ML15280A305
| ML15280A305 | |
| Person / Time | |
|---|---|
| Site: | Davis Besse  |
| Issue date: | 09/03/2014 |
| From: | FirstEnergy Corp, FirstEnergy Nuclear Operating Co |
| To: | Advisory Committee on Reactor Safeguards, Office of Nuclear Reactor Regulation |
| Shared Package | |
| ML15280A293 | List: |
| References | |
| L-15-310, TAC ME4640 C-CSS-099.20-063, Rev 01 | |
| Download: ML15280A305 (66) | |
Text
Attachment F Tornado and Wind Loads Calc. No:
Sheet No:
Sheet Rev.:
C.CJ1 C-CSS-099.20-063 Rev.-006-1 of 4 000 Tornado loads The pressure at any point of the structure is calculated as the product of the dynamic wind pressure (q) times the pressure coefficient, Cp. This coefficient changes direction (i.e.,
positive or negative) as a function of the location within the structure.
Per Ref.
10 Table 4(f), for cylindrical structures like the shield building, the pressure coefficient is function of the angle a, as shown in Figure 1
and Table 1.
In this calculation, the pressure distribution for h/d =
1 is used in the finite element model along with a pressure coefficient for the roof Cpe =
-1 per Ref.
10 table 4(e). This pressure this distribution is intended to increase hoop stresses in the building.
- Cylinder, surface load Smooth surfaces h/d*\\
Slack wcrkmg Cpt= rO 1
Stack closed CL.=>>-0.8 Figure 1: Distribution of wind pressures around cylinder (Ref 10. Table 4(f))
a 0
15 30 45 60 75 90 105 120 135 150 165 180 h/d 1
1 0.8 0.1
-0.7
-1.2
-1.6
-1.7
-1.2
-0.7
-0.5
-0.4
-0.4
-0.4 7
1 0.8 0.1
-0.8
-1.7
-2.2
-2.2
-1.7
-0.8
-0.6
-0.5
-0.5
-0.5 25 1
0.8 0.1
-0.9
-1.9
-2.5
-2.6
-1.9
-0.9
-0.7
-0.6
-0.6
-0.6 1.510 1.00 0.80 0.10
-0.71
-1.24
-1.65
-1.74
-1.24
-0.71
-0.51
-0.41
-0.41
-0.41 Table 1: C coefficient as a function of the h/d ratio, values for the shield building (i.e., h/d =1.51) are interpolated (Ref 10. Table 4(f))
Attachment F Tornado and Wind Loads Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev.-89e-2 of 4 000 The energy of a fluid immersed in wind stream can by calculated per Bernoulli's theorem, which for the situation shown in figure 2 results in below equation:
1 2
1
,2
-Pv0
+po=-pv
+p where p is the wind density, V is the wind velocity, p0 is the static pressure of the wind approaching the cylinder and the term 0.5pV02 is the dynamic pressure of the free wind stream which is designated by q; p and 0.5pV2 are the static and dynamic wind pressures of the fluid along its path.
Figure 2: Flow around a cylinder for large Reynolds numbers.
For Davis Besse the following parameters apply per USAR 3.3.1:
h := (809.5 - 584)/? =
225.5-./r d:=
144/*
V := 300mph p:=
0.0765 \\pcf q := - \\T = 0.23-ksf 2
g P-t :=
3psi = 0.432-ksf d-4q = 2.185 x 10 Total elevation exposed to wind Cylinder diameter A degree of conservatism is added to the tornado model by assuming constant tornado wind velocity, USAR Section 3.3.2.1.1 Standard air density Dynamic wind pressure Pressure drop associated with tornado funnel, assumed to act concurrently with the force due to a 300 mph wind. USAR Section 3.3.2.2 larger than 2.3lb0-5
Attachment F Tornado and Wind Loads Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev.S9&
3 of 4 000 Wind pressure
<0)
(4)
Pe(a) := Hnterp[Cpe",Cpe
,a)-q AP(a) := Pi - Pe(a) a:= 0,0.01.. 7T 120 60 120 210 330 240 300 210 240 300 270 270 Pe [psf]
P[psf]
Figure 3: Wind pressure distribution around shield building
Attachment F Tornado and Wind Loads Calc. No:
Sheet No:
Sheet Rev.:
CO I
C-CSS-099.20-063 Rev.-eee-4 of 4 000 J
Wind loads Similar to Tornado loads, wind loads applied to the Shield Building are calculated below Vw := 9Qmph Wind velocity pw := 0.0765\\pcf Standard air density 1
Pw qw:=--Vw-=0.02hksf
6S5A32-yflbf Wind pressure Pew(a) := linterp[cpe°,Cp(,4,a)-gw Dynamic wind pressure Cpi= -0.8 per Table 4(f) of ASCE 3269 larger than 2.31b05 a:
0,0.01..77 120 90 60 210 300 240 300 270 270 Pe [psf]
P[psf]
Figure 4: Wind pressure distribution around shield building 30
Attachment G:
ANSYS Static Analysis Input and Output Calc. No:
C-CSS-099.20-063, Rev.-See o° i
Sheet No:
1 of 1 T^H Sheet Rev.:
000 Attachment G:
The ANSYS input and output files are stored in the folder i/nf-W C-is.
fjtlprinaJ fllti**
^h.ch pw prewJ-*^-
4to?~cc-Soea.
Attachment H ANSYS 13.0 Validation Project:
Shield Building Design Basis Calculation Calc. No:
C-CSS-099.20-063 Rev. 001 Sheet No:
1 Sheet Rev.:
000 Validation of ANSYS Mechanical APDL Release 13.0 (CE 498)
This Attachment contains 8 sheets and one electronic disk.
The verification of ANSYS is a two-step process involving (1) the validation the program COMPARE and (2) The validation of ANSYS Mechanical APDL Release 13.0 (CE 498) using TestBench - My Suite Manager computer program.
Validation of the COMPARE Program Files used for the verification of the program compare are listed in table 1 below and included electronically in the subdirectory verification\\compare.
Name CMPOPT DIFOPT ERRS 1
7 ERRS Abnormal GOOD ERRS Abnormal TEST GOOD 1
7 GOOD Abnormal OUT 1
7 OUT Abnormal GOOD OUT Abnormal TEST TEST 1
7 TEST Abnormal Description Compare options file ANSYS supplied file Error file reported by compare after verifying compare tolerances Error file reported by compare after verifying abnormal end of GOOD file Error file reported by compare after verifying abnormal end of TEST file GOOD file for verifying compare tolerances GOOD file for verifying abnormal end of TEST file OUT/DIFF file from verifying compare tolerances OUT/DIFF file reported by compare after verifying abnormal end of GOOD file OUT/DIFF file reported by compare after verifying abnormal end of TEST file TEST file for verifying compare tolerances TEST file for verifying abnormal end of TEST file The following compare tolerances are used for the verification of validation the program COMPARE and the validation of ANSYS Mechanical APDL Release 13.0 (CE 498) using TestBench - My Suite Manager computer program:
COMPARE PROGRAM VALIDATION System being validated:
Computer performing validation:
ANSYS Mechanical APDL R.13 FRED104068 OS OS Windows x64 Windows 7 Enterprise Tolerances Used Indicate any changes made to the numerical tolerances listed below that were necessary for the system being verified Description la. Almost zero (Good file) lb. Almost zero (Test file) 2.Absolute value
- 3. Fractional difference
- 4. Absolute difference Ignore difference if lAl<T& lBl<T lAl<T& lBl<T lA+Bl<T lA-Bl/X<T l A-B l <T Default tolerance 1.00E-06 1.00E-06 1.00E-10 1.00E-04 1.00E-06 Changed to Same Same Same Same Same
Attachment H ANSYS 13.0 Validation Project:
Shield Building Design Basis Calculation Calc. No:
C-CSS-099.20-063 Rev. 001 Sheet No:
2 Sheet Rev.:
000 The following table lists the results of the validation of the tolerances of the program compare. Refer to files listed above and reported in the subdirectory verification\\compare.
COMPARE PROGRAM VALIDATION Output Item checked
- 1. Integer values (change into value)
- 2. Real number values (change number in approp. signif. digit)
- 3. Real number sign (change sign of real number)
- 4. Exponent value (alter exponent value sign)
- 5. Alphanumeric string (alter one character of string)
- 6. Missing line (delete a line)
- 7. Additional line (add arbitrary line)
Acceptable YES YES YES YES YES YES YES Not Acceptable COMPARE PROGRAM VALIDATION COMPARE
SUMMARY
TESTING RESULTS If the contents of the ERRS file is the basis for determining that comparisons are acceptable (rather than mdividual review of each OUT f.le),
then the following tests must be performed to ensure that the file is being written correctly. If auxiliary programs were used for evaluation, attach validation that these work correctly.
i Item checked
- 1. Abnormal termination of GOOD file
- 2. Abnormal termination of TEST file 3
Number of compare differences not 0 4
Number of absolute value differences not 0
- 5. Proper handling of a comparison rerun; ERRS file is correct and complete after running (at least) items 1 to 4 Acceptable YES YES YES YES YES Not Acceptable COMPARE PROGRAM VALIDATION Were auxiliary programs used for results evaluation?
Yes NoX ACCEPTANCE COMPAPE identifier (as it arr°=irc 'rnMPARF output): COMPARE REL 4.4 UP20050506 WINDOWS The COMPARE program ha.
Originator:
Reviewer:
, been validated as indicated above and was found to be a<
SHEN WANG xeptabl HOAN-KEE KIM Date:
Date:
4/19/2012 4/19/2012 Validation of ANSYS9 Mechanical APDL
Attachment H ANSYS 13.0 Validation Project:
Shield Building Design Basis Calculation Calc. No:
C-CSS-099.20-063 Rev. 001 Sheet No:
3 Sheet Rev.:
000 After completion of above validation steps, the verification of ANSYS Mechanical APDL was conducted using the procedures presented in Chapter 4 of ANSYS Verification Testing Package User's Guide for Windows.
This attachment validates machine ID FRED104068 for performing analysis using a controlled copy of ANSYS Mechanical APDL Release 13.0 CE498.
This computer has been used for all the finite element analyses included in this calculation.
The validation has been completed following the "ANSYS Verification Testing Package" provided by ANSYS. ANSYS TestBench and mySuiteManager were installed in machine ID FRED101588 and 836 test problems were run and compared against a benchmark; the validation reports are included electronically in the subdirectory verificationVeports. Out of the 836 test problems, 7 failures were encountered. The output and difference files for each of the test cases reported as failures are listed below and included electronically in the subdirectory verification\\failures.
Name c3-100081a.diff c3-100081a.lis.out c3-106987.diff c3-106987.lis.out pertl85-fmhgls.diff pertl85-fmhgls.lis.out pertl9O-dpgO3s.diff pertl90-dpg03s.lis.out vml98.diff vml98.lis.out vmc8.diff vmc8.lis.out vmrO29-t5-189.diff vmr029-t5-189.lis.out Description Differences file for test case c3-100081a output file for test case c3-100081a Differences file for test case C3-106987 output file for test case C3-106987 Differences file for test case pertl85-fmhgls output file for test case pertl85-fmhgls Differences file for test case pertl9O-dpgO3s output file for test case pertl90-dpg03s Differences file for test case vml98 output file for test case vml98 Differences file for test case vmc8 output file for test case vmc8 Differences file for test case vmrO29-t5-189 output file for test case vmrO29-t5-189 The following is a description of each of these failures and their resolution:
Test Case Description Issue c3-100081a Large deflection prestress modal analysis with cyclic symmetry, testing all 3 main symmetric eigensolvers (LANB,LANPCG,SNODE) using SOLVE approach COMPARE DIFFERENCE FOUND AT NG= 1503 NT-1503
Attachment H ANSYS 13.0 Validation Project:
Shield Building Design Basis Calculation Calc. No:
C-CSS-099.20-063 Rev. 001 Sheet No:
4 Sheet Rev.:
000 Resolution G=
4 3642.654166014 T=
4 3624.686354136 COMPARE DIFFERENCE FOUND AT G=
5 7839.404314666 T=
5 7788.737934515 COMPARE DIFFERENCE FOUND AT G=
6 7897.845677113 T=
6 7819.328657511 COMPARE DIFFERENCE FOUND AT G=
3 4631.068468008 T=
3 4636.715510286 COMPARE DIFFERENCE FOUND AT G=
4 4651.371673153 T=
4 4636.926189697 COMPARE DIFFERENCE FOUND AT G=
3 6362.115422840 T=
3 6341.754873313 COMPARE DIFFERENCE FOUND AT G=
4 6381.274327552 T=
4 6358.811035217 COMPARE DIFFERENCE FOUND AT G=
5 8235.156470653 T=
5 8247.189920852 COMPARE DIFFERENCE FOUND AT G=
6 8465.816957159 T=
6 8283.978094141 COMPARE DIFFERENCE FOUND AT G=
2 2772.852082144 T=
2 2770.070354634 COMPARE DIFFERENCE FOUND AT G=
4 6182.306941345 T=
4 6098.180195954 COMPARE DIFFERENCE FOUND AT G=
5 8658.586330589 T=
5 8680.502338480 COMPARE DIFFERENCE FOUND AT G=
6 8840.098133016 T=
6 8731.291430469 13 numerical differences among the NG= 1504 NT= 1504 NG= 1505 NT= 1505 NG= 1545 NT= 1545 NG= 1546 NT= 1546 NG= 1576 NT= 1576 NG= 1577 NT= 1577 NG= 1578 NT= 1578 NG= 1579 NT= 1579 NG= 1608 NT= 1608 NG= 1610 NT= 1610 NG= 1611 NT= 1611 NG= 1612 NT= 1612 benchmark solution (G) and test solution (T).
