ML19161A391
| ML19161A391 | |
| Person / Time | |
|---|---|
| Site: | Seabrook  |
| Issue date: | 06/10/2019 |
| From: | Harmon, Curran, Harmon, Curran, Spielberg & Eisenberg, LLP, C-10 Research & Education Foundation |
| To: | Atomic Safety and Licensing Board Panel |
| SECY RAS | |
| References | |
| RAS 55035, ASLBP 17-953-02-LA-BD01, 50-443-LA-2 | |
| Download: ML19161A391 (117) | |
Text
UNITED STATES OF AMERICA NUCLEAR REGULATORY COMMISSION ATOMIC SAFETY AND LICENSING BOARD In the Matter of NEXTERA ENERGY SEABROOK, LLC (Seabrook Station, Unit 1)
Docket No. 50-443-LA-2 ASLBP No. 17-953-02-LA-BD01 Hearing Exhibit Exhibit Number:
Exhibit
Title:
INT023 Simpson Gumpertz & Heger Document No. 170444-L-003 Rev. 1, Response to RAI-D8-Attachment 1 Example Calculation of Rebar Stress For a Section Subjected to Combined Effect of External Axial Moment and Internal ASR (Enclosure 4 to Letter SBK-L-18074) to SBK-L-18074 Simpson Gumpertz & Heger Document No. 170444-L-003 Rev. 1, "Response to RAI-DS-Attachment 1 Example Calculation of Rebar Stress For a Section Subjected to Combined Effect of External Axial Moment and Internal ASR."
SIMPSON GUMPERTZ & HEGER PROJECT NO:
170444 I
Engineering of Structures and Building Enclosures DATE:
Dec 2017 CLIENT:
NextEra Energy Seabrook BY:
MR.M.Gargari
SUBJECT:
Examele Calculation of Rebar Stress VERIFIER:
A. T. Sarawit RESPONSE TO RAl-D8-ATTACHMENT 1 EXAMPLE CALCULATION OF REBAR STRESS FOR A SECTION SUBJECTED TO COMBINED EFFECT OF EXTERNAL AXIAL AND MOMENT AND INTERNAL ASR
- 1.
REVISION HISTORY Revision 0: Initial document.
- 2.
OBJECTIVE OF CALCULATION The objective of this calculation is to provide an example calculation of rebar stress used in parametric studies 1 and 2 in response to RAl-08.
- 3.
RESULTS AND CONCLUSIONS Table 1 summarizes the tensile stress in rebars corresponding to constant axial force and moment with an increasing ASR expansion. The results are also plotted in Figure 1 b. This data is used to draw diagrams similar to what presented in Figure 3b of parametric study 1.
- 4.
DESIGN DATA I CRITERIA Diagrams presented in the response to RAl-08 are extracted for two extreme sections one with minimum reinforcement ratio and the other with maximum reinforcement ratio. There is no other criteria.
- 5.
ASSUMPTIONS 5.1 Justified assumptions The concrete material is represented by compression only elastoplastic material with compressive strain cutoff of 0.003. This simple constitutive model satisfactorily captures the response of concrete in compression because stresses are not near reaching the compressive strength. Attachment 2 Appendix H provides a comparison study between the stresses in rebars of the critical component of two structures (with high and low compressive stress in concrete) computed using two different constitutive models for concrete, namely:
Response to RAl-08-Attachment 1 1
Revision 0
Accurate model that uses Kent and Park concrete response in compression Simple model/idealized model which is an elastoplastic model with compressive stress cutoff at compressive strain of 0.003 The concrete strength in tension is conservatively neglected.
5.2 Unverified assumptions There are no unverified assumptions.
- 6.
METHODOLOGY As an example calculation, Case I for a section with high reinforcement ratio is considered. The section is 2ft thick with 3000psi concrete that is reinforced with #11@6in. on both faces. The point corresponding to case I is highlighted on P-M interaction diagram provided in Figure 1. The amount of axial force and moment for Case I are -128.5kip/ft and 174.2kip-ft/ft, respectively.
To calculate the diagram in parametric study 1, the axial force and moment are kept constant while the internal ASR load is increased. Such a diagram is presented in Figure 3 of the response to RAl-08. For the second parametric study, specific ASR expansion is selected and the amount of moment is increased. The calculation presented here provides an example for both parametric studies. In fact, the loading sequence does not matter.
The stress in rebars is calculated considering the following steps:
- 1)
The geometry including thickness, rebar size, spacing, etc. are provided.
- 2)
The compatibility and equilibrium equations are satisfied for concrete and steel when the concrete undergoes expansion due to internal ASR. Consequently, the initial stresses in concrete and steel are calculated.
- 3)
Appropriate material model are assigned for concrete and steel. Specifically, elastic material for steel and an elastoplastic material for concrete are used.
- 4)
Section is discretized into 20 layers, and appropriate functions are developed to facilitate the calculation of strain and stress at middle of each layer. Steel layers are also used at the center of rebars at each faces.
- 5)
By knowing the value of axial force "P" (P = -128.5kip/ft), the curvature value "<p" is iterated to minimize the difference between the target moment (M = 17 4.2kip-ft/ft) and the moment from sectional analysis based on inputted axial force and trial curvature.
- 6)
Using the developed functions, the strain and consequently stress are calculated for each steel fiber and at the farthest edge of the concrete compressive fiber.
Response to RAl-08-Attachment 1 2
Revision 0
- 7.
REFERENCES There are no references
- 8.
COMPUTATION 8.1. Strain in Steel and Concrete due to Internal ASR expansbn Input Data ASR expansion Measured crack index Threshold factor Material properties Compressive strength of concrete Young's modulus of concrete Yield strength ofsteel Young's modulus of steel Geometry Width of fibers Total thickness or height Area of concrete Area of tensile reinforcement
(#8@12 in.)
Number of reinforcement in row, e.g. equal to 2 for tensile and compressive Depth to reinforcement mm Ecr := 0.8-m Fthr := I Ee:= 3 l 20ksi fy := 60ksi Es := 29000ksi b := 12in h := 24in Ac := b*h = 288*in2
- 6. 2 As:= 2* 1.5 m SteelNum := 2 d := 20.3i Finding the strain in steel and concrete by satisfying compatibility and equilibrium Initial Guess Initial mechanical strain in concrete Initial strain in steel Compatibility equation Response to RAl-08-Attachment 1 Eo.conc := 0 Eo.steel := 0 Given 3
Revision 0
Equilibrium equation Initial strain in concrete and steel 8.2. Sectional Analysis Input Data Concrete Material Model Constitutive model for concrete Steel Material Model Constitutive model for steel Response to RAl-08-Attachment 1 ans := Find( Ea.cone, Ea.steel)
MATconc(E) :=
0 if E > 0 0 if E < -0.003 (Ee* E) otherwise
~ MATconc( Ee)_ 2
"' e ksi Ci3 --
-4
- 0.01 50
,-, g MATstee](Es) i2 0
~
ksi
{/] --
- 50
- 0.01
- 5x l0 4
0 Strain
-3 0
0.01 Strain Revision 0
Concrete Fibers Number offibers Height of fibers Concrete fiber coordinates Concrete fiber strain Concrete fiber stress Concrete fiber force Reinforcement/Steel fibers Depth to reinforcement fiber Area of reinforcement fiber Steel fiber strain Steel fiber stress Steel fiber force Response to RAl-08-Attachment 1 ConeNum := 20 h
Cone8 :=
1.2* in ConeNum Coney :
for i E 1.. ConeNum h
ConeH ans.+-- - - + --- + (i - l)*ConeH I
2 2
ans Conec:( co.cone, c, (fl) :=
for i E 1.. ConeNum ansi +-- c 0 cone + c - tp* Coney i ans Conecr( co.cone, c, (fl) :=
for I E 1.. ConeNum ansi +-- MAT cone( Co nee( co.cone, c, (fl) i) ans ConeF( co.cone, c, (fl) :=
for i E 1.. ConeNum ansi +-- Conecr( co.cone, c, (fl) i. ( b* ConeH) ans Steely1 := -(d -~) = -8.3-in h
Steely := d - -
= 8.3* m 2
2
. 2 SteelAs :=As= 3.12*m I
. 2 SteelAs :=As= 3.12*m 2
Steele:( co.steel, c, (fl) :=
for i E 1.. SteelNum ansi +-- co.steel + c - tp* Steelyi ans Steelcr( c 0 steel> c, (fl) :=
for i E 1.. SteelNum ansi +-- MA Tsteel( Steele( co.steel> c, (fl) i) ans SteelF( co.steel> c, (fl) :=
for i E 1.. SteelNum ans1. +-- Steelcr( co.steel> c, (fl): Steel As.
I I
ans 5
Revision 0
Initial Stress State Initial stress in concrete Concretea := Conca( so.cone, 0, 0)
Initial stress in steel Axial Equilibrium Force( so.cone, so.steel> E:, tp) :=
ans 1 ~ 0 for i E 1.. ConcNum ansl ~ ansl + ConcF(e:oconc,i::,tp).
I ans2 ~ 0 for i E 1.. Stee!Num ans2 ~ ans2 + Stee!F( co.steel> E:, tp).
I ans ~ ans 1 + ans2 Moment Equilibrium Moment( so.cone, So.steel> E:, tp) :=
ans 1 ~ 0 for i E 1.. ConcNum ansl ~ ansl + -1
- ConcF( E: 0 cone> E:, tp):Concy.
I I
ans2 ~ 0 for i E 1.. Stee!Num ans2 ~ ans2 + -1
- Stee!F( E: 0 steel, E:, tp): Steely.
I I
ans ~ ans 1 + ans2 Response to RAl-08-Attachment 1 6
Revision 0
Solution Known parameters Axial force Iteration Curvature Solve for strain at centroid Axial strain at centroid (initial guess)
Axial force equilibrium Sectional forces Stress and strain in concrete and steel Steel fiber stress and strain Concrete fiber stress and strain Maximum compressive strain in concrete p := - 128.52kip
<l> := 0.000046*_!__
in f(x) := Force( Eo.conc>Eo.steel>X,<j>) - P Ecent := root( f( Xa), Xa) = -7.471 x 10- 5 Force( E0 cone, E0 steel> Ecent> ¢) = - 128.52* kip M oment( Ea.cone, Ea.steel, Ecent, ¢) = I
- kip* ft Concretey := Coney Requires iteration Concrete£
- Concrete£ ConcNum ConcNum-1 ( h
)
- 4 Emax.comp :=
- Coney
... = -7.608 x 10 Cone
- Cone 2
ConcNum-1 y ConCNum y ConCNum-1
+Concrete£ ConcNum-1 Maximum compressive stress in concrete Response to RAl-08-Attachment 1 7
Revision 0
- 9.
TABLES Table 1: Stress in rebars of 2ft thick section with high reinforcement ratio for P=-128.52kip/ft and M=17 4.24ki p-ft/ft Total stress in steel (ksi)
Maximum initial stress in compressive stress Cl (mm/m) concrete (ksi)
Curvature, qi (1/in)*
Rebar1 Rebar1 in concrete (ksi) 0 0
0.00007 19.737
-13.961
-2.31 0.4 9.655 0.000056 22.869
-4.089
-2.334 0.8 19.311 0.000046 28.217 6.072
-2.374 1.2 28.966 0.00004 35.511 16.255
-2.457 1.6 38.622 0.000038 44.377 26.084
-2.624 2
48.277 0.0000375 53.851 35.799
-2.821
- The curvature needs to be found iteratively to satisfy the moment equilibrium Example in Section 8
- 10.
FIGURES
-600 1-400
~ -200
~
200 400 ~-------~~-------~
-400
-300
-200
-100 0
100 200 300 400 Moment (kip-ft/ft)
P-M interaction Ultimate strength
- W orlcing stress (b) Location of Case I in P-M interaction 70 60 50
,,;;-g 40
~ 30
"" "' 20
..c ell p::
10 0
25
-10 Internal ASR (mm/m)
-<r-Case I -Internal ASR only (b) Stress in the critical rebar of Case I Figure 1: Results for Case I Response to RAl-08-Attachment 1 8
Revision 0
SIMPSON GUMPERTZ & HEGER I
Engineering of Structures and Building Enclosures CLIENT:
NextEra Energy Seabrook
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures PROJECT NO: __
1'-'-70"""'4'"-'-44-'-----
DATE: ---~F~e~b=20~1~8 ___
BY: ---~M~R~
. M=*~G=ar~qa=ri~--
VERIFIER: --~A~
. T~.
S=a=ra~w~it __
RESPONSE TO RAl-08-ATTACHMENT 2 EVALUATION OF MAXIMUM STRESS IN REBARS OF SEABROOK STRUCTURES
- 1.
REVISION HISTORY Revision 0: Initial document.
Revision 1: Revised pages 9, 10, 11 and 12 from Revision 0 to 1. The revision was made to remove footnotes 'a' and 'b' which identified CEB results to be preliminary, and WPC/PH and EMH results to be pending final review. Revised pages 1 to update Revision history section.
Revised page 13 to update revision of references 7 and 8.
- 2.
OBJECTIVE OF CALCULATION AND SCOPE The objective of this calculation is to evaluate the stress in rebars of the structures at NextEra Energy (NEE) Seabrook Station in Seabrook, New Hampshire for in-situ load combinations considering unfactored normal operating loads when adding the loads due to ASR.
All demands are from the ASR susceptibility evaluation of each structure.
The scope of this calculation includes the following structures:
Control Room Makeup Air Intake structure (CRMAI)
Residual Heat Removal Equipment Vault structure (RHR)
Containment Enclosure Building (CEB)
Enclosure for Condensate Storage Tank (CSTE)
Main steam and feed water west pipe chase and Personnel Hatch (WPC/PH)
Containment Equipment Hatch Missile Shield structure (CEHMS)
Containment Enclosure Ventilation Area (CEVA)
Safety-Related Electrical Duct Banks and Manholes (EMH) W01, W02, W09, and W13 through W16 Response to RAl-08-Attachment 2 1
Revision 1
SIMPSON GUMPERTZ & HEGER I Engineering of Structures and Building Enclosures CLIENT:
NextEra Energy Seabrook PROJECT NO: ---'-"'17~0~44~4 ___
DATE: ----=De=c~2=0-'-"'17 ___
BY: ----~M~R~.
M~*~G=a"-"rg=ar~i __
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures VERIFIER: --~A~.-'-"'T.~S=a=ra~w~it __
- 3.
RESULTS AND CONCLUSIONS Stress evaluation results are listed below:
The structure is evaluated for the load combinations listed in Section 4. The load combination listed below controls the calculation of maximum stress in rebars.
D + L + E +To+ Eo + He+ FrHR.Sa (LC2)
The stress in rebars of all structural components remain below yield strength. The following components give the highest stress in rebars:
Rebars along the horizontal strip of east exterior wall of the RHR structure at approximate elevation of -30 ft are stressed to 56.5 ksi subjected to LC2. The high stress is expected to occur in localized area, and therefore, the moment can distributed to mid span in susceptibility evaluation of the structure [3]. In addition, the stresses are expected to less because of the conservatism including a limited model of PAB as connected to RHR as explained in Section 6.3.
The maximum axial stress of 55.6 ksi is expected in rebars of the wall above east corner of Electrical Penetration at EL +45 ft subjected to LC2 in CEB.
Rebars along the horizontal strip at east wall of CRMAI structure are expected to experience tensile stress as high as 43.3ksi. The Cl/CCI value over the walls of the structure is zero, and the induced demands are mainly due to relative expansion of the base mat with respect to walls.
Rebars in the east-west direction at the base slab of CEVA are expected to be stressed to 44 ksi if the Cl value increases 200% beyond the current state. As explained in Section 6.6, the actual value is expected to be less because of the conservatism in computing unfactored demands due to original loads.
- 4.
DESIGN DATA I CRITERIA In response to RAl-08 request, the maximum stress in the rebars of Seabrook structures is calculated and compared with yielding strength of rebars (fy = 60ksi). In this evaluation, the following in-situ load combinations (also called service load and unfactored normal operating load) are considered:
D + L + E + To + Sa (In-situ condition, LC1 )
D + L + E + To + Eo + He + h HR.Sa (In-situ condition plus seismic load, LC2)
Response to RAl-08-Attachment 2 2
Revision 0
SIMPSON GUMPERTZ & HEGER I Engineering of Structures and Building Enclosures CLIENT:
NextEra Energy Seabrook
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures PROJECT NO: --~17~0~44~4~----
DATE: _____
De~c~2~0~17 ___
BY: -----"M"'"R-"-. =M"'-. G=a=r=ga=ri'----
VERIFIER: --~A~.T~.
S=a=ra=w=it ___
where D is dead load, L is live load, E is lateral earth pressure, Ta is operating temperature, Ea is the operating basis earthquake (OBE), He is dynamic earth pressure due to OBE, and Sa is ASR load. Operating temperature To is only applicable to the WPC/PH. For the second in-situ load combination, ASR loads are further amplified by a threshold factor (FrnR) to account for the future ASR expansion.
- 5.
METHODOLOGY To calculate the stress in rebars of structural components subjected to in-situ load combinations, sectional analysis based on fiber section method is used. In this method, the cross section is discretized into fibers (or layers), and an appropriate material model is assigned to each fiber. Figure 1 demonstrates a typical fiber section discretization. The total moment and axial force are calculated by integrating force over all fibers.
The concrete material is represented by compression only elastoplastic material with compressive strain cutoff of 0.003. This simple constitutive model satisfactorily captures the response of concrete in compression because stresses are not near reaching the compressive strength. Appendix H provides a comparison study between the stresses in rebars of the critical component of two structures (with high and low compressive stress in concrete) computed using two different constitutive models for concrete, namely:
Accurate model that uses Kent and Park concrete response in compression Simple model/idealized model which is an elastoplastic model with compressive stress cutoff at compressive strain of 0.003 Both models are schematically depicted in Figure 2a. The concrete strength in tension is conservatively neglected. Reinforcing steel bars are modeled using elastic perfectly plastic material in compression and tension. Figure 2b demonstrates the steel material model used for the section analysis. The initial slope (Young modules) are 29,000 ksi for steel and 57,000.fl'c for concrete.
In this evaluation the ASR load effect causes:
Response to RAl-08-Attachment 2 3
Revision 0
SIMPSON GUMPERTZ & HEGER I Engineering of Struc tures and Building Enclosures CLIENT:
NextEra Energy Seabrook PROJECT NO: --~17~0~44~4~----
DATE: ----~D~e~c=20~1~7 ___
BY: ____
~M~R~*~
M~
. G~a=r~qa~ri~-~
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures VERIFIER: __
_,_,A-'--'-
.T~
. S=a=ra=WI=
- t~---
The axial force and bending moment that are induced by ASR expansion of other components (adjacent structural component)
The internal stress in rebars due to ASR expansion of the component itself The latter induces tensile stress in rebars and compressive stress in concrete that is called initial stress state. The effect of internal ASR expansion is considered by adding autogenous strain to the concrete and steel material. The input strain magnitude is set to be the ASR strain value measured over the specific component, and the output strains (initial strain in concrete and steel after application of ASR strain) are calculated by satisfying equilibrium and compatibility equations. If a member does not show any sign of internal ASR or the internal ASR expansion of the member was conservatively set equal to zero during ASR susceptibility evaluation of the structure, the initial stress in concrete and rebar are set to zero.
The critical sections that governed the calculation of threshold factor of each structure are selected for the evaluation, and demands due to combined effects of internal ASR expansion and induced ASR expansion of other components are computed with methods used in susceptibility evaluation of the structures. Appendix J provides Run ID logs. These demands are added to the demands subjected to original design loads, and the stress in rebars are calculated.
