ML15280A311
| ML15280A311 | |
| Person / Time | |
|---|---|
| Site: | Davis Besse  |
| Issue date: | 09/03/2014 |
| From: | FirstEnergy Nuclear Operating Co |
| To: | Advisory Committee on Reactor Safeguards |
| Shared Package | |
| ML15280A293 | List: |
| References | |
| L-15-310, TAC ME4640 C-CSS-099.20-063, Rev 1 | |
| Download: ML15280A311 (46) | |
Text
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 1
of 32 000 Interaction Diagram Region C-1 Circumferential Properties Material
/
- = 4000/75/
Compressive strength fy
- = 55ksi REDUCED Ec := 57000-^/c-psi Es := 29000fai ecu:= 0.003 Strength reduction factors 4>t := 0.9
<pc :=
0.7 4>ca := 0.8 Section properties h := 30m b :=
12m d :=
\\in Ag :=
\\in Compression capacity n :=
last(d)
/ VA^ + 0.85-/cU-/i - VAS Tension capacity I.F. rebar#8@ 12 O.F. rebar#11 @ 12 r
fh m
Mc :=
^c-V
/}, -As
- - </.
-21 Mi-kip-ft Mr :
<6r-V
\\-fy-As
- - - d.
= 34.939-kip-ft 7=0
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 2 of 32 000 Sibr
[Kip]
800 675 550 425 300 175 50
-75
/
s i
\\
-0
-400
-300
-200
-100 100 200 300
, [Kip-ft]
Control points interaction diagram 0
1 2
3 4
5 6
7 8
9 10 0
-116.3
-81.4
-65.2 0
77.5 261.2 355.2 478.1 659.7 753.3 753.3 kip 4>Mn =
0 1
2 3
4 5
6 7
8 9
10 0
34.9 77.2 95.9 163.1 237.1 377.3 346.4 317.6 233.9 165 0
kip-ft
<pP'n =
0 1
2 3
4 5
6 7
8 9
10 0
-116.3
-81.4
-66.2 0
109.5 332.5 412.6 520.7 687.5 753.3 753.3 kip
<t>M'n =
400 0
1 2
3 4
5 6
7 8
9 10 0
34.9
-7.3
-24.8
-92.3
-196.5
-372.8
-344.7
-329.5
-259.4
-213.6 0
kip-ft
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.
C-CSS-099.20-063 Rev. 001 3 of 32 000 Interaction Diagram Region C-1 Meridional:
Properties Material p
- = 4000/w Compressive strength
^:= 29000to'
&o^= 0.003
/$p,:= fy
' Es Strength reduction factors Section properties h := 30m o
\\2iti nNA (4\\
(
L21 Xn2
- "Ur
^~ll.5.1.27jm Compression capacity Tension capacity I.F. rebar#10@ 12 O.F. rebar#10@8
^ 4-L
(
M*s=*c2s Vy sj\\
/-o
- -d.
l
=-24.447-Jkip-y5f 2
/ J
\\-l
--d.
=31.432-Jkip-^
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 4 of 32 000
¥* [Kip]
800 675 550 425 300 175 50 r
r
\\
^SC Jo
/
-0
'-500
-375 Control points interaction diagram
-250
-125 0
125
' [Kip-ft]
250 375 0
1 2
3 4
5 6
7 8
9 10 0
-171.5
-120
-100.7 0
82.4 256.2 343.9 479.6 681.5 786.1 786.1 kip 4>Mn =
0 1
2 3
4 5
6 7
8 9
10 0
31.4 92.7 114.2 211.8 288.2 419.8 382.8 348.1 253.9 175.5 0
kip-ft 4>P'n =
0 1
2 3
4 5
6 7
8 9
10 0
-171.5
-120
-103.1 0
105.7 317.9 395.7 518.1 706.7 786.1 786.1 kip
<pM'n =
500 0
1 3
4 5
6 7
8 9
10 0
31.4
-29.9
-48.7
-147.9
-247
-413.5
-381.4
-358.9
-276.9
-219.9 0
kip-ft
Attachment B P-M interaction curves Interaction Diagram Region C-2 Circumferential Properties Material fc
- = 4000/w/
Compressive strength fy
- = 55ksi REDUCED Ec := 57000-//c psi Es := 29000ksi ecu:=
0.003 Strength reduction factors ct>c :=
0.7 Section properties h := 30in b := 12m d\\-
\\in AQ :=
\\in
[.26 J
[\\.56j Compression capacity Tension capacity Calc. No:
Sheet No:
Sheet Rev.:
I.F. rebar#8@12 O.F.
rebar#11 @ 12 Yl r
v r
a th j =0 C-CSS-099.20-063 Rev. 001 5 of 32 000 rfJU-27.175-^-./?