Attachment H ANSYS 13.0 Validation Project:
Shield Building Design Basis Calculation Calc. No:
C-CSS-099.20-063 Rev. 001 Sheet No:
5 Sheet Rev.:
000 Test Case Description Issue Resolution Test Case Description Issue Resolution Modal frequencies calculated using SNODE symmetric eigensolver (T) differ by up to 2.15%,
with respect to the benchmark solution (G) as documented in c3-100081a.diff file and shown above, which affects the quality of the solution. Therefore large deflection prestress modal analyses with cyclic symmetry should not be run in the subject machine using the SNODE symmetric eigensolver.
C3-106987 Mass Summary when MASS21 has no Translational Mass. Corrects Class 3 error for Releases prior to 13.0; which were showing mass summary with incorrect total mass that affected the participation factors as well.
COMPARE DIFFERENCE FOUND AT NG=
932 NT=
932 G=indows Process ID:
2876 T=indows Process ID:
7436 1 inconsequential difference among the benchmark solution (G) and test solution (T). The difference is due to the process ID as documented in c3-106987.diff file and shown above, which does not affect the quality of the solution. Therefore the run is deemed successful.
Pertl85-ftnhgls Objective:
The objective of this test case is to verify linear perturbed modal solve with thermal loading and also verify freqs, strain, stress results for solidl85 with reference run using modal solve.
Materials: hyper-Ogden Element features: mixed formulation, full integration
==
Description:==
A plate is modeled and meshed with solidl85 elements. The plate is constrained at one end.
Non-linear static solve is performed with thermal loading and pressure applied on the top surface for bending.Pre-stressed modal solve is then performed using two approaches Case 1: PSOLVE Case 2: Linear perturbed analysis Expected results:
Eigenvalues and elastic strains obtained from easel and case2 should match. Stresses do not match as expected for hyperelastic materials.
The thermal strains should be the same before and after the linear perturbed analysis.
COMPARE DIFFERENCE FOUND AT NG=
510 NT=
510 G=
349 12.824
-37.488 24.664 3.0547
-4.2542
-0.67934E-01 T=
349 12.824
-37.489 24.664 3.0549
-4.2547
-0.67674E-01 1 difference among the benchmark solution (G) and test solution (T). The maximum differences are in the order of 0.45% or less and are inconsequential.
Attachment H ANSYS 13.0 Validation Project:
Shield Building Design Basis Calculation Calc. No:
C-CSS-099.20-063 Rev. 001 Sheet No:
6 Sheet Rev.:
000 Test Case PERT190-DPG03S Objective:
The objective of this test case is to verify linear perturbed modal solve with thermal loading and also verify eigenvalue, stress and strain results for solshl90 with reference run. All results are compared in global coordinate, element and layer coordinates.
Materials: linear elastic anisotropic Element features: layered structural solids using pure displacement formulation, esys defined.
Store data for top and bottom for all layers.
==
Description:==
A solid beam is meshed with solshl90 elements. The beam is constrained at one end. Pressure is applied on the top surface for bending. Thermal loading are also applied.
Pre-stressed modal solve is then performed using two approaches Linear perturbed analysis and, PSOLVE Expected results:
Results match for the two cases in all coordinates. The thermal strains should be the same before and after the linear perturbed analysis.
Issue COMPARE DIFFERENCE FOUND AT NG=
612 NT=
612 G=
4-0.86490E+06 0.26139E-01-67300.
0.19381E+06 -69162.
0.25187E+06 T=
4-0.86490E+06 0.26239E-01-67300.
0.19381E+06 -69162.
0.25187E+06 COMPARE DIFFERENCE FOUND AT NG=
613 NT=
613 G=
5-0.86941E+06 0.18716E-01-81530.
0.22605E+06-68664.
0.24843E+06 T=
5-0.86941E+06 0.18835E-01-81530.
0.22605E+06-68664.
0.24843E+06 COMPARE DIFFERENCE FOUND AT NG=
614 NT=
614 G=
10 0.86941E+06 0.21773E-01 81530.
0.22605E+06-68664.
-0.24843E+06 T=
10 0.86941E+06 0.21891E-01 81530.
0.22605E+06-68664.
-0.24843E+06 COMPARE DIFFERENCE FOUND AT NG=
615 NT=
615 G=
9 0.86490E+06 0.29184E-01 67300.
0.19381E+06-69162.
-0.25187E+06 T=
9 0.86490E+06 0.29283E-01 67300.
0.19381E+06-69162.
-0.25187E+06 COMPARE DIFFERENCE FOUND AT NG=
616 NT=
616 G=
14 0.39267E+06-0.57305E-02 43355.
58878.
-19366.
-0.12499E+06 T=
14 0.39267E+06-0.57546E-02 43355.
58878.
-19366.
-0.12499E+06 COMPARE DIFFERENCE FOUND AT NG=
617 NT=
617 G=
15 0.39285E+06-0.49118E-02 41992.
52034.
-16141.
-0.12553E+06 T=
15 0.39285E+06-0.49406E-02 41992.
52034.
-16141.
-0.12553E+06 COMPARE DIFFERENCE FOUND AT NG=
618 NT=
618 G=
20-0.39285E+06-0.56597E-02-41992.
52034.
-16141.
0.12553E+06 T=
20-0.39285E+06-0.56886E-02-41992.
52034.
-16141.
0.12553E+06 COMPARE DIFFERENCE FOUND AT NG=
619 NT=
619 G=
19-0.39267E+06-0.64782E-02-43355.
58878.
-19366.
0.12499E+06
Attachment H ANSYS 13.0 Validation Project:
Shield Building Design Basis Calculation Calc. No:
C-CSS-099.20-063 Rev. 001 Sheet No:
7 Sheet Rev.:
000
.9-0.39267E+06-0.65023E-02-43355.
58878.
-19366.
0.12499E+06 COMPARE DIFFERENCE FOUND AT NG=
724 NT=
724 G=
4 0.26277E-01-0.93725E+06 5049.0
-0.20564E+06-22319.
7703.0 T=
4 0.26376E-01-0.93725E+06 5049.0
-0.20564E+06-22319.
7703.0 COMPARE DIFFERENCE FOUND AT NG=
725 NT=
725 G=
5 0.18354E-01-0.94066E+06 -10273.
-0.23624E+06-22346.
-2462.9 5
0.18472E-01-0.94066E+06-10273.
-0.23624E+06-22346.
-2462.9 COMPARE DIFFERENCE FOUND AT NG=
726 NT=
726 G=
10 0.21410E-01 0.94066E+06 10273.
-0.23624E+06 22346.
-2462.9 T=
10 0.21528E-01 0.94066E+06 10273.
-0.23624E+06 22346.
-2462.9 COMPARE DIFFERENCE FOUND AT NG=
727 NT=
727 G=
9 0.29322E-010.93725E+06-5049.0
-0.20564E+06 22319.
7703.0 T=
9 0.29420E-01 0.93725E+06-5049.0
-0.20564E+06 22319.
7703.0 COMPARE DIFFERENCE FOUND AT NG=
728 NT=
728 G=
14 -0.57602E-02 0.43277E+06 3250.2
-61977.
-2255.7 771.06 T=
14-0.57847E-02 0.43277E+06 3250.2
-61977.
-2255.7 771.06 COMPARE DIFFERENCE FOUND AT NG=
729 NT=
729 G=
15 -0.49805E-02 0.43312E+06 1714.4
-54480.
-2258.5
-246.53 T=
15-0.50096E-02 0.43312E+06 1714.4
-54480.
-2258.5
-246.53 COMPARE DIFFERENCE FOUND AT NG=
730 NT= 730 G=
20-0.57285E-02-0.43312E+06-1714.4
-54480.
2258.5
-246.53 T=
20-0.57575E-02-0.43312E+06-1714.4
-54480.
2258.5
-246.53 COMPARE DIFFERENCE FOUND AT NG=
731 NT=
731 G=
19-0.65080E-02-0.43277E+06-3250.2
-61977.
2255.7 771.06 T=
19-0.65324E-02-0.43277E+06-3250.2
-61977.
2255.7 771.06 COMPARE DIFFERENCE FOUND AT NG=
839 NT=
839 G=
14-0.57602E-02 0.43277E+06 3250.2
-61977.
-2255.7 771.06 T=
14 -0.57847E-02 0.43277E+06 3250.2
-61977.
-2255.7 771.06 COMPARE DIFFERENCE FOUND AT NG=
840 NT=
840 G=
15-0.49805E-02 0.43312E+06 1714.4
-54480.
-2258.5
-246.53 T=
15-0.50096E-02 0.43312E+06 1714.4
-54480.
-2258.5
-246.53 COMPARE DIFFERENCE FOUND AT NG=
841 NT=
841 G=
20-0.57285E-02-0.43312E+06-1714.4
-54480.
2258.5
-246.53 T=
20-0.57575E-02-0.43312E+06-1714.4
-54480.
2258.5
-246.53 COMPARE DIFFERENCE FOUND AT NG=
842 NT=
842 G=
19-0.65080E-02-0.43277E+06-3250.2
-61977.
2255.7 771.06 T=
19-0.65324E-02-0.43277E+06-3250.2
-61977.
2255.7 771.06 Resolution 20 differences among the benchmark solution (G) and test solution (T). The differences are in the order of 0.7% or less and are inconsequential.
Attachment H ANSYS 13.0 Validation Project:
Shield Building Design Basis Calculation Calc. No:
C-CSS-099.20-063 Rev. 001 Sheet No:
8 Sheet Rev.:
000 Test Case Description Issue Resolution Test Case Description Issue Resolution Test Case Description Issue Resolution VM198 Large Strain In-plane Torsion Test For details refer to ANSYS Mechanical APDL Verification Manual.
COMPARE DIFFERENCE FOUND AT NG= 1759 NT= 1759 G=RELEASE 0.0 UPDATE 0
CUSTOMER 00000000 T=RELEASE 0.0 UPDATE 0
CUSTOMER 00203236 COMPARE DIFFERENCE FOUND AT NG= 3161 NT= 3161 G=RELEASE 0.0 UPDATE 0
CUSTOMER 00000000 T=RELEASE 0.0 UPDATE 0
CUSTOMER 00203236 2 inconsequential differences among the benchmark solution (G) and test solution (T). The difference is due to the customer number as documented in VM198.diff file and shown above, which does not affect the quality of the solution. Therefore the run is deemed successful.
VMC8 Aluminum Bar Impacting a Rigid Boundary. For details refer to ANSYS Mechanical APDL Verification Manual.
COMPARE DIFFERENCE FOUND AT NG= 1029 NT= 1029 G=STORAGE COMPLETE FOR 38 DATA POINTS T=STORAGE COMPLETE FOR 42 DATA POINTS 3 differences among the benchmark solution (G) and test solution (T) as follows:
1.
Different time history data point sampled and therefore inconsequential.
VmrO29-t5-189 Large deflection of a curved elastic cantilever under transverse end load. For details refer to ANSYS Mechanical APDL Verification Manual.
COMPARE DIFFERENCE FOUND AT NG=
629 NT= 629 G=
EQUILITER 7 COMPLETED. NEW TRIANG MATRIX. MAX DOF INC=
34.52 T=
EQUIL ITER 7 COMPLETED. NEW TRIANG MATRIX. MAX DOF INC=
30.46 1 difference among the benchmark solution (G) and test solution (T) due to DOF increments used for iterative solution; therefore inconsequential and the run is deemed successful.
ACCEPTANCE ANSYS identifier: ANSYS Mechanical APDL Release 13.0 (Build: 20101012) CE498 ANSYS Mechanical APDL Release 13.0 CE498 program has been validated as indicated above and was found to be acceptable Originator:
SHEN WANG Date:
4/19/2012 Reviewer:
HOAN-KEE KIM Date:
4/19/2012
Attachment I
Calc. No:
C-CSS-099.20-063 Rev.