12in Calculation is performed for unit width Actual concrete member Response to RAl-08-Attachment 2 Rebar 1 Rebar 2 Stress f,1~----
~ Strain Steel material model Stress Concrete material model Fiber section discretization and material models 4
Revision 0
SIMPSON GUMPERTZ & HEGER I Engineering of Structures and Building Enclosures CLIENT:
NextEra Energy Seabrook
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures PROJECT NO: --~17~0~44~4~----
DATE: ----=De=c'-=2=0_,_,17 ___
BY: ____
~M~R~
- =M~
G=a~rg=a=ri __ ~
VERIFIER: --~A.~T~.
S=a=ra=w=it ___
Figure 1 - Schematic representation of fiber section method Stress Stress
-0.003 Strain E,
+------
- ----+ Strain Idealized model
< 1-fy (a) Concrete material model (b) Steel material model Figure 2 - Concrete and steel material model
- 6.
ANALYSIS AND EVALUATION COMPUTATIONS This section summarizes the maximum stress that are computed in rebars and concrete of several Seabrook structures at critical sections.
6.1 Control Room Makeup Air Intake structure The stress in rebars of the critical components of CRMAI structure that governed the calculation of threshold factor is calculated and presented in Appendix A. Calculation of the threshold factor for the CRMAI structure is primarily governed by axial-flexure interaction along the horizontal strip of the east wall that occurs at the middle of the wall [1 ]. A threshold factor of 1.4 was determined from evaluation of the CRMAI structure, which indicates that ASR-related demands are amplified by 40% beyond the factored values.
Tables 1 and 2 summarize the stress in rebars of east wall and base mat of CRMAI structure.
As can be seen from the table, the maximum axial stress is 43.3 ksi expected to form in a horizontal rebar of the walls close to the interior of the structure. The maximum stress in base mat that has highest ASR expansion within the structure is 39.1 ksi. Both stresses are below the yield strength of rebars.
Response to RAl-08-Attachment 2 5
Revision 0
SIMPSON GUMPERTZ & HEGER I
Engineering of Structures and Building Enclosures CLIENT:
NextEra Energy Seabrook
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures 6.2 Containment Enclosure Building PROJECT NO: --~17~0~44~4 ___
DATE: ----=De=c=2=01~7 ___
BY: ----=M~R~.
M=*~G=a~rg=ar~i __
VERIFIER: --~A~.T~*~S=ar=aw=it~---
The stress in rebars at the critical section of the CEB structures is calculated and presented in Appendix B. The calculated threshold factor was 1.3 [2]. Tables 1 and 2 summarize the stress in rebars at two critical locations. The maximum axial stress of 55.6 ksi is expected in rebars of the wall above east corner of Electrical Penetration.
6.3 Residual Heat Removal Equipment Vault The stress in rebars of the critical components of RHR structure that governed the calculation of threshold factor is calculated and presented in Appendix C. Calculation of the threshold factor for the RHR structure is primarily governed by axial-flexure interaction along the horizontal strip along the south side of the east exterior wall [3]. A threshold factor of 1.2 was determined from evaluation of the RHR structure, which indicates that ASR-related demands are amplified by 20% beyond the factored values.
Tables 1 and 2 list the stress in horizontal rebars of east exterior wall, and the stress in vertical rebars in west and east interior walls of RHR structure. As can be seen from the table, the maximum tensile stress of 59.5 ksi is expected in the vertical rebars of the east interior wall due to LC2. However, the RHR walls are designed to span horizontally between intersecting walls; and therefore, the vertical rebars are not part of the main load path for the RHR. Figure C1 shows the contour plots of vertical strains in the interior walls due to LC1. The contour plots show that the overall vertical strains are reasonable compared to the yielding strain of rebars.
Localized strain concentration is observed close to the door openings at approximate El. (-) 30 ft. and El.(-) 45 ft.
The next highest tensile stress is 56.5 ksi calculated for the horizontal rebars of exterior east wall. The specific section also governed the determination of threshold factor for the RHR structure. As explained in the susceptibility evaluation of RHR [3], moment can distribute to mid span and along the width of the wall, therefore, localized strain concentration is not of concern.
The majority of the stresses that develop at this location are due to the RHR connection to PAB.
The PAB foundation locally stiffens the connection between the RHR and the PAB which attracts the moment demand about the vertical axis in the east exterior wall of the RHR. In addition, the PAB base slab is subject to uplift pressure from backfill expansion which in turns Response to RAl-08-Attachment 2 6
Revision 0
SIMPSON GUMPERTZ & HEGER I Engineering of Structures ond Building Enclosures CLIENT:
NextEra Energy Seabrook
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures PROJECT NO: --~17~0~44~4 ___
DATE: ----~De~c~2~01~7 ___
BY: ----~M~R~
. M~*~G~a~rq=ar~i __
VERIFIER: ----'A""".T,,__,,.-"'S=ar=aw=it,__ __
induces forces in the RHR external walls near the connection. The stresses in the RHR evaluation and as reported here are conservative due to only including a limited model of PAB as connected to RHR which introduces extra overturning moment as well as the expected vertical shear force at this connection.
6.4 Condensate Storage Tank Enclosure The stress in rebars of the critical components of CSTE structure that governed the calculation of threshold factor is calculated and presented in Appendix D. Selection of threshold factor for the CSTE structure is primarily governed by hoop tension at the top of the tank enclosure wall and vertical moment at the base of the tank enclosure wall [4]. A threshold factor of 1.6 was determined from evaluation of the CSTE structure, which indicates that ASR-related demands are amplified by 60% beyond the factored values.
Tables 1 and 2 summarize the stress in rebars of the tank enclosure wall of the CSTE structure.
As can be seen from the table, the maximum axial stress of 26. 7 ksi is expected to form in vertical rebars at the bottom of the tank enclosure wall.
6.5 Containment Equipment Hatch Missile Shield The stress in rebars of the critical components of CEHMS structure that governed the calculation of threshold factor is calculated and presented in Appendix E. Selection of threshold factor for the CE HMS structure is primarily governed by out-of-plane moment at the base of east wing wall [5]. A threshold factor of 1.5 was determined from evaluation of the CEHMS structure, which indicates that ASR-related demands are amplified by 50% beyond the factored values.
Tables 1 and 2 summarize the stress in rebars of east wing wall of CEHMS structure. The maximum axial stress is 41.6 ksi expected to form in vertical rebars of the east wing wall at top of the column.
6.6 Containment Enclosure Ventilation Area The stress in rebars of the critical components of CEVA structure that governed the calculation of threshold factor is calculated and presented in Appendix F. Selection of threshold factor for the CEVA is primarily governed by out-of-plane moment at the base slab located in Area 3 (Areas are defined in Ref. 6). A threshold factor of 3.0 was determined from evaluation of the Response to RAl-08-Attachment 2 7
Revision 0
SIMPSON GUMPERTZ & HEGER I Engineering of Structures and Building Enclosures CLIENT:
NextEra Energy Seabrook
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures PROJECT NO: __
_,_17'""0'"""'44_,_4,__ ___
DATE: ----=De=cc.-=2=0~17 ___
BY: ____
~M=R=
- =M-'-
. G=a=r=qa=ri~-~
VERIFIER: --~
A~.T_,_. S=a~ra=w=it~---
CEVA structure, which indicates that ASR-related demands are amplified by 200% beyond the factored values.
Tables 1 and 2 summarize the stress in rebars at the base slab. The maximum computed axial stress in rebars of the base mat is 44 ksi. However, as explained in Appendix F, the original design calculation did not provide demands due to unfactored load cases/combinations; hence, a conservative value was selected for the evaluation of rebar stress presented in Appendix F.
6.7 West Pipe Chase and Personnel Hatch The stress in rebars at the critical flexural section of the WPC/PH structures is calculated and presented in Appendix I. The threshold factor of 1.8 was calculated based on out-of-plane shear of the WPC west wall [7]. Tables 1 and 2 summarize the stress in rebars at the base of the WPC north wall, the critical tensile stress location.
A maximum tensile stress of 44.4 ksi develops in horizontal rebars of the WPC north wall.
6.8 Electrical Manholes The stress in rebars at the critical flexural section of the EMH W13 and W15 is calculated and presented in Appendix G. The calculated threshold factor was 3.7 [8].
Tables 1 and 2 summarize the stress in rebars in EMH W13 and W15. A maximum tensile stress of 27.0 ksi develops in the horizontal rebars of EMH W13 and W15.
Response to RAl-08-Attachment 2 8
Revision 0
SIMPSON GUMPERTZ & HEGER I Engineering of Structures and Building Enclosures PROJECT N 0: ~~~1~70~4~4~4~~~~-
DATE:
Feb 2018 CLIENT:
NextEra Energy Seabrook BY:
MR. M. Garqari
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures VERIFIER:
A.T. Sarawit Table 1 - Stress in rebars of structural components subjected to LC1 Total stress in Maximum Maximum Internal steel (ksi) compressive compressive Component Item ASR Location stress in mechanical (mm/m)
Rebar1 Rebar2 concrete (ksi) strain in concrete M = 5.2 (kip-ft/ft)
East wall, horizontal strip, East Wall 0
at the middle of the wall 36.2 26.8 0
>O p = 49.8 (kip/ft)
~
0:::
(.)
M = 20.8 (kip-ft/ft)
North-south strip, at Base mat 0.99 intersection with south 27.8 26.4
-0.28
-8.96e-5 p = -28.4 (kip/ft) walls M = 459.5 (kip-ft/ft)
Between Mechanical &
Wall 0.60 Electrical Penetration at 27.1 5.60
-2.21
-6.61e-4 p = -141.2 (kip/ft)
Elev. -30ft.
co w
u M = -39.6 (kip-ft/ft)
Wall between Mechanical Wall 0.10
& Electrical Penetration, 24.6 2.73
-0.71
-1.88e-4 P= 14.1 (kip/ft) below personal hatch East exterior M = -98.5 (kip-ft/ft)
East exterior wall, wall 0.75 horizontal strip, at the 46.9 11.4
-1.9
-6.09e-4 p = -35.0 (kip/ft) approximate El. (-) 30 ft 0:::
East interior M = 28.6 (kip-ft/ft)
East interior wall, vertical
- c:
wall 0.0 strip, at the approximate 41.6 5.5 0.0
>O 0:::
p = 37.2 (kip/ft)
El. (-) 45 ft West interior M = 11.0 (kip-ft/ft)
West interior wall, vertical wall 0.0 strip, at the approximate 26.5 12.5 0.0
>O p = 30.8 (kip/ft)
El. (-) 30 ft Response to RAl-08-Attachment 2 9
Revision 1
SIMPSON GUMPERTZ & HEGER I Engineering of Structures ond Building Enclosures PROJECTN0 : ~~~1~70~4~4~4~~~~-
DATE:
Feb 2018 CLIENT:
NextEra Energy Seabrook BY:
MR. M. Garqari
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures VERIFIER:
A T. Sarawit Table 1 - (Continue)
Internal Total stress in Maximum Maximum Component Item ASR Location steel (ksi) compressive compressive stress in mechanical strain (mm/m)
Rebar1 Rebar 2 concrete (ksi) in concrete w
Tank M = 41.0 (kip-ft/ft)
Bottom of tank enclosure I-Enclosure 0.43 15.8 8.6
-0.68
-1.89e-4
(/)
wall, vertical direction u
Wall P=-12.9 (kip/ft)
(/)
M = 159.6 (kip-ft/ft)
East wing East wing wall, at
- c:
0.72 23.4 15.0
-0.78
-2.50e-4 w
walls p = -8.3 (kip/ft) intersection with column u
<(
M = 83.7 (kip-ft/ft)
Base slab rebar along Base slab 0.31 32.8 5.1
-0.89
-2.8e-4 w
east-west direction u
p = 1.7 (kip/ft)
M = 3.8 (kip-ft/ft)
- c:
North wall below pipe a..
North wall 0.24 7.8 6.6
-0.07
-0.22e-4 (3
break beam a..
p = 19.1 (kip/ft) 3:
M = 7.4 (kip-ft/ft)
- c:
W13/W15 0.25 W13/W15 walls 11.2 5.6
-0.28
-9.61 e-6 p = -3.2 (kip/ft) w Response to RAl-08-Attachment 2 10 Revision 1
SIMPSON GUMPERTZ & HEGER I Engineering of Structures a nd Building Enclosures PROJECTN0 : ~~~1~7~04~4~4~~~~~
DATE:
Feb 2018 CLIENT:
NextEra Energy Seabrook BY:
MR. M. Gargari
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures VERIFIER:
A.T. Sarawit Table 2 - Stress in rebars of structural components subjected to LC2 Internal Total stress in Maximum Maximum Component Item FrnR ASR Location steel (ksi) compressive compressive stress in mechanical strain (mm/m)
Rebar1 Rebar2 concrete (ksi) in concrete M = 7.7 (kip-ft/ft)
East wall, horizontal strip, East Wall O**
at the middle of the wall 43.3 29.6 0
>O p = 57.6 (kip/ft)
~
1.4 et::
()
M = 26.5 (kip-ft/ft)
North-south strip, at Base mat 0.99 intersection with south 39.1 37.3
-0.33
-1.06e-4 p = -32.3 (kip/ft) walls M = 614.7 (kip-ft/ft)
Between Mechanical &
Wall 1.3 0.60 Electrical Penetration at 42.5 1.97
-2.68
-8.51e-4 ID p = 10.5 (kip/ft)
Elev. -30ft.
w
()
M =22.8 (kip-ft/ft)
East side of Electrical Wall 1.3 0.10 Penetration at Elev. 45ft.
55.6 12.9
-1.33
-3.67e-4 p = 52.8 (kip/ft)
East exterior M=-119.5 (kip-ft/ft)
East exterior wall, wall 0.75 horizontal strip, at the 56.5 13.8
-2.1
-6.73e-4 p = -40.8 (kip/ft) approximate El. (-) 30 ft et::
East interior M = 33.0 (kip-ft/ft)
East interior wall, vertical
- i:
wall 1.2 0.0**
strip, at the approximate 59.5*
17.7 0.0
>O et::
p = 60.9 (kip/ft)
El. (-) 45 ft West interior M = 13.4 (kip-ft/ft)
West interior wall, vertical wall 0.0**
strip, at the approximate 36.6*
19.6 0.0
>O p = 44.4 (kip/ft)
El. (-) 30 ft Response to RAl-08-Attachment 2 11 Revision 1
SIMPSON GUMPERTZ & HEGER I Engineering of Structures and Building Enclosures PROJECTN0:~~~1~7=04~4~4~~~~~
DATE:
Feb 2018 CLIENT:
NextEra Energy Seabrook BY:
MR. M. Garqari
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures VERIFIER:
A.T. Sarawit Table 2 - (Continued)
Internal Total stress in Maximum Maximum Component Item FrHR ASR Location steel (ksi) compressive compressive stress in mechanical strain (mm/m)
Rebar1 Rebar2 concrete (ksi) in concrete w
Tank M = 65.7 (kip-ft/ft)
Bottom of tank enclosure I-Enclosure 1.6 0.43 26.7 13.9
-1.11
-3.08e-4
(/)
wall, vertical direction
(.)
Wall P=-12.9 (kip/ft)
(/)
M=311.6 (kip-ft/ft)
East wing East wing wall, at
- c:
1.5 0.72 41.6 20.8
-1.52
-4.87e-4 w
walls p = -0.7 (kip/ft) intersection with column
(.)
<(
M = 83.7 (kip-ft/ft)
Base slab rebar along Base slab 3.0 0.31 44.0 20.6
-1.08
-3.46e-4 w
east-west direction
(.)
p = 1.7 (kip/ft)
M = 78.8 (kip-ft/ft)
- c:
North wall below pipe a..
North wall 1.8 0.24 44.4 8.0
-1.36
-4.37e-4 u
break beam a..
p = 34.4 (kip/ft)
- J:
- c:
M = 0 (kip-ft/ft)
W13/W15 3.7 0.25 W13/W15 walls 27.0 24.5
-0.30
-9.69e-5 w
p = 23.6 (kip/ft)
- Vertical strips (strips that engage vertical rebars) are not part of primary load path for RHR, and therefore, are not designed following ACI 318 strength design method. These members do not need to be considered for the evaluation of stress in rebars.
Response to RAl-08-Attachment 2 12 Revision 1
SIMPSON GUMPERTZ & HEGER I
Engineering of Structures and Building Enclosures PROJECT NO: --~17~0~44~4 ___
DATE: ----~Fe=b~2~01~8 ___
CLIENT:
NextEra Energy Seabrook BY: ----=M=R=.
M=*~G~a~rq=ar~i __
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures VERIFIER: ___
A~.T~*~S=ar=aw~it~---
- 7.
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
REFERENCES Simpson Gumpertz & Heger Inc., Evaluation of Control Room Makeup Air Intake Structure, 160268-CA-08 Rev. 0, Waltham, MA, May 2017.
Simpson Gumpertz & Heger, Inc., Evaluation and Design Confirmation of As-designed CEB 150252-CA-02 Rev 1, Waltham, MA, Dec. 2017.
Simpson Gumpertz & Heger Inc., Evaluation of Residual Heat Removal Equipment Vault, 160268-CA-06 Rev. 0, Waltham, MA, Dec 2016.
Simpson Gumpertz & Heger Inc., Evaluation of Condensate Storage Tank Enclosure Structure, 160268-CA-03 Rev. 0, Waltham, MA, Dec. 2016.
Simpson Gumpertz & Heger Inc., Evaluation of Containment Equipment Hatch Missile Shield Structure, 160268-CA-02 Rev. 0, Waltham, MA, Oct.
2016.
Simpson Gumpertz & Heger Inc., Evaluation of Containment Enclosure Ventilation Area, 160268-CA-05 Rev. 0, Waltham, MA, Mar. 2017.
Simpson Gumpertz & Heger, Inc., Evaluation of Main Steam and Feedwater West Pipe Chase & Personnel Hatch Structures 170443-CA-04 Rev. 0, Waltham, MA, Jan. 2018.
Simpson Gumpertz & Heger, Inc., Evaluation of Seismic Category I Electrical Manholes - Stage 1160268-CA-12 Rev. 0, Waltham, MA, Jan.
2018.
Response to RAl-08-Attachment 2 13 Revision 1
SIMPSON GUMPERTZ & HEGER I
Engineering of Structures and Building Enclosures CLIENT:
NextEra Energy Seabrook
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures APPENDIX A PROJECT NO:
170444 DATE: ---~D=
ec~2=0~17~--
BY: ----=
M~R=
.M=.G=a=
rq=a~r i __
VERIFIER: --~A~.
T~*~S=ar=
awi
=*~t __
TENSILE STRESS IN REBARS OF CONTROL ROOM MAKEUP AIR INTAKE STRUCTURE A1.
REVISION HISTORY Revision 0: Initial document.
A2.
OBJECTIVE OF CALCULATION The objective of this calculation is to compute the maximum tensile stress that can form in the rebars of Control Room Makeup Air Intake (CRMAI) structure.
A3.
RES UL TS AND CONCLUSIONS Table A 1 summarizes the tensile stress in rebars of the CRMAI structure calculated at critical locations.
The maximum tensile stress is 43.3 ksi computed for the horizontal rebar of east wall close to the interior of the structure and subjected to the second In Situ load combination.
Besides, although the stress due to internal ASR expansion is high for the base mat, the stress due to loading is small. Therefore, base mat does not govern the calculation of the maximum stress in rebars.
A4.
DESIGN DATA I CRITERIA See Section 4 of the calculation main body (Cale. 160268-CA-08 Rev. 0).
AS.
ASSUMPTIONS A5.1 Justified assumptions There are no justified assumptions.
AS.2 Unverified assumptions There are no unverified assumptions.
Response to RAl-08 Attachment 2 Appendix A
- A Revision 0
AG.