-d)
=34.939-kip-ft
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 6 of 32 000
[Kip]
800 675 550 425 300 175 50
-75
\\
y
-0
"-400
-300
-200
-100 100 200 300 n [Kip-ft]
Control points interaction diagram 0
1 2
3 4
5 6
7 8
9 10 0
-116.3
-81.4
-65.2 0
77.5 261.2 355.2 478.1 659.7 753.3 753.3 kip (pMn =
0 1
2 3
4 5
6 7
8 9
10 0
34.9 77.2 95.9 163.1 237.1 377.3 346.4 317.6 233.9 165 0
kip-ft
<pp'n =
0 1
2 3
4 5
6 7
8 9
10 0
-116.3
-81.4
-66.2 0
109.5 332.5 412.6 520.7 687.5 753.3 753.3 kip 4>M'n =
400 0
1 2
3 4
5 6
7 8
9 10 0
34.9
-7.3
-24.8
-92.3
-196.5
-372.8
-344.7
-329.5
-259.4
-213.6 0
kip-ft
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.
C-CSS-099.20-063 Rev. 001 7 of 32 000 Interaction Diagram Region C-2 Meridional Properties Material
£^:= AOOOpsi Compressive strength
£^=
oOksi
£^.= 0.003
&#i'~ fy ~
s Strength reduction factors Section properties f 4 A
^0.79^
2 Compression capacity
^:=
last(d)
L Tension capacity I.F. rebar#8@12 O.F. rebar#10@12 H
T-
/
X 1 fyAs\\--d\\U-\\%A%-kip-fi 7=0 M
, ^
r.
h x\\
^^
L 7
Vz
/J 7=0
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 8 of 32 000
[Kip]
800 675 550 42b 300 175 50
/5
/
/
f
}
\\
\\
'-400
-300
-200
-100 0
100
$Mn [Kip-ft]
200 300 Control points interaction diagram 0
1 2
3 4
5 6
7 8
9 10 0
-111.2
-77.9
-62.4 0
78.8 269.8 351.5 474 662.5 750.7 750.7 kip
<pMn =
0 1
2 3
4 5
6 7
8 9
10 0
23.8 64.2 82.1 146.7 222.4 369.4 340.9 318.4 236.5 172.2 0
kip-ft 4>P'n =
0 1
2 3
4 5
6 7
8 9
10 0
-111.2
-77.9
-63.1
-0 99.5 316.4 390.7 503.1 681.5 750.7 750.7 kip 4>M'n =
400 0
1 2
3 4
5 6
7 8
9 10 0
23.8
-16.7
-33.8
-98.6
-193.7
-364.6
-339.9
-326.6
-253.9
-205.3 0
kip-ft
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 9 of 32 000 Interaction Diagram Region C-3 Circumferential:
Properties Material fc'-=
V=
Ec--
Es-=
£cu Strengtr
<£<=
Re section h:=
b:=
d:=
= 4000psi Compressive strength 55ksi REDUCED 57000-^
29Q00ksi
=
0.003 i reduction factors
=
0.9
=
0.7 properties 30m 12m
( 4^l rL56\\ 2
\\in As :=
hn
\\2b) s
\\\\.56)
Compression capacity n
- =
-.=
Tension last{d)
eh
'(p
'\\f
%Ac~r"0.85 'j r
\\ u h y
A c
\\\\
co.
c y
^^^
s c
i
^^^
j i
capacity I.F.
rebar#11 @ 12 O.F.
rebar#11 @ 12 Mc~ tc 2, PAsj\\2 ~di)\\
hP n
r f
w
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 10 of 32 000 5b:
¥>n [Kip]
800[
675 425 iUU 175 50 Ib J
/
1
\\
- \\
V
/
-0
-500
-375
-250
-125 0
[Kip-ft]
125 250 375 Control points interaction diagram
<t>Pn =
0 1
2 3
4 5
6 7
8 9
10 0
-154.4
-108.1
-90.5 0
95.1 294.4 383 505.9 687.5 775.6 775.6 kip
<j>Mn =
0 1
2 3
4 5
6 7
8 9
10 0
0 55.5 75.3 163.9 253.1 407.8 371.9 343.1 259.4 195.1 0
kip-ft (j)p'n =
0 1
2 3
4 5
6 7
8 9
10 0
-154.4
-108.1
-90.5 0
95.1 294.4 383 505.9 687.5 775.6 775.6 kip 4>M'n =
500 0
1 2
3 4
5 6
7 8
9 10 0
0
-55.5
-75.3
-163.9
-253.1
-407.8
-371.9
-343.1
-259.4
-195.1 0
kip-ft
Attachment B P-M interaction curves Interaction Diagram Region C-3 Meridional: LC100-400 Properties Material f-\\= 4000/wj Compressive strength Jfa.=
29000iks/
&*!= °003 Strength reduction factors r$v&<.'~
Section properties Mr 30in Compression capacity Tension capacity Calc. No:
Sheet No:
Sheet Rev.:
I.F.