In-Plane Shear Check Sheet No:
1 of 2 Sheet Rev, m
Ultimate Strength Design FM5:= 6.8/kM44/M5.5// = 2.186 x 10J/b>
MS line break load V
15604-A:;/? + FMS Total Shear at EL565 under SSE+ MS line break D =
\\iA-ft Diameter of the SB t =
30-in Wall thickness neglecting concrete cover (j) =
0.85 PerACI 318-63, Section 1504 d:=
t - Sin Effective depth for in plane shear check, neglecting 5" concrete on the outside face fc 4000-psi fy
=
55-ksi r
2 ai
\\_D
- (D - 2d) J Consider SB equvalent to a square block of shear walls, half of total Ac.= 0.5n concrete area take the global shear V
- =
4>-2 If
-psi-A Concrete shear capacity, perACI 318-63, Section 1701 Fc= 7.19 x
\\03-kip V
=
V v
=
1.06 x 10
-kip Shear force to be taken by reinforcement s:=\\2in Rebar spacing V-s
=
1.574-m-ACI 318-63, Eqn 17-4 A
-j
- = 0.79i<<2 + 1.0-1.56/k2 Provided shear reinforcement, conservatively using C2 circumferential rebar Avprovide = 2-35"2 Av = i-574"2 Sufficient margin exists
Attachment 1
In-Plane Shear Check Paga Calc. No:
Sheet No:
Sheet Rev.:
4ufO C-CSS-099.20-063 Rev. "666 2 of 2
°°'
nnf\\
OOl l
Working Stress Design V
- = 9i53kip Total Shear at EL565 under OBE fc := 4000-pi/
fallow := ^.6-ksi Ac = 6.688 x 104m2 Vc :=
l.l Jf~psi-Ac-\\,11 Concrete shear capacity, perACI 318-63. Section 1201 Allowable increased by 1/3 perACI 318-63, Section 1004 6.188 x \\Q3-kip o3*7p y
- _ y
_ y
_ 3 665 x io3.*7p Shear force to be taken by reinforcement s:=\\2in Rebar spacing
^provide := 0.79m2+1.0-1.56m2
=
10.83-fai vprovide Provided shear reinforcement, conservatively using C2 circumferential rebar OK OR fallow D
= 1.533-/*2
Attachment J Shield Building Sectional Analysis Calc. No:
C-CSS-099.20-063 Rev. 999 Sheet No:
1 of 29 a
Sheet Rev.:
000 1^
ZF Section Capacity Davis Besse Shield Building The equations presented in this section are derived using strain compatibility and equilibrium concepts as described in detail in the main body of the calculation. The figure below and the following consideration are used for this purpose.
Plane sections before bending remain plane after bending The stress strain behavior of concrete and steel is known f:.
h/2 M initial Bending Total strain stress Internal Forces External Forces Concrete (s
) and steel (ss) strains are calculated using strain compatibility as follows:
-cm c-d,
-y
£cm+£o cp:
The concrete resultant (C) and its moment arm (yb) are calculated by integrating the concrete stress/c(ec) that acts on each infinitesimal concrete area b(6)dy.
Note that 6(d) is the width of the concrete section a location d.
y0
= Max(0,c-hi)
C =
fc{ec)- b{y)dy Distance from the neutral axis to the first concrete fiber under compression.
Internal resultant of concrete compression
= c -
f (e \\b(y)y dy Location of concrete compression measured from the top concrete fiber C
The concrete and steel stresses are calculated using appropriate constitutive laws, as those given below.
In general any type of constitutive behavior can be used. Conservatively, the concrete tensile capacity is ignored.
Attachment J Shield Building Sectional Analysis Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 000-2 of 29 000
£c ~
Unconfined concrete model per Park and Paulay 1975 0.85/c-(l.2 -
100-ec)
// £c > 0.002
/<<*(<<*)
Elastoplastic steel model Internal steel forces Equilibrium of the reinforced concrete section is verified as follows n
/=0 Pure compression capacity HH Pure tension capacity Material Properties
/c
= 4000/75/
jc =
\\50pcf a = 0.0000055 Ec = 57000 Es = 29000fo/
v = 0.25 w = 3.6 x 10 ksi
- =
0.003
= 0.00013 Concrete compressive strength Rebar yielding stress Concrete unit weight Concrete and rebar coefficient of thermal expansion (1/F)
Concrete modulus of elasticity Rebar modulus of elasticity Concrete Poisson's ratio Yielding strain Concrete crushing strain Concrete tensile cracking strain
Attachment J Shield Building Sectional Analysis Calc. No:
Sheet No:
Sheet Rev.
C-CSS-099.20-063 Rev. 969-oO(
3 of 29 000 f"
<<= = 8 Modular ratio
/c[psi]
4000 3000 2000 1000 1
1 1
1
[ksi]
60" 40" 20" 0.001 0.002 0.003 0.003 Concrete Figure 1: Stress strain curves used for the calculations Geometry The overall dimensions of the SB building are presented in the figure below. The original construction opening (53ft
- 46.5ft) is located at 305 52' 13", while the new opening (24ft
- 33.5 ft) is located at 323 13' 24" (Refs.
3 & 4).
-L 801-0 EL. 565-0
\\
i EL 1 1
72-6" i
i SGR opening 24'x33.5 i
i Construction opening 53'x46.5' EL 837'-6" EL 604'-0" EL 579'-0" 326.7° 323° 305°52'13" 234.1° 144 ft
Attachment J Shield Building Sectional Analysis Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 000 4of29 000 Ill h=
V
<<i' Ac:
Rd-ow
°a Ao 2.5ft 144//
=71ft
->Re-t
=n{R;-Rr)
=125/5-+3in
=80/J
- =asir[Ow*(2-^-)]-(i
- =Oat
- o--=Re\\\\Rf-\\-\\
='*fi Reinforcement Shell thickness f"
SB cylinder diameter Cylinder exterior radius Cylinder interior radius Cylinder cross section area Exterior radius of spherical dome Opening width Opening arclength Cross sectional area of opening Opening location from the upper most compressive fiber The following figure shows the rebar retails for concrete section above and below the proposed location for the new SGR
- opening, Ref. 7b.
- 8@1Z OPNGTOPEL637-6" OPNC
<Exceroted from Ref.
7O>
4 EL 629'-3'
- io@ir
- B@1?
- 11@12*
Attachment J Shield Building Sectional Analysis Calc. No:
C-CSS-099.20-063 Rev 000 OO\\
Sheet No:
5 of 29
^
Sheet Rev.:
000
^ w^
Rc :=
10.15ft Roj =
lift -Sin-
\\Alin-123m*
2 Rlf-=
69.5ft + 3in+ 0.791.5/<<
i :=
12/n Aifa := 0.79/<<2 ceill
- 223 radius to centerline of shield building O.F.
rebar radius I.F.
rebar radius rebar spacing Area of outside face rebar (above EL 629-3")
Area of inside face rebar (above EL 629-3")
Area of outside face rebar (below EL 629-3")
Area of inside face rebar (below EL 629-3")
number of exterior bars used in half circle Rbar.a := Rbai{nb'A6 'Re>Ro.f>Ri.f<Aof.a'Ai.f.a)
Rbar.b :~ Rbat[nb'Ad >Re>Ro.f'Ri.f'Ao.f.b>Ai.f.b)
Asa'=Rbar.a Independent loads Self weight WD :=
5210kip 2
m d'-R
<1>
bar. a in
<0>
2 Asb := Rbar.b ln 4
db:= Har.b
& := WD tt := 'J 519ft <:<631.5ft,-
Dome weight
- R.
I SB weight at elevation z Wj{:)-jc-A0-(631.5fi-:)
Wj{z)
Ac-ac := a(629.5ft) = 39.2-ksf average stress at elevation 629.5'
Attachment J Shield Building Sectional Analysis Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev.-96e-OO K
6 of 29 000 8x10 d
[ft]
initial strain due to dead load redistribution s0 (EL 629'-3")
Seismic Loads The inertiai seismic forces (vertical and horizontal) reported in the original design of the SB (Ref.
8c) are used herein to calculate the seismic demand for the SGRP.
It must be noted that per Ref.
2, Davis Besse Maximum Possible Earthquake with a 0.15g peak ground acceleration (PGA) is consistent with NRC RG 1.29 definition of SSE; while the Maximum Probable Earthquake, with a 0.08g PGA is consistent with the definition of Operating Basis Earthquake (OBE).
Safe Shutdown Earthquake (SSE)+MS Line Break (Rp)
The horizontal E'^and vertical £'. SSE inertiai loads reported in Ref. 8c are provided below, with Rp lateral load added at EL643 and EL660. As can be seen, the shear, bending moment and axial load (K'(,
A/';,
/>',)
are derived from the inertiai forces (£'
£'_), which is conservative since the inertiai response is not always in phase as implied in the calculations below.
Elevation Inertiai forces (Horizontal SSE)
Inertiai forces (Vertical SSE)
EL--
i 0
1 2
3 4
6 7
8 9
- o u
12 0
812.77 801.05 774.52 748.00 720.00 692.00 660.00 646.50 643.00 609.00 603.00 589.50 570.75 ft 0
1 2
3 4
6 7
8 9
10 11 12 0
2442.90 2688.80 2511.90 2171.20 1828.20 1587.00 1982.00 271.00 1679.00 332.00 140.00 145.00 25.00 kip E'.=
0 1
2 3
4 6
7 8
9 10 11 12 0
1167.40 1344.20 1399.10 1348.20 1254.60 1177.70 711.93 223.46 469.29 321.00 135.29 174.73 144.34 kip 12 12 12 Viz) :=
'xy;
Attachment J Shield Building Sectional Analysis Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 000 Co I 7 of 29 000
^
Elevation (ft) 800 700 600 I
\\
S37.5
^604 800 Elevation (ft) 637.5 604.
5000 10000 15000 20000 SSE Shear Force (kip) 0 1000000 2000000 3000000 4000000 SSE Bending Moment (kip.ft) 800 70C Elevation (ft) 600-6: 7.5 0
2000 4000 6000 8000 10000 SSE Vertical Force (kip)
Shear, Bending Moment and Axial Seismic Demands for Safe Shutdown Earthquake (SSE)
Attachment J Shield Building Sectional Analysis Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. 960- OOI 8 of 29 ooo Operating Basis Earthquake (OBE)
The horizontal E and vertical E. OBE inertial loads reported in Ref. 8c are provided below. As can be seen, the shear, bending moment and axial load (Vr M,, P) are derived from the inertial forces (£^, £.), which is conservative since the inertial response is not always in phase as implied in the calculations below.
Elevation EL--
i 0
1 2
3 4
5 6
7 8
9 10 11 12 0
812.77 801.05 774.52 748.00 720.00 692.00 660.00 646.50 643.00 609.00 603.00 589.50 570.75 12 i =
f)
Elevation (ft) ft Inertial forces
( Horizontal OBE)
Inertial forces (Vertical OBE) 0 1
2 3
4 5
6 7
8 9
10 11 12 0
1544.40 1699.20 1585.20 1367.70 1150.60 1000.30 557.20 172.00 367.10 211.90 89.30 92.50 15.40 kip E.=
0 1
2 3
4 5
6 7
8 9
10 11 12 0
808.33 931.55 971.52 935.58 869.68 813.14 486.98 152.19 318.75 210.14 88.32 107.82 77.52 12 12 i = 0 i = n 800 700 600 I
i 637.5
\\
604 800 Elevation (ft) kip 637.5 604 0
5000 10000 OBE Shear Force (kip) 0 500000 1000000 1500000 2000000 OBE Bending Moment (kip.ft)
Attachment J Shield Building Sectional Analysis Calc. No:
C-CSS-099.20-063 Rev.-OOO-Sheet No:
9 of 29 Sheet Rev.:
000 800 Elevation (ft) 700" 600" "I
637.5 601 0
2000 4000 6000 8000 OBE Vertical Force (kip)
Shear, Bending Moment and Axial Seismic Demands for Operating Basis Earthquake (SSE)
LOAD COMBINATIONS As discussed in section 7.6, the governing load combination for the SB permanent condition is D + E' +TA+Rp This combination is used next to check the structural adequacy of the restored opening at the elevation shown in the next page:
Accident load conditions Vertical demand D + E'+Rp LC-1 V
- P'/h Vertical demand D + E'+Rp LC-2 p
= wT(hc \\ + P'/h.
cbk
\\
ck)
\\
ck Normal operation load conditions
- =
0..9 Bending demand D + E'+Rp Initial stress due to dead load redistribution v~
Bending demand D + E'+Rp Initial stress due to dead load redistribution LC-3 Vertical demand D + E
- Hhc Bending demand D + E Initial stress due to dead load redistribution
£>
- = crfh on
\\'Ckj
Attachment J Calc. No:
Shield Building Sectional Analysis Sheet No:
Sheet Rev C-CSS-099.20-063 Rev. W9- £>°<
10 of 29
^^
Governing load combinations Elevation Axial load (D-E'z)
Bending Moment (D+E'w)
Initial LC-1 hc =
0 1
2 3
4 5
6 7
8 9
0 579.00 602.00 615.20 619.30 623.40 627.50 629.25 631.50 635.50 638.50 fi Pc =
0 1
2 3
4 5
6 7
8 9
0 3.4-104 3-104 2.9-104 2.8-104 2.7-104 2.7-104 2.6-104 2.6-104 2.5-104 2.5-104 kip Mc =
0 1
2 3
4 5
6 7
8 9
0 2.8-106 2.4-106 2.1-106 2.1-106 2-106 1.9-106 1.9-136 1.8-106 1.8-106 1.7-106 kip-ft aQ =
0 1
2 3
4 5
6 7
8 9
stress (D) 0 46.7 43.3 41.3 40.7 40.1 39.5 39.2 38.9 38.3 30.4 ksf Elevation Axial load (D+E'z)
Bending Moment (D+E'
)
Initial stress (D)
LC-2 hc =
0 1
2 3
4 5
6 7
8 9
0 579.00 602.00 615.20 619.30 623.40 627.50 629.25 631.50 635.50 638.50 f<
Pcb =
0 1
2 3
4 5
6 7
8 9
0 5.3-104 4.9-104 4.7-104 4.6-104 4.5-104 4.5-104 4.4-104 4.4-104 4.3-104 4.3-104 kip Mcb =
0 1
2 3
4 5
6 7
8 9
0 2.8-106 2.4-106 2.1-106 2.1-106 2-106 1.9-106 1.9-106 1.8-106 1.8-106 1.7-106 kip-ft
<Joh =
0 1
2 3
4 5
6 7
8 9
0 46.7 43.3 41.3 40.7 40.1 39.5 39.2 38.9 38.3 30.4 ksf Elevation Axial load (D-Ez)
Bending Moment (D+E
)
Initial stress (D)
LC-3 hc =
0 1
2 3
4 5
6 7
8 9
0 579.00 602.00 615.20 619.30 623.40 627.50 629.25 631.50 635.50 638.50 fi Pcn =
0 1
2 3
4 5
6 7
8 9
0 3.7-10<
3.3-104 3.1-10<
3.1-104 3-104 2.9-10" 2.9-10" 2.9-10" 2.8-10" 2.7-10" kip Mcn =
0 1
2 3
4 5
6 7
8 9
0 1.6-106 1.4-106 1.3-106 1.3-106 1.2-106 1.2-106 1.2-106 1.1-106 1.1-106 1.1-106 kip-ft am-0 1
2 3
4 5
6 7
8 9
0 46.7 43.3 41.3 40.7 40.1 39.5 39.2 38.9 38.3 30.4 ksf
Page 5 of 5 Attachment J Shield Building Sectional Analysis Calc. No:
C-CSS-099.20-063 Rev.-9S9-CCl Sheet No:
11 of 29 Sheet Rev.:
969 ooi I
Calculation of Section Capacity The bending moment of the SB is calculated for the elevations indicated above 0.e., for the vector of elevations h). Results are presented below in the form of rebar strain versus section moment plots. For the sake of clarity, only elevations 602',
619.3', 629.25' and 638.5' are plotted. For comparison purposes the maximum moment demands at elevation 602' (2.4 x 10*6 kip.ft) and 638.5' (1.7 x 10*6 kip.ft) are included in the plots. As can be seen the moment demand is well below the moment capacity of the SB. Furthermore, no yielding of the rebar {zmzx < ey) takes place for the subject maximum demands.
