ML18004A007: Difference between revisions
StriderTol (talk | contribs) (Created page by program invented by StriderTol) |
StriderTol (talk | contribs) (Created page by program invented by StriderTol) |
||
(5 intermediate revisions by the same user not shown) | |||
Line 2: | Line 2: | ||
| number = ML18004A007 | | number = ML18004A007 | ||
| issue date = 01/02/2018 | | issue date = 01/02/2018 | ||
| title = | | title = La - | ||
| author name = | | author name = | ||
| author affiliation = NRC | | author affiliation = NRC | ||
Line 16: | Line 16: | ||
=Text= | =Text= | ||
{{#Wiki_filter: | {{#Wiki_filter:SeabrookLANPEm Resource From: SeabrookLAHearingFile Resource Sent: Tuesday, January 02, 2018 2:42 PM To: SeabrookLANPEm Resource Attachments: 170444-L-001 Rev. 0.pdf 1 | ||
Hearing Identifier: Seabrook_LA_NonPublic Email Number: 1341 Mail Envelope Properties (8d5e0168125e4699b25984c1e541eb8d) | |||
==Subject:== | ==Subject:== | ||
== | Sent Date: 1/2/2018 2:41:42 PM Received Date: 1/2/2018 2:41:52 PM From: SeabrookLAHearingFile Resource Created By: SeabrookLAHearingFile.Resource@nrc.gov Recipients: | ||
The structural evaluation of the Containment Enclosure Ventilation Area (CEVA), referenced above, showed that its north wall between EL +3 and +19 ft was bowed outward with a maximum out-of-plumbness of 1.25 in., measured during SGH field observation in February 2017. The referenced calculation showed that the wall can move by | "SeabrookLANPEm Resource" <SeabrookLANPEm.Resource@nrc.gov> | ||
at the point of maximum bowing) before conducting a more robust analysis or repairing the wall becomes necessary. The bowing limit of 1.5 in. was | Tracking Status: None Post Office: HQPWMSMRS01.nrc.gov Files Size Date & Time MESSAGE 3 1/2/2018 2:41:52 PM 170444-L-001 Rev. 0.pdf 619783 Options Priority: Standard Return Notification: No Reply Requested: No Sensitivity: Normal Expiration Date: | ||
in the wall with | Recipients Received: | ||
Mr. Edward Carley - | |||
6 November 2017 Mr. Edward Carley Engineering Supervisor - License Renewal NextEra Energy Seabrook, LLC. | |||
P.O. Box 300, Lafayette Road Seabrook, NH 03874 Project 170444 - License Amendment Request & NRC Review Support, NextEra Energy Seabrook Station, Seabrook, NH Reference - Evaluation of Containment Enclosure Ventilation Area (CEVA), | |||
Calculation 160268-CA-055HY (FP101122), 22 March 2017 Document Number: 170444-L-001 | |||
==Dear Mr. Carley:== | |||
The structural evaluation of the Containment Enclosure Ventilation Area (CEVA), referenced above, showed that its north wall between EL +3 and +19 ft was bowed outward with a maximum out-of-plumbness of 1.25 in., measured during SGH field observation in February 2017. The referenced calculation showed that the wall can move by an additional 25% (reaching to 1.5 in. | |||
at the point of maximum bowing) before conducting a more robust analysis or repairing the wall becomes necessary. | |||
The bowing limit of 1.5 in. was calculated conservatively in the referenced calculation by neglecting the compression reinforcement in calculating the moment-curvature behavior of the wall. The limit of bowing is recalculated as shown in Attachment A considering the compression reinforcement in the moment-curvature calculation, and including the effects of upward vertical movement of CEVA. The upward movement of CEVA can impose vertical tension in the north wall of CEVA. Accordingly, moment-curvature relationships are calculated at different levels of tension. | |||
At each level of axial force, a limiting curvature is determined to avoid unacceptable behavior. As explained in Attachment A, the curvature value of 0.003 1/in. corresponds either to the buckling of compression reinforcement (for cases with low level of axial tension) or rupture of tension reinforcement (for cases with high level of axial tension). Conservatively, 90% of this curvature value (0.0027 1/in.) is selected for computing the maximum bowing that the wall can resist. | |||
The computed moment-curvature relationships are assigned to a finite element model of the wall, and nonlinear analyses are performed to determine the lateral displacement at which the curvature of the wall at the point of maximum bowing reaches the limiting curvature. Figure A2 in Attachment A shows that 2 in. of lateral wall deformation induces curvature of 0.0027 1/in. in the wall with a low level of axial force, while the same displacement induces curvature of 0.0023 1/in. | |||
in the wall with a high level of axial tension. Therefore, the wall can resist a lateral bowing of 2 in. | |||
Mr. Edward Carley - Project 170444 6 November 2017 Document No. 170444-L-001 Revision 0 before buckling or rupture of the vertical reinforcement will occur (with 10% margin), and it is recommended that the wall be retrofitted prior to it experiencing 2 in. of bowing. | |||