rebar#11 @ 12 O.F. rebar#11 @12 n
j=0 !yAsA2 r
A, ^
\\ f A
(h C-CSS-099.20-063 Rev. 001 11 of 32 000
-d^O-kipft i)\\
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 12 of 32 000
[Kip]
-2
-500
-375
-250
-125 125 250 375 500 Control points interaction diagram 0
1 2
3 4
5 6
7 8
9 10 0
-168.5
-117.9
-100 0
93.3 287.3 369.8 498.4 693 784.3 784.3 kip 4>Mn =
0 1
2 3
4 5
6 7
8 9
10 0
0 60.3 80.2 177 264.4 414.2 380.1 352 264.4 197.4 0
kipft
<t>p'n =
0 1
2 3
4 5
6 7
8 9
10 0
-168.5
-117.9
-100
-0 93.3 287.3 369.8 498.4 693 784.3 784.3 kip (pM'n =
0 1
2 3
4 5
6 7
8 9
10 0
0
-60.3
-80.2
-177
-264.4
-414.2
-380.1
-352
-264.4
-197.4 0
kipft
Attachment B Calc. No:
C-CSS-099.20-063 Rev. 001 P-M interaction curves Sheet No:
13 of 32 Sheet Rev.:
000 Interaction Diagram Region C-4 Circumferential Properties Material
/
- = 4000psi Compressive strength fy
- = 55ksi REDUCED Ec := 57000-Jfc-psi Es := 29000/bi ecu:=
0.003
£
f
- E
£y Jy
^s Strength reduction factors
<pt :=
0.9 Section properties h := 30m b :=
12m (4\\
f2-1.56^
2 d :=
\\in A. :=
\\in Compression capacity n :=
last(d)
Tension capacity I.F.
rebar#11 @6 O.F.
rebar#11 @6
r (h
X\\
Mc - 0c 2, p'^\\2 ~ dj)\\ ~ OkiP'fi n
r r*"*
\\i Mf - ^ 2,
["^'^;' [2 dJ)\\ "
^ ^
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 14 of 32 000 1x10" 825
[Kip]
475 300 125
-50
-225
-400
\\
-0
-600
-450
-300
-150 150 300 450 600 Control points interaction diagram 0
1 2
3 4
5 6
7 8
9 10 0
-308.9
-216.2
-115.5 0
105 284.4 379.3 532.2 743.9 865.8 865.8 kip 0
1 2
3 4
5 6
7 8
9 10 0
0 104.2 199.3 307.5 402 540.2 478.6 422.3 311.1 217.1 0
kipft 0
1 2
3 4
5 6
7 8
9 10 0
-308.9
-216.2
-115.5
-0 105 284.4 379.3 532.2 743.9 865.8 865.8 kip
<pM'n =
0 1
2 3
4 5
6 7
8 9
10 0
0
-104.2
-199.3
-307.5
-402
-540.2
-478.6
-422.3
-311.1
-217.1 0
kip-ft
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.
C-CSS-099.20-063 Rev. 001 15 of 32 000 Interaction Diagram Region C-4 Meridional:
Properties Material
^:= 4000/75/
Compressive strength
^:= 29000ksi
&>>>;= °003
/WW" V
S Strength reduction factors Section properties Mr 3Oin Compression capacity
^:=
last(d)
Tension capacity I.F. rebar#11 @ 12 O.F. rebar#11 @12 n
A/I
>1
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 16 of 32 000
[febr 800T 675
[Kip]
- 500
- 375
- 250
- 125 Control points interaction diagram 0
1 2
3 4
5 6
7 8
9 10 0
-168.5
-117.9
-100 0
93.3 287.3 369.8 498.4 693 784.3 784.3 kip 4>Mn =
0 1
2 3
4 5
6 7
8 9
10 0
0 60.3 80.2 177 264.4 414.2 380.1 352 264.4 197.4 0
kip-ft 4>P'n =
0 1
2 3
4 5
6 7
8 9
10 0
-168.5
-117.9
-100
-0 93.3 287.3 369.8 498.4 693 784.3 784.3 kip
<j)M'n =
500 0
1 2
3 4
5 6
7 8
9 10 0
0
-60.3
-80.2
-177
-264.4
-414.2
-380.1
-352
-264.4
-197.4 0
kip-ft
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 17 of 32 000 Interaction Diagram Region C-5 Circumferential:
Properties Material fc
- = AOOOpsi Compressive strength
/
- = 55ksi REDUCED Ec := 51000-Ifcpsi Es := 29000ksi ecu:= 0.003 Strength reduction factors
<pt :=
0.9 4>c :=
0.7 Section properties h := 30m b :=
12m d:=
^4N 15
,26, in Compression capacity n
- =
last(d) v=
1
,1
.33
.33
.33 1.56>
1.56 1.56y 2
b-h -
Tension capacity I.F.
rebar#11 @9 O.F.
rebar#11 @9
= 0-kip-ft
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 18 of 32 000 m
[Kip]
1x10 825 650 475 300 125
-50
-225
/
/
/
-0
-500
-375
-250
-125 125 250 375 n [Kip-ft]
Control points interaction diagram 0
1 2
3 4
5 6
7 8
9 10 0
-308.1
-215.7
-120.5
-0 74.9 203.6 389.1 540.1 754.6 865.3 865.3 kip
<j)Mn =
0 1
2 3
4 5
6 7
8 9
10 0
0 104.2 194.8 306.3 369.9 451.5 407.1 369.2 276.5 200.3 0
kip-ft 4>P\\X =
0 1
2 3
4 5
6 7
8 9
10 0
-308.1
-215.7
-120.5 0
74.9 203.6 389.1 540.1 754.6 865.3 865.3 kip (pM'n =
500 0
1 2
3 4
5 6
7 8
9 10 0
0
-104.2
-194.8
-306.3
-369.9
-451.5
-407.1
-369.2
-276.5
-200.3 0
kip-ft
Attachment B P-M interaction curves Interaction Diagram Region C-5 Meridional:
Properties Material
/>
- = 4000/w; Compressive strength 4^=
60fcsi C
J
/\\J\\J\\J' ll f,
' Uol J^.= 29QQ0ksi
/^*/:= Jy ~
s Strength reduction factors Section properties h :=
30in b
'.=
YIXyi
//A f 4
]
( 1.56 l
2 Compression capacity Tension capacity Calc. No:
C-CSS-099.20-063 Rev. 001 Sheet No:
19 of 32 Sheet Rev.:
000 I.F. rebar#11 @ 12 O.F.
rebar#11 @12 r
t u m
j =o
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.