In fact the demand will have to be increased by a factor of approximately 2 to produce yielding of the upper most rebar.
7.0x10 EL. 602' EL. 619.30' EL. 629.25' EL. 638.50' Section moment as a function of the maximum steel strain for different elevations along the SGR opening
Attachment J Shield Building Sectional Analysis Calc. No:
C-CSS-099.20-063 Rev.-GGG OO\\
Sheet No:
12 of 29 Sheet Rev.:
000
-yo\\S LOCAL TEMPERATURE EFFECTS (LC-1)
Thermal stresses due to temperature gradients (TA) are combined with the stresses due to extemal loading demand (D+E'+Rp with E'z acting up) according to the following procedure:
1.
Calculate the location on the neutral axis under (D+E1) demand.
2.
Calculate the maximum steel strain and stress for the rebar in the SGR opening 3.
Calculate the maximum tension developed in the opening using the rebar stresses calculated above.
4.
Use the maximum tension from step 4 to calculate the thermal moments and stresses due to a temperature differential of 125°F corresponding to TA Neutral axis location The location of the neutral axis is calculated next for the elevations hc along the height of the SGR opening.
k:=
0 Elevation hc
= 579/?
Pc
=3Ax\\04kip Mc
= 2.8 x
\\06-kip-ft a0
46.7-ksf guess c :
o.oi-*
eci-.=
0.00013
- := if(hck ~ s29-5fi*Asa*
Given c>Q c
- =
c ec
- =
eci+ a ck ck Cl Ec
°k
/t:=
1 Elevation hc
= 602ft Pc
=3xl04fap Mc
= 2.4 x 106-kip-ft K
K
<rn
=433-ksf guess:
c:=0A-h eci :=
0.0003 Given
\\:= Find(c,£j cc
- = c e
- =£*+<r i\\
\\
Cl>
ck ck Cl E
Ec
°k
Attachment J Shield Building Sectional Analysis k:=
2 Elevation hr
=
ck Pr
= 2.9 x guess c
Given c>0 P<p(c, k:=
3 Elevation h.
ck
%=2.8x guess Given c>0 Ptpfc (C)-Fin
- =
4 Elevation hr ck guess Given c>0
- =
Fir 615.2//
0 kip Mr k
- =
0.01-A
£c/:
(c'£c/)
V=
= 619.3/
104top M£ c:=0A-h ea
,ed,d,As,fc,a0
= 623 Aft 4
10 Aip A/£ c-0.0l-h
£c dA f
d(c,ec) c^
= 2.1 x
\\06-kip-ft
=
0.0003 A
d\\= P c
ec
- = £ci
= 2.1 x
\\06-kip-ft
- = 0.00003
^5
= 2 x 106-kip-ft
- = 0.0003
^5 Calc. No:
Sheet No:
Sheet Rev.:
c0
= 41.3-fc/
s-=(f(f>ck> 629.5ft,A^
M<p(c,eci,d,As,fc,a0 V
1 o-o
= 40.7-fa/
- =if(hc
> 629.5ft,Asa,
\\'£ci' s' c'a 1
Ec k
cr.
= 40.1-is/
- = if(n^ 629.5ft,Asa, Mpfce
-dA f
a 1
C-CSS-099.20-063 13 of 29 000
>Asb)
/o) = %
°kd°YM<k Asb) d\\=M Rev.-eee-t>oi
Attachment J Shield Building Sectional Analysis k:=
5 Elevation
/?
=
ck V2-7x guess Given c>0 P<p(c.
( °]
wrFmd k:=
6 Elevation h,
=
ck Pc
=2.6x ck guess c
Given c> 0
\\
k:=l Elevation h.
=
ck
\\
%=2.6x 621.5ft
\\04kip
- =
0.1-/7
£ci,d,As,fc (c £
\\
\\c'£ci) 629.3^:
- =
0.3-h 631.5^
Difficult to converge, c :=
0.45-Pv(c,£cl
£cr
<k-
\\
£ci:-
°k
'ck'=
solve
= 1.9 x 106
=
0.000003
= 1.9 x 106
=
0.00003
°)
ck
°
= 1.8 x 106 by hand h
£ci := 0.000083 4, :=
- =
c
£(
W X=l£x 10
^)-<<>>
1 kip-ft As Cl Calc. No:
Sheet No:
Sheet Rev.:
o-0 39.5-jfcx/
= ;/^> 629.5^,^a)
Mtp^c,£ci,d,Asfc,cr 1
=,/^> 629.5^,^,
f cr k
> 629.5ft,Asa,Asb^
lO6-A/p/r t
C-CSS-099.20-063 Rev.-QQO-OO
\\
14 of 29 000
^
- sb) o/o) = ^
Asb)
°k
°)
ck
Attachment J Shield Building Sectional Analysis k:=
8 Elevation V
guess Given a
k-9 Elevation V
hc
=635.5^
2.5 x 104 kip
c:=0.1-A
- >0 P(p(c,eci,d,As,f
= Find(c,£c^
hc
=
638.5./?
K 2.5 x 10* kip Solve by hand c:=
0.45-A Mip(c,eci,d,As
£CT-fc^o
= 1.8x 106-
=
0.000003
= 1.7 x 106
= 0.00009 rf0^ = 2.5 x
,J"\\ =
1.7 C
kip-fl As
- =£a kip-fi As io4,,
xlO6
- =
£ci Calc. No:
Sheet No:
Sheet Rev.:
a0
= 38.3-jb/
- = iffh> 629.5ft,Asa, V
cr.
= 30.4-ksf
°k l
C-CSS-099.20-063 Rev.-969-CO(
15 of 29
^u 000
^
Attachment J Shield Building Sectional Analysis Calc. No:
C-CSS-099.20-063 Rev:-9G6-SheetNo:
16 of 29 Sheet Rev.:
000 f
Maximum strain and stresses The maximum tension and compression strain and stresses are reported next for the each elevation of interest along the SGR opening height. As can be seen below, tensile strains are larger than the concrete cracking strain (ss/st >1),
therefore the concrete will fully crack during the SSE.
£-k-=£ w=£ fSi
= £srEs fse
= £seEs Jem,
Jc[ £c, 'J c k
V k
Elevation Neutral axis location Maximum tensile strain IUF.
Maximum tensile strain O.F.
Maximum tensile stress I.F.
Maximum tensile stress O.F.
Maximum compressive stress Maximum compression strain Maximum tensile strain I.F.
(Normalized by crushing strain)
Normalized by yielding strain hc =
hc =
0 1
2 3
4 5
5 7
S 9
0 1
2 3
4 5
6 7
8 S
0 579.00 602.00 615.20 619.30 623.40 627.50 629.25 631.50 635.50 638.50 Elevation 0
579.00 602.00 615.20 619.30 623.40 627.50 629.25 631.50 635.50 638.50 ft 0
1 2
3 4
5 6
7 8
9 0
55.1 58.5 62 62.9 63.9 65 65.5 64.8 58.6 64.8 fi
~cu 0
1 2
3 4
5 6
7 8
9 0
0.08 0.07 0.06 0.06 0.06 0.06 0.05 0.05 0.05 0.05
'SI 0
1 2
3 4
5 6
7 8
9 0
-0.23
-0.18
-0.15
-0.15
-0.14
-0.13
-0.13
-0.13
-0.15
-0.11 Maximum tensile strain O.F.
Normalized by yielding strain Maximum tensile strain I.F.
Maximum tensile strain O.F.
Normalized by cracking strain Normalized by cracking strain fi
=
0 1
2 3
4 5
6 7
8 9
0
-0.23
-0.19
-0.16
-0.15
-0.14
-0.13
-0.13
-0.13
-0.15
-0.12 SI 0
1 2
3 4
5 6
7 8
9 0
-3.61
-2.87
-2.41
-2.29
-2.18
-2.06
-2.02
-2.00
-2.32
-1.79
~se 0
1 2
3 4
5 6
7 8
9 0
-3.67
-2.S2
-2.45
-2.33
-2.21
-2.1
-2.05
-2.03
-2.36
-1.82
Attachment J Shield Building Sectional Analysis Calc. No:
C-CSS-099.20-063 Rev.-eee-Sheet No:
17 of 29 Sheet Rev.:
000 Til1v The figure below shows the distribution of rebar strains through the SB cross-section for different elevations along the SGR opening height (tensile strains are positive). As expected, the maximum tensile strains take place at the SGR opening location.
6x10 4x10" 2x10 Rebar strain cs
-2x10
-4x10 4
4 E.L. 579 E.L. 602
E.L. 615.2 E.L. 619.3 V
T PS)
C..L,. Oz 3.4 E.L. 627.5 E.L. 629.5
--* E.L. 631.5 C
T
£3 5.5 EL. 638.5 0
4 0
25 100 125 150 50 75 Rebar location d
[ft]
Rebar strain distribution through the SB cross section for different elevations along the SGR opening Maximum tensile and compressive stresses are reported below, as can be seen the rebar stresses are about 20% of the yielding stress.
Similarly, the compressive stresses are about 20% of the concrete compression strength. Therefore the SB remains elastic during the site SSE.
Elevation Maximum tensile stress I.F.
Maximum tensile stress O.F.
Maximum compressive stress 0
1 2
3 4
5 6
7 8
9 0
579.00 602.00 615.20 619.30 623.40 627.50 629.25 631.50 635.50 638.50 ft 0
1 2
3 4
5 6
7 8
9 0
-13.8
-11
-9.2
-8.8
-8.3
-7.9
-7.7
-7.6
-8.8
-6.8 ksi 0
1 2
3 4
5 6
7 8
9 0
-14
-11.1
-9.3
-8.9
-8.4
-8
-7.8
-7.7
-9
-6.9 ksi Jem 0
1 2
3 4
5 6
7 8
9 0
918.5 782.9 704.5 681 657.5 633.9 623.8 606.4 624.8 572.1 psi
Attachment J Shield Building Sectional Analysis Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev.-eee- <=>°<
18 of 29 000 if Maximum tensile and corresponding compressive forces The figure below, shows a typical cross section of the SB, through the elevation proposed for the SGR opening. As can be seen, external moment and axial demands (P-M) generate maximum compression (Pc) and tension (Pt) forces at the upper most and lower most portions of the building cross section, respectively. Maximum tensile and compressive forces are calculated here for D +
E' load combination. These forces are used to calculate the thermal stresses developed in the cross section.