METHODOLOGY The critical demand that controlled the selection of threshold factor of the CRMAI structure was axial-flexure interaction along the horizontal strip of the east wall and close to the middle which is considered for evaluation. Additionally, the north-south strip of the base mat is also considered to check a location with high internal ASR expansion. Finite element analyses are conducted to calculate the axial force and bending moment at critical sections of the structure. The FE model and analysis method are similar to what explained in susceptibility evaluation of CRMAI structure [A 1 ]. The axial force and bending moments are calculated using section cuts method. The computed demands are:
LC1 for the walls: M = 5.2 kip-ft/ft, P = 49.8 kip/ft LC1 for the base mat: M = 20.8 kip-ft/ft, P = -28.4 kip/ft LC2 for the walls: M = 7.7 kip-ft/ft, P = 57.6 kip/ft LC2 for the base mat: M = 26.5 kip-ft/ft, P = -32.3 kip/ft To calculate the stress in rebars subjected to a combination of axial force and bending moment, sectional analysis based on fiber section method, as explained in calculation main body, is used. The calculation is conducted per 1 foot width of the walls/slabs, and each section is discretized into 20 fibers. An example calculation that evaluates the stress in rebars of the east wall is presented in Section A8. The Cl value for the base mat was 0.99 mm/m which included in the analysis to find the initial stress state due to internal ASR alone. Value of zero internal ASR is used for the walls as it leads to conservative demands.
A7.
REFERENCES
[A 1]
Simpson Gumpertz & Heger Inc., Evaluation of Control Room Makeup Air Intake structure, 160268-CA-08 Rev. 0, Waltham, MA, May 2017.
[A2]
United Engineers & Constructors Inc., Seabrook Station Structural Design Drawings.
[A3]
United Engineers & Constructors Inc., Design of Makeup Air Intake Structure, MT-28-Calc Rev. 2, Feb. 1984.
Response to RAl-08 Attachment 2 Appendix A
-A Revision 0
AS.
COMPUTATION A8.1. Strain in Steel and Concrete due to lnternalASR expansion Input Data ASR expansion Measured crack index Threshold factor Material properties Compressive strength of concrete Young's modulus of concrete Yield strength of steel Young's modulus of steel Geometry Width of fibers Total thickness or height Area of concrete Area of tensile reinforcement
(#8@12 in.)
Number of reinforcement in row, e.g. equal to 2 for tensile and compressive Depth to reinforcement mm Ecr:= O-m F1hr := 1.4 fc := -3ksi Ee := 3120ksi fy := 60ksi Es:= 29000ks*
b := 12i h := 24in Ac:= b*h = 288*in2 As:= 0.79in2 SteelNum := 2 d := 20.Si Ref. [A1)
Ref.[A2)
Finding the strain in steel and concrete by satisfying compatibility and equilibrium Initial Guess Initial mechanical strain in concrete Initial strain in steel Compatibility equation Equilibrium equation Response to RAl-08 Attachment 2 Appendix A Eo.conc := 0 Eo.steel := 0 Given Fthr" Ec1 = Eo.steel -
Eo.conc ans := Find( Eo.conc, Eo.stee1)
-A Revision 0
Initial strain in concrete and steel A8.2. Sectional Analysis Input Data Concrete Material Model Constitutive model for concrete Steel Material Model Constitutive model for steel Response to RAl-08 Attachment 2 Appendix A MATeone(E:) :=
0 if > 0 fe fe if E < -
Ee (Ee* E:) otherwise 0
~ MATeone( Ee)_ 2
~
ksi
(/) --
- 4
- 0.01
-£
- fy if E < _ Y Es (Es* E:) otherwise I
50 -
~ MATsteeI( Es)
~
0 -
~
ksi
(/) -- - 0.05
- A - 3
- 5x10 0
Strain I
I I
0 0.05 Strain Revision 0
Concrete Fibers Number of fibers Height of fibers Concrete fiber coordinates Concrete fiber strain Concrete fiber stress Concrete fiber force Reinforcement!Stee/ fibers Depth to reinforcement fiber Area of reinforcement fiber Steel fiber strain Steel fiber stress Steel fiber force Response to RAl-08 Attachment 2 Appendix A ConcNum := 20 h
ConcH :=
1.2* in ConcNum Coney :
for i E 1.. ConcNum h
ConcH ans.+-- -- + --- + (i - l)*ConcH I
2 2
ans Con cc( Ea.cone, E, tp) :=
for i E 1.. ConcNum ansi +--Ea.cone+ E - tp*Concyi ans Cancer( Ea.cone, E, tp) :=
for i E 1.. ConcNum ansi +-- MAT cone( Con cc( Ea.cone, E, tp) i) ans ConcF(c c en) *=
fio1*
0 E 1.. ConcNum
"'o.conc,c,,.-
- ans. +-- Conccr(Eo cone, E, tp): ( b* ConcH)
I I
ans Steely1 := -(d -~) = -8.S*in h
Steely := d - -
= 8.5*m 2
2
. 2 SteelAs := As= 0.79* m I
9. 2 SteelAs := As= 0.7 *m 2
Steele( Ea.steel, E, tp) :=
for i E 1.. SteelNum ansi +-- Ea.steel + E - tp* Steelyi ans Steelcr( Ea.steel> E, tp) :=
for I E 1.. SteelNum ansi +-- MA Tsteel( Steele( Ea.steel, E, tp) i) ans SteelF( Ea.steel, E, tp) :=
for i E 1.. SteelNum ans. +-- Steelcr( Ea.steel> E, tp): Steel As.
I I
I ans
-A Revision 0
Initial Stress State Initial stress in concrete Concretecr := Cone er( S0 cone, 0, 0)
Initial stress in steel Axial Equilibrium Force(so.conc,So.steebs,tp) :=
ansl +--- 0 for i E 1.. ConcNum ans 1 +--- ans 1 + ConcF( s 0 cone, s, tp).
I ans2 +--- 0 for i E 1.. Stee!Num ans2 +--- ans2 + Stee!F( so.steel> s, tp).
I ans +--- ans 1 + ans2 Moment Equilibrium Moment( So.cone, So.stee], s, tp) :=
ans 1 +--- 0 for i E 1.. ConcNum ans I +--- ans I + -1
- ConcF( so.cone, s, tp): Coney.
I 1
ans2 +--- 0 for i E I.. Stee!Num ans2 +--- ans2 + -1
- Stee!F( So.steeb s, tp): Steely.
I 1
ans +--- ansl + ans2 Response to RAl-08 Attachment 2 Appendix A
-A Revision 0
Solution Known parameters Axial force Iteration Curvature Solve for strain at centroid Axial strain at centroid (initial guess)
Axial force equilibrium Sectional forces p := 57.6kip
X,cp) - P Ecent := root( f( Xa), Xa) = 1.257 X 10- 3 Requires iteration Foree(Eo.conc,Eo.steel> Ecent><P) = 57.6*kip Moment( Ea.cone> Ea.steel> Ecent' <P) = 7.697* kip*ft Stress and strain in concrete and steel Steel fiber stress and strain Coneretey := Coney Concrete fiber stress and strain Maximum compressive strain in concrete Coneretee: - Coneretee: ConcNum ConcNum-1 (h ) Emax.comp :=
- - - Coney
... = 9.223 x Coney - Coney 2 ConcNum-1 ConcNum ConcNum-1 + Coneretee: ConcNum-1 Maximum compressive stress in concrete Response to RAl-08 Attachment 2 Appendix A - A Revision 0 A9. TABLES Table A 1: Stress in re bars at critical locations of CRMAI structure subjected to LC1 Total demands for sustained load (In Situ condition, Total stress in steel Maximum LC1) (ksi) compressive Component Item stress in Demand Location Rebar1 Rebar2 concrete (ksi) Out-of-plane 5.2 Walls moment (kip-ft/ft) East wall, horizontal strip, at the 36.2 26.8 0 middle of the wall Axial force (kip/ft) 49.8 Out-of-plane 20.8 Base mat moment (kip-ft/ft) North-south strip, at intersection with 27.8 26.4 -0.28 south walls Axial force (kip/ft) -28.4 Table A2: Stress in rebars at critical locations of CRMAI structure subjected to LC2 Total demands for sustained loads plus OBE amplified Total stress in steel Maximum with threshold factor (In Situ condition, LC2) (ksi) compressive Component Item stress in Demand Location Rebar1 Rebar 2 concrete (ksi) Out-of-plane 7.7 Walls moment (kip-ft/ft) East wall, horizontal strip, at the 43.3 29.6 0 middle of the wall Axial force (kip/ft) 57.6 out-ot-plane 26.5 Base mat moment (kip-ft/ft) North-south strip, at intersection with 39.1 37.3 -0.33 south walls Axial force (kip/ft) -32.3 Example in Section A8 A10. FIGURES There are no figures. Response to RAl-08 Attachment 2 Appendix A -A Revision 0 SIMPSON GUMPERTZ & HEGER I Engineering of Structures and Building Enclosures CLIENT: NextEra Energy Seabrook
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures APPENDIX B PROJECT NO:
170444 DATE: ---~D~ec~2~0~17~--
BY: ----~O~O~E~rb~av~--
VERIFIER: ___
A~T~S~a~ra~w~it __
TENSILE STRESS IN REBAR AND CONCRETE OF CONTAINMENT ENCLOSURE BUILDING STRUCTURE B1.
REVISION HISTORY Revision 0: Initial document.
B2.
OBJECTIVE OF CALCULATION The objective of this calculation is to compute the maximum tensile stress that can form in the rebars and the maximum compressive stress that can form in concrete sections of the Containment Enclosure Building (CEB) structure.
B3.
RESULTS AND CONCLUSIONS Table 81 through 84 summarizes the stress results in rebar and concrete sections of the CEB structure calculated at critical locations. The Maximum tensile stress is 55.6 ksi in the wall at the east side of electrical penetration at Elev. 45 ft subjected to the second in-situ load combination (LC2).
B4.
DESIGN DATA I CRITERIA See Section 4 of the calculation main body (Cale. 150252-CA-02 Rev. 1 ).
B5.
ASSUMPTIONS B5.1 Justified assumptions There are no justified assumptions.
B5.2 Unverified assumptions There are no unverified assumptions.
Response to RAl-08 Attachment 2 Appendix B
- B Revision 0
- 86.
METHODOLOGY The critical demands that control the selection of the threshold factor for the CEB structure are out-of-plane moment and axial load interaction at various sections of the wall surface. Finite element analyses were conducted to calculate the axial force and bending moment at these locations due to ASR load [B1].
To calculate the stress in rebars subjected to a combination of axial force and bending moment, sectional analysis based on fiber section method, as explained in calculation main body, is used. The calculation is conducted per 1 foot width of the walls, and each section is discretized into 20 fibers. An example calculation that evaluates the stress in the vertical rebars at the section of the wall on the east side of the electrical penetration and at Elev. 45 ft. is presented in Section B8. The ASR expansion of the CEB wall is included in the analysis to find the initial stress state due to internal ASR alone.
- 87.
REFERENCES
[B1]
Simpson Gumpertz & Heger Inc., Evaluation of Containment Enclosure Building Structure, 150252-CA-02 Rev. 1, Waltham, MA, Dec 2017.
[B2]
United Engineers & Constructors Inc., Seabrook Station Structural Design Drawings.
Response to RAl-08 Attachment 2 Appendix B
- B Revision 0
- 88.
COMPUTATION 88.1. Strain in Steel and Concrete due to Internal ASR expansion Input Data ASR expansion Measured crack index Threshold factor Material properties Compressive strength of concrete Young's modulus of concrete Yield strength of steel Young's modulus of steel Geometry Width of fibers Total thickness or height Area of concrete Area of tensile reinforcement Number of reinforcement in row, e.g. equal to 2 for tensile and compressive Depth to reinforcement Response to RAl-D8 Attachment 2 Appendix B mm ScJ := 0.10 - m F1hr := 1.3 fc := -4ksi Ee := 360Sksi fy := 60ksi E5 := 29000ks*
b := 12in h := !Sin A,, := b*h = 180*in2 SteelNum := 2 d := !Sin - 3.60in = I l.4*i 3 -
Ref. [81]
Ref. [82]
Revision 0
Finding the strain in steel and concrete by satisfying compatibility and equilibrium Initial Guess Initial mechanical strain in concrete Initial strain in steel Compatibility equation Equilibrium equation Initial strain in concrete and steel 88.2. Sectional Analysis Input Data Concrete Material Model Kent & Park Model Strain at Peak compressive strength Strain at 50% compressive strength Model parameter Residual compressive strength Constitutive model for concrete
~
co.cone := 0 co.steel := 0 Given ans := Find( e:o.conc, co.steel)
Eco := - 0.002!
fc 3 - 0.002*-
psi 3
E:sou := ----- = -3.667 x 10-fc
+ 1000 psi 0.5 z := ---- = - 300 MAT cone( e:) :=
min[fc.res Jc{ I - Z* ( e: - Eco)] if e: < Eco
~[ ~~ - (,:)']
- f 'ro < ' <O 0 if 0
- ::; e:
o,..._-------~
~ MAT cone( e:c)_ 2
~
ksi
[/) --
- 4
- 0.01 0
Strain Response to RAl-08 Attachment 2 Appendix B 4 -
Revision 0
Steel Material Model Constitutive model for steel
-£
-fy if E < _ Y Es (E5*c:) otherwise I
I 50
~
~
~ MATstee1{c:s)
~
0
~
~
ksi
(;) -
I
- 0.05 0
0.05 Concrete Fibers Strain Number of fibers ConeNum := 20 Height of fibers h
ConeH :=
0.75*in ConeNum Concrete fiber coordinates Coney :
for i E 1.. ConeNum h
Cone8 ans. +-- -- + --- + (i - l)*Cone8 I
2 2
ans Concrete fiber strain Conei Eo.conc, E, t.p) :=
for i E 1.. ConeNum ansi +-- Eo.conc + E - i.p*Coneyi ans Concrete fiber stress Cone er( Eo.conc, E, i.p) :=
for I E 1.. ConeNum ansi +-- MAT cone( Cone1,,( Eo.conc, E, i.p) i) ans Concrete fiber force Conep( Eo.conc, E, t.p) :=
for i E 1.. ConeNum ansi +-- Cone er( Eo.conc, E, i.p) i. ( b* ConeH) ans Response to RAl-08 Attachment 2 Appendix B
- B Revision 0
Reinforcement!Steel fibers Depth to reinforcement fiber Area of reinforcement fiber Steel fiber strain Steel fiber stress Steel fiber force Initial Stress State Initial stress in concrete Initial stress in steel Axial Equilibrium Response to RAl-08 Attachment 2 Appendix B Steely1 := -(d -~) = -3.9*in h
9
- Steely := d - -
= 3. *m 2
2
. 2 SteelAs :=As = l*m I
Steel As := As = l *in 2 2
Steele:( Ea.steel> E, lp) :=
for i E 1.. SteelNum ansi +-- Ea.steel + E - lp* Steely i ans Steela( Ea.steel> E, lp) :=
for 1 E 1.. SteelNum ansi +-- MAT steel( Steele( Ea.steel, E, lp) i) ans SteelF( Ea.steel, E, lp) :=
for i E 1.. SteelNum ans1. +-- Steelcr( Ea.steel, E, lp).
- SteelAs.
1 1
ans Concretecr := Conca( Ea.cone, 0, 0)
Force(Eo.conc,Eo.steel> E,lp) :=
ansl +-- 0 for i E 1.. ConcNum ans 1 +-- ans 1 + ConcF( E 0 cone, E, lp) i ans2 +-- 0 for i E 1.. SteelNum ans2 +-- ans2 + SteelF( E 0 steel> E, lp).
1 ans +-- ans 1 + ans2
- B Revision 0
Moment Equilibrium Solution Known parameters Axial force Iteration Curvature Solve for strain at centroid Axial strain at centroid (initial guess)
Axial force equilibrium Sectional forces Stress and strain in concrete and steel Steel fiber stress and strain Concrete fiber stress and strain Response to RAl-08 Attachment 2 Appendix B Moment( So.cone, So.steel> s, i.p) :=
ans 1 +--- 0 for i E 1.. ConeNum ans 1 +--- ans 1 + -1
- Conep( so.cone, s, i.p): Coney.
I I
ans2 +--- 0 for i E 1.. Stee!Num ans2 +--- ans2 + -1
- Stee!p( S0 steel> s, i.p): Steely.
I I
ans +--- ans 1 + ans2 p := 52.80kip f(x) := Foree(so.conc,Sosteel>X,cp)- P Scent := root( f( Xo), Xo) = 1.063 x 10- 3 Requires iteration Foree(so.conc,So.steel,Scent,¢) = 52.S*kip Moment( so.cone> So.steel> Scent>¢) = 22.807* kip*ft Coneretey := Coney
- B Revision 0
Maximum compressive strain in concrete Concrete£
- Concrete£ ConCNum ConCNum-1 (h
)
-4 max.comp:=
- Coney
... = -3.67 x 10 Coney
- Coney 2
ConcNum-1 ConCNum ConCNum-1
+Concrete£ ConcNum-1 Maximum compressive stress in concrete
- 89. TABLES Table 81. Stress in Rebar and Concrete of Structural Components Subjected to LC1 Standard Case Total stress in steel Maximum (ksi) stress and Comp.
Demand Location strain in Rebar1 Rebar2 concrete (ksi) [in.fin.]
Wall M = 459.5 (kip-ft/ft)
Wall near
-2.21 36 in.
foundation.
27.1 5.60
[-6.61e-4]
P=-141.2 (kip/ft)
Horz. cut.
Wall M = 1.94 (kip-fUft)
Wall above Elec.
0.0 15 in.
13.2 7.18
[2.25e-5]
p = 20.33 (kip/ft)
Horz. cut.
Wall M = -39.58 (kip-ft/ft)
Below personal
-0.71 24.6 2.73 27 in.
p = 14.07 (kip/ft) hatch. Vert. cut.
[-1.88e-4]
Wall M = -34.00 (kip-ft/ft)
Side of personal
-0.57 19.5 2.78 27 in.
P=11.05 (kip/ft) hatch. Vert. cut.
[-1.49e-4]
Response to RAl-08 Attachment 2 Appendix B
- B Revision 0
Table 82. Stress in Rebar and Concrete of Structural Comaonents subiected to LC2 Standard Case Total stress in steel Maximum (ksi) stress and Comp.
Demand Location strain in Rebar1 Rebar2 concrete (ksi) [in.fin.]
Wall M = 614.7 (kip-ft/ft)
Wall near
-2.68 36 in.
foundation.
42.5 1.97
[-8.507e-4]
p = 10.48 (kip/ft)
Horz. cut.
Wall M = 432.1 (kip-ft/ft)
Wall near
-2.48 36 in.
foundation.
20.6 2.16
[-7.69e-4]
p = -391.3 (kip/ft)
Horz. cut.
Wall M =22.81 (kip-ft/ft)
Wall above Elec.
-1.33 15 in.
55.6 12.9
[-3.67e-4]
p = 52.80 (kip/ft)
Horz. cut.
Wall M = -12.92 (kip-ft/ft)
Wall above Elec.
-0.78 15 in.
17.2 3.96
[-2.042e-4]
p = 4.70 (kip/ft)
Horz. cut.
Wall M = -6.57 (kip-ft/ft)
Below personal 0.0 25.9 19.7 27 in.
p = 57.80 (kip/ft) hatch. Vert. cut.
[5.05e-4]
Wall M = -92.23 (kip-ft/ft)
Below personal
-1.54 37.0
-1.17 27 in.
P=-15.28 (kip/ft) hatch. Vert. cut.
[-4.32e-4]
Wall M= -1.18 (kip-ft/ft)
Side of personal 0.0 22.5 21.4 27 in.
p = 55.82 (kip/ft) hatch. Vert. cut.
[6.00e-4]
Wall M = -80.76 (kip-ft/ft)
Side of personal
-1.29 27.8
-0.83 27 in.
p = -21.38 (kip/ft) hatch. Vert. cut.
[-3.55e-4]
Response to RAl-08 Attachment 2 Appendix B
- B Revision 0
Table 83. Stress in Rebar and Concrete of Structural Components Subjected to LC1 Standard-Plus Case Total stress in steel Maximum (ksi) stress and Comp.