C-CSS-099.20-063 Rev. 001 20 of 32 000 tfcbr 80Q
[Kip]
-75
-20t
- 500
- 375
- 250 Control points interaction diagram 0
1 2
3 4
5 6
7 8
9 10 0
-168.5
-117.9
-100 0
93.3 287.3 369.8 498.4 693 784.3 784.3 kip
<pMn =
0 1
2 3
4 5
6 7
8 9
10 0
0 60.3 80.2 177 264.4 414.2 380.1 352 264.4 197.4 0
kip-ft 4>P'n =
0 1
2 3
4 5
6 7
8 9
10 0
-168.5
-117.9
-100
-0 93.3 287.3 369.8 498.4 693 784.3 784.3 kip
<pM'n =
0 1
2 3
4 5
6 7
8 9
10 0
0
-60.3
-80.2
-177
-264.4
-414.2
-380.1
-352
-264.4
-197.4 0
kip-ft
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.
C-CSS-099.20-063 Rev. 001 21 of 32 000 Interaction Diagram Region D-1 Circumferential:
Properties Material fc
- = 4000/75/
Compressive strength f
- =
60ksi Ec := 57000-//c psi Es :=
29000te" ecu:= 0.003 Strength reduction factors 4>f:=0.9
<pc := 0.7 4>ca :=
0.8 Section properties h :=
2Ain b :=
Ylin
( 4 ^
f 0.79^
?
Compression capacity
/i :=
last(d)
Pc = *ca*c\\fy EA^ + ^-fc{b-h " ^ll L
Tension capacity I.F. rebar#8@12 O.F. rebar#9@12 Mc := 0C- ^
l/y -As
- j - - ^ J
= -5.8$-kiP-ft 7=0
^^
L j
V^
/J 7=0
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 22 of 32 000 Ibr 700 600
¥*n [Kip]
-250
-187.5
-125
-62.5 Control points interaction diagram
<t>Pn =
0 1
2 3
4 5
6 7
8 9
10 0
-96.7
-67.7
-53.5 0
69.1 206.5 275.3 371.3 516.8 605.1 605.1 kip
<pMn =
0 1
2 3
4 5
6 7
8 9
10 0
7.6 35.6 48.6 92 141.9 225.5 214.9 205.7 162.5 114.3 0
kipft ct>P'n =
0 1
3 4
5 6
7 8
9 10 0
-96.7
-67.7
-53.7
-0 77.8 224.9 292.1 384.1 525.1 605.1 605.1 kip 4>M'n =
0 1
2 3
4 5
6 7
8 9
10 0
7.6
-20.5
-33.3
-76.7
-132.5
-222.7
-214.3
-208.3
-168
-125.2 0
kip-ft
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.
C-CSS-099.20-063 Rev. 001 23 of 32 000 Interaction Diagram Region D-1 Meridional:
Properties Material
/V:= 4000/m; Compressive strength J^=
60ksi
&r 29000ksi Strength reduction factors Section properties Compression capacity Tension capacity I.F. rebar#8@12 O.F. rebar#9@12 MjoJ-= &C
/
/v'^r d.
= 5.88-kip-ft 7=0
_fy'Asj\\i j)\\ = 1-5' ip'ft
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 24 of 32 000
[Kip]
700 600 500 400 300 200 100 0
/
_ ^"^st-
\\
Q
-250
-187.5
-125
-62.5 62.5 125 187.5 250 Control points interaction diagram 0
1 2
3 4
5 6
7 8
9 10 0
-96.7
-67.7
-53.5 0
69.1 206.5 275.3 371.3 516.8 605.1 605.1 kip
<pMn =
0 1
2 3
4 5
6 7
8 9
10 0
7.6 35.6 48.6 92 141.9 225.5 214.9 205.7 162.5 114.3 0
kip-ft
<pp:n =
0 1
2 3
4 5
6 7
8 9
10 0
-96.7
-67.7
-53.7
-0 77.8 224.9 292.1 384.1 525.1 605.1 605.1 kip
<pM'n =
0 1
2 3
4 5
6 7
8 9
10 0
7.6
-20.5
-33.3
-76.7
-132.5
-222.7
-214.3
-208.3
-168
-125.2 0
kip-ft
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.
C-CSS-099.20-063 Rev. 001 25 of 32 000 Interaction Diagram Region D-2 Circumferential:
Properties Material fc--=
v=
Ec-=
Es--
£cu-Strength
<pc-.