Compression Tension Stress dueto External Full cross section External forces Forces Internal forces Maximum compression (Pc) and tension (Pt) forces per unit length maxk-Ai.f.afSi,'Ao.f.ffse
^max Elevation Maximum tensile force Maximum compressive force 0
1 2
3 4
5 6
7 8
9 0
579.00 602.00 615.20 619.30 623.40 627.50 629.25 631.50 635.50 638.50 max 0
1 2
3 4
5 6
7 8
9 0
-44.2
-35.1
-29.5
-28.1
-26.7
-25.3
-24.7
-15.8
-18.4
-14.2 kip
~max 0
1 2
3 4
5 6
7 8
9 0
330.7 281.8 253.6 245.1 236.7 228.2 224.6 218.3 224.9 206.0 kip
Attachment J Shield Building Sectional Analysis Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev.-99eC>>ol 19 of 29 000 Thermal stresses In the following analysis, 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 for a concrete section without a compression zone For a rotationally restrained section without a compression zone, 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
Initial stress Compression 7f
/
i Exterior Cold Aa
's =nA's(c'iff-Aa) h/2 Section Temperature Uncracked Gradient stresses Cracked stresses final stress Internal Forces External Demand Linear thermal gradient and stresses in the lower most concrete section of the SB crTt(AT,N,d,d\\t,b,As,A>s):=
a0 *~ --
Act lOOpsi Act I
< rook n-AA ar(f 0.5t
+ Aa
- n-A'A an Aa s
° 0.5t
-(N),Aa fx 9
0.5t
)
0.5t fcmax fs ycmax J
Attachment J Shield Building Sectional Analysis Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rey.JMX 20 of 29 000 Lk Thermal stresses for a concrete section with a compression zone For a rotationally restrained section with a compression zone, 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 equations below.
interior Initial stress F's =KA's(
Exterior Section Temperature Uncracked Gradient stresses Cracked stresses F, =
final stress Internal Forces Linear thermal gradient and stresses in the upper most concrete section of the SB aTc{AT,N,d,d\\t,b,As,A'^ :=
aQ *- --AT-a-Ec Aa WQpsi Aal
<- root n'AsX°'~o7t
~{n~ l)'A'sX°"oJt ~
Aa-b\\
t t
i i
-(AO t
cxo-Aal
- f. *-n\\cr0
+ Aal 0.5t a
/.<<--(<<-
1)-
a0 Aal U
0.5t
)
Jcmax
- ~
fs fs
/cmax h/2 External Demand
Attachment J Shield Building Sectional Analysis Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev.-©ee-21 of 29 000 Thermal stresses under tension and compression load
-f{AT, a-f{AT,N,d,d',t,b,A
,A'sj :=
aTc(AT, N,d,d>J,b,A
,A's)
\\t,b,As,A's^
if Im(aJ({AT\\N,d,d\\t,b,A$,As) \\
Okip-ft Shell section properties d
- =--l3+
1.41 +
\\i t
2
{
2 d'
- =
if) hr
< 629.5ft,- - f 3 +
1 + ]/<<,-
k
\\
ck 2
I 2
J 2
AT :=
125 b:=
\\ft 3 +
1 + -
\\in I.F.
rebar O.F.
rebar O.F. rebar location I.F.
rebar location Temperature gradient Elevation I.F.
rebar O.F.
rebar Unit width I.F.
rebar location O.F.
rebar location hc =
0 1
2 3
4 5
6 7
8 9
0 579.00 602.00 615.20 619.30 623.40 627.50 629.25 631.50 635.50 638.50 ft A'
=
0 1
2 3
4 5
6 7
8 9
0 1.27 1.27 1.27 1.27 1.27 1.27 1.27 0.79 0.79 0.79
- in A.
=
0 1
2 3
4 5
6 7
8 9
0 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.3 1.3 1.3 in d' =
0 1
2 3
4 5
6 7
8 9
0 10.4 10.4 10.4 10.4 10.4 10.4 10.4 10.5 10.5 10.5 in d =
0 1
2 3
4 5
6 7
8 9
0 10 10 10 10 10 10 10 10 10 10 in Thermal stresses and strains under tension load
- =
-a
,d
,d'
,t,b,A
,A' k
k k
sk
's.max
fs.
Es£y
Attachment J Shield Building Sectional Analysis Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev.-6©&-
22 of 29 000 Elevation O.F rebar stress Maximum rebar strain ratio I.F rebar stress (Normalized by sy)
Concrete stress 0
1 2
3 4
5 6
7 8
9 0
579.00 602.00 615.20 619.30 623.40 627.50 629.25 631.50 635.50 638.50 ft f,=
0 1
2 3
4 5
6 7
8 9
0
-19.3
-16.6
-15.3
-15.1
-14.9
-14.7
-14.6
-14.8
-15.2
-14.5 ksi e s.max 0
1 2
3 4
5 6
7 8
9 0
-0.32
-0.28
-0.26
-0.25
-0.25
-0.24
-0.24
-0.25
-0.25
-0.24
/., =
0 1
2 3
4 5
6 7
8 9
0
-5.8
-2.7
-1.6
-1.4
-1.2
-1.0
-1.0
-1.0
-1.4
-0.8 Thermal stresses and strains under compression load f
'sc.
Asc.
'cc.
- =-aT(AT-Cmnr
,d
,d>
,t,b,A,
\\
'max k
k k
sk sk Elevation O.F rebar stress Maximum rebar strain (Normalized by e
) O.F 0
1 2
3 4
5 6
7 8
9 0
579.00 602.00 615.20 619.30 623.40 627.50 629.25 631.50 635.50 638.50 ft fsc.
=
0 1
2 3
4 5
6 7
8 9
0 0.2
-1.1
-1.8
-2.1
-2.3
-2.6
-2.7
-2.8
-2.6
-3.1 ksi £ sc.max 0
1 2
3 4
5 6
7 8
9 0
0
-0.02
-0.03
-0.03
-0.04
-0.04
-0.04
-0.05
-0.04
-0.05 A,
=
ksi fc
=
0 1
2 3
4 5
6 7
8 9
0 0.0
-3.9 155.7 184.7 211.3 235.8 246.0 226.4 168.6 258.6
'sc.max
Jsc.
Esey I.F rebar stress Concrete stress 0
1 2
3 4
5 6
7 8
9 0
12.0 10.9 10.2 10.0 9.8 9.6 9.5 9.5 9.7 9.2 frr
=
psi 0
1 2
3 4
5 6
7 8
9 0
2083.1 1928.3 1833.5 1804.1 1774.3 1744 1730.9 1717.9 1742.7 1670.7 psi
Attachment J Calc. No:
Shield Building Sectional Analysis Sheet No:
Sheet Rev.:
LOCAL TEMPERATURE EFFECTS (LC-2)
C-CSS-099.20-063 Rev.-ee&- °°\\
23 of 29 H
000 oU<<W For the sake of completeness, thermal stresses are also calculated here considering that the vertical component of the site SSE is acting down, which results in maximum compressive stresses. Under this scenario, the section capacity is checked a 2 critical locations, EL 629.25' and EL.
579'.
Note that, for the reinforcement pattern above the SGR opening the maximum bending moment take place at EL 629.25'.
Neutral axis location The location of the neutral axis is calculated next for the elevations EL 629.25' and EL.
579.
k:=
0 Elevation hc
= 579/r EL0 := hck Pcb
=5.3x 104 kip Mb=2.Sx\\06kip-ft aob
=
k k
0 guess c := O.8/2
£ci 5= 0.00012 As := '\\hck ~ 629'5j Given c>0
- = Find[c,e A
c b
'= c
£cb
- = e
+ ^ob k:=
6 Elevation h.
= 629.3ft EL,
- =
fc.
k
]
ck pch
=4.4xl04fo>
Mb
= 1.9 x
\\06kip-ft a b
=
k k
k guess c := 0.5-h eci := 0.0003 A* '= '\\hck ' 629' Given c> 0 u^ci^fc,ob/oyuchk (C)-Find(ce) c
-c s
- +-U
{**}*
m{C'£a>
C°bl' C
- l"
£a+ Eca°b0
^Asa>Asb) 39.2-ksf V^sb)
Attachment J Shield Building Sectional Analysis Maximum strain and stresses The maximum tension and compression strain SGR opening location.
k :=
0..
1
£seb. := £s\\ ccb, <Re ~ Ro.f>£cb, ~ ~T'aobn fsi
'= £sib'Es fse
- = £sebEs fcmb,:=fc(£cb,'fc)
Calc. No:
Sheet No:
Sheet Rev.:
and stresses are reported
-ob/o]
C-CSS-099.20-063 Rev.-9©e <&
24 of 29
^
000
^ jM next for the each elevation of interest along the Maximum tensile strain I.F.
Maximum tensile strain O.F.
Maximum tensile stress I.F.
Maximum tensile stress O.F.
Maximum compressive stress Maximum tensile and compressive stresses are reported below. To account for compressive stress concentrations around the opening, the maximum compressive stress calculated above is conservatively increased by 300 psi, based on the maximum compressive stresses due dead load redistribution reported in FENOC Calculation C-CSS-099.20-045, Rev.1.
Elevation Maximum compressive stress 0 D+E1
( 579
^
(6.6\\
EL=\\
\\ft f
=
[ksi
{6293/
se
{4.6 J Cross section properties A's:=
0 As
- =
0 d:=
0 d :--- l3+
1.41 + ]in 12 I
2
)
r t
f 1.27" d'
- =
if\\ hr
< 619.5ft,- -
3 +
1 +
k
\\ck 2
y 2j AT :=
125 b:=
\\ft F.
Maximum compressive stress Maximum compressive stress D+E' D+E' + stress concentration
^856.9^
d':=
0 Al56.9"\\
cm cmb
^ 906.5 )
I.F.
rebar O.F.
rebar I.F. rebar location O.F.
rebar location Temperature gradient Unit width
Attachment J Shield Building Sectional Analysis Calc. No:
C-CSS-099.20-063 Rev.-©QG-Sheet No:
25 of 29 Sheet Rev.:
000 Maximum compressive load Maximum compressive and tensile forces are calculated here for D +
E' load combination (E'z acting down). These forces are used to calculate the thermal stresses developed in the cross section.
Tmax, := 'lf(hc, S 629-5fi>Ao.f.afse+ Ai.f.dfsi ^o.f.ffse
+ ALf.ffsi,)
Cmax'= fern'tb Elevation Maximum tensile force (indicating no tension)
Maximum compressive force
( 579
^
(20.7
^629.3 y
^14.4 Thermal stresses and strains under compression load As can be seen the rebar compressive stresses are about 20% of the yielding stress similarly, the concrete compressive stresses are about 60%
of the compressive strength.
Per Ref.
1 Section 3.8.2.3.4, the factor for compression is 0.7.
Therefore the SB remains elastic under LC-2 load combination; thus meeting the acceptance criteria. Note that it is conservative to use a factor of 0.7 for compression since the SB sectional behavior is flexural.
sc.,.
f,sc.
Elevation 579
\\
,d
,d'
,t,b,A.
,A' k
k k
sk O.F rebar stress
-sc.max fsc.
= 0 fsc.
Es£y fsc.
= 0
- = 0 O.F rebar strain (Normalized by £y)
EL=\\
\\ft
' 629.3.U oa
I.F rebar stress
'13.7"
' sc.max Concrete stress 123319 U
Attachment J Shield Building Sectional Analysis Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev..GOO-c>>o\\
26 of 29 000 ALLOWABLE STRESS CHECK AND CRACK WIDTH CALCULATION The maximum crack width is calculated for normal operation conditions per the requirement of Ref.
- 1. The critical loading condition (LC-3) for this check occurs when the vertical component of the site OBE is acting up, while the region of interest (i.e. the opening area) is in tension, which results in maximum tensile stresses and thus in maximum cracking.
Under this scenario.the section capacity is checked a 2 critical locations, EL 629.25' and EL.
579'.
Note that, for the reinforcement pattern above the SGR opening the maximum bending moment take place at EL 629.25'.
Neutral axis location The location of the neutral axis is calculated next EL 629.25' and EL.
584' along the height of the SGR opening.
k:=
0 Elevation hc
= 519ft 0
~
ck Prrt
= 3.7 x \\04kip guess:
c:=0.5-h Given c>0
- Mrr,
= 1.6 x l06kip-fi
£cj :=
0.00003 A-.=
1 1
m
\\:=Find{c,ec^
c
- = c ecn:=eci+ -c
~ci) u u
^c k:=
6 Elevation hc
= 629.3ft Prn
= 2.9 x 10 kip
- Mrr,
=
1.2 x 10
-kip-ft ann=30A-ksf guess:
c:=0.9-h eci:= 0.00005 A$:= iffhc
>629.5ft,Asa,Asb Given c> 0
, eci, d,As,fc,
\\:=Find(c,e^
c
- = c cil l
£ci+
Attachment J Shield Building Sectional Analysis Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev.-999-o=>(
27 of 29 000 Maximum strain and stresses The maximum tension and compression strain and stresses are reported next for the each elevation of interest along the SGR opening location.
k:=
0..
1
£senk
nk'Re + Ri.f'£cnk
£
^on^c ccn,'Re + Ro.f>£cn, ~ yaon0>a he
£series Jcmn.
Jcl £cnk << c Maximum tensile strain I.F.
Maximum tensile strain O.F.
Maximum tensile stress I.F.
Maximum tensile stress O.F.
Maximum compressive stress Maximum tensile and compressive stresses are reported below, as can be seen the rebar stresses are about 3% of the yielding stress, while the compressive stresses are about 10%
of the concrete compression strength. Therefore the SB remains elastic during the site OBE.
Elevation 579 EL =
l
\\ft
\\ 629.3.U Cross section properties Maximum tensile stress O.F.
D+E Maximum compressive stress D+E 530.8 381.3 As.
= 0 d:= 0 d':= 0
< 629.5ft,Aifb,Aifa d
- = -- l3+
1.41 +pi I
2
\\
2
)
dV=if\\
1.27\\
t hr
< (,29.5ft,- -
3 +
1 +
\\in,- -
3 +
1 + -
\\in 2
J AT := 78 b
- =
\\ft I.F.
rebar O.F.
rebar I.F.
rebar location O.F. rebar location Temperature gradient Unit width
Attachment J Shield Building Sectional Analysis Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev.-eee-oo<
28 of 29 nnn Maximum tensile and compressive load Maximum tensile and compressive forces are calculated here for D + E load combination (E acting up). These forces are used to calculate the thermal stresses developed in the cross section.