Demand Location strain in Rebar1 Rebar2 concrete (ksi) [in.fin.]
Wall M = 459.2 (kip-ft/ft)
Wall near
-2.21 36 in.
foundation.
27.1 5.58
[-6.61e-4]
p = -142.2 (kip/ft)
Horz. cut.
Wall M = 1.69 (kip-ft/ft)
Wall above Elec.
0.0 15 in.
12.5 7.34
[4.03e-5]
p = 19.88 (kip/ft)
Horz. cut.
Wall M = -39.25 (kip-ft/ft)
Below personal
-0.71 24.6 2.73 27 in.
p = 13.92 (kip/ft) hatch. Vert. cut.
[-1.88e-4]
Wall M = -33.66 (kip-ft/ft)
Side of personal
-0.57 19.3 2.79 27 in.
P=11.03 (kip/ft) hatch. Vert. cut.
[-1.47e-4]
Response to RAl-D8 Attachment 2 Appendix B
- B Revision 0
Table 84. Stress in Rebar and Concrete of Structural Components Subjected to LC2 Standard-Plus Case Total stress in steel Maximum (ksi) stress and Comp.
Demand Location strain in Rebar1 Rebar2 concrete (ksi) [in.fin.]
Wall M = 614.4 (kip-ft/ft)
Wall near
-2.68 36 in.
foundation.
42.4 1.97
[-8.51e-4]
p = 9.38 (kip/ft)
Horz. cut.
Wall M = 431.8 (kip-ft/ft)
Wall near
-2.48 36 in.
foundation.
20.6 2.19
[-7.67e-4]
p = -392.3 (kip/ft)
Horz. cut.
Wall M =22.45 (kip-ft/ft)
Wall above Elec.
-1.32 15 in.
54.9 12.8
[-3.62e-4]
p = 52.29 (kip/ft)
Horz. cut.
Wall M=-13.08 (kip-ft/ft)
Wall above Elec.
-0.78 15 in.
17.1 3.90
[-2.06e-4]
p = 4.25 (kip/ft)
Horz. cut.
Wall M = -6.24 (kip-ft/ft)
Below personal 0.0 25.9 19.7 27 in.
p = 57.62 (kip/ft) hatch. Vert. cut.
[5.05e-4]
Wall M = -91.80 (kip-ft/ft)
Below personal
-1.54 37.0
-1.17 27 in.
p = -15.46 (kip/ft) hatch. Vert. cut.
[-4.32e-4]
Wall M = -0.85 (kip-ft/ft)
Side of personal 0.0 22.4 21.5 27 in.
p = 55.76 (kip/ft) hatch. Vert. cut.
[6.07e-4]
Wall M = -80.25 (kip-ft/ft)
Side of personal
-1.29 27.5
-0.81 27 in.
p = -21.39 (kip/ft) hatch. Vert. cut.
[-3.52e-4]
- 89. Figures There are no figures Response to RAl-08 Attachment 2 Appendix B
- B Revision 0
SIMPSON GUMPERTZ & HEGER I
Engineering of Structures and Building Enclosures CLIENT:
NextEra Energy Seabrook
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures APPENDIX C PROJECT NO:
170444 DATE: ---~D~ec~2=0~17~--
BY: ----~G~.
~Ts=a~m=pr=as~-
VERIFIER: --~
A~
. T~*~S=ar=awi~
- t~-
TENSILE STRESS IN REBARS OF RESIDUAL HEAT REMOVAL EQUIPMENT VAULT STRUCTURE C1.
REVISION HISTORY Revision 0: Initial document.
C2.
OBJECTIVE OF CALCULATION The objective of this calculation is to compute the maximum tensile stress that can form in the reinforcing steel rebars of Residual Hear Removal Equipment Vault (RHR) structure.
C3.
RESULTS AND CONCLUSIONS Table C1 summarizes the tensile stress in rebars of the RHR structure calculated at critical locations. The maximum tensile stress is 59.5 ksi computed for the vertical rebar of east interior wall at approximate El.(-) 45 ft. and subjected to the second in situ load combination. However, per RHR susceptibility evaluation [C1] and original design calculation [C3], the vertical rebars are not the primary load path.
Essentially, the wall were designed to span horizontally. The next highest stress value is 56.5 ksi that is computed for the east exterior wall.
C4.
DESIGN DATA I CRITERIA See Section 4 of the calculation main body (Cale. 160268-CA-06 Rev. 0).
CS.
ASSUMPTIONS C5.1 Justified assumptions There are no justified assumptions.
C5.2 Unverified assumptions There are no unverified assumptions.
Response to RAl-08 Attachment 2 Appendix C
- C Revision 0
C6.
METHODOLOGY The most critical stress demand in the horizontal rebars of the RHR structure is primarily due to the axial-flexure interaction along the vertical section cut in the south side of the east exterior wall. The highest stress demand in the vertical rebars of the RHR structure is primarily due to tension in the east and west interior walls.
Finite element analyses are conducted to calculate the axial force and bending moment at critical sections of the structure. The FE model and analysis method are similar to what explained in susceptibility evaluation of RHR structure [C1]. The axial force and bending moments are calculated using the method of section cuts.
Sectional analysis based on fiber section method is used to calculate the stress in the rebars of a section of a wall subjected to a combination of axial force and bending moment, as explained in calculation main body. Each wall section is discretized into 20 fibers of 1 ft width. An example calculation that evaluates the stress in the rebars of the east exterior wall is presented in Section C8. The Cl value for the exterior wall was 0. 75 mm/m which included in the analysis to find the initial stress state due to internal ASR alone.
Zero internal ASR is used for the interior walls.
Figure C1 shows the contour plots of vertical strains in the interior walls due to LC1. The contour plots show that the overall vertical strains are reasonable compared to the yielding strain of rebars (i.e., 0.02% in/in). Localized strain concentration is observed close to the door openings at approximate El. (-) 30 ft. and El. (-) 45 ft.. Ductile distribution of local demands along the width of the interior walls is possible. As a result, localized strain concentration is not of concern.
C7.
REFERENCES
[C1]
Simpson Gumpertz & Heger Inc., Evaluation of Residual Heat Removal Equipment Vault, 160268-CA-06 Rev. 0, Waltham, MA, August 2017.
[C2]
United Engineers & Constructors Inc., Seabrook Station Structural Design Drawings.
[C3]
United Engineers & Constructors Inc., Analysis and Design of Vault Walls up to El. 23 ft.,
PB-30 Cale Rev. 9, Dec. 2002.
Response to RAl-08 Attachment 2 Appendix C
- C Revision 0
CB.
COMPUTATION CB.1 Strain in Steel and Concrete due to Internal ASR expansion Input Data ASR expansion Measured crack index Threshold factor Material properties Compressive strength of concrete Young's modulus of concrete Yield strength ofsteel Young's modulus of steel Geometry Width of fibers Total thickness or height Area of concrete Area of tensile reinforcement
(#8@9 in.)
Number of reinforcement in row, e.g. equal to 2 for tensile and compressive Depth to reinforcement mm Ecr := 0.75 - m F1hr := 1.0 fc := -3ksi Ee := 3 I 20ksi fy := 60ksi Es := 29000k;i b := 12in h := 24i Ac:= b*h = 288*in2 12. 2
. 2 As:= 0.79* -
m = l.0)3*m 9
SteelNum := 2 d := 20.Sin Ref. [C1]
Ref.[C2]
Finding the strain in steel and concrete by satisfying compatibility and equilibrium Initial Guess Initial mechanical strain in concrete Initial strain in steel Compatibility equation Equilibrium equation Initial strain in concrete and steel Response to RAl-08 Attachment 2 Appendix C Ea.cone:= 0 Ea.steel := 0 Given (Ec"Ac)*Eo.conc + (Es*As*Stee!Num}Eo.steel = 0 ans := Find( Ea.cone, Ea.steel)
- C Revision 0
C8.2 Sectional Analysis Input Data Concrete Material Model Constitutive model for concrete Steel Material Model Constitutive model for steel Response to RAl-08 Attachment 2 Appendix C MATeone(E:) :=
0 if > 0 fe fe if< -
Ee (Ee* s) otherwise 0
~ MATconc( Ee)_ 2
~
ksi
(/) --
,..--, g MATstee1(i=:s)
~
ksi
(/) --
-4
- 0.01
-£
-fy if< _ Y Es (E5*s) otherwise I
50
~
0 r
- 50 r
- 0.05
- C 0 Strain I
I I
0 0.05 Strain Revision 0
Concrete Fibers Number of fibers Height of fibers Concrete fiber coordinates Concrete fiber strain Concrete fiber stress Concrete fiber force Reinforcement/Steel fibers Depth to reinforcement fiber Area of reinforcement fiber Steel fiber strain Steel fiber stress Steel fiber force Response to RAl-08 Attachment 2 Appendix C ConcNum := 20 h
ConeH :=
1.2* i ConeNum Coney :
for i E 1.. ConeNum h
Cone8 ans.+-- -- + --- + (i - l)*Cone8 I
2 2
ans Cone,;:( Ea.cone, E, <.p) :=
for i E 1.. ConeNum ansi +-- Ea.cone+ E - tp*Coneyi ans Conecr( Ea.cone, E, <.p) :=
for i E 1.. ConeNum ansi +-- MAT cone( ConeE( Ea.cone, E, <.p) i) ans ConeF( Ea.cone, E, <.p) :=
for i E 1.. ConeNum ansi +-- Conecr(Eo.conc,E,<.p)i*(b*ConeH) ans Steely 1 := -( d - ~) = -8.5* in h
Steely := d - -
= 8.5*m 2
2
. 2 SteelAs := As= 1.053-m 1
. 2 SteelAs := As= l.053*m 2
Stee!E( Ea.steel> E, <.p) :=
for i E 1.. SteelNum ansi +-- Ea.steel + E -
<.p* Steelyi ans Steelcr( Ea.steel, E, <.p) :=
for i E 1.. SteelNum ansi +-- MA Tsteel( Stee!E( Ea.steel> E, <.p )i) ans SteelF( Ea.steel, E, <.p) :=
for i E 1.. SteelNum ans1. +-- Steelcr( Ea.steel, E, <.p) : Steel As.
I I
ans
- C Revision 0
Initial Stress State lnttial stress in concrete Concretecr := Cone er( s o.cone, 0, 0) lnttial stress in steel Rebarcr := Steelcr( so.steel, 0, 0)
Axial Equilibrium Force( So.cone, So.steel> s, tp) :=
ansl ~ 0 for i E 1.. ConcNum ansl ~ ansl + ConcF(soconc,s,tp).
I ans2 ~ 0 for i E 1.. Stee!Num ans2 ~ ans2 + Stee!F( E:0 steel> s, tp).
I ans ~ ans 1 + ans2 Moment Equilibrium Moment( so.cone, so.steel, s, tp) :=
ans 1 ~ 0 for i E 1.. ConcNum ans 1 ~ ans 1 + - 1
- ConcF( so.cone, s, tp): Coney.
I I
ans2 ~ 0 for i E 1.. Stee!Num ans2 ~ ans2 + - 1
- Stee!F( so.steel> s, tp): Steely.
I I
ans ~ ans 1 + ans2 Response to RAl-08 Attachment 2 Appendix C
- C Revision 0
Solution Known parameters Axial force Iteration Curvature Solve for strain at centroid Axial strain at centroid (initial guess)
Axial force equilibrium Sectional forces Stress and strain in concrete and steel Steel fiber stress and strain Concrete fiber stress and strain Maximum compressive stress in concrete Response to RAl-08 Attachment 2 Appendix C p := -35kip 1
¢ := -0.000072--
in f(x) := Force(i::o.conc,Eo.steei>X,¢) - P Ecent := root( f( Xo), Xo) = 3.028 x 10- 4 Requires iteration Moment( Eo.conc> co.steel> Ecent> ¢) = -100.015
- kip*ft Concretey := Coney
- C Revision 0
C9.
TABLES Table C1: Stress in rebars at critical locations of RHR structure subjected to LC1 Total demands for sustained load (In Situ Total stress in steel (ksi)
Maximum condition, LC1) compressive Component Item stress in Demand Location Rebar1 Rebar2 concrete (ksi)
Moment about the vertical East exterior wall, vertical
-98.5 Wall global axis strip, at the approximate El.
46.9 11.4
-1.9 (kip-ft/ft)
(-) 30 ft Axial force
-35.0 (kip/ft)
Moment about the horizontal East interior wall, horizontal 28.6 Wall global axis strip, at the approximate El.
41.6 5.5 0.0 (kip-ft/ft)
(-) 45 ft Axial force 37.2 (kip/ft)
Moment about the horizontal 11.0 West interior wall, horizontal global axis Wall strip, at the approximate El.
26.5 12.5 0.0 (kip-ft/ft)
Axial force
(-) 30 ft 30.8 (kip/ft)
Table C2: Stress in rebars at critical locations of RHR structure subjected to LC2 Total demands for sustained load (In Situ Total stress in steel (ksi)
Maximum condition, LC1) compressive Component Item stress in Demand Location Rebar 1 Rebar2 concrete (ksi)
Moment about the vertical East exterior wall, vertical global axis
-119.5 Wall strip, at the approximate El.
56.5 13.8
-2.1 (kip-ft/ft)
(-) 30 ft Axial force
-40.8 (kip/ft)
Moment about the horizontal East interior wall, horizontal 33.0 Wall global axis strip, at the approximate El.
59.5 17.7 0.0 (kip-ft/ft)
(-) 45 ft Axial force 60.9 (kip/ft)
Moment about the horizontal 13.4 West interior wall, horizontal global axis Wall (kip-ft/ft) strip, at the approximate El.
36.6 19.6 0.0 Axial force
(-) 30 ft 44.4 (kip/ft)
Response to RAl-08 Attachment 2 Appendix C
- C Revision 0
C10.
FIGURES
- I
- L*.*[1t:.-0J
. ~ :..... r.-1:.*::t
~ *~.:.. r.- i:>:;
~ :J
- t. ~1!5:
M oo~::
' :n:c:.;-IJ]
, "T)?S-l:rl
. 01)ll f!Z
, IJQl'JE i Figure C1: Contour plots of vertical strains in the interior walls due to LC1 Response to RAl-08 Attachment 2 Appendix C
- C Revision 0
SIMPSON GUMPERTZ & HEGER I
Engineering of Structures and Building Enclosures CLIENT:
NextEra Energy Seabrook
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures APPENDIX D PROJECT NO:
170444 DATE: ---~D=ec,,_,2=
0_,_,17 __
BY: -------'-'RW"'-'-'-'K=ee'"'"'n"""-
e __
VER! FIER: ----'-"A T_,_,S=a=ra,_,_,w_,_,_it __
TENSILE STRESS IN REBARS OF CONDENSATE STORAGE TANK ENCLOSURE STRUCTURE D1.
REVISION HISTORY Revision 0: Initial document.
D2.
OBJECTIVE OF CALCULATION The objective of this calculation is to compute the maximum tensile stress that can form in the rebars of the Condensate Storage Tank Enclosure (CSTE) structure.
D3.
RESULTS AND CONCLUSIONS Table 01 summarizes the tensile stress in rebars of the CSTE structure calculated at critical locations. The Maximum tensile stress is 26.7 ksi at the bottom of the tank enclosure wall subjected to the second in situ load combination (LC2).
D4.
DESIGN DATA I CRITERIA See Section 4 of the calculation main body (Cale. 160268-CA-03 Rev. 0).
D5.
ASSUMPTIONS D5.1 Justified assumptions There are no justified assumptions.
D5.2 Unverified assumptions There are no unverified assumptions.
Response to RAl-08 Attachment 2 Appendix D
- D Revision 0
- 06.
METHODOLOGY The critical demands that control the selection of the threshold factor for the CSTE structure are hoop tension at the top of the tank enclosure wall, and vertical moment at the base of the tank enclosure wall.
Finite element analyses were conducted to calculate the axial force and bending moment at these locations due to ASR load [D1].
To calculate the stress in rebars subjected to a combination of axial force and bending moment, sectional analysis based on fiber section method, as explained in calculation main body, is used. The calculation is conducted per 1 foot width of the walls, and each section is discretized into 20 fibers. An example calculation that evaluates the stress in the vertical rebars at the base of the tank enclosure wall is presented in Section D8. The ASR expansion of the tank enclosure is included in the analysis to find the initial stress state due to internal ASR alone.
- 07.
REFERENCES
[D1]
Simpson Gumpertz & Heger Inc., Evaluation of Condensate Storage Tank Enclosure Structure, 160268-CA-03 Rev. 0, Waltham, MA, Dec 2016.
[D2]
United Engineers & Constructors Inc., Seabrook Station Structural Design Drawings.
[D3]
United Engineers & Constructors Inc., Condensate Storage Tank Mat and Wall Reinforcement, MT-21, Rev. 3, Jan. 1984.
Response to RAl-08 Attachment 2 Appendix D
- D Revision 0
- 08.
COMPUTATION 08.1. Strain in Steel and Concrete due to lntemalASR expansion Input Data ASR expansion Measured crack index Threshold factor Material properties Compressive strength of concrete Young's modulus of concrete Yield strength ofsteel Young's modulus of steel Geometry Width of fibers Total thickness or height Area of concrete Area of tensile reinforcement
(#11@12 in.)
Number of reinforcement in row, e.g. equal to 2 for tensile and compressive Depth to reinforcement mm Ecr := 0.43 - m Fthr := 1.6 fc := -4ksi Ee:= 3605ksi fy := 60ks Es:= 29000ks*
b := 12in h := 24in Ac:= b*h = 288*in2 6" 2 As:=l.5m SteelNum := 2 d := 20.3in Ref. [01]
Ref.[02]
Finding the strain in steel and concrete by satisfying compatibility and equilibrium Initial Guess Initial mechanical strain in concrete Initial strain in steel Compatibility equation Equilibrium equation Response to RAl-08 Attachment 2 Appendix D Ea.cone := 0 Ea.steel := 0 Given Fthr" Ec1 = Ea.steel - Ea.cone ans := Find( Ea.cone, Ea.steel)
- D Revision 0
Initial strain in concrete and steel 08.2. Sectional Analysis Input Data Concrete Material Model Constitutive model for concrete Steel Material Model Constitutive model for steel Response to RAl-D8 Attachment 2 Appendix D MATconcCc) :=
0 if E: > 0 fc fc if E: < -
Ee (Ec*c) othe1wise 0
~
~ MATconc( Ee)_ 2
~
ksi Ul --
- 0.01 MATsteeJ(E:) :=
-£
-fy if E: < _ Y Es (E5*c) otheiwise I
50 -
~
g MATstee!( c:s)
~
0 -
~
ksi ifJ -- - 0.05
- D - 5xl0 -3 0
Strain I
' 1 I
0 0.05 Strain Revision 0
Concrete Fibers Number of fibers Height of fibers Concrete fiber coordinates Concrete fiber strain Concrete fiber stress Concrete fiber force Reinforcement/Steel fibers Depth to reinforcement fiber Area of reinforcement fiber Steel fiber strain Steel fiber stress Steel fiber force Response to RAl-08 Attachment 2 Appendix D ConcNum:= 20 h
ConcH :=
1.2* i1 ConcNum Coney :
for i E 1.. ConcNum h
ConcH ans.*- - -
+ --- + (i - l)*ConcH I
2 2
ans Co nee( co.cone, c, i.p) :=
for i E 1.. ConcNum ansi *- co.cone + c - i.p* Concyi ans Cancer( co.cone, c, i.p) :=
for i E 1.. ConcNum ansi *- MAT cone( Conce( co.cone, c, lp) J ans ConcF( co.cone, c, i.p) :=
for i E 1.. ConcNum ansi *- Cancer( c 0 cone, c, i.p \\*(b*ConcH) ans Steely 1 := - ( d - ~) = - 8.3* in h
Steely := d - -
= 8.3* m 2
2
. 2 SteelAs := As = l.56*m I
. 2 SteelAs := As= l.56*m 2
Steele( co.steel> c, i.p) :=
for i E 1.. SteelNum ansi *-co.steel + c - lp*Steelyi ans Steeler( c0 steel> c, lp) :=
for i E 1.. SteelNum ansi *- MA Tsteel( Steele( co.steel, c, lp) J ans SteelF( co.steel, c, lp) :=
for i E 1.. SteelNum ans1. *- Steeler( co.steel, c, lp): Steel As.
