) Se ahear ettf f nese, consequently, depende on the asial stif fness of the bars crossing the crack.
More recent works regarding the.. ear transfer representation in i5 A first step 11f ted approach involves the a s etemption tha t the connection with the ameared crack concept try to incorporate aume of i
shear ettsfnese depende only on the crack opening, and that this le a
the aspects pre'viously neglected.
.{
dItermined by the external forces which cause the cracking.
De capability of the reinforcement of providing the additional tonelle suyukosturk (5.1 b 5.17, 5.18, 5.391 ha s prenanted a constitutive
)
force le postulated, and this may be true only if the reinforcement relation which takes into account both the asial ettf fnese of the bar s f
crossing the crack and the dowel action. Ef fective shear F19141ttee ha s not yielded under the external load.
Al so, the frictional L
i have been formula ted for concrete blocks with uniformly distributed
/
character of the shear force is Aeglected, by e smsning tha t a finite rtletion esists between shear slip and shear force.
reinforcement and parallet equidistant cracks.
Incremental A
2,nstitutive rela tion ships within the content of three-dimensional e
Rio approach ha s bees adopted in connection with a discrete Finite Element Analyste have been e stahl t ehad.
In this a pproach,
{
concrete is checked at each integration point of the elemunts where j
crack repre sen ta tion, by Ngo and Scordells [5 50].
If a crack to
~.
of the link element is reduced to aero, stress and strain histories are follased. If upon a load increment e
established, the ettf fnese Ky i
e j
, (-
4
?
i
,, p 292 FINITE ELEMENT ANALYSIS
/
REINFORCED CONCRETE 29)
M the principal stress in the 4th direction at an integration point exceeds the tonelle strength of concrete, a t that integration point a crack t o defined in the direction perpendicular to the ith direction, and the constitutive law of concrete is accordingly modified.
%e appropria te modificatoin of the shear rigidity torme have been a
determined 15.17] from a generalization of Ege.
(5.21) and (5.25)
(involving the effe2t ef the straine normal to the crack plane)
D h
combined with a statistical analysis of eve 11able esperimental data.
ceach weanau Basant 15.0) has developed a stress-displacement constitutive relation k
i for rough cracks.
He material model developed to for a reinforced k
shear dehametiea m en displacemens enconhmMy ecesa e-b concrete plate with a parallel set of ContinuDue through cracks inclined to a system of reinforcing not of bare (rig.
5.3 2 p. with 6
M this model the ef fect of cracks in concrete le described by a relation y
involve s 6,, 6,, 0,,,
O g
t ha t i.e.,
the tangential and normal f
nn f
displacement components on a crack.
If the oppaatte surfsces of a
/
rough crack are in constant, and if the normal streme acrose the cract t
[r
.,I
- "*"F e
t la zero or constant, any relative tangential displacement 0 telip) between the opposite susfaces of a crack is accompanied by tt normal
' ~ ' " - -
displacement 6n (crack dilatancy). If 6, le kept con stant, any t 6
ahear determation witadespiecoment consenuay acess e b will alwa ys produce normal compressive essess o tranesitted a m es nn the crack by aggregate interlock which te regarded a s a manifestation of f riction.
]
As an average over large crack a rea s and many cracks, the b) 4 relation betwnen nn*
nt, a nd 0,f 6 le considered to be a material t
OS-l Agro-os ee ar,eoeoigel and g gy property, similar to streme-strain relations, and to, te gwneral, in
~
the following forms a3 04
' d o"
~ o a '
'4 6 '
g nn nn at n
(5.37) uw
> =
03 f.6s.[h# af. 4t.*Jt2h damckp muur semer) do*
8 8
d6 U
8 nt tn tt t,
d"'
- 02S.
l o24 I
in which 8,,, B,ge...
are crack stiffnese coef ficients which depend 02 Cedesm ond DelM
. orellow boams n'
O*U U
and possibly also other state parametere. assed t
nn*
nt N%'C/G=G240-2Sosp wa.guine end schnots kh on the available test data, by adopting a teset general forsmalation the
%g incremental constitutive relationship dd= Cat ho s been derived in which C to the incremental stiffness matrio of cracked reinforced concrete, O t2*s N
~ 9g,gma o,
w referred to cracs coordin.tes a and t.
The formulation to suit.ble s'%g *%
for two-dimensional incremental finite elasment analysis of cracked concrete reinforced by a regular not of ba r e.
Dowel action and
,,,, N kinking of the bare in the cracks le neglected. thloading and cyclic
,6 aa g;,;,
Tenmie swam nornme as stack s,s to'* A ew loading are not con.idered.
o A staplified form of this model has later been offered by Ba sa n t and Tsuba ki (5.9).
nie etspler, linearized model employs a secant Fi9 5*31 (a) Shear Deformation, (b) Iteduced Shear Modulus att f fnese matris for the cracked concrete, and it to ba sed on the vs. Tensile Normal Strain.
eleple idea s of friction coef ficient and dilatancy ratio for the crack 4
Slip. M ue, stiffnese matrices for concrete with frictional cracks in one ( mee D3 5.28) and two directions have been developed. The o-N
-