>Ao.f.afse
. + Ai.f.afsi,'Ao.f.bfse. + Ai.f.ffsi max^
Cmax'=fcmtb Elevation 579 629.3 Maximum tensile force
(-13.8^
T'=
-5.3 r Maximum compressive force fonts' Cmm =
I
\\kip max I 326.4 J Thermal stresses and strains under compressive load As can be seen the maximum concrete compressive stress within the region of interest (i.e., the opening) under LC 3 is less than 1800 psi, which is lower than the admissible compressive stress per Ref.
1 Section 3.8.2.2.6 of 2680 psi.
Therefore the SB remains elastic under this load combination; thus meeting the acceptance criteria.
4=
- = 0 fsc.
- = 0 fee.
- = ° t
Jsn.
' sn.
\\
'en.
- = ~(r7/AT,-Cmax
,d
,d' k
k k
- -k r#m Elevation 579 Thermal stresses and strains under tensile load EL=\\
ft
,629.3/
O.F rebar stress Lr I.F rebar stress
[ksi 9.8 Concrete stress fcn- = Il628.5 As can be seen the maximum tensile rebar stress is 9 ksi, which is lower than the admissible tensile stress per Ref.
1 Section 3.8.2.2.6 of 32.4 ksi. Therefore the SB remains elastic under this load combination; thus meeting the acceptance criteria.
f,r
= 0 J sn.
' sn.
= 0 fee
= 0 fcen.
\\
.^^1,-7^^^^^
Elevation 579 EL =
629.3 O.F rebar stress
'-8.9s I.F rebar stress f-426.8' I
338.7 Concrete stress A78.3' psi
Attachment J Shield Building Sectional Analysis Calc. No:
Sheet No:
Sheet Rev.:
C-CSS-099.20-063 Rev. -906-29 of 29 000 The maximum concrete crack width is calculated as per Ref.
10 and compared with the allowable maximum crack width (0.01 in) required in the original design of SB (Ref.
- 1) as detailed below.
tb:=
( 3 +
1.41 +
\\l A
- =
2-tb-b R:=
0.000091- \\--R\\ - 5 \\in,Qin I in 2
I ksi I
in maxk Elevation
( 579 EL=\\
\\ft I 629.3 Maximum crack width
-vl_v 0.0000^1 o.ooooj
-in
Attachment K: Evaluation of Temperature Rise in a Concrete Wall Exposed to High Energy Line Breaks Calc. No:
C-CSS-099.20-063, Rev.-eee-SheetNo:
1 of 4 ooi Sheet Rev.:
000 Attachment K Evaluation of Temperature Rise in a Concrete Wall Exposed to High Energy Line Breaks Originator (Print, Sign & Date)
R.Vijaykumar VjS^A-le^
(Bechtel)
^
Reviewer/Design Verifier (Print, Sign
& Date) r y
J.T.Chan jfc^J^
(Bechtel) f f-Approver (Print, Sign & Date)
A-LVieira^j^^^
(Bechtel)
Attachment K: Evaluation of Temperature Rise in a Concrete Wall Exposed to High Energy Line Breaks Calc. No:
C-CSS-099.20-063, Rev.-99e-SheetNo:
2 of 4 oo, Sheet Rev.:
000 This attachment demonstrates that, for a 30 inch concrete wall exposed to a high energy line break, the temperature rise in the concrete wall is negligible.
The attachment evaluates the temperature rise in the Shield Building (SB) concrete wall under the conditions of the following three high energy line breaks:
- 1) Main Feedwater Line Break (MFWLB) [1]
- 2) Steam Generator Blowdown High Energy Line Break (SGBD HELB) [2], and
- 3) Main Steam Line Break (MSLB) [3].
The maximum atmosphere temperature for the three high energy line breaks is obtained from References [1],
[2], and [3] as follows:
36" MSLB Room 602 602A 601E 600/601W 601A-1 601A-2 3L Maximum Temp., F 379 385 378 373 390 285 Comment
<600s MFWLB
[11 Room 303 314 304 313 404 Maximum Temperature, F
"1
"^
"^
323
<212
<212
<212 Comment
Room 208 236 303 314 annulus 105/113/225 115 100/101 Maximum Temperature, F
208 301 196 266 376 212 232 168 Comment
<120s The thermal response of the concrete wall in response to the vapor temperature transient is calculated using a transient one-dimensional heat conduction model to a semi-infinite solid with a convective heat transfer boundary condition to one side of the wall.
The rationale for the use of the semi-infinite model will be made clear by an inspection of the results.
The results for the transient temperature distribution in the wall are calculated as (Reference [4], page 204, Equation 5.48):
T(x,t) -
Tj Too ~ ^i Where:
T(x,t)
=
T, Too
=
transient (°F) hx h2at t+ )][*
)1 Temperature in the wall as a function of time and distance from the steam-facing surface (°F)
Initial temperature of the concrete wall (°F)
Temperature of the room atmosphere (steam), assumed to be constant over the time of the
Calc. No:
C-CSS-099.20-063, Rev.-999 Sheet No:
3 of 4 Sheet Rev.:
000 Attachment K: Evaluation of Temperature Rise in a Concrete Wall Exposed to High Energy Line Breaks erfc
=
Complimentary error function x
=
Distance from the steam-facing surface in the concrete wall (ft) h
=
Heat transfer coefficient between the wall and steam in Btu/hr-ft2-°F k
=
Thermal conductivity of Concrete = 1.48 BTU/hr-ft-T (Reference [1], sheet 3) rho
=
density of concrete = 150 lbm/ft3(Reference [1], sheet 3)
Cp
=
specific heat of concrete = 0.24 BTU/lbm-T (Reference [1], sheet 3) a
=
thermal diffusivity = k/rho/cp = 0.041 fr/hour t
=
time from the start of the accident (hour)
The 36" MSLB bounds all accident sequences due to the maximum temperature and maximum time interval; here it is conservatively assumed that the maximum temperature of 390 °F occurs over the entire time period of 600 s, even though, in reality such high temperatures are attained only for a few seconds. With Ti = 120 °F, Too
=390 °F, and by setting the surface heat transfer coefficient to very high value, it is possible to revert back to constant surface temperature boundary condition (Equation 5.43, page 203, [4]).
(2)
The results for concrete wall temperature as a function of time, using Equation (2) are given in Figure 1.
420 390 360
£330 l 300 270 m
l 240
'210 180 150 120
x=o l--X = linch
- X = 2inch
- -X = 3inch X= 6 inch i
at 100 200 300 400 500 600 700 Time (s)
Figure 1
Concrete wall temperature as a function of time for an initial wall temperature of 120 °F, and a room atmosphere temperature of 390 °F Figure 1 shows that for a conservative assumed constant steam temperature of 390°F applied over the entire accident sequence of 600 s, and with an infinite heat transfer coefficient, the temperature exceeds a temperature of 149°F in the first 2 inches into the wall (measured from the hot end).
Even if the transient time is arbitrarily
Attachment K: Evaluation of Temperature Rise in a Concrete Wall Exposed to High Energy Line Breaks Calc. No:
C-CSS-099.20-063, Rev:-GQG-Sheet No:
4 of 4
<s°^
Sheet Rev.:
000 extended to 30 minutes, the wall temperature at 4 inches does not exceed 147°F.
This analysis is very conservative, since it is assumed that the maximum temperature occurs over the entire transient.
As shown in Figure 2, there is no temperature gradient in the wall beyond 3 inches.
For the three HELB sequences, the temperature effect in 30 inches of concrete wall is very small.
Therefore, for the structural evaluation of the concrete wall, the thermal impact of the HELB sequence(s) can be ignored.
420 390 9
12 15 18 21 24 Distance Along the Wall (inches) 27 30 Figure 2 Concrete wall temperature as a function of distance along the wall for an initial wall temperature of 120 °F, and Atmosphere temperature of 390 °F References 1.
C-NSA-000.02-005, "Main Feedwater Line Breaks and Cracks in the Auxiliary Building," Rev. 002.
2.
C-NSA-000.02-006, "Steam Generator Blowdown Line Breaks in the Auxiliary Building", Rev. 001.
3.
C-NSA-000.02-016, "36 Inch main Steam Line Breaks in Rooms 601 and 602," Rev.000.
4.
Frank. P. Incropera and David P. DeWitt, "Fundamentals of Heat and Mass Transfer, Second Edition, John Wiley and Sons, 1985, Pages 203-204.
Attachment L:
ACI Code Compliance of Shield Building with Observed Laminar Cracking Calc. No:
C-CSS-O99.20-063, Rev. 001 Sheet No:
Iofl3 Sheet Rev:
000 Attachment L:
ACI Code Compliance of Shield Building with Observed Laminar Cracking
Attachment L:
ACI Code Compliance of Shield Building with Observed Laminar Cracking Calc. No:
C-CSS-099.20-063, Rev. 001 Sheet No:
2 of 13 Sheet Rev:
000 This attachment provides code compliance review of the existing Shield Building with observed laminar cracking for ACI 318-63 code (Table 1) and ACI 307-69 code (Table 2).
It shall be noted that the Shield Building is an existing structure that was originally designed and constructed to comply with USAR and applicable code provisions of ACI 318-63 (using ultimate strength design method) and ACI 307-69 (using working stress design method). The only change to the structure is the observed laminar cracking near the outer reinforcement layer as described in Refs.
19a-e and
- 25. To address this new condition, this calculation (C-CSS-099.20-063) has been developed to illustrate compliance with USAR and the applicable Codes (ACI 318-63 and ACI 307-69). Since the Shield Building is an existing structure, many of the provisions related to materials, testing, quality, construction, and details of reinforcement for the as constructed Shield Building are deemed to be compliant with the USAR and the ACI 318-63 and ACI 307-69 Codes.
Also note that per summary section of ACI 307-69, this Code gives supplemental provisions using working stress design method, besides those given in the Building Code (ACI 318), for concrete chimneys or other structures with hollow circular cross sections. Therefore, for topics not explicitly covered by ACI 307-69, the design provisions in ACI 318-63 are used.
The tables in this attachment supplement the main body of the calculation, by focusing on the compliance of the new design calculation to the relevant sections of the Codes that are affected by the observed laminar cracking.
The following Code Compliance categories are used in these tables:
Not applicable: For provisions that do not apply to the new design basis calculation.
Not affected by laminar cracking:
For provisions related to Shield Building aspects that are not covered by the new design calculation, such as materials, reinforcement details, etc. These provisions are deemed to be compliant during original design and construction.
Yes - not affected by laminar cracking:
For provisions that are covered in the new design basis calculation but are not affected by the laminar cracking, such as wind and earthquake loads, design methodology, etc. These provisions are found to be compliant based on the new design basis calculation.
Yes - affected by laminar cracking: For provisions that are potentially affected by the laminar cracking but are found to be compliant based on the new design basis calculation.
For example, provisions related to rebar strength, allowable stresses, etc. The provisions falling in this category are highlighted in the Tables.
Attachment L:
ACI Code Compliance of Shield Building with Observed Laminar Cracking Calc. No:
C-CSS-O99.20-063, Rev. 001 Sheet No:
3 of 13 Sheet Rev:
000 Table 1: CODE COMPLIANCE OF THE EXISTING SHIELD BUILDING WITH OBSERVED LAMINAR CRACKING FOR ACI 318-63 CODE ACI 318-63 Code Provisions Chapter-l:
General requirements 101 - Scope 102 - Permits and drawings 103-Inspection 104 - Approval of special systems of design or construction Chapter-2:
Load tests of structures Chapter-3:
Definitions Chapter-4:
Materials Chapter-5:
Concrete quality Chapter 6:
Mixing and placing concrete Chapter-7:
- Formwork, embedded pipes, and construction joints Code Compliance Not affected by laminar cracking/Not applicable Not applicable Not applicable Not applicable Not applicable Not affected by laminar cracking Not affected by laminar cracking Not affected by laminar cracking Not applicable Descriptions 101-a:
The minimum requirements for the design of reinforced concrete have been incorporated by following all the applicable requirements of this Code.
101-b:
The general building code is not applicable.
101-c:
Special structures consideration is not applicable.
Shield building cylinder design is carried out using elastic analysis consistent with USAR and the industry standards.
The permits and drawings are not applicable for existing structure.
The concrete work site inspection, curing and temperature records are not applicable for existing structure.
No special systems of design are used.
Special systems of construction are not applicable for an existing structure.
Load testing of in-place concrete systems is not carried out and thus not applicable This section is not affected as no new materials are used.
All the material requirements were met during construction. The detailed condition assessment and core testing showed that in-place concrete was of sound quality and exceeded its specified design strength - See Section 3.0 of the calculation.
This section is not affected as no new materials are used.
All the material requirements were met during construction. The detailed condition assessment and core testing showed that in-place concrete was of sound quality and exceeded its specified design strength -See Section 3.0 of the calculation.
This section is not affected as no new materials are used.
All the material requirements were met during construction. The detailed condition assessment and core testing showed that in-place concrete was of sound quality and exceeded its specified design strength - See Section 3.0 of the calculation.
Not applicable for existing structure.