Section h:=
b:=
d:=
-- AQOQpsi Compressive strength 60ta'
- 510W-jf-p7i 29000ksi
=
0.003
- fy + Es i reduction factors 0.9
=
0.7 properties 12m I
1
j I
2 m
/4_ :=
\\in UoJ S
U56J Compression capacity n
- =
Tension pt---
last(d) capacity LC100-400 I.F. rebar#8@ 12 O.F.
rebar#11 @12 l
r
/- -d. I
=-21.56-fa>-/f 2
^J
- -rf.
1
\\ = 21.12-kip-ft
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 26 of 32 000
[Kip]
700 587.5 475 362.5 250 137.5 25
-87.5
/
/
\\
\\>
-0
'-250
-187.5
-125
-62.5 62.5 125 187.5
[Kip-ft]
Control points interaction diagram 0
1 2
3 4
5 6
7 8
9 10 0
-126.9
-88.8
-71.8
-0 62.3 176.3 251.8 359.6 516.8 622.8 622.8 kip cpMn =
0 1
2 3
4 5
6 7
8 9
10 0
27.7 64.1 79.4 134.3 178.3 245.7 230.5 213.6 162.5 102.4 0
kip-ft
<t>p'n =
0 1
2 3
4 5
6 7
8 9
10 0
-126.9
-88.8
-73.4 0
92.2 243.7 313.4 406.2 547.3 622.8 622.8 kip 4>M'n =
250 0
1 2
3 4
5 6
7 8
9 10 0
27.7
-8.7
-22.5
-77.7
-142.5
-235.2
-228.5
-223.1
-182.8
-142.8 0
kip-ft
Attachment B P-M interaction curves Interaction Diagram Region D-2 Meridional:
Properties Material
/
- = 4000ps!
Compressive strength far 60ksi
&,:= 29000fo<<
/6jv"= fy ~
s Strength reduction factors Section properties Compression capacity Tension capacity Calc. No:
Sheet No:
Sheet Rev.:
I.F. rebar#8@ 12 O.F. rebar#11 @12 7=0 r
(h 7=0 C-CSS-099.20-063 Rev. 001 27 of 32 000
= -2\\.56-kipft
= 21.12-kip-ft
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 28 of 32 000 700 587.5 475 362.5
[Kip]
137.5 187.5 125
- 62.5 62.5 125 187.5 250 Control points interaction diagram 0
1 2
3 4
5 6
7 8
9 10 0
-126.9
-88.8
-71.8
-0 62.3 176.3 251.8 359.6 516.8 622.8 622.8 kip
<pMn =
0 1
2 3
4 5
6 7
8 9
10 0
27.7 64.1 79.4 134.3 178.3 245.7 230.5 213.6 162.5 102.4 0
kipft 4>P'n =
0 1
2 3
4 5
6 7
8 9
10 0
-126.9
-88.8
-73.4 0
92.2 243.7 313.4 406.2 547.3 622.8 622.8 kip
<pM'n =
0 1
2 3
4 5
6 7
8 9
10 0
27.7
-8.7
-22.5
-77.7
-142.5
-235.2
-228.5
-223.1
-182.8
-142.8 0
kipft
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 29 of 32 000 Interaction Diagram Region D-3 Circumferential:
Properties Material fc
- = 4000/w Compressive strength Jy Ec := 57000-Jf~p7i Es -
29000ksi ecu := 0.003 Strength reduction factors 4>t := 0.9
<f>c := 0.7 Section properties h := 2\\in b :=
Xlin
( 4~\\
(
1.56 2
d:=
\\in A. :=
\\in
\\10J s
\\2-\\.56J Compression capacity n :=
last(d)
P
- =
(b d>r
/*,
7 A c + 0.85 -fr
\\ b h y
A c
cu c
y
/
j j
11
/
i j
Tension capacity I.F. rebar#11 @ 12 O.F. rebar#11 @6 M, :=
0,-
f.-Ac d.
= Db.lbkipft t
jL, I
y sj y2 j)\\
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 30 of 32 000
[Kip]
700 575 450 325 200 75
-50 1/5 X
V*
\\
y
-300
-212.5
-125
-37.5 50
[Kip-ft]
137.5 225 312.5 Control points interaction diagram 0
1 2
3 4
5 6
7 8
9 10 0
-252.7
-176.9
-99.3 0
50.1 117.8 215.5 357.3 547.3 696.7 696.7 kip 4>Mn =
0 1
2 3
4 5
6 7
8 9
10 0
56.2 125.2 180.4 249.1 281 319 293.7 255.8 182.8 92.3 0
kip-ft
<pp'n =
0 1
2 3
4 5
6 7
8 9
10 0
-252.7
-176.9
-92.3
-0 100.9 254.3 340.2 451.9 609.1 696.7 696.7 kip 4>M'n =
400 0
1 2
3 4
5 6
7 8
9 10 0
56.2
-12.9
-71.5
-135.4
-204
-297.7
-289.5
-275.1
-224
-176.2 0
kip-ft
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.
C-CSS-099.20-063 Rev. 001 31 of 32 000 Interaction Diagram Region D-3 Meridional:
Properties Material
£^:= 4000psf Compressive strength JE^j.=
29000fcs;
&^= °003
&pj~ Jy
- s Strength reduction factors Mrt6\\'
Section properties h := 24m f4Y fL56V 2 Compression capacity L
Tension capacity I.F.
rebar#11 @ 12 O.F. rebar#11 @12 n
r
/ u M
^:= ^C-V U,-^ \\--d.