I I
ans
- D Revision 0
Initial Stress State Initial stress in concrete Concretecr := Conccr( s o.cone, 0, 0)
Initial stress in steel Rebarcr := Steelcr( So.steel> 0, 0)
Axial Equilibrium Force( So.cone, So.steel> s, tp) :=
ans 1 ~ 0 for i E 1.. ConcNum ans 1 ~ ans 1 + ConcF( so.cone, s, tp).
I ans2 ~ 0 for i E 1.. SteelNum ans2 ~ ans2 + SteelF( So.steel, s, tp).
I ans ~ ans 1 + ans2 Moment Equilibrium Moment( so.cone, s 0 steel, s, tp) :=
ans 1 ~ 0 for i E 1.. ConcNum ansl ~ ansl + - l*ConcF(so.conc,s,tp).-concy.
I I
ans2 ~ 0 for i E 1.. SteelNum ans2 ~ ans2 + - 1
- SteelF( so.steel> s, tp): Steely.
I I
ans ~ ansl + ans2 Response to RAl-08 Attachment 2 Appendix D 6 -
Revision 0
Solution Known parameters Axial force Iteration Curvature Solve for strain at centroid Axial strain at centroid (initial guess)
Axial force equilibrium Sectional forces p := - 12.9kip f(x) := Force( So.cone, So.steel> x, <P) - P Scent := root( f( Xo), Xo) = 6. 778 X 10- S Requires iteration Force( So.cone> So.steel> Scent>¢) = - 12.9* kip Moment( so.cone> 0 steel> Scent> <P) = 65.634* kip*ft Stress and strain in concrete and steel Steel fiber stress and strain Concrete fiber stress and strain Maximum compressive strain in concrete Concretey := Coney Concrete£
- Concrete£
(
)
ConCNum ConCNum-1 h
max.comp:= ---------------. -
- Coney
... = - 3.066 x Coney
- Coney 2
ConcNum-1 ConcNum ConCNum-1
+Concrete£ ConcNum-1 Maximum compressive stress in concrete Response to RAl-08 Attachment 2 Appendix D
- D Revision 0
- 09.
TABLES Table 01: Stress in rebars at critical locations of CSTE structure subjected to LC1 Total demands for sustained load (In Total stress in steel (ksi)
Maximum Situ condition, LC1) compressive Component Item stress in Demand Location Rebar1 Rebar2 concrete (ksi)
Out-of-plane 0
moment (kip-Wft)
Top of tank enclosure wall, 16.3 16.3
-0.14 horizontal direction Tank Axial force (kip/ft) 41.4 Enclosure Wall Out-of-plane 41 moment (kip-Wft)
Bottom of tank enclosure 15.8 8.6
-0.68 wall, vertical direction Axial force (kip/ft)
-12.9 Table 02: Stress in rebars at critical locations of CSTE structure subjected to LC2 Total demands for sustained loads plus Maximum Component Item OBE amplified with threshold factor (In Total stress in steel (ksi) compressive Situ condition, LC2) stress in Demand Location Rebar1 Rebar2 concrete (ksi)
Out-of-plane 0
Top of tank enclosure wall, moment (kip-Wft) horizontal direction 26.0 26.0
-0.23 Tank Axial force (kip/ft) 66.2 Enclosure Wall Out-of-plane 65.7 moment (kip-Wft)
Bottom of tank enclosure 26.7 13.9
-1.11 wall, vertical direction Axial force (kip/ft)
-12.9 010.
FIGURES Example in Section DB There are no figures.
Response to RAl-DB Attachment 2 Appendix D
- D Revision 0
r lMPSON GUMPERTZ & HEGER I
Engineering of Structures and Building Enclosures CLIENT:
NextEra Energy Seabrook
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures APPENDIX E PROJECT NO: _
_____,1-'-70=--4'-'4-'-4 __
DATE: ---~F~eb~2~0~
17~--
BY: ----~M~R=.M~.G
~a~rg~a~
ri __
VERIFIER: --~A~
. T~
- ~S=ar=aw=it~-
TENSILE STRESS IN REBARS OF CONTAINMENT EQUIPMENT HATCH MISSILE SHIELD STRUCTURE E1.
REVISION HISTORY Revision 0: Initial document.
Revision 1: Revised page E-1 to update Revision history section. Revised page E-2 from Revision 0 to 1 to make editorial correction references to Section A8 to E8.
E2.
OBJECTIVE OF CALCULATION The objective of this calculation is to compute the maximum tensile stress that can form in the rebars of Containment Equipment Hatch Missile Shield (CEHMS) structure.
E3.
RESULTS AND CONCLUSIONS Table E1 summarizes the tensile stress in rebars of the CEHMS structure calculated at critical locations.
The maximum tensile stress is 41.2 ksi computed for the eat wing wall at the intersection with the column.
E4.
DESIGN DATA I CRITERIA See Section 4 of the calculation main body (Cale. 160268-CA-02 Rev. 0).
E5.
ASSUMPTIONS E5.1 Justified assumptions There are no justified assumptions.
E5.2 Unverified assumptions There are no unverified assumptions.
Response to RAl-08 Attachment 2 Appendix E
- E Revision 1
E6.
METHODOLOGY The critical demand that governed the computation of the threshold factor of CEHMS structure was bending of east wind wall at the intersection with column. At this location the demands are:
ASR load with threshold factor: M = 168 kip-ft/ft, P = 2.06 kip/ft (Appendix C of Ref. E1)
Unfactored ASR load: M = 112.1 kip-ft/ft, P = 1.4 kip/ft (threshold factor was 1.5)
Original unfactored demands excluding the OBE: M = 47.5 kip-ft/ft, P = -9.7 kip/ft (Sheet 30 to 45 of Ref. E3)
Original unfactored demands including the OBE: M = 143.6 kip-ft/ft, P = -2.72 kip/ft (Sheet 30 to 45 of Ref. E3)
To calculate the stress in rebars subjected to a combination of axial force and bending moment, sectional analysis based on fiber section method, as explained in calculation main body, is used. The calculation is conducted per 1 foot width of the wall, and each section is discretized into 20 fibers. An example
!calculation that evaluates the stress in rebars of the east wing wall is presented in Section E8. The Cl value of the wall was 0. 72 mm/m which included in the analysis to find the initial stress state due to internal ASR alone.
E7.
REFERENCES
[E1]
Simpson Gumpertz & Heger Inc., Evaluation of Containment Equipment Hatch Missile Shield structure, 160268-CA-02 Rev. 0, Waltham, MA, Oct 2016.
[E2]
United Engineers & Constructors Inc., Seabrook Station Structural Design Drawings.
[E3]
United Engineers & Constructors Inc., Equipment Hatch Shield Wall, CE-6-Calc Rev. 3, Aug.
1998.
Response to RAl-08 Attachment 2 Appendix E
- E Revision 1
ES.
COMPUTATION E8.1. Strain in Steel and Concrete due to Internal PS R expansion Input Data ASR expansion Measured crack index Threshold factor Material properties Compressive strength of concrete Young's modulus of concrete Yield strength of steel Young's modulus of steel Geometry Width offibers Total thickness or height Area of concrete Area of tensile reinforcement
(#11@6 in.)
Number of reinforcement in row, e.g. equal to 2 for tensile and compressive Depth to reinforcement mm E:c1 := 0.72 - m Fthr := 1.5 fc := -3ksi Ee:= 3120ksi fy := 60ksi Es := 29000ksi b := 12in h := 42in Ac:= b*h = 504*in2 As := 2* l.56in2 SteelNum := 2 d := 36.88i Ref.[E1]
Ref.[E2]
Finding the strain in steel and concrete by satisfying compatibility and equilibrium Initial Guess Initial mechanical strain in concrete Initial strain in steel Compatibility equation Equilibrium equation Response to RAl-08 Attachment 2 Appendix E E:o.conc := 0 E:o.steel := 0 Given ans := Find( so.cone, E:o.stee1)
- E Revision 0
Initial strain in concrete and steel E8.2. Sectional Analysis Input Data Concrete Material Model Constitutive model for concrete Steel Material Model Constitutive model for steel Response to RAl-08 Attachment 2 Appendix E MATeone(E:) :=
0 if E: > 0 fe fe if E: < -
Ee (Ee* E:) otherwise 0
~
~ MATeone(c:e)_ 2
~
ksi
(/} --
- 4
- 0.01 MATsteeJ(E:) :=
-£
- fy if E: < _
Y Es (E5*c) otherwise I
50 -
~
g MATstee1(c:s)
~
0....
~
ksi
(/} -- - 0.05
- E - 5x10 -3 0
Strain I
I I
0 0.05 Strain Revision 0
Concrete Fibers Number offibers Height of fibers Concrete fiber coordinates Concrete fiber strain Concrete fiber stress Concrete fiber force Reinforcement/Steel fibers Depth to reinforcement fiber Area of reinforcement fiber Steel fiber strain Steel fiber stress Steel fiber force Response to RAl-08 Attachment 2 Appendix E ConcNum := 20 h
ConcH :=
2.l*i ConcNum Coney :
for i E 1.. ConcNum h
ConcH ans. +-- -- + --- + (i - 1 )- ConcH I
2 2
ans Con cc:( co.cone, c, i.p) :=
for i E 1.. ConcNum ansi +-- co.cone+ c - tp*Concyi ans Conccr( co.cone, c, i.p) :=
for i E 1.. ConcNum ansi +-- MAT cone( Con cc:{ co.cone, c, i.p) i) ans ConcF( co.cone, c, i.p) :=
for i E 1.. ConcNum ans. +-- Conccr(c 0 cone, c, i.p). * ( b* ConcH)
I I
ans Steely1 := -(d -~) = -15.88*in Steely := d - ~ = 15.88*in 2
2
. 2 SteelAs := As= 3.12*m 1
. 2 SteelAs :=As= 3.12*m 2
Steele( co.steel, c, i.p) :=
for i E 1.. SteelNum ansi +-- co.steel + c - tp* Steelyi ans Steel er( co.steel> c, i.p) :=
for I E 1.. SteelNum ansi +-- MA Tsteel( SteelE( co.steel, c, i.p) i) ans SteelF( c t 1 c <n) *=
"or 1" E 1.. SteelNum
'-o.s ee '""',-
- 11 ans1. +-- Steelcr( co.steel, c, i.p). *Steel As.
I I
ans
- E Revision 0
Initial Stress State Initial stress in concrete Concretecr := Conccr( S 0 _conc, 0, 0)
Initial stress in steel Axial Equilibrium Force( so.cone, So.steel> s, tp) :=
ansl +--- 0 for i E 1.. ConcNum ans 1 +--- ans 1 + ConcF( s 0 cone, s, tp).
I ans2 +--- 0 for i E 1.. Stee!Num ans2 +--- ans2 + Stee!F( 0.steeb s, tp).
I ans+--- ansl + ans2 Moment Equilibrium Moment( So.cone, So.steel, s, tp) :=
ans 1 +--- 0 for i E 1.. ConcNum ans 1 +--- ans 1 + -1
- ConcF( so.cone, s, tp): Coney.
I I
ans2 +--- 0 for i E 1.. Stee!Num ans2 +--- ans2 + -1
- Stee!F( S 0 steel, s, tp): Steely I
I ans +--- ans 1 + ans2 Response to RAl-D8 Attachment 2 Appendix E
- E Revision 0
Solution Known parameters Axial force Iteration Curvature Solve for strain at centroid Axial strain at centroid (initial guess)
Axial force equilibrium Sectional forces p := -0.7kip f(x) := Force( co.cone, co.steel> x, <P) - P ccent := root(f(Xo),Xo) = l.037x 10- 4 Requires iteration Force(co.conc,co.steebccent><P) = - 0.7*kip Moment( co.cone, co.steel> ccent> <P) = 311. 755 *kip* ft Stress and strain in concrete and steel Steel fiber stress and strain Concretey := Coney Concrete fiber stress and strain Maximum compressive strain in concrete ConcreteE
- ConcreteE ConcNum ConcNum-1 ( h
)
cmax.comp :=
- Coney
... = - 4.876 x Cone
- Cone 2
ConcNum-1 y ConCNum y ConcNum-1
+ ConcreteE ConCNum-1 Maximum compressive stress in concrete Response to RAl-08 Attachment 2 Appendix E
- E Revision 0
E9.
TABLES Table E1: Stress in rebars at critical locations of CEHMS structure subjected to LC1 Total demands for sustained load (In Situ condition, Total stress in steel Maximum LC1)
(ksi) compressive Component Item stress in Demand Location Rebar1 Rebar2 concrete (ksi)
Out-of-plane 159.6 East wing moment (kip-tuft)
East wing wall, at intersection with 23.4 15.0
-0.78 walls column Axial force (kip/ft)
-8.3 Table E2: Stress in rebars at critical locations of CEHMS structure subjected to LC2 Total demands for sustained loads plus OBE amplified Total stress in steel Maximum with threshold factor (In Situ condition, LC2)
(ksi) compressive Component Item stress in Demand Location Rebar1 Rebar2 concrete (ksi)
Out-of-plane 311.6 East wing moment (kip-tuft)
East wall, horizontal strip, at the 41.6 20.8
-1.52 wall middle of the wall Axial force (kip/ft)
-0.7 Example in Section EB E10.
FIGURES There are no figures.
Response to RAl-08 Attachment 2 Appendix E
- E Revision 0
SIMPSON GUMPERTZ & HEGER I
Engineering of Structures and Building Enclosures CLIENT:
NextEra Energy Seabrook
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures APPENDIX F PROJECT NO:
170444 DATE: ---~D=ec~2=0~17~--
BY: ----=M"--'R=.M=.G=a"'-"rq=a"'-ri __
VER! FIER: ---'-'A"--. T""".-"'S=ar_,,_awi
=*_,_
t __
TENSILE STRESS IN REBARS OF CONTAINMENT ENCLOSURE VENTILATION AREA F1.
REVISION HISTORY Revision 0: Initial document.
F2.
OBJECTIVE OF CALCULATION The objective of this calculation is to compute the maximum tensile stress that can form in the rebars of Containment Enclosure Ventilation Area (CEVA) structure.
F3.
RESULTS AND CONCLUSIONS Table F1 summarizes the tensile stress in rebars of the CEVA structure calculated at critical locations. The maximum tensile stress is 44.0 ksi computed for the rebars of the base slab along east-west direction.
F4.
DESIGN DATA I CRITERIA See Section 4 of the calculation main body (Cale. 160268-CA-05 Rev. 0).
F5.
ASSUMPTIONS F5.1 Justified assumptions There are no justified assumptions.
F5.2 Unverified assumptions There are no unverified assumptions.
Response to RAJ-DB Attachment 2 Appendix F
- F Revision 0
F6.
METHODOLOGY The critical demand that governed the computation of the threshold factor of CEVA structure was bending moment of the base slab in Area 3 subjected to seismic load combinations that act parallel to east-west direction [F1]. The original calculation of CEVA structure [F3] does not provide unfactored demand values; therefore, in this evaluation, the factored load is conservatively divided by the minimum load factor in the load combination and used in calculating rebar stress:
ASR load with threshold factor: M = 28.7 kip-ft/ft P = O (Appendix C of Ref. F1)
Unfactored ASR load: M = 9.56 kip-ft/ft, P = O (threshold factor was 3.0)
Original unfactored demands incxluding the OBE: M = 77/1.4 = 55 kip-ft/ft, P = 2.44/1.4 = 1.43 kip/ft (Sheet 16 of Ref. F3). Note that the value of 1.4 was the load factor applied to the dead load in the combination (minimum load factor)
To calculate the stress in rebars subjected to a combination of axial force and bending moment, sectional analysis based on fiber section method, as explained in calculation main body, is used. The calculation is conducted per 1 foot width, and each section is discretized into 20 fibers. An example calculation that evaluates the stress in rebars of the base slab is presented in Section F8. The Cl value of all components was set equal to 0.31 mm/m which included in the analysis to find the initial stress state due to internal ASR alone.
F7.
REFERENCES
[F1]
Simpson Gumpertz & Heger Inc., Evaluation of Containment Enclosure Ventilation Area, 160268-CA-05 Rev. 0, Waltham, MA, Mar. 2017.
[F2]
United Engineers & Constructors Inc., Seabrook Station Structural Design Drawings.
[F3]
United Engineers & Constructors Inc., Containment Enclosure Ventilation Area, EM-33-Calc Rev.
4, Jan. 1986.
Response to RAl-08 Attachment 2 Appendix F
- F Revision 0
F8.
COMPUTATION F8.1. Strain in Steel and Concrete due to Internal ASR expansvn Input Data ASR expansion Measured crack index Threshold factor Material properties Compressive strength of concrete Young's modulus of concrete Yield strength of steel Young's modulus of steel Geometry Width of fibers Total thickness or height Area of concrete Area of tensile reinforcement
(#9@12 in.)
Number of reinforcement in row, e.g. equal to 2 for tensile and compressive Depth to reinforcement mm cc1 := 0.31-m Fthr := 3 fc := -3ksi Ee := 3 I 20ksi fy := 60ksi Es := 29000ksi b := 12in h := 30i Ac := b*h = 360*in2 1
- 2 As:=
m SteelNum := 2 d := 26.4in Ref. [F1]
Ref.[F2]
Finding the strain in steel and concrete by satisfying compatibility and equilibrium lnttial Guess lnttial mechanical strain in concrete lnttial strain in steel Compatibility equation Equilibrium equation Response to RAl-08 Attachment 2 Appendix F co.cone:= 0 co.steel := 0 Given Fthr' cc1 = co.steel - co.cone ans := Find( co.cone, co.steel)
- F Revision 0
Initial strain in concrete and steel F8.2. Sectional Analysis Input Data Concrete Material Model Constitutive model for concrete Steel Material Model Constitutive model for steel Response to RAl-0 8 Attachment 2 Appendix F MATeone(E:) :=
0 if E: > 0 fe fe if E: < -
Ee (Ee* E:) otherwise 0
~
~ MA Tconc( E:e)_ 2 Vl
~
ksi
(/) --
- 4
- 0.01 MATsteeJ(E:) :=
- f
- fy if E: < _ Y Es (Es*e) otherwise I
50 -
~
g MATsteeI( es)
~
0 -
~
ksi Ul -- - 0.05
- F - 5xl 0- 3 0
Strain I
I I
0 0.05 Strain Revision 0
Concrete Fibers Number of fibers Height of fibers Concrete fiber coordinates Concrete fiber strain Concrete fiber stress Concrete fiber force Reinforcement/Steel fibers Depth to reinforcement fiber Area of reinforcement fiber Steel fiber strain Steel fiber stress Steel fiber force Response to RAl-08 Attachment 2 Appendix F ConcNum := 20 h
ConcH :=
1.5* i ConcNum Coney :
for i E 1.. ConcNum h
ConcH ans.+- -- + --- + (i - l)*ConcH 1
2 2
ans ConcE( c 0 cone, c, (jJ) :=
for i E 1.. ConcNum ansi +- co.cone + c - tp* Concyi ans Conccr( co.cone, c, tp) :=
for i E 1.. ConcNum ansi +- MAT cone( ConcE( co.cone, c, (jJ) i) ans ConcF( co.cone, c, (jJ) :=
for i E 1.. ConcNum ans. +- Conccr(c0 cone, c, tp): ( b* ConcH)
I I
ans Steely1 := -(d -~) = -11.4*in h
Steely := d - -
= 11.4*m 2
2
. 2 SteelAs :=As= l *m I
. 2 SteelAs :=As= l*m 2
Steele( co.steel> c, (jJ) :=
for i E 1.. SteelNum an\\ +- co.steel+ c - tp* Steelyi ans Steel ( c-t 1 c- "') *=
fio1*
1° E 1.. SteelNum cr "'o.s ee,c-,.,-
- ans SteelF( co.steel> c, (jJ) :=
for i E 1.. SteelNum ans1. +- Steeicr( co.steel> c, tp): Steel As.