Attachment L:
ACI Code Compliance of Shield Building with Observed Laminar Cracking Calc. No:
C-CSS-099.20-063, Rev. 001 Sheet No:
4 of 13 Sheet Rev:
000 ACI 318-63 Code Provisions Chapter-8:
Details of reinforcement 801 - Hooks and bends 802 - Cleaning reinforcement 803 - Placing reinforcement 804-Spacing of bars 805 - Splices in reinforcement 806 - Lateral reinforcement 807 - Shrinkage and temperature reinforcement 808 - Concrete protection for reinforcement Chapter-9:
Design (general considerations) 901:
Design of methods 902:
Design loads 903:
Resistance to wind, earthquake, and other forces 904:
Frame analysis-General 905:
Frame analysis - Details 906:
Requirements for T-beams 907:
Effective depth of beam or slab Code Compliance Not affected by laminar cracking Not affected by laminar cracking Yes - not affected by laminar cracking Yes - not affected by laminar cracking Yes - not affected by laminar cracking Yes - not affected by laminar cracking Yes - not affected by laminar cracking Not applicable Not applicable Descriptions No new reinforcement is added - existing reinforcement meets the requirements.
No new reinforcement is added - existing reinforcement meets the requirements.
Detailed condition assessment and testing confirmed that reinforcement is not affected by laminar cracking and that there is no path for moisture to penetrate to the subterranean laminar cracking and the reinforcement.
The reinforcement is sufficiently protected with at least 3 inches of concrete cover and recently applied coating - See Section 3.0 of the calculation.
The design is carried out using Part IV -B (Ultimate Strength Design) of ACI 318-63 which is consistent with the original design and construction.
See main body of the calculation.
The design loads used are those described in the USAR. See main body of the calculation.
The design loads used are those described in the USAR. See main body of the calculation.
Shield Building is a cylindrical shell. Therefore, typical frame analysis is not applicable. A standard linear elastic finite element model analysis is carried out to accurately represent the Shield Building.
See Appendix 3E of USAR and main body of the calculation.
The stiffness, loading and resulting member forces such as moment, axial load and shear are obtained using detailed FEM. See main body of the calculation.
No T-Beams are involved.
No beams or slabs are involved in the calculation.
Attachment L:
ACI Code Compliance of Shield Building with Observed Laminar Cracking Calc. No:
C-CSS-099.20-063, Rev. 001 Sheet No:
5 of 13 Sheet Rev:
000 ACi 318-63 Code Provisions 908:
Distance between lateral supports 909:
Control of deflections 910: Deep beams 911:
Minimum reinforcement of flexural members 912:
Limiting dimensions of columns 913:
Limits for reinforcement of columns 914:
Bending moments in columns 915:
Length of columns 916:
Strength reductions for length of compression members 917:
Transmission of column load through floor system 918:
Anchorage requirements
-General 919:
Anchorage of web reinforcement 920:
Transfer of moments and effect of openings in slabs and footings Code Compliance Not applicable Not applicable Not applicable Not affected by laminar cracking Not applicable Not affected by laminar cracking Not applicable Not applicable Descriptions No beams are involved in the calculation.
No explicit deflection requirements are included in either USAR or DCM. The reason for this is that such deflection checks are generally applicable to building type of structures where excessive deflection can cause damage to non-structural/architectural elements.
However, the SB is a very stiff cylindrical structure, the expected deflection due to seismic or wind load effects will be negligible from serviceability point of view. To substantiate this point, Calc VS01/B01-003, Pg. 3-24 shows that the lateral displacement at the dome due to SSE is 0.642". Consider a nominal 250' as the SB height from the base ring foundation elevation 565', the ratio of lateral displacement to height of structure is 1/4672 [i.e, 0.6427(250x12")], which is much smaller than what a typical building may experience. This clearly shows that the SB stiffness is so large such that there should not be any deflection concerns. Also note that Att. A of this calculation confirms that the laminar cracking does not affect the structural stiffness of the SB.
No deep beams are involved.
No new reinforcement is added - existing reinforcement meets the requirements.
No columns are included in the DB calculation.
No new reinforcement is added - existing reinforcement meets the requirements.
No web reinforcement is involved.
No unbalanced force is involved between columns and slabs. The openings have been designed and detailed in the original calculation and there is no impact of laminar cracking on the openings.
Attachment L:
ACI Code Compliance of Shield Building with Observed Laminar Cracking Calc. No:
C-CSS-O99.2O-O63, Rev. 001 Sheet No:
6 of 13 Sheet Rev:
000 ACI 318-63 Code Provisions 921:
Torsion Chapter-10:
Working Stresses Design (WSD) 1001:
General 1002:
Allowable stresses in concrete 1003:
Allowable stresses in reinforcement 1004:
Allowable stresses -
Wind and Earthquake forces Chapter-11:
Flexural computations (WSD)
Chapter-12:
Shear and diagonal tension (WSD) 1201: Shear stress 1202: Web reinforcement 1203: Stirrups 1205: Stress restriction 1206: Web reinforcement restriction 1207: Shear stress in slabs and footings 1208: Lightweight aggregate concrete Chapter-13:
Bond and anchorage (WSD)
Chapter-14:
Reinforced concrete columns (WSD)
Code Compliance Not applicable Not applicable Yes - not affected by laminar cracking Not applicable Yes - not affected by laminar cracking Not applicable Yes - not affected by laminar cracking Not applicable Not applicable Not applicable Descriptions No beam torsion is involved.
The design is primarily done by strength design Part IV-B of ACI 318-63 and some applicable portions of WSD using ACI 307-69.
The design is primarily done by strength design Part IV-B of ACI 318-63 and some applicable portions of WSD using ACI 307-69. In absence of shear design provisions in ACI 307-69, working stress design provisions in ACI 318-63 are used for compliance, using the allowable shear stress in concrete given in this Section and Section 1004.
The design is primarily done by strength design Part IV-B of ACI 318-63 and some applicable portions of WSD using ACI 307-69.
See "Descriptions" for Section 1002.
The design is primarily done by strength design Part IV-B of ACI 318-63 and some applicable portions of WSD using ACI 307-69.
In absence of shear design provisions in ACI 307-69, working stress design provisions in Sections 1201-1203 of ACI 318-63 are used for compliance.
The design is primarily done by strength design of ACI 318-63 and some applicable portions of WSD using ACI 307-69.
The design is primarily done by strength design of ACI 318-63 and some applicable portions of WSD using ACI 307-69.
The design is primarily done by strength design of ACI 318-63 and some applicable portions of WSD using ACI 307-69.
Attachment L:
ACI Code Compliance of Shield Building with Observed Laminar Cracking Calc. No:
C-CSS-099.20-063, Rev. 001 Sheet No:
7 of 13 Sheet Rev:
000 ACI 318-63 Code Provisions Chapter! S:
General strength and serviceability requirements (USD) 1501: Definition 1502: General requirements 1503:
Assumptions 1504:
Safety provisions 1505:
Design strengths for reinforcement 1506:
Design loads 1507:
Control of deflections Code Compliance Yes - not affected by laminar cracking Yes - not affected by laminar cracking Yes - not affected by laminar cracking Yes - affected by laminar cracking Yes - not affected by laminar cracking Not applicable Descriptions All applicable requirements are met as discussed below:
(a)
All applicable provisions of Part IV-B comply, (b)
Bending moment in axially loaded members (shell elements of the cylinder) is included in the FEM analysis - See main body of the calculation, (c)
Analysis is based on elastic theory - See FEM analysis discussion in main body of the calculation.
No continuous flexural members are involved. No adjustments are needed in FEM analysis results for Hp^ign purpose.
The assumptions made for design of concrete in main body of the calculation are the same as listed in (a) through (s) of 1503.
(a) Strengths are computed in accordance with Part IV-B. See main body of the calculation, (b) The strength reduction coefficient used are the same as in 1504.
(c) The strength capacities used are based on Section 3.8.2.2.3 and Appendix 3E of USAR and same as used in the original design basis calculation.
Section 301 of ACI 318-63 defines the minimum yield strength of reinforcement as the minimum value determined in tension according to applicable ASTM specifications; this corresponds to the testing of individual rebar in tension tests. The reinforcement design strength is limited to 60 ksi for vertical and inner horizontal hoops in this calculation, while it is conservatively limited to only 55 ksi for outer hoop bars in the laminar cracking regions. Note that << l<<i iq nnt hping dpfinpri as the minimum vield strength of reinforcement, but is being used as its limiting design strength in this calculation. The 55 ksi is based on test results, which were obtained using a bond and development test procedure that is typically used for such tests and forms the basis for the Code equations.
Note that the Code specified value of 60 ksi is to provide a general limiting strength for design. The actual yield is generally higher and is not used in the design.
In that sense, the 55 ksi limit provides a similar but an even a lower limit for design that was developed conservatively using the acceptable test protocol and is thus consistent with the Code. The use of lower allowable design strength (less than 60 ksi specified) increases the design safety margin over and above the minimum specified in the Code. See Section 3.3 of the calculation for further discussions.
The design loads are those specified in Section 3.8.2.2.4 of USAR.
See main body of the calculation.
See "Descriptions" for Section 909
Attachment L:
ACI Code Compliance of Shield Building with Observed Laminar Cracking Calc. No:
C-CSS-099.20-063, Rev. 001 Sheet No:
8 of 13 Sheet Rev:
000 ACI 318-63 Code Provisions 1508:
Control of cracking Chapter lfi:
Flexural computations (USD) 1601:
Rectangular beams with tension reinforcement only 1602:
Rectangular beams with compression reinforcement 1603:
1-and T-sections 1604:
Other cross sections Chapter-17:
Shear and diagonal tension (USD) 1701:
Ultimate shear strength 1702:
Web reinforcement 1703:
Stirrups 1704:
Bent bars 1705:
Stress restrictions 1706:
Web reinforcement restrictions 1707:
Shear stress in slabs and footings Code Compliance Yes - not affected by laminar cracking Yes - affected by laminar cracking Not applicable Yes - affected by laminar cracking Yes - not affected by laminar cracking Yes - not affected by laminar cracking Yes - not affected by laminar cracking Not applicable Yes - not affected by laminar cracking Yes - not affected by laminar cracking Not applicable Descriptions (a) Only deformed bars are used.
The detailing meets the USAR as constructed, (b) The design yield strength of reinforcement is limited to 60 ksi or less. See main body of the calculation.
Flexural strengths are determined at element level based on methodology consistent with this section (See main body of the calculation).
The design is carried out using only 55 ksi strength for the outer hoop bars.
No 1-or T-sections included in the DB calculation.
The shell elements are designed based on general FEM analysis using assumptions in Section 1503.
See main body of the calculation. The design is carried out using only 55 ksi strength for the outer hoop bars.
See main body of the calculation.
Web reinforcement is not required by design - See main body of the calculation.
Stirrups are not required by design - See main body of the calculation.
No bent bars are provided in the original construction.
Shear stress is less than the specified limit in 1705 (b).
See main body of the calculation.
Web reinforcement is not required by design - See main body of the calculation.
No slabs or footings are included in the calculation.
Attachment L:
ACI Code Compliance of Shield Building with Observed Laminar Cracking Calc. No:
C-CSS-099.20-063, Rev. 001 Sheet No:
9 of 13 Sheet Rev:
000 ACI 318-63 Code Provisions 1708:
Lightweight aggregate concretes Chapter-18:
Bond and anchorage (USD)
Chapter-19:
Combined axial compression and bending (USD) 1901:
General requirements 1902:
Bending and axial load capacity of short members (rectangular sections with bars in one or two faces) 1903:
Bending and axial load of short members (circular sections with bars circularly arranged) 1904:
Bending and axial load of short members (square sections with bars circularly arranged)
Chapter-20:
Joists and two-way slabs Chapter-21:
Flat slabs with square or rectangular panels Chapter-22:
Reinforced concrete walls Code Compliance Not applicable Yes -affected by laminar cracking Yes -affected by laminar cracking Yes -affected by laminar cracking Yes -affected by laminar cracking Not applicable Not applicable Not applicable Not applicable Descriptions Lightweight aggregate is not used.
The existing reinforcement meets the USAR and Code requirements for anchorage.
To evaluate the effect of laminar cracking on bond of reinforcement, detailed testing was carried out, the summary of which is provided in Section 3.0 of the calculation and Ref.24. The testing indicated that in the presence of laminar cracks, it is conservative to conclude that the lap-spliced #11 bars with a 79-inch splice length can achieve bar stresses on the order of 55 ksi or more. Therefore, for design purposes, reinforcement strength for the outer hoop bars in the cracked regions is reduced to 55 ksi (instead of 60 ksi specified in USAR) to provide a larger safety margin for the reinforcement in the affected areas. Also see "Description" for Section 1505.
The general requirements are met using moment-axial (P-M) interactions for the shell elements. See main body of the calculation. The design is carried out using only 55 ksi strength for the outer hoop bars.
The general requirements are met using moment-axial (P-M) interactions for the shell elements. See main body of the calculation. The design is carried out using only 55 ksi strength for the outer hoop bars.
Shield building shell elements have reinforcement on both faces. The requirements are met using moment-axial (P-M) interactions for the shell elements. See main body of the calculation. The design is carried out using only 55 ksi strength for the outer hoop bars.
No circular sections with circular bars -The design of the shell elements is carried out using P-M interaction. See main body of the calculation.
No square sections with circular bars - The design of the shell elements is carried out using P-M interaction. See main body of the calculation.