]
=-1.503x \\6~H-kipft
^"^
L 7 V^
/J 7=0
[
fh
\\]
-14 A^:= ^. V
-/
-As
- - d.
= 1.932 x 10
-fcip-jft 7=0
Attachment B P-M interaction curves Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 32 of 32 000 Hbr n [Kip]
700 587.5 47 b
- 462.5 250 137.5 2i
-87.5
/
/
/
of
\\
-0
'-300
-225
-150 Control points interaction diagram
- 75 75 150 225 300 0
1 2
3 4
5 6
7 8
9 10 0
-168.5
-117.9
-100 0
79.3 202.1 281 390.1 547.3 647.2 647.2 kip
<f>Mn =
0 1
2 3
4 5
6 7
8 9
10 0
0 47.6 63.1 134.9 189.7 262.9 250 233.9 182.8 126.9 0
kip-ft (pp'n =
0 1
2 3
4 5
6 7
8 9
10 0
-168.5
-117.9
-100
-0 79.3 202.1 281 390.1 547.3 647.2 647.2 kip
<pM'n =
0 1
2 3
4 5
6 7
8 9
10 0
0
-47.6
-63.1
-134.9
-189.7
-262.9
-250
-233.9
-182.8
-126.9 0
kip-ft
Attachment C Calc. No:
C-CSS-099.20-063 Rev. 001 Thermal moments Sheet No:
1of14 Sheet Rev.:
000 Thermal Moments: Circumferential direction In the following analysis, at first the thermal stress distribution is determined for un cracked concrete and then concrete cracking is considered and the neutral axis is shifted until force equilibrium is achieved between the internal forces and external demand. Thermal stresses are calculated herein using the assumptions of ACI 307-69 (see supplement to Ref.
9a), which are summarized as follows:
(a)
The inner (hot) part is restrained from expanding freely by the outer part and the outer part is stretched by the restrained inner part.
(b)
There is a
neutral surface between the inner and outer
- parts, where the elongation due to temperature is unrestricted and therefore free of temperature stresses.
(c)
For a particular elevation, the temperature gradient through the shell thickness is the same along the building circumference.
Therefore the original circular shape of the building is not altered by the temperature gradient.
(d)
Horizontal sections remain horizontal after temperature changes.
(e)
The temperature gradient through the thickness of the building shell is linear (i.e., a straight line).
(f)
The tensile strength of concrete is neglected.
Per Davis-Besse Design Criteria Manual Rev 25, The following material properties are used in the analysis:
fc
= 4000psi Concrete compressive strength
/
55ksi Rebar yielding stress (REDUCED) 7 150pcf Concrete unit weight a = 0.0000055 Coefficient of thermal expansion (1/F)
Ec = 57000 If psi = 3605-ksi Concrete modulus of elasticity E
= 29000ksi Rebar modulus of elasticity i/=0.25 Concrete Poisson's ratio e
=
Yielding strain s
ecu := 0.003 Concrete crushing strain t s 30in = 2.5ft Shield building thickness td a 24in = 2ft Dome thickness Es Modular ratio n =
= a Ec
Attachment C Thermal moments Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 2 of 14 000 Thermal stresses for a concrete section under compression load For a rotationally restrained section under compressive load, thermal gradients result in bending stresses as shown in the figure below.
For an uncracked section, the maximum concrete stress is given linear. However, since the tensile strength of concrete is ignored, thermal tensile stresses results in concrete cracking. This cracking shifts the location of the neutral axis until equilibrium is achieved between the concrete in compression and the reinforcement in tension, as given the enuations below.
interior Initial stress F',=nA'i(a'irAa) h/2 Fs =n final stress Temperature Uncracked Cracked Internal Gradient stresses stresses Forces Linear thermal gradient and stresses in a section under compression External Demand MTc(AT,N,d,d\\t,b,As,A's):=
Acr <r-WOpsi Acr]
< root n-A-\\ <rn
+ Aa\\ - (n -
d'
\\
Act
...,Aa 0.5t
)
-(AO
- 0
)
a°"oJt + A(Tl)
F
<<- -(n - D-A1 [aQ- - Aal\\
s s\\yU 0.5t
)
Cc <~
7 7 -v
-O-Q-V 4
F-d b
H Aa-1 2
s-d'-
b Cc t
h 2
6-t (ao A
kd\\
si
-Acrl\\
a0 J
Attachment C Thermal moments Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 3 of 14 000 Thermal moments for concrete sections under tension load For a rotationally restrained section under tensile load, thermal gradients result in bending stresses as shown in the figure below. For an uncracked section, the maximum concrete stress is linear. However, since the tensile strength of concrete is ignored, the external tension plus thermal tensile stresses results in concrete cracking. This cracking shifts the location of the neutral axis until equilibrium is achieved by tension in the reinforcement, as given by below; where the different terms are explained in the main body of the this calculation.