I I
ans
- F Revision 0
Initial Stress State Initial stress in concrete Concrete" := Conca-( Eo.conc, 0, 0)
Initial stress in steel Axial Equilibrium Force( Eo.conc, Eo.steel> E, tp) :=
ans 1 ~ 0 for i E 1.. ConcNum ansl ~ ansl + ConcF(c:oconc,c:,tp).
I ans2 ~ 0 for i E 1.. Stee!Num ans2 ~ ans2 + Stee!F( Eo.steel> E, tp).
I ans ~ ans 1 + ans2 Moment Equilibrium Moment( Eo.conc, E 0 steel> E, tp) :=
ans 1 ~ 0 for i E 1.. ConcNum ansl ~ ansl + -1 *ConcF( Eo.conc, c:, tfl):Concy.
I I
ans2 ~ 0 for i E 1.. Stee!Num ans2 ~ ans2 + - 1
- Stee!F( E 0 steel> E, tp): Steely I
I ans ~ ans 1 + ans2 Response to RAl-08 Attachment 2 Appendix F
- F Revision 0
Solution Known parameters Axial force Iteration Curvature Solve for strain at centroid Axial strain at centroid (initial guess)
Axial force equilibrium Sectional forces p := l.74kip 1
X,¢)- P Ecent := root( f( Xa), Xa) = 2.299 x 10- 4 Requires iteration Foree(Eo.conc,Eo.steel>Ecent,¢) = 1.74-kip Moment(Eoconc,Eosteel,Ecent,<P) = 83.675-kip*ft Stress and strain in concrete and steel Steel fiber stress and strain Coneretey := Coney Concrete fiber stress and strain Maximum compressive strain in concrete ConereteE - ConereteE ConcNum ConcNum-1 ( h ) - 4 Emax.comp := - Coney ... = -3.453 x 10 Cone - Cone 2 ConcNum-1 y ConCNum y ConcNum-1 + ConereteE ConcNum-1 Maximum compressive stress in concrete Response to RAl-08 Attachment 2 Appendix F - F Revision 0 F9. TABLES Table F1: Stress in rebars at critical locations of CEVA structure subjected to LC1 Total demands for sustained load (In Situ condition, Total stress in steel Maximum LC1) (ksi) compressive Component Item stress in Demand Location Rebar1 Rebar2 concrete (ksi) Out-of-plane 64.5* Base slab moment (kip-tuft) Base slab at Area 3 32.8 5.1 -0.89 Axial force (kip/ft) 1.74*
- These demands are computed conservatively by including OBE and dividing the total factor demand by the minimum load factor in the load combination in the original design calculation.
Table F2: Stress in rebars at critical locations of CEVA structure subjected to LC2 Total demands for sustained load (In Situ condition, Total stress in steel Maximum LC1) (ksi) compressive Component Item stress in Demand Location Rebar1 Rebar2 concrete (ksi) Out-of-plane 83.7 Base slab moment (kip-tuft) Base slab at Area 3 44.0 20.6 -1.08 Axial force (kip/ft) 1.74 Example in Section FS F10. FIGURES There are no figures. Response to RAl-08 Attachment 2 Appendix F - F Revision 0 r lMPSON GUMPERTZ & HEGER I Engineering of Structures and Building Enclosures CLIENT: NextEra Energy Seabrook
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures APPENDIX G PROJECT NO: _
____,1-'-70"""'4'"'"44-'-----
DATE: -------'--F=eb'--'2=0-"'18'----
BY: ____
__,__,_RW~Ke=e=n=-e __
VERIFIER: --~AT~S~a~ra~w~it __
TENSILE STRESS IN REBARS OF STAGE 1 ELECTRICAL MANHOLES G1.
REVISION HISTORY Revision 0: Initial document.
Revision 1: Revised pages G-1 and G-2 from Revision 0 to 1 to update references of calculation revision from A to 0. Revised page G-1 to update Revision history section.
G2.
OBJECTIVE OF CALCULATION The objective of this calculation is to compute the maximum tensile stress that can form in the rebars of the Stage 1 Electrical Manhole (EMH) structures.
G3.
RESULTS AND CONCLUSIONS Table G1 summarizes the tensile stress in rebars of the EMH calculated at critical locations. The maximum tensile stress is 27 ksi in EMH W13/W15 subjected to the second in situ load combination (LC2).
G4.
DESIGN DATA I CRITERIA I See Section 4 of the calculation main body (Cale. 160268-CA-12 Rev. 0).
G5.
ASSUMPTIONS G5.1 Justified assumptions There are no justified assumptions.
G5.2 Unverified assumptions There are no unverified assumptions.
Response to RAl-08 Attachment 2 Appendix G
- G Revision 1
G6.
METHODOLOGY The critical demands that control rebar tension in the Stage 1 EMH are horizontal moment and horizontal tension in EMH W13 and W15. Finite element analyses were conducted to calculate the axial force and bending moment at these locations due to ASR load [G1].
To calculate the stress in rebars subjected to a combination of axial force and bending moment, sectional analysis based on fiber section method, as explained in calculation main body, is used. The calculation is
- conducted per 1 foot width of the walls, and each section is discretized into 20 fibers. An example calculation that evaluates the stress in the horizontal rebars in the walls of EMH W13 and W15 is presented in Section G8. The ASR expansion of the EMH is included in the analysis to find the initial stress state due to internal ASR alone.
G7.
REFERENCES
[G1]
Simpson Gumpertz & Heger Inc., Evaluation of Seismic Category I Electrical Manholes - Stage 1, I
160268-CA-12 Rev. 0, Waltham, MA, Jan 2018.
[G2]
United Engineers & Constructors Inc., Seabrook Station Structural Design Drawings.
Response to RAl-08 Attachment 2 Appendix G
- G Revision 1
GS.
COMPUTATION G8.1. Strain in Steel and Concrete due to lntemalASR expansion Input Data ASR expansion Measured crack index Threshold factor Material properties Compressive strength of concrete Young's modulus of concrete Yield strength of steel Young's modulus of steel Geometry Width of fibers Total thickness or height Area of concrete Area of tensile reinforcement
(#6@12 in.)
Number of reinforcement in row, e.g. equal to 2 for tensile and compressive Depth to reinforcement mm cc1 := 0.25 -
m Fthr := 3.7 fc := -3ksi Ee:= 3120ksi fy := 60ksi Es:= 29000ks' b := 12in h := 18in Ac:= b*h = 216*in2 0
. 2 As:=
.44m SteelNum := 2 d := 15.625in Ref. [G1]
Ref.[G2]
Finding the strain in steel and concrete by satisfying compatibility and equilibrium Initial Guess Initial mechanical strain in concrete Initial strain in steel Compatibility equation Equilibrium equation Response to RAJ-DB Attachment 2 Appendix G co.cone := 0 co.steel := 0 Given Fthr' cc1 = co.steel - co.cone ans := Find( co.cone, co.steel)
- G Revision 0
Initial strain in concrete and steel G8.2. Sectional Analysis Input Data Concrete Material Model Constitutive model for concrete Steel Material Model Constitutive model for steel Response to RAJ-08 Attachment 2 Appendix G MATeone(E) :=
0 if E > 0 fe fe if E < -
Ee (Ee* E) otherwise 0
~ MATeonc(c:e)_ 2
~
ksi
(/) --
- 4
- 0.01
- f
- fy if E < _ Y Es (E5*c:) otherwise I
50 -
g MATsteei(c:s)
~
0...
~
ksi t/) -- - 0.05
- G -3
- 5x10 0
Strain I
I 0
0.05 Strain Revision 0
Concrete Fibers Number of fibers Height of fibers Concrete fiber coordinates Concrete fiber strain Concrete fiber stress Concrete fiber force Reinforcement/Steel fibers Depth to reinforcement fiber Area of reinforcement fiber Steel fiber strain Steel fiber stress Steel fiber force Response to RAl-08 Attachment 2 Appendix G ConcNum := 20 h
ConcH :=
0.9*in ConcNum Coney :
for i E 1.. ConcNum h
ConcH ans.*- -- + --- + (i - l)*ConcH I
2 2
ans Con cc( co.cone, c, (fl) :=
for i E 1.. ConcNum ansi *- c 0 cone + c - tp* Concyi ans Con cu( co.cone, c, (fl) :=
for i E 1.. ConcNum ansi *- MAT cone( Cone,,:( co.cone, c, (fl) i) ans ConcF( co.cone, c, (fl) :=
for i E 1.. ConcNum ans.*- Concu(coconc,c,y:i): (b*ConcH)
I I
ans Steely1 := -(d -~) = - 6.625*in h
Steely := d - -
= 6.625* m 2
2 SteelAs := As = 0.44*in2 I
SteelAs := As= 0.44*in2 2
Steele( co.steel, c, y:i) :=
for i E 1.. SteelNum ansi *- co.steel + c - tp* Steely i ans Steel ( c t 1 c
(('\\) *=
fior 1° E 1.. SteelNum u co.s ee, "', Y ans SteelF( c0 steel, c, (fl) :=
for i E 1.. SteelNum ans1. *- Steelu( co.steel> c, (fl): Steel As.
I I
ans
- G Revision 0
Initial Stress State lnttial stress in concrete Concretecr := Cone er( so.cone, 0, 0) lnttial stress in steel Axial Equilibrium Force( So.cone, So.steel> s, tp) :=
ans 1 ~ 0 for i E 1.. ConcNum ansl ~ ansl + Concp(soconc,s,tp).
I ans2 ~ 0 for i E 1.. SteelNum ans2 ~ ans2 + Steelp( S0 steel> s, tp).
I ans ~ ans 1 + ans2 Moment Equilibrium Moment( S0 cone, so.steel, s, tp) :=
ans 1 ~ 0 for i E 1.. ConcNum ans 1 ~ ans 1 + -1
- Concp( so.cone, s, tp): Coney.
I I
ans2 ~ 0 for i E 1.. Stee!Num ans2 ~ ans2 + - 1
- Steelp( S0 steel> s, tp): Steely.
I I
ans ~ ans 1 + ans2 Response to RAl-08 Attachment 2 Appendix G
- G Revision 0
Solution Known parameters Axial force Iteration Curvature Solve for strain at centroid Axial strain at centroid (initial guess)
Axial force equilibrium Sectional forces p := - 4.4kip
cP) = - 4.4* kip Moment( Eo.conc > co.steel> Ecent> cP) = 9.679* kip* ft Stress and strain in concrete and steel Steel fiber stress and strain Concretey := Coney Concrete fiber stress and strain Maximum compressive strain in concrete ConcreteE - ConcreteE ConCNum ConCNum-1 ( h ) - 5 Emax.comp := - Coney ... = -9.69 x 10 Coney - Coney 2 ConcNum-1 ConCNum ConCNum-1 + ConcreteE ConcNum-1 Maximum compressive stress in concrete Response to RAl-DB Attachment 2 Appendix G - G Revision 0 G9. TABLES Table G1: Stress in rebars at critical locations of EMH subjected to LC1 Total demands for sustained load (In Total stress in steel (ksi) Maximum Situ condition, LC1) compressive Component Item stress in Demand Location Rebar1 Rebar2 concrete (ksi) Out-of-plane 7.4 EMH moment (kip-tuft) W13/VV15 wall 11.2 5.6 -0.28 W13/W15 Axial force (kip/ft) -3.2 Table G2: Stress in rebars at critical locations of EMH subjected to LC2 Total demands for sustained loads plus Maximum OBE amplified with threshold factor (In Total stress in steel (ksi) compressive Component Item Situ condition, LC2) stress in nt>m~nn I nc,.tion Roh-.r 1 Rnh-.r? concrete (ksi) EMH Out-of-plane W13/W15 9.3 moment (kip-tuft) W13/VV1 5 wall 27.0 24.5 -0.30 Axial force (kio/ftl -4.4 Example in Section GB G10. FIGURES There are no figures. Response to RAl-08 Attachment 2 Appendix G - G Revision 0 SIMPSON GUMPERTZ & HEGER PROJECT NO: 170444 I Engineering of Structures and Building Enclosures DATE: ---~D~ec~2~0~17~-- CLIENT: NextEra Energy Seabrook BY: ----=M~R-~M~.G~a~rq=a=ri __
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures VERIFIER: --~A~.
T~*~S=ar~awi=*t~-
APPENDIX H EVALUATING THE PERFORMANCE OF A SIMPLE ELASTO-PLASTIC MATERIAL MODEL FOR CONCRETE TO BE USED FOR EVALUATION OF REBAR STRESS H1.
REVISION HISTORY Revision 0: Initial document.
H2.
OBJECTIVE OF CALCULATION The objective of this calculation is to compare the rebar stresses computed by using two different using constitutive models for concrete, and justify the at the simple material model provides a satisfactory results.
H3.
RES UL TS AND CONCLUSIONS The stress in rebars are computed using two constitutive models for concrete. The stress in rebars obtained using both models are very close indicating the simple model captures the concrete behavior satisfactorily. This is due to steel ratios in the components of Seabrook structures which is less than the maximum ratio allowed by the code. Therefore concrete crushing and post-linear response of the concrete does not impact the response noticeably.
CRMAI:
Stress in Rebar 1: 39.1 (simple model, Appendix A) and 39.01 (accurate model)
Stress in Rebar 2: 37.3 (simple model, Appendix A) and 37.16 (accurate model)
Stress in concrete: -0.33 (simple model, Appendix A) and -0.328 (accurate model)
CEHMS:
Stress in Rebar 1: 41.6 (simple model, Appendix E) and 42.1 (accurate model)
Stress in Rebar 2: 20.8 (simple model, Appendix E) and 19.3 (accurate model)
Stress in concrete: -1.5 (simple model, Appendix E) and -1.4 (accurate model)
H4.
DESIGN DATA I CRITERIA There are no design data.
Response to RAl-08 Attachment 2 Appendix H
- H Revision 0
HS.
ASSUMPTIONS HS.1 Justified assumptions There are no justified assumptions.
HS.2 Unverified assumptions There are no unverified assumptions.
HG.
METHODOLOGY Stress in rebars at the base mat of CRMAI and at the east wing wall of CEHMS structures are computed using a more accurate constitutive model of Kent and Park [H4] in compression, and the results are compared with the stresses obtained from the simple model as explained in the main body. The stresses in rebars from the simple model are provided in Appendix A and E for CRMAI and CEHMS structures respectively. Section H8 provides a sample calculation for rhe base mat of CRMAI structures.
H7.
REFERENCES
[H1]
Simpson Gumpertz & Heger Inc., Evaluation of Control Room Makeup Air Intake structure, 160268-CA-08 Rev. 0, Waltham, MA, May 2017.
[H2]
United Engineers & Constructors Inc., Seabrook Station Structural Design Drawings.
[H3]
United Engineers & Constructors Inc., Design of Makeup Air Intake Structure, MT-28-Calc Rev. 2, Feb. 1984.
[H4]
Dudley. C. Kent, and Robert Park, Flexural members with confined concrete, ASCE Journal of Structural Division, 97 (ST7), 1969-1990, 1971.
H8.
COMPUTATION H8.1. Strain in Steel and Concrete due to Internal ASR expansion Input Data ASR expansion Measured crack index Threshold factor Material properties Compressive strength of concrete Young's modulus of concrete Response to RAl-08 Attachment 2 Appendix H mm sc1 := 0.99 -
m Fthr := 1.4 fc := -3ksi Ee:= 3 J 20ksi
- H Ref. [H1]
Revision 0
Yield strength ofstee I fy := 60ksi Young's modulus of steel Es := 29000ksi Geometry Width of fibers b := 12in Ref.[H2]
Total thickness or height h := 36i Area of concrete Ac := b*h = 432*in2 Area of tensile reinforcement As := 0.79in2
(#8@12 in.)
Number of reinforcement in row, SteelNum := 2 e.g. equal to 2 for tensile and compressive Depth to reinforcement d := 32.~
Finding the strain in steel and concrete by satisfying compatibility and equilibrium Initial Guess Initial mechanical strain in concrete Initial strain in steel Compatibility equation Equilibrium equation Initial strain in concrete and steel H8.2. Sectional Analysis Input Data Concrete Material Model Kent & Park Model Strain at Peak compressive strength Strain at 50% compressive strength Response to RAl-08 Attachment 2 Appendix H co.cone:= 0 co.steel := 0 Given ans := Find( co.cone, co.steel) cco := - 0.002 csou :=
fc 3 - 0.002*-
=-ps_i =*-4.5 x I0- 3 fc
+ 1000 psi
- H Revision 0
Model parameter 0.5 z := --- = -200 Residual compressive strength Constitutive model for concrete MAT eoneC E:) :=
min[fe.res,fe{ 1 - Z* ( E: - ceo)] if c < ceo
~[ ~~ -UJ'] ;, ° < £ <D 0 if 0:::; c
,-.._ g MATeone( e:e)- 2
</>
</>
~
ksi
[/J --
-4
- 0.01
- 5xl0 -3 Strain Steel Material Model Constitutive model for steel
-£
-fy if c < _!_
Es (E5*c) otherwise I
I 50 -
g MATstee1(e:s)
</>
0
~
ksi
[/J --
- 50,_
- 0.05 0
Strain Response to RAl-DS Attachment 2 Appendix H
- H 0 I
0.05 Revision 0
Concrete Fibers Number of fibers Height of fibers Concrete fiber coordinates Concrete fiber strain Concrete fiber stress Concrete fiber force Reinforcement/Steel fibers Depth to reinforcement fiber Area of reinforcement fiber Steel fiber strain Steel fiber stress Steel fiber force Response to RAl-08 Attachment 2 Appendix H ConcNum := 20 h
ConcH :=
1.8* in ConcNum Coney :
for i E 1.. ConcNum h
ConcH ans.~ - -
+ --- + (i - l )*ConcH I
2 2
ans Conce( Ea.cone, E, lp) :=
for i E 1.. ConcNum an\\~ Ea.cone+ E - lp*Concyi ans Con cu( Ee.cone, E, lp) :=
for i E 1.. ConcNum ansi ~ MAT cone( Con cc( Ee.cone, E, lp) i) ans ConcF( Ea.cone, E, lp) :=
for i E 1.. ConcNum ansi ~ Concu( Ea.cone> E, lp) i*( b*ConcH) ans Steely1 := -(d -~) = - 14.S*in h
Steely := d - -
= 14.5*m 2
2 9. 2 SteelAs := As = 0.7 *m I
9. 2 SteelAs :=As = 0.7 *m 2
Steele( E0 steel, E, lp) :=
for i E 1.. SteelNum an\\ ~ Ee.steel + E - lp* Steelyi ans Stee!cr( Ea.steel> E, lp) :=
for 1 E 1.. SteelNum ansi ~ MA Tsteel( Steele( E0 steel> E, lp) i) ans SteelF( Ee.steel> E, lp) :=
for i E 1.. SteelNum ans. ~ Stee!cr( Ea.steel, E, (fl): Steel As I
I I
ans
- H Revision 0
Initial Stress State Initial stress in concrete Concretecr := Conca-( Ea.cane, 0, 0)
Initial stress in steel Axial Equilibrium Force( Ea.cane, Ea.steel> E, tfl) :=
ans 1 ~ 0 for i E 1.. ConcNum ans l ~ ansl + ConcF(Eacanc,E,tp).