No joists or two-way slabs are included in the calculation.
No flat slabs are included in the calculation.
Attachment L:
ACI Code Compliance of Shield Building with Observed Laminar Cracking Calc. No:
C-CSS-O99.20-063, Rev. 001 Sheet No:
10 of 13 Sheet Rev:
000 ACI 318-63 Code Provisions 2201: Structural design of walls 2202: Empirical design of walls 2203: Walls as grade beams Chapter-23:
Footings Chapter-24:
Precast concrete Chapter-25:
Composite concrete f lexural construction Chapter-26:
Prestressed concrete Code Compliance Yes - affected by laminar cracking Not applicable Not applicable Not affected by laminar cracking Not applicable Not applicable Not applicable Descriptions 2201 - Shield Building cylindrical walls are designed for the applicable loading per USAR using a detailed FEM analysis. See main body of the calculation.
The design is carried out using only 55 ksi strength for the outer hoop hars.
The empirical design is not used.
The walls are not used as grade beams.
Laminar cracking does not affect the foundation ring mat. The basemat is not included in the calculation. See main body of the calculation.
No precast concrete is included in the design.
No composite concrete is included in the design.
No prestressed concrete is included in the design.
Attachment L:
ACI Code Compliance of Shield Building with Observed Laminar Cracking Calc. No:
C-CSS-099.20-063, Rev. 001 Sheet No:
11 of 13 Sheet Rev:
000 Table 2: CODE COMPLIANCE OF THE EXISTING SHIELD BUILDING WITH OBSERVED LAMINAR CRACKING FOR ACI 307-69 CODE ACI 307-69 Code Provisions Chapter 1-General 1.1-Scope 1.2-Drawings and computations 1.3-Regulations Chapter 2 - Materials Chapter 3 - Construction Requirements Chapter 4 -
Design of Chimney Shell 4.1-General 4.2-Wind Forces Code Compliance Not affected by laminar cracking Not affected by laminar cracking Not affected by laminar cracking Not affected by laminar cracking Not affected by laminar cracking Yes - affected by laminar cracking Not applicable Descriptions The design of Shield Building has been performed using the working stress design methodology given in this Code.
The guidelines given in this Code have been used to calculate the design demands in the Shield Building shell for thermal loading.
No new drawings are prepared, and computations are approved per applicable guidelines.
1.3.1 - The design of the Shield Building conforms to the regulatory requirements prescribed in the USAR and Davis Besse Design Criteria Manual. See main body of the calculation.
1.3.2-This subsection is not applicable, since it pertains to height restrictions for chimneys.
This section is not affected as no new materials are used.
All the material requirements were met during construction.
The detailed condition assessment and core testing showed that in-place concrete was of sound quality and exceeded its specified design strength - See Section 3.0 of the calculation.
This section is not affected as no new materials are used.
All the material requirements were met during construction.
The detailed condition assessment and core testing showed that in-place concrete was of sound quality and exceeded its specified design strength - See Section 3.0 of the calculation.
Shield Building has been designed to resist the dead loads, wind and earthquake loads, and temperature effects in both vertical and circumferential directions. The new design evaluation of the Shield Building has been performed using the element level results from the finite element analysis using ANSYS, as described in the Appendix 3E of USAR. The concrete and reinforcement stresses for working stress design load combinations are calculated and combined using a methodology (i.e. thin shell theory) consistent with the requirements provided in this Section and the Code Supplements (Sections 7.5 and 7.8 and Attachment E of the calculation). The working level stresses are shown to not exceed the allowable stresses meeting Section 4.9 requirement (allowable stresses are reduced to account for the reduced design strength of outer circumferential reinforcement).
The wind loads are based on the USAR and Davis Besse Design Criteria Manual (Section 7.4 of the calculation).
Attachment L:
ACI Code Compliance of Shield Building with Observed Laminar Cracking Calc. No:
C-CSS-099.20-063, Rev. 001 Sheet No:
12 of 13 Sheet Rev:
000 ACI 307-69 Code Provisions 4.3 - Wind and dead load stresses - No openings 4.4 - Wind and dead load stresses - At openings 4.5 - Earthquake design 4.6 - Vertical temperature stresses 4.7-Circumferential temperature stresses 4.8 - Combined stresses due to dead loads, temperature, and wind (or earthquake) 4.9 - Allowable Stresses Chapter 5 - Design Curves Appendix 1 - Chimney Linings Appendix 2 - Accessories Supplement - Equations for Stress due to Wind and Dead Load (Derivation of Equations)
Code Compliance Yes - not affected by laminar cracking Not applicable Yes - not affected by laminar cracking Yes - affected by laminar cracking Yes - not affected by laminar cracking Not Applicable Not Applicable Yes - not affected by laminar cracking Descriptions See discussion for Section 4.1 and Code Supplements.
The earthquake loads are based on the USAR and Davis Besse Design Criteria Manual (Section 7.4 of the calculation).
See discussion for Section 4.1 and Code Supplements.
The concrete and reinforcement allowable stresses given in this Section are the maximum limiting values. Since the design strength (not the yield strength)of the outer circumferential reinforcement is conservatively limited to 55ksi, instead of using the yield strength value of 60 ksi as the reinforcement design strength, the allowable stresses for concrete and outer circumferential reinforcement are also conservatively reduced in direct proportion of the considered design strength to the specified minimum yield strength of reinforcement. Since the stresses do not exceed reduced allowable given in this Section the Code requirement is met. Also see "Description" for ACI 318-63, Section 1505 in Table 1.
This Chapter provides the design curves as supplemental tools to facilitate the calculation of stresses using Chapter
- 4. These design curves are based on the equations given in Chapter 4 and the Code Supplements. Based on the discussion for Section 4.1, the provisions in this Chapter are also met for the new design evaluation of the Shield Building.
This Appendix is not applicable since no lining is used in the Shield Building.
This Appendix is not applicable since it applies specifically to concrete chimneys.
See "Descriptions" for Section 4.1.
Attachment L:
ACI Code Compliance of Shield Building with Observed Laminar Cracking Calc. No:
C-CSS-099.20-063, Rev. 001 Sheet No:
13 of 13 Sheet Rev:
000 ACI 307-69 Code Provisions Supplement - Derivation of Equations for Stress due to Wind and Dead Load where Two openings occur not Diametrically opposite Supplement - Equations for Temperature Gradient and Thermal Stresses through Chimney Shell Code Compliance Not Applicable Yes - not affected by laminar cracking Descriptions This Supplement is not applicable since the new design evaluation of Shield Building does not consider multiple openings.
As described in "Descriptions" for Section 4.1, the new design calculation of the Shield Building is based on the element level results from the finite element analysis using ANSYS. The structural demands due to thermal loads are calculated manually using the same bases as given in this Supplement and are combined with the structural demands due to other (mechanical) loads using a methodology consistent with the Supplement (Sections 7.6 and 7.7 and Attachment C of the calculation). Since the same set of concepts and basic principles of engineering mechanics are used to derive the structural demands for thermal loads, the provisions given in this Supplement are met.
Attachment M:
Memos from Outside Industry Experts Calc. No:
C-CSS-099.20-063, Rev. 001 Sheet No:
1 of 5 Sheet Rev.:
000 Attachment M Memos from Outside Industry Experts
Attachment M:
Memos from Outside Industry Experts Calc. No:
C-CSS-099.20-063, Rev. 001 Sheet No:
2 of 5 Sheet Rev.:
000 Action Required:
No Due Date:
N/A August 22, 2013 Mr. Jon Hook Design Engineering Manager FENOC Davis-Besse Nuclear Power Station 5501 North State Route 2 Oak Harbor, OH 43449 Subject Bechtel Job Number 25593 Letter/File No.:
25583-000-TCM-GEG-00010 Mtnos from Prof. Sozen and Prof. Darwin related to the rorthodotoov used In the Davis-Bessie Shield Building Design Bases Calculation
Reference:
N/A
Dear Mr. Hook:
Attached are the memos from Prof. Mete Sozen dated August 10, 2013, and Prof. David Darwin dated Jury 31,2013 documenting their review of the methodology used in the Davis-Bessie shield building design bases calculation..
Professor Sozen is a Kettelhut Distinguished Professor of Structural Engineering at Purdue University. He obtained his PHD degree in Civil Engineering at University of Illinois, Urbana in 1957. He was given the rank of professor in 1963. His current research focuses on vulnerability assessment of building and transportation structures, development of numerical nonlinear models for dynamic responses of reinforced structures, and effect of explosion and impact on buildings. He has been involved in tests of a wide range of structural elements, assemblies and structures in the laboratory and in the field.
Professor Darwin is a Deane E. Ackers Distinguished Professor at University of Kansas.
He has extensive experimental and analytical expenence in the field of bond and development of reinforcement. He is a past chair and current member of ACI Committee 408 on Bond and Development of Reinforcement. He developed the ACl Committee 408 expression for development in splice lengths, which accurately coversi bars with yield strengths between 40 and 120ksi and for concrete with strengths ranging from 2000 to SOOOpsi. He ateo developed ASTM A944 Beam-End Test, BECHTCL P0WE1 COIFOWTIOM
Attachment M:
Memos from Outside Industry Experts Calc. No:
C-CSS-099.20-063, Rev. 001 Sheet No:
3 of 5 Sheet Rev.:
000 Mr. Jon Hook August 22, 2013 25593-000-TCM-GEG-OOO10 Page 2 of 2 which is used to evaluate relative bond strength. He has been involved with bond studies since 1981.
Note that in Professor Darwin's memo, the technical paper 'Effect of laminar Cracking on Davis-Besse Shield Building Design Basis Calculations" is inactive, but the contents of this paper have been fully Included in the Calculation C-CSS-099.20-063, Rev.OOO.
If you have any questions or comments, please call me at 301-229-8087.
- Regards, Douglas Dismukes Project Engineer
Enclosure:
- 1) Memo from Prof. Mete Sozen dated August 10, 2013 (1 Page)
- 2) Memo from Prof. David Darwin dated Jury 31,2013 (1 Page)
Bechtet C. Ravotta J. Munshi H.Liu W. Hickerson FENQC G. Michael J. Hook T.Henry FirstEnergy acknowledges receipt of correspondence number 25593-000-TCM-GEG-00010.
Received by Date:
Please acknowledge receipt and return to:
Bechtel Power Corporation 5275 Westview Drive Frederick, MD 21703 Mail Stop BP4-2C4 Attn:
Project Administrator
Attachment M:
Memos from Outside Industry Experts Calc. No:
C-CSS-099.20-063, Rev. 001 Sheet No:
4 of 5 Sheet Rev.:
000 25553-COC-TCM-GEG-OCC10 Aacnnenti.i)
TO:
Dr. Javeed Munshi FROM: MeteSozen LuiM RE:
Bechtel Power Corporation Report, "Davis-Besse Shield Building Design Basis Calculations,"
03/26/2013 DATE:
10 August 2013 Thank you for giving me the opportunity to review your report on the study of the D-B 5hieW Building.
The twelve tests carried out in Bowen Laboratory confirmed in every instance that neither the strength nor the stiffness of the 79-in. and 120-m. splices of the ffll bars would be affected by the presence of cracks in the plane of the splices of the outer circumferential reinforcement. From the viewpoint of strength and stiffness requirements of ACI 31&-63 and AQ 307-69, there is no need indicated for modifying the original design model of the D-B Shell. And it follows that the current analysis will show that the code requirements will be satisfied.
With respect to servkeabiSty and durability: The history of the D-B Shell over the past decades is the most convincing indicator of its promised positive behavior in the future.
The Bowen tests have revealed no negative effects of the cracks on stiffness and strength of the spfices.
The behavior to date of the existing shell answers all reasonable questions with respect to durability.
I do not see any reason why the response of the shell to the anticipated earthquake would be handicapped by problems with the splices of the circumferential reinforcement.
I agree with your decision not to change the model used for analysis of the shidd struaure with respect to requirements of Ad 318 and Ad 307. Therefore, I conclude that the curreitt re-evaluations will be found satisfactory in accordance with both ACI specifications cited.
Attachment M:
Memos from Outside Industry Experts Calc. No:
C-CSS-099.20-063, Rev. 001 Sheet No:
5 of 5 Sheet Rev.:
000 255&3-00C-TCM-G SG-O0010 Anacrment (2)
MEMORANDUM TO: Javeed Munshi FROM: Daxid Darwin DATE: My 31.2013
SUBJECT:
Review of "Effect of Laminar Crackins on Davis-Besse Shield Building Design Basis Calculations." 25593-O0O-GS3-GEG-00017. Rev.001 I have reviewed the subject paper along with my memorandum to you dated July 13, 2012, and the report of our experimental work. SL Repon 12-2.
The purposed methodology for incorporating the effect of laminar cracking in design corresponds with die findings of our stud}*. Those findings, in essence, demonstrate that under the test conditions, which were more severe than observed in the Shield Building, 79-in. lap splices of No.
11 bars can develop a stress on the order of 55 ksi. According to the paper, mat value of bar stress is to be used in the new design basis calculations.
I believe this approach is both realistic and practicaL Given that the splice lengths exceed those required by the ACI Code at the rime of the design. ACI 31 S-63. and that the requirements for control of cracking m that code are met I feel that the purposed methodology is appropriate for establishing compliance with me provisions of the 1963 ACI Building Code~