interior f
d' d
Exterior Cold Section Temperature Uncracked Gradient stresses Cracked stresses final stress Internal Forces External Demand Linear thermal gradient and stresses for a section under tension UTt[AT,N,d,d',t,b,As,A'sy.=
Act <- WOpsi Act]
<r-won n-AA crn
+ Aa\\ - n-A'\\ crn Act] - (N),Acr\\
I H
0.5t
)
s{° 0.5t
)
J n-A-\\ crn
+ Act]
s y
° o5t
)
F'. <r- -n-A'-l
<rn Aal s
sy
° ost
)
IF -d-F'-d)
Thermal moment under tension or compression load Thermal moments for section under tension or compression are calculated by combining the equations presented above as follows:
Mj{AT,N,d,d\\t,b,As,A's):=
MTc(AT,N,d,d\\t,b,As,A's)
MTt(AT,N,d,d',t,b,As,A's) if Im[MTc[AT,N,d,d\\t,b,As,A's))
- Okip-ft
Attachment C Thermal moments Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 4 of 14 000 Note: No thermal moments within Reaions C5 Region C1 & C2 section properties A'$1 := 0.79in2 As] := 1.56in2 dl:^2-Wn d'j :=
-j - (4)in b :=
lft Region C3 section properties A's2 := L56in2 AS2
'=
1.56in d'2 :=-- {4)in Region C4 section properties A's3 := 2-1.56in2 As3 := 2-1.56in2 d3-=-- (4)in t
a d :=
(4)in j
2 I.F.
rebar O.F. rebar I.F. rebar location O.F.
rebar location Unit width I.F.
rebar O.F.
rebar I.F.
rebar location O.F.
rebar location Unit width I.F. rebar O.F.
rebar I.F.
rebar location O.F.
rebar location Unit width
Attachment C Thermal moments Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 5 of 14 000 Region D1 section properties A's5 := 0.79in2 As5 := l.Oin2 d'5 := - (4) in Mr ]f Region D2 section properties A's6 := 0.79in2 As6 := 1.56in2 ld "6 :=
(4)in d'6:=j-(4)in Region D3 section properties A's7~ 1.56in2 As7:=2-1.56in2 d
---(4)in 7'
2 ld d'7 :=
(4)in I.F.
rebar O.F.
rebar I.F.
rebar location O.F.
rebar location Unit width I.F. rebar O.F.
rebar I.F.
rebar location O.F.
rebar location Unit width I.F.
rebar O.F.
rebar I.F.
rebar location O.F.
rebar location Unit width
Attachment C Thermal moments Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 6 of 14 000 AT :=
78 Nq\\= -60kip, Moment (kip.ft/ft)
-55kip 110 99 88 77 66 55 44 33 22 11 0
- x.
60 Variation
. 80kip X
X X
X X
X X
X X
X X
x X
- X
^Xv "x
>v Compres'siorK
- v
- 44
-28 of thermal moment Temperature gradient Range of hoop forces in the n
X X
X X
X X
X X
X X
X
\\
Tension X
\\
x X \\
^£*
\\\\ \\
^^
\\ X X
^
\\
\\
N-_<X"
^
x
\\
^SC
_<*^^
-12 4
20 36 Membrane force (kip/ft) as function of hoop load for normal cylinder for dead load C1&C2 C3
- C4 Dl D3 52 68 84 100 operation temperature
Attachment C Thermal moments Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 7 of 14 000 Ne:= -75kip,-70kip.. 120kip Temperature gradient Range of hoop forces in the cylinder for dead load 160 144 128 112 96 Moment (kip.ft/ft) 8C 64 48 32 16 X
X X
'x X
X
- \\
Vs X
X X
X 4
X X
0 Cl &C2 C3
- C4 Dl D2 D3 X
X X
x Tension Compressor
-80
-58
-36
-14 30 52 74 96 118 140 Membrane force (kip/ft)
Variation of thermal moment as function of hoop load for accident temperature
Attachment C Calc. No:
C-CSS-099.20-063 Rev. 001 Thermal moments Sheet No:
8 of 14 Sheet Rev.:
000 Thermal Moments: Meridional direction In the following analysis, at first the thermal stress distribution is determined for un cracked concrete and then concrete cracking is considered and the neutral axis is shifted until force equilibrium is achieved between the internal forces and external demand. Thermal stresses are calculated herein using the assumptions of ACI 307-69 (see supplement to Ref.
9a), which are summarized as follows:
(a)
The inner (hot) part is restrained from expanding freely by the outer part and the outer part is stretched by the restrained inner part.
(b)
There is a
neutral surface between the inner and outer
- parts, where the elongation due to temperature is unrestricted and therefore free of temperature stresses.
(c)
For a particular elevation, the temperature gradient through the shell thickness is the same along the building circumference.
Therefore the original circular shape of the building is not altered by the temperature gradient.
(d)
Horizontal sections remain horizontal after temperature changes.
(e)
The temperature gradient through the thickness of the building shell is linear (i.e., a straight line).
(f)
The tensile strength of concrete is neglected.
Per Davis-Besse Design Criteria Manual Rev 25, The following material properties are used in the analysis:
fc
= 4000psi Concrete compressive strength
/
60ksi Rebar yielding stress 7C 150pcf Concrete unit weight a = 0.0000055 Coefficient of thermal expansion (1/F)
Ec m 57000 Ifc -psi = 3605-ksi Concrete modulus of elasticity E
= 29000ksi Rebar modulus of elasticity v= 0.25 Concrete Poisson's ratio
/y e
=
Yielding strain Es ecu := 0.003 Concrete crushing strain t = 30in = 2.5ft Shield building thickness td m 24in = 2ft Dome thickness Es Modular ratio n =
= o Ec
Attachment C Thermal moments Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 9 of 14 000 Thermal stresses for a concrete section under compression load For a rotationally restrained section under compressive load, thermal gradients result in bending stresses as shown in the figure below.