I ans2 ~ 0 for i E 1.. Stee!Num ans2 ~ ans2 + Stee!F( Ea steel, E, tp).
1 ans ~ ans 1 + ans2 Moment Equilibrium Moment( Ea.cane, Ea.steel, E, tp) :=
ans 1 ~ 0 for i E 1.. ConcNum ans 1 ~ ans 1 + -1
- ConcF( Ea.cane, E, tp): Coney.
I I
ans2 ~ 0 for i E 1.. Stee!Num ans2 ~ ans2 + -1
- Stee!F( Ea.steel> E, tp): Steely.
1 I
ans ~ ans 1 + ans2 Response to RAl-08 Attachment 2 Appendix H
- H Revision 0
Solution Known parameters Axial force Iteration Curvature Solve for strain at centroid Axial strain at centroid (initial guess)
Axial force equilibrium Sectional forces p := - 32.3kip
:= 0.0000022.2-m f(x) := Foree(co.conc,co.steel>x,<f>)- P ccent := root(f(Xo),Xo) = -2.724 x 10- 5 Requires iteration Foree(co.conc,co.steel>ccent>) = -32.3*kip Moment( co.cone, co.steel, ccent, <!>) = 26.431 *kip* ft Stress and strain in concrete and steel Steel fiber stress and strain Concrete fiber stress and strain Maximum compressive strain in concrete Coneretey := Coney ConereteE
- ConereteE
(
)
ConCNum ConcNum-1 h
cmax.comp := ---------------. - - Coney
... = -1.124 x Cone
- Cone 2
ConcNum-1 y ConCNum y ConcNum-1
+ ConereteE ConCNum-1 Maximum compressive stress in concrete Response to RAl-08 Attachment 2 Appendix H
- H Revision 0
H9.
TABLES There are no tables.
H10.
FIGURES There are no figures.
Response to RAl-08 Attachment 2 Appendix H
- H Revision 0
r lMPSON GUMPERTZ & HEGER I Engineering of Structures ond Building Enclosures CLIENT:
NextEra Energy Seabrook
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures APPENDIX I PROJECT NO: -~1~70~4~44~--
DATE: ---~F=eb~2=0~18~--
BY: ----~RW~Ke=e=ne~--
VERIFIER: ___
A~T~S=a~ra=w~it __
TENSILE STRESS IN REBARS OF WEST PIPE CHASE STRUCTURE
- 11.
REVISION HISTORY Revision 0: Initial document.
Revision 1: Revised pages 1-1 and 1-2 from Revision 0 to 1 to update references of calculations revision from A to 0. Revised 1-1 to update Revision history section.
- 12.
OBJECTIVE OF CALCULATION The objective of this calculation is to compute the maximum tensile stress that can form in the rebars of the West Pipe Chase (WPC) structure.
- 13.
RESULTS AND CONCLUSIONS Table 11 summarizes the tensile stress in rebars of the WPC structure calculated at critical locations. The Maximum tensile stress is 44 ksi at the base of the WPC north wall subjected to the second in situ load combination (LC2).
- 14.
DESIGN DATA I CRITERIA I See Section 4 of the calculation main body (Cale. 170443-CA-04 Rev. 0).
- 15.
ASSUMPTIONS 15.1 Justified assumptions There are no justified assumptions.
15.2 Unverified assumptions There are no unverified assumptions.
Response to RAl-08 Attachment 2 Appendix I 1 -
Revision 1
- 16.
METHODOLOGY The critical demands that control rebar tension in the WPC structure are horizontal moment and horizontal tension near the base of the WPC north wall. Finite element analyses were conducted to calculate the axial force and bending moment at these locations due to ASR load [11].
To calculate the stress in rebars subjected to a combination of axial force and bending moment, sectional analysis based on fiber section method, as explained in calculation main body, is used. The calculation is conducted per 1 foot width of the walls, and each section is discretized into 20 fibers. An example calculation that evaluates the stress in the horizontal rebars at the base of the WPC north wall is presented in Section 18. The ASR expansion of the WPC north wall is included in the analysis to find the initial stress state due to internal ASR alone.
- 17.
REFERENCES
[11]
Simpson Gumpertz & Heger Inc., Evaluation of the Main Steam and Feedwater West Pipe Chase I
and Personnel Hatch Structures, 170443-CA-04 Rev. 0, Waltham, MA, Jan 2018.
[12]
United Engineers & Constructors Inc., Seabrook Station Structural Design Drawings.
[13]
United Engineers & Constructors Inc., Analysis and Design of MS&FW Pipe Chase - West, EM-20, Rev. 7, February 1986 Response to RAl-08 Attachment 2 Appendix I 2 -
Revision 1
- 18.
COMPUTATION 18.1. Strain in Steel and Concrete due to Internal ASR expansion Input Data ASR expansion Measured crack index Threshold factor Material properties Compressive strength of concrete Young's modulus of concrete Yield strength of steel Young's modulus of steel Geometry Width of fibers Total thickness or height Area of concrete Area of tensile reinforcement
(#11@12 in.)
Number of reinforcement in row, e.g. equal to 2 for tensile and compressive Depth to reinforcement mm ccr := 0.24 - m Fthr := 1.0 fc := -3ksi Ee:= 3120ksi fy := 60ksi Es := 29000ks b := 12i1 h := 24i Ac:= b*h = 288*in2
. 2 As := 1.56m SteelNum := 2 d := 20.3 in Ref. [11]
Ref.[12]
Finding the strain in steel and concrete by satisfying compatibility and equilibrium Initial Guess Initial mechanical strain in concrete Initial strain in steel Compatibility equation Equilibrium equation Response to RAl-08 Attachment 2 Appendix I co.cone:= 0 co.steel := 0 Given Fthr' ccr = co.steel - co.cone ans := Find( co.cone, co.steel) 3 -
Revision 0
Initial strain in concrete and steel 18.2. Sectional Analysis Input Data Concrete Material Model Constitutive model for concrete Steel Material Model Constitutive model for steel Response to RAl-08 Attachment 2 Appendix I MATconc(E) :=
0 if E > 0 fc fc if E < -
Ee (Ee* E) otherwise 0
~ MA Tconc( cc)_ 2
~
ksi if) --
-4
- 0.01
-£
- fy if E < __!_
Es (Es* E) otherwise I
50 -
- @, MATsteeI( cs)
~
0 -
~
ksi
.n -- - 0.05 4 -
-3
- 5x10 0
Strain I
'1 I
0 0.05 Strain Revision 0
Concrete Fibers Number offibers Height of fibers Concrete fiber coordinates Concrete fiber strain Concrete fiber stress Concrete fiber force Reinforcement/Steel fibers Depth to reinforcement fiber Area of reinforcement fiber Steel fiber strain Steel fiber stress Steel fiber force Response to RAl-08 Attachment 2 Appendix I ConeNum := 20 h
ConeH :=
1.2* in ConeNum Coney :
for i E 1.. ConeNum h
Cone8 ans.~ - - + --- + (i - l)*ConeH 1
2 2
ans Co nee:( c 0 cone, c, tp) :=
for i E 1.. ConeNum ansi ~ co.cone+ c - tp*Coneyi ans Cone ( c c rn) *=
"or 1* E 1.. ConeNum cr "'o.conc, "',.,..
- 1' ansi ~ MAT cone( Co nee:( co.cone, c, tp) i) ans ConeF( co.cone, c, tp) :=
for i E 1.. ConeNum ansi ~ Conecr( co.cone, c, tp) i. ( b* ConeH) ans Steely 1 := -( d - ~) = -8.3* in Steely := d - ~ = 8.3* in 2
2
. 2 Steel As := As = 1.56* m I
. 2 Steel As := As = 1.56* m 2
Steele:( co.steel, c, tp) :=
for i E 1.. SteelNum ansi ~ co.steel + c - tp* Steelyi ans Steelcr( co.steel> c, tp) :=
for 1 E 1.. SteelNum ansi ~ MA Tsteei( Steele:( co.steel> c, tp \\)
ans SteelF( co.steel, c, tp) :=
for i E 1.. SteelNum ans1. ~ Steelcr( co.steel, c, tp). *Steel As.
l I
ans 5 -
Revision 0
Initial Stress State Initial stress in concrete Concretecr := Conca-( 0.conc, 0, 0)
Initial stress in steel Axial Equilibrium Force( a.cone, a.steel>, tp) :=
ans I f- 0 for i E I.. ConcNum ansl f-ansl + Concp(E:oconc,E:,tp).
I ans2 f- 0 for i E 1.. Stee!Num ans2 f-ans2 + Steelp( 0.steel> E:, tp).
I ans f-ans 1 + ans2 Moment Equilibrium Moment( a.cone, a.steel, E:, i.p) :=
ans I f- 0 for i E 1.. ConcNum ansl f-ansl + -1 *Concp( E:o.conc' E:, i.p) :Coney.
I I
ans2 f- 0 for i E 1.. Stee!Num ans2 f-ans2 + - 1
- Steelp( 0 steel> E:, tp): Steely I
I ans f-ans 1 + ans2 Response to RAl-0 8 Attachment 2 Appendix I 6 -
Revision 0
Solution Known parameters Axial force Iteration Curvature Solve for strain at centroid Axial strain at centroid (initial guess)
Axial force equilibrium Sectional forces p := 19.lkip
X, <P) - P Ecent := root( f( Xo), Xo) = 3.004 x 10- 5 Requires iteration Force(c:o.conc>Eo.steel>Ecent><P) = 19.l *kip Moment( co.cone> Ea.steel> Ecent> <P) = 3.784* kip*ft Stress and strain in concrete and steel Steel fiber stress and strain Concrete,, := Coney Concrete fiber stress and strain Maximum compressive strain in concrete ConcreteE - ConcreteE ConCNum ConCNum-1 (h ) -5 Emaxcomp :=
- - - Coney
... = - 2.072 x 10 Coney - Coney 2 ConcNum-1 ConCNum ConCNum-1 + ConcreteE ConcNum-1 Maximum compressive stress in concrete Response to RAl-08 Attachment 2 Appendix I 7 - Revision 0
- 19.
TABLES Table 11: Stress in rebars at critical locations of WPC structure subjected to LC1 Total demands for sustained load (In Total stress in steel (ksi) Maximum Situ condition, LC1) compressive Component Item stress in Demand Location Rebar 1 Rebar 2 concrete (ksi) Out-of-plane 3.8 WPC North moment (kip-tuft) Base of wall, horizontal 7.8 6.6 -0.07 Wall direction Axial force (kip/ft) 19.1 I Example in Section 18 Table 12: Stress in rebars at critical locations of WPC structure subjected to LC2 Total demands for sustained loads plus Maximum OBE amplified with threshold factor (In Total stress in steel (ksi) compressive Component Item Situ condition, LC2) stress in Demand Location Rebar1 Rebar2 concrete (ksi) WPC North Out-of-plane 78.8 Base of wall, horizontal Wall moment (kip-tuft) direction 44.4 8.0 -1.36 Axial force (kip/ft) 34.4 110. FIGURES There are no figures. Response to RAl-08 Attachment 2 Appendix I 8 - Revision 0 APPENDIXJ SIMPSON GUMPERTZ & HEGER I Engineering of Structures and Building Enclosures CLIENT: NextEra Energy Seabrook
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures PROJ ECTN0:~~-1~7~0~44~4-'--~~~-
DATE:
Dec. 201 7 BY:
MR. M. Garqari VERIFIER:
A.T. Sarawit COMPUTER RUN IDENTIFICATION LOG SIMPSON GUMPERTZ & HEGER I
Engineering of Structures and Building Enclosures Client:
NextEra Energy Seabrook Page 1
of _4 __ _
Project:
Evaluation of maximum stress in rebars of Seabrook structures Project No.:
170444 Subcontract No.:
N/A Calculation No.:
RAl-08 Attachment 2 Run No.
Title ProgramNer.A Hardware Date Files 1
CRMAI subjected to unfactored load (sustained loading) including ASR load CRMAI subjected to unfactored load (sustained loading) 2 plus OBE including ASR load that has been amplified by threshold factor CEB Standard Case subjected to unfactored loads 3
(sustained loading) including ASR and OBE. For OBE load case, ASR loads are amplified by threshold factor.
CEB Standard-Plus Case subjected to unfactored loads 4
(sustained loading) including ASR and OBE. For OBE load case, ASR loads are amplified by threshold factor.
RHR subjected to unfactored sustained loads (i.e., non 5
ASR loads), unfactored ASR loads, and unfactored seismic loads considering unit acceleration (i.e., 1 g).
6 CSTE subjected to ASR load Response to RAl-08 Attachment 2 Appendix J ANSYS 15.0 Structural ANSYS 15.0 Structural ANSYS 15.0 Structural ANSYS 15.0 Structural ANSYS 15.0 Structural ANSYS 15.0 Structural
- J Cluster3g8 10/12/2017 Cluster3g 8 10/12/2017 Cluster3g8 11/22/2017 Cluster3g 8 11/22/2017 Cluster3g 8 10/12/2017 Cluster3g 8 11/11/2016 Revision 0 Note C Note C Note C Note C Note C Note C EP 3.1 EX3.4 R2 Date: 1 Sept 2012
SIMPSON GUMPERTZ & HEGER I
Engineering of Structures and Building Enclosures CLIENT:
NextEra Energy Seabrook
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures Run No.
Title ProgramNer.A 7
WPC/PH subjected to ASR load Notes:
A ANSYS 15.0 Structural is QA verified B
Cluster3g information is provided below:
Model: Compute Blade E55A2 Serial Number: 4600E70 T201000293 Manufacturer: American Megatrends Inc.
ANSYS 15.0 Structural Operating System: Microsoft Windows NT Server 6.2 (x64)
C Input and output files for ANSYS computer runs are listed in Table J 1.
Response to RAl-08 Attachment 2 Appendix J
- J PROJECT N0: ~~~1~7~04~4~4~~~~~
DA TE:
Dec. 2017 BY:
MR. M. Gargari VERIFIER:
A.T. Sarawit Hardware Date Cluster3g 8 11/09/2017 Revision 0 Files Note C I
EP 3.1EX 3.4 R2 Date: 1 Sept 2012
SIMPSON GUMPERTZ & HEGER I
Engineering of Structures and Building Enclosures PROJECT NO: -~1~70~4~44~---
DATE: ---~D=e=c
.~
20~1~7 ___
CLIENT:
NextEra Energy Seabrook BY: ---~M~R~.
M=*~G=a~rg=ar~i __
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures VERIFIER: --~A~.T~*~S=ar=aw~it~---
Table J 1. Input and output files for AN SYS computer runs Run No.
Input FilesA Output FilesA 1
CRMAl_SUS.db8 CRMAI - SUS.rst 2
CRMAI SUS OBE.db8 CRMAI SUS OBE.rst 3
SR Rebar Stress A 10 r0.db8 SR Rebar Stress A 10 rO.lxx 4
SR Rebar Stress 87 r0.db8 SR Rebar Stress 87 rO.lxx Non ASR Loads Non ASR Loads RHR_ILC_02.db RHR ILC 02.rst RHR_ILC_03.db RHR_ILC_03.rst RHR ILC 05.db RHR_ILC_05.rst RHR_ILC_ 16.db RHR ILC 16.rst ASR Loads ASR Loads RHR ILC 09.db RHR_ILC_09.rst 5
RHR_ILC_ 10.db RHR_ILC_ 10.rst Seismic 1g Seismic 1g RHR ILC 06.db RHR_ILC_06.rst RHR ILC 07.db RHR_ILC_07.rst RHR_ILC_08.db RHR ILC 08.rst RHR_ILC_ 13.db RHR ILC 13 rst RHR ILC 14.db RHR ILC 14.rst 6
WPC.dbc WPC.rst Notes:
A Input and output files are provided on RAl-Attachment-CD. File type descriptions are as follows.
- .db= ANSYS database file containing the model (nodes, elements, properties, boundary conditions, loads, etc.).
- .rst = ANSYS result file containing forces, moments, reactions, displacements, etc.
- .lxx = ANSYS load case file containing forces, moments, reactions, displacements, and other structural response output for load cases and load combinations.
B Each structure has been analyzed for two load combination as follows:
D + L + E +To+ Sa (In-situ condition, LC1)
D + L + E +To+ Eo +He+ FrnR.Sa (In-situ condition plus seismic load, LC2)
C Each structure is analyzed for ASR load only. The original design demands are extracted from original design calculation.
D The description of the input and output files for Run No. 5 is following:
RHR_ILC_02: Self-Weight:
RHR_ILC_03: Hydrostatic Pressure Outside RHR_ILC_05: Live Load RHR_ILC_06: Seismic North-South with 1g acceleration RHR_ILC_07: Seismic East-West with 1g acceleration RHR_ILC_08: Seismic Vertical with 1g acceleration RHR ILC 09: In structure ASR Response to RAl-08 Attachment 2 Appendix J
- J Revision 0
SIMPSON GUMPERTZ & HEGER I Engineering of Structures and Building Enclosures CLIENT:
NextEra Energy Seabrook
SUBJECT:
Evaluation of maximum stress in rebars of Seabrook structures RHR ILC 10: Concrete fill RH R_I LC_ 13: Seismic South-North with 1 g acceleration RHR_ILC_14: Seismic West-East with 1g acceleration RH R_I LC_ 16: Backfill Soil Static Pressure Response to RAl-08 Attachment 2 Appendix J
- J PROJECT NO: --~17~0~44~4~----
DATE: ____
~D~e=c.~2=0~17~--~
BY: ____
~M~R~*~M~*~G~a~rg=a~ri __ ~
VERIFIER: --~A~
. T~*~S~ar~a~w~it ___
Revision 0 to SBK-L-18074 Simpson Gumpertz & Heger calculations supporting the response provided to RAI 010 regarding cracked section properties used for the evaluation of the RHR vault and Spent fuel pool walls.
SIMPSON GUMPERTZ & HEGER I Engineering of Structures and Building Enclosures CLIENT NextEra Energy Seabrook SUBJECT Verification of cracked section properties: RHR structure Calculation attachment PROJECT N0. __
~17~0~44~4~--
DATE ____
3~1~M=a~v~2~0~18~_
BY Georqios Tsampras CHECKED BY MR. M. Garqari Flexural Cracking of 2 ft. thick east exterior wall 1.0 Revision History Revision 0. lnrrial document.
2.0 Objective of Calculation The objective of this calculation attachment is to verify current cracked section properties used for the evaluation of the Residual Heat Removal (RHR) structure east exterior wall when considering ASR loading pre-compressive effect on the cracking moment calculation and to determine if such results affect negatively the current results for the evaluation of the RHR.
3.0 Assumptions No assumptions are considered in this calculation attachment.
4.0 Methodology The highest demand-to-capacity (D/C) ratio in the RHR walls is reported at the east exterior wall due to interaction of horizontal axial compression and bending about the vertical axis (see Appendix E of 160268-CA-06 [1 ]). Therefore, RHR east exterior wall is selected for the verification.
In Appendix E of 160268-CA-06 [1] Section E6.4.1 the bending moment demand was calculated considering uncracked section properties for bending about the vertical axis. In Appendix E of 160268-CA-06 Section E6.4.3 [1] the effective moment of inertia of cracked concrete is calculated according to ACl318-14 Table 6.6.3.1.1 (b) [2] considering the factored moment and axial load demands. The ratio of effective over gross moment of inertia calculated in Appendix E of 160268-CA-06 Section E6.4.3 [1] is compared with the ratio of effective over gross moment of inertia calculated considering the modified ACI 318-71 Eqn 9-4 [3, 4] including the compressive stress due to ASR expansion effects.