For an uncracked section, the maximum concrete stress is given linear. However, since the tensile strength of concrete is ignored, thermal tensile stresses results in concrete cracking. This cracking shifts the location of the neutral axis until equilibrium is achieved between the concrete in compression and the reinforcement in tension, as given the enuations below.
Initial stress interior AT" F's =nA',(a'srAar)
Exterior Section Temperature Uncracked Gradient stresses Cracked stresses final stress Internal Forces External Demand Linear thermal gradient and stresses in a section under compression MTc[AT,N,d,d',t,b,As,A's) :=
2 Aa <r-lOOpsi Aal
< root n-A 1
-a-Q-t-b
,. + Aa\\-(n-Acrb
.,/
d' A
A A A Cn Aa
..., Aa s {
° 0.5t
)
-Aa^
1
-(N)
Fs<-n-As-\\er0-0.5t
+ Acrl d'
Fr t- -in - 1)-A
aQ Aal U
0.5t
)
'aO-vb Aal-b
+
1-1/
Attachment C Thermal moments Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 10 of 14 000 Thermal moments for concrete sections under tension load For a rotationaily restrained section under tensile load, thermal gradients result in bending stresses as shown in the figure below. For an uncracked section, the maximum concrete stress is linear. However, since the tensile strength of concrete is ignored, the external tension plus thermal tensile stresses results in concrete cracking. This cracking shifts the location of the neutral axis until equilibrium is achieved by tension in the reinforcement, as given by below; where the different terms are explained in the main body of the this calculation.
Initial stress interior f
d' d
m Exterior Cold Section Temperature Uncracked Gradient stresses Cracked stresses Internal Forces External Demand Linear thermal gradient and stresses for a section under tension MTj(AT,N,d,d\\t,b,As,A's) :=
Aa <- lOOpsi Aal <- root. n-AA crn
+ Act] -n-A'A crn Aa\\ - (N),Acr\\
L S\\U 0.5t
)
s{° 0.5t J
0 0.5f j
F's
^<<A'5-
- Acrl 0.5t J
Thermal moment under tension or compression load Thermal moments for section under tension or compression are calculated by combining the equations presented above as follows:
Mj[AT,N,d,d\\t,b,As,Als):=
MTc(AT,N,d,d\\t,b,As,A's)
MTt(AT,N,d,d\\t,b,As,A's) if Im(MTc(AT,N,d,d',t,b,As,A's))
- Okip-ft
Attachment C Thermal moments Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 11 of 14 000 Note: No thermal moments within Reaion C5 Region C1 section properties A's]
- = 13.7m Asl := 1.5-1.27in2 di
- =
4in 1
2 t
d'j
- =
(4) in b :=
1ft Region C2 section properties A's2
- = 0.79in As2
- =
1.27in d'2 :=
-j - (4)in Region C3 & C4 section properties A'sj
- =
1.56in A$j
- =
1.56in d3 := - (4)in d'3 :=-- (4)in Note that conservatively, that 1/2 of the the center line rebar is I.F.
rebar O.F.
rebar I.F.
rebar location O.F.
rebar location Unit width I.F.
rebar O.F. rebar I.F. rebar location O.F.
rebar location Unit width I.F.
rebar O.F.
rebar I.F.
rebar location O.F.
rebar location Unit width moved to each the O.F and I.F
Attachment C Thermal moments Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 12 of 14 000 Region D1 section properties A's4 := 0.79in2 As4 := l.Oin2 d
4-2 d'4 -=-J- (4) in Region D2 section properties A's5 :=
0.79in As5 := 1.56in2 d5:=j- (4)in fd d's :=
(4) in J
2 Region D3 section properties A's6 := 7.56m2 As6 := 7.56m2
{d d6:=
(4)in d'6:=j-(4)in I.F. rebar O.F.
rebar I.F.
rebar location O.F. rebar location Unit width I.F.
rebar O.F. rebar I.F. rebar location O.F. rebar location Unit width I.F.
rebar O.F.
rebar I.F. rebar location O.F.
rebar location Unit width
Attachment C Thermal moments Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 13 of 14 000 AT :=
78 Nff:= -60kip,-55kip..80kip Temperature gradient Range of hoop forces in the cylinder for dead load Moment (kip.ft/ft) 45 36 27 18
-60
-44
-28 12 20 36 52 68 84 100 Membrane force (kip/ft)
Variation of thermal moment as function of meridional load for normal operation temperature
Attachment C Thermal moments Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 001 14 of 14 000
- = -75kip,-70kip.. 120kip Temperature gradient Range of hoop forces in the cylinder for dead load 140 126 112 Moment (kip.ft/ft) 70 56 42 28 14
-80
-58
-36
-14 8
30 52 74 Membrane force (kip/ft) 96 118 140 Variation of thermal moment as function of meridional load for accident temperature