5.0 Results and Conclusions The effective moment of inertia of cracked concrete calculated in Appendix E of 160268-CA-06 [1] Section E6.4.3 is equal to 35% of the gross moment of inertia of uncracked concrete. The effective moment of inertia of cracked concrete calculated using the modifiedACI 318-71 Eqn 9-4 [3, 4] including the compressive stress due to ASR expansion effects is equal to 23% of the gross moment of inertia of uncracked concrete. Thus, the demands are expected to reduce when the modified ACI 318-71 Eqn 9-4 [3, 4] is used to calculate the effective moment of inertia. As a result, the evaluation of the RHR structure presented in160268-CA-06 is conservative and rr is not affected.
Response to RAl-D10 Attachment 1
-A1 Revision 0
6.0 Computations Below are the demands atthe support of the Eastexteriorwall-2 ft thick wall between El.(-) 32 ft to(-) 40 ft with uncracked section properties in flexure about the vertical axis from Section E6.4.1 160268-CA-06 [1 ].
Horizontal axial load due to 1.0Sa Horizontal axial load due to 1.40+ 1.7L +1.7E ASR effects load combination multiplier Threshold factor Total horizontal axial load Bending Moment about the vertical axis due to 1.0Sa Bending Moment about the vertical axis due to 1.40+ 1.7L +1.7E Total bending Moment about the vertical axis
!bf NBOI := 4.8031E+02*-.-
m
!bf Nc02 := -5.6331E+03*-.-
m SFSa := 1.6 kth := 1.2 3 !bf Nsup u 2 := Nco2 + k1h*SFSa*NBOl = -4.7109 x 10 *-.-
m lbf*in MBOI := - l.1382E+05* -. -
m lbf*in Mc02 := - 2.4120E+04*-.-
m Msup u 2 := Mco2 + k1h* SF Sa* MBo! = - 242.6544* kip*_!'!
ft Calculation of effective moment of inertia of cracked concrete using the modified ACI 318-71 Eqn 9-4 [3, 4] including the compressive stress due to ASR expansion effects.
Wal thickness Gross moment of inertia of uncracked concrete One foot long section width Compressive stress due to compressive load Concrete Strength Cracking stress Response to RAl-0 10 Attachment 1 tw := 2ft 3
4 tw 3 in lg := -
= l.152x 10 *-
12 m
b := 12in c*
- Nsup u 2
-- -- = 392.5754ps1 b
fc := 3000psi fr := 7.5*~ fc*psi = 410.7919psi
- A 1 Revision 0
Size of reinforcing bar in the wall at the section cut Reinforcing bar area Reinforcing bar spacing Total reinforcing bar area per length in the wall at the location of the section cut Depth of concrete section Steel modulus Concrete modulus Ratio of steel modulus over concrete modulus Cracked moment of inertia Cracking moment Effective cracked moment of inertia [ACI 318-71 Eqn 9-4]
(defined as a function of Ma)
Response to RAl-010 Attachment 1
~:= 9in)
(A,b*in2) 2 As :=
= l.0533*in b
d := 20.5in E5 := 29000ksi Ee := 57000*~fe*psi
( n := :: = 9.2889 )
b
- 1 B := -- = l.2265*in n*As
(..J2*d*B + 1 - 1) kd :=
= 5.0237*in B
3 b*kd 2
+ n*A5*(d - kd)
. 4 J
In Ier:= -------- = 237.5526*-
b in Reference [4]
2 Mer Mer in
(
)3 [ (
)3]
4 Iersup_MD:=
1 1
- lg + 1 -
1 J
- Ier=266.9122*-.-
Msup_u_2 Msup_u_2 lil Iersup MD
= 0.2317 lg
- A 1 Revision 0
7.0 References
[1] Simpson Gumpertz & Heger Inc., Appendix E: Evaluation of Residual Heat Removal Equipment Vault, Report 160268-CA-06, August 2017, Waltham, Revision O
[2]American Concrete Institute, Building Code Requirements for Structural Concrete and Commentary, ACI 318-14, 2014
[3]American Concrete Institute, Building Code Requirements for Structural Concrete and Commentary, ACI 318-71, 1972
[4] Simpson Gumpertz & Heger Inc., Methodology for the analysis of seismic category I structures with concrete affected by Alkali-Silica Reaction, Methodology Document 170444-MD-01, Waltham, Revision 1 Response to RAl-010 Attachment 1
-A1 Revision 0
SIMPSON GUMPERTZ & HEGER I
Engineering of Structures and Building Enclosures PROJECT NO: --~17~0~44~4~--
DATE: ---~3~1
~M=ay'-=20~1=
8 __
CLIENT:
NextEra Energy Seabrook BY: ____
~N~E=C=a=st=a~ne=d=a __
SUBJECT:
Verification of Cracked Section Properties: SFP Walls VERIFIER: __
~A~T~S=
ar~aw=it. __
1.0 Revision History Revision 0. Initial document.
2.0 Objective of Calculation Calculation Attachment Flexural Cracking of 6ft Thick SFP Walls The objective of this calculation attachment is to verify the cracked section properties used for the evaluation of the Spent Fuel Pool (SFP) walls in the Fuel Storage Building (FSB) when taking into account the ASR pre-compression effect has on delaying the onset of flexural cracking and determine if such effect negatively impact the current FSB evaluation results.
3.0 Assumptions No assumptions are considered in this calculation attachment.
4.0 Methodology The highest demand-to-capacity (D/C) ratio in the SFP walls is reported at the north wall due to interaction of vertical axial compression and bending about the horizontal axis. This SFP north wall is selected for the verification. For completeness, cracked section properties of this SFP north wall due to interaction of horizontal axial compression and bending about the vertical axis are also verified. The highest D/C ratio due to bending about horizontal axis is 0.9 and corresponds to load combination C03 (Table 10, Calculation 160268-CA-09). The highest D/C ratio due to bending about vertical axis is 0.5 and corresponds to load combination C03. Load combination C03 considers an ASR load factor of 2.0 and a threshold factor of 1.2 to account for potential future ASR expansion.
Field inspection of accessible SFP walls show that they are already cracked. Cracking can be initiated by factors other than flexural loads, such as thermal gradients. Original design calculation for the SFP mat and walls uses fully-cracked moment of inertia (lcr) for the calculation of demands due to thermal gradients in the SFP walls.
The ratio of lcr to the gross moment of inertia (lg) is 0.13 when evaluating bending about the horizontal axis. The ratios of the effective moment of inertia (le) to lg corresponding to the un-cracked section moment due to operational and accidental thermal gradients are 0.15 and 0.14, respectively. The above results justify the use of_lcr in the original design calculation for the evaluation of temperature bending demands about the horizontal axis in the SPF walls.
The ratio of lcr to lg is 0.09 when evaluating bending about the vertical axis. The ratios of le to lg corresponding to the un-cracked section moment due to operational and accidental thermal gradients are 0.11 and 0.10, respectively. The above results justify the use of lcr in the original design calculation for the evaluation of temperature bending demands about the vertical axis in the SPF walls.
The evaluation of the SFP walls in CA-09 is performed based on a ratio of le to lg of 0.25. To verify the use of this ratio, the cracking moment (Mer) is re-calculated taking into account the ASR pre-compression effect has on delaying the onset of flexural cracking. The le to lg ratio is then calculated based on this re-calculated Mer forthe un-cracked section moment due to operational and accidental thermal gradients.
Response to RAl-010 Attachment 2
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5.0 Results and Conclusions The ratios of le to lg about the horizontal axis due to operational and accidental thermal gradients when taking into account the ASR loading pre-compressive effect due to load combination C03 are 0.16 and 0.15, respectively. These ratio values do not exceed the used ratio value of 0.25.
The ratios of le to lg about the vertical axis due to operational and accidental thermal gradients when taking into account the ASR loading pre-compressive effect due to load combination C03 are 0.30 and 0.21, respectively. The ratio value due operational thermal gradient slightly exceed the used ratio value of 0.25. The associated current DIC ratio is 0.5. Section 6.3 estimates the corresponding D/C ratio when le/lg has a value of 0.30. The moment demand is estimated by amplifying the current moment demand by the ratio of le/lg value of 0.30 to le/lg value of 0.25. The updated DIC ratio is calculated as 0.6.
Based on the above results, it is concluded that accounting for the ASR loading pre-compression effect in calculating the Mer does not impact negatively the current results for the evaluation of the FSB.
6.0 Computations 6.1 Bending About Horizontal Axis Section properties are obtained from Page 1-06 of Calculation 160268-CA-09 Appendix I thickness of cross section depth to reinforcement unit width concrete compressive strength area of tension steel
(#11 @ 12 in) yield strength of tension steel concrete elastic modulus steel elastic modulus ASR Loading Demands h := (6* 12)in = 6 ft d
h l.41in
- =
- 3.5m - l.128m - -- = 66.7*in 2
b:= 1ft fpc := 3000psi As := l.56in 2 fy := 60000psi Ee := 3120000psi Es := 29000000psi The controlling combination load for the evaluation of the SFP North Wall is C03 (Section Cut40 in Table 10, Calculation 160268-CA-09). Factored ASR axial compression demand and including the threshold factor of 1.2 applied in the vertical direction of the SFP north wall are obtained from FSB_UC model of the FSB (Section 6.2, Calculation 160268-CA-09). Axial compression demand due to the thermal gradient is not considered since the wall is free to translate in the upward direction.
Threshold factor ASR loading factor of2.0 for combination load C03 and affected by 20% reduction in ASR load (Table 6 of Methodology Document170444-MD-O 1)
Response to RAl-010 Attachment 2 TF:= 1.2 ASR F := 1.6
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Unfactored ASR compression force.
Factored ASR compressive stress due to combination load C03 Temperature Loading Demands
!bf kip Pu:= 3737.5 -
= 44.9*-
in ft ASR_F*TP*Pu finitial := ----- = lOOpsi h
The temperature moment demands for the un-cracked section of the wall are calculated based on thermal gradients defined in the original design calculation for the SFP mat and walls (FB-17) and considering fixed-fixed boundary condttions. Modeling as fixed-pinned boundary condttions leads to bending demands that are up to 1.5 times larger than that obtained using fixed-fixed boundary condttions. Therefore, the use off1Xed-f1Xed boundary condttions for bending about the horizontal direction is conservative.
Operational Temperature:
Temperature at top Temperature at bottom Coefficient ofThermal Expansion for concrete Gross moment of inertia Operational thermal moment based on un-cracked section Accidental Temperature:
Temperature at top Temperature at bottom Accidental thermal moment based on un-cracked section Determine Mer Ratio of steel to concrete elastic moduli modulus of rupture
[ACI 318-71 Section 9.5.2.2]
Cracking moment [ACI 318-71 Eqn 9-5]
Response to RAl-010 Attachment 2 T1 := 175*
0P
- 6 (
1 )
- = 5.5* 10 3
b*h 5. 4 Ig := -- = 3.732 x 10 *m 12
( Tt - Tb)
Ec*(Ig)-
2-Mtgo :=
= 1371.4-ktp*ft 0.5-h Jy,:= 212*
0P
~:= -10*
0 P
( Tt -Tb)
Ec*(Ig)* * -
2-M1ga :=
1645.7*ktp*ft 0.5-h n := rounct( :: ) = 9 (fr + f;nitial) *lg Mer:
= 44l*kip*ft 0.5*h
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Compute Cracked Moment of Inertia Distance to neutral axis of cracked section Fully cracked moment of inertia Ratio of fully cracked moment of inertia to gross moment of inertia Effective cracked moment of inertia [ACI 318-71 Eqn 9-4]
(defined as a function of Ma)
(~
b*d
) n*As kd :=
1 + -- - 1.-- = ll.375*in n*As b
3 b*kd 2
4. 4 Icr:=--+n*As*(d-kd) =4.881 x 10 *m 3
Icr
= 0.131 lg l*- Ie/lg I o.s*~\\~---+--------+---t---+----+------t--*
0.6 *----+---~l\\
-t----+-----+----t-------*------------+-----+-----1
\\
0 4 1-----j----l~---j-----t----t-----t------------~---<---- 1
. -----------------~-------- ----------------
021
~. _
- ---*-~-*-----+-----+----4----+-----l
--- ---- - ----- - - - -- ------ ----- :zs 00 300 600 900 1200 1500 1800 2100 2400 2700 3000 Moment Demand (kip*ft) le/ lg Ratio for Bending about Horizontal Axis Ieng Ratio at Uncracked Section Temperature Moment Demand Ratio of effective moment of inertia to gross moment of inertia at moment demand for an un-cracked section due to operational temperature.
Ratio of effective moment of inertia to gross moment of inertia at moment demand for an un-cracked section due to accidental temperature.
Response to RAl-010 Attachment 2
-A2 le(Mtgo)
-'----'-- = 0.16 lg le(Mtga)
---=0.15 lg Revision 0
6.2 Bending AboutVerticalAxis Section properties are obtained from Page 1-03 of Calculation 160268-CA-09 Appendix I depth to reinforcement area of tension steel
(#9@ 12in)
ASR Loading Demands l.128in d := h - 3.5m - --- = 67.9*m NV\\
2 As := 1.00in2
/WM The controlling combination load for the evaluation of the SFP North Wall is C03 (Section Cut 38 in Table 10, Calculation 160268-CA-09). Factored ASR axial compression demand and including the threshold factor of 1.2 applied in the horizontal direction of the SFP north wall are obtained from FSB_UC model of the FSB (Section 6.2, Calculation 160268-CA-09). Axial compression demand due to the thermal gradient is not considered. The restraint and inward pressure effects due to ASR expansion of the concrete backfill at the west side of the north wall leads to large axial compression demands. Including the axial compression demand due to temperature is considered to double-count the compressive effect and thus too conservative since its effect is only developed due to the restraint e~ct of the corcre1e backfill.
Unfactored ASR compression force.
ASR compressive stress due to combination load C03 Temperature Loading Demands
!bf kip p := 21098 -
= 253.2*-
NJN in ft ASR_F*TF*Pu
~ =
=563psi h
The temperature moment demands for the un-cracked section of the wall are calculated based on thermal gradients defined in the original design calculation for the SFP mat and walls (FB-17) and considering fixed-fixed boundary conditions. Fixed boundary conditions for bending about vertical axis are judged adequate due to the restraint effects of the thick west wall of the SFP and north wall of the cask loading pool. Therefore, the same temperature moment demands considered in the evaluation for bending about the horizontal axis are used.
Determine Mer Cracking moment [ACI 318-71 Eqn 9-5]
(fr + ~nitia!) *lg Mer :=
= 841*kip*ft MMM/\\
0.5*h Compute Cracked Moment of Inertia Distance to neutral axis of cracked section Fully cracked moment of inertia Response to RAl-D10 Attachment 2
(~
b
- d
) n*As kd :=
1 + -- - 1 *-- = 9.373*in MNI n*As b
3 b*kd 2
4 4
Icr := -- + n*As*(d - kd) = 3.416 x 10 *in
/WM 3
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Ratio of fully cracked moment of inertia to gross moment of inertia Effective cracked moment of inertia [ACI 318-71Eqn9-4]
(defined as a function of Ma)
Icr
= 0.092 lg
\\
F ie/lg I 0.&1-+----+------1\\\\
-+----t---+----t---t----t-------i 0.61---*-
\\
o.4
--+----+--
I'
------- l ---~~--------- --
o.2 1~---f------1f-----l----+----+--~-"::::---+----+---+----l
-- -------------- ---- it25
1----+----+---....J 0
0 300 600 900 1200 1500 1800 Moment Demand (kip*ft) le /lg Ratio for Bending about Vertical Axis Ieng Ratio at Uncracked Section Temperature Moment Demand Ratio of effective moment of inertia to gross moment of inertia at moment demand for an un-cracked section due to operational temperature.
Ratio of effective moment of inertia to gross moment of inertia at moment demand for an un-cracked section due to accidental temperature.
Response to RAl-010 Attachment 2
-A2 2100 2400 Ie(Mtgo)
---=0.3 lg Ie(Mtga)
---=0.21 lg 2700 3000 Revision 0
6.3 Evaluation of DIC Ratio for Bending about Vertical Axis in the SFP North Wall Axial compression demands in the horizontal direction and bending demands about the vertical direction in the SFP north wall are obtained from FSB_FC model of the FSB. The demands correspond to Section Cut 38. (Section 6.2, Calculation 160268-CA-09).
Unfactored ASR axial compression demand Unfactored ASR bending demand Factored ASR axial compression load due to combination load C03 Factored ASR bending demand due to combination load C03 Factored axial tension load due to combination load C03 w/oASR loading Factored bending demand due to combination load C03 w/oASR loading (opposite toASR moment)
Factored axial compression load due to combination load C03 Factored bending demand due to combination load C03
!bf kip PASR:= 17793-.-=213.5*-
m ft MAsR := 359990 lb~*in = 360* kip*ft m
ft kip PASR C03 := ASR F*TF*PASR = 410*-
ft kip* ft MASR C03 := ASR F*TF*MASR = 691*--
ft
!bf kip Pc03 := -94.808-.- = -1.1*-
m ft
!bf* in kip* ft Mc03 := -13921-.- = -13.9*--
m ft kip Puc03 := PASR C03 + Pc03 = 408.8*-
ft kip* ft MuC03 := MAsR C03 + Mco3 = 677.3*--
ft Amplification factor for Muc03.The amplification factor to estimate the moment demand when accounting for the ASR loading compressive effect (finitial) is conservatively calculated by the factor between the ratios of the effective moment of inertia le w~h and without finitial.
0.30 I
- = -
= 1.2 amp 0.25 Factored amplified bending demand due to combination load C03 PM capacfy diagram file (From spColumn w~ adjusted capacfy factors)
Load PM capacity diagram for section cut 38 Response to RAl-010 Attachment 2
(
)
kip*ft Muc03_amp := lamp' MuC03 = 812.7*ft PMD := "0072 _ 0083 _ 0083 _ 0406 _ 0406.PMD" PM_File := READFILE(PMD, "delimited")
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Extract PM capacity curve Compression capacity Cap axial compression to the design limit.
Demand point:
Compute OCR for PM Interaction Response to RAl-010 Attachment 2 PM CapM := submatrix(PM File,2,rows(PM File), 1, 1)* kip* ft ft PM CapP := submatrix(PM File,2,rows(PM File),2,2)* kip ft
[
(
As)
As J kip Pn:= 0.7*0.80* 0.85-fpc* h-2b + 2b*fy = 1298.l*ft PM_ CapP _capped :=
retval rows( PM_ CapP) +-- 0 for rowi E 1.. rows(PM _ CapP) retval
. +-- min(PM CapP
., Pn) rowi rowi retval kip* ft PM_DM := Muco3_amp = 812.712*ft kip PM_DP := Puco3 = 408.813-ft 1
demandAngle +-- angl
(.-
), ( :-- )
kip* ft kip ft ft best P +-- 0.0 best M +-- 0.0 best_ AngleDelta +-- 99999 for ci E 1.. rows( PM_ CapP _capped)
{
PM CapM. PM CapP capped *1 thisAngle +-- angl
(-.
) Cl,
(.-)
cl k1p*ft kip ft ft angleDelta +-- thisAngle - demandAngle if I angleDeital < best_AngleDelta best_ AngleDelta +-- I angleDeital best_P +-- PM_CapP_cappedci best_M +-- PM_CapMci d=~dLffi~ ~ [(¥)f + m;)]'
o~acifyLffi~ ~ [t~;~r + [~:)]'
demandLength return ----=-
capacity Length
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l.5x 103 ------ - ---
i. *------------ 0°<?~
-~<?-0--0 --------------- ------------------
0 o 0 o 00 00
- i******.... ******i**
ldO'------f o
o ~\\ ---
500. *******-****-********----
- -***-*---~*-*-*--*-**
- -*-**-*-**-**--*------***-*-* *-----*---~---*-***-*-*----**-*-*--*-****
........................................................................................................................................... !~.
0
- 500
- 2x I03
- lxl03 000 PM Capacity, uncapped
- PM Capacity, capped
- PMDemand
/
--~- !...........................................
0 Moment, kip*ft/ft Axial Force Moment Interaction Diagram for Section 38 Response to RAl-010 Attachment 2
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