The site visit report (170444-SVR-01-R0, FP101192-00) for the recent measurements indicates that the wall moved outward since the previous measurements; bulging has increased to 1-7/16 in. Additionally, at a localized area, hammer sounding indicated portions of the concrete cover potentially susceptible to separation, especially at areas with larger horizontal cracks. Therefore, sensitive equipment or processes should be protected against possible falling pieces of concrete cover from this wall before it is retrofitted. | |||
Sincerely yours, Said Bolourchi Michael Mudlock, P.E. | |||
Senior Principal Senior Project Manager NH License No. 14808 I:\BOS\Projects\2017\170444.00-LARS\Workspace\CEVA North Wall\170444-L-001 Rev. 0.docx | |||
PROJECT NO: 170444 DATE: Nov 2017 CLIENT: NextEra Energy Seabrook BY: MR.M.Gargari | |||
==SUBJECT:== | ==SUBJECT:== | ||
Evaluation of Additional Displacement for the North Wall of CEVA VERIFIER: I. Baig ATTACHMENT A MOMENT CURVATURE RELATION FOR THE CEVA NORTH WALL A1. REVISION HISTORY Revision 0: Initial document. | |||
[A3] | A2. OBJECTIVE OF CALCULATION The objective of this calculation is to compute moment-curvature diagrams for the north wall of Containment Enclosure Ventilation Area (CEVA) structure subjected to different tensile force. | ||
}} | A3. RESULTS AND CONCLUSIONS Figure A2 presents moment-curvature diagram for the wall section subjected to different tensile force. As can be seen from the figure, by increasing the magnitude of tensile force, the failure mode changes from compressive rebar buckling to tensile rebar rupture. For all cases, the point of severe damage initiation approximately corresponds to curvature value of 0.003 (1/in.). Accordingly, this point is selected as a limiting curvature and the wall is allowed to deform up to this curvature. | ||
Figure A3 provides a comparison between two cases, one with accounting for the effect of compressive rebars and the other one without considering the compressive rebars. As can be seen from the figure, including the resistance offered by compressive reinforcement does not affect the ultimate capacity noticeably, however, it increases the ductility of a section. | |||
A4. DESIGN DATA / CRITERIA See Section 4 of the calculation main body (160268-CA-05 Rev.0). | |||
A5. ASSUMPTIONS A5.1 Justified assumptions There are no justified assumptions. | |||
A5.2 Unverified assumptions There are no unverified assumptions. | |||
Attachment A -A Revision 0 | |||
A6. METHODOLOGY To calculate the moment-curvature diagrams, sectional analysis based on fiber section method for integrating over the cross section is used. In this method, the cross section is discretized into fibers (or layers subjected to unidirectional bending), and an appropriate material model is assigned to each fiber. | |||
Figure A1 demonstrates a typical fiber section discretization. In this study, each section is discretized into 20 fibers/layers. The concrete material is represented by Kent and Park [A5] model in compression and Stevens exponential softening model in tension [A3]. Reinforcing steel bars are modeled using elastic perfectly plastic material with strain cutoff of 0.007 in tension and accounting for inelastic buckling model of Kashani et al. [A4] in compression. | |||
Moment-curvature diagrams are then calculated for axial tension of 0, 10, 30 and 60 kips. Each point is derived by selecting an axial force, and then changing curvature value and calculating the moment. Figure A2 presents the computed moment-curvature diagrams. | |||
An additional study is conducted to show the effect of including or excluding compressive reinforcement. | |||
The study shows accounting for the effect of compressive rebars increases the ductility of a member as presented in Figure A3; therefore, the member can accommodate more displacement. | |||
A7. REFERENCES | |||
[A1] Simpson Gumpertz & Heger Inc., Evaluation of Containment Enclosure Ventilation Area, 160268-CD-05 Rev. 1, Waltham, MA, Mar. 2017. | |||
[A2] United Engineers & Constructors Inc., Seabrook Station Structural Design Drawings. | |||
[A3] Yuan Lu, and Marios Panagiotou. "Three-dimensional cyclic beam-truss model for nonplanar reinforced concrete walls." Journal of Structural Engineering, 2013, 140(3): 04013071. | |||
[A4] Mohammad M. Kashani, Laura N. Lowes, Adam J. Crewe, Nicholas A. Alexander, Phenomenological hysteretic model for corroded reinforcing bars including inelastic buckling and low-cycle fatigue degradation, Computer and Structures, 156 (1), 58-71, 2015. | |||
[A5] Dudley. C. Kent, and Robert Park, Flexural members with confined concrete, ASCE Journal of Structural Division, 97 (ST7), 1969-1990, 1971. | |||
Attachment A -A Revision 0 | |||
A8. COMPUTATION Geometry Rebar diameter db 1.128in Reinforcement ratio 2 2 1 in 3 | |||
6.944 u 10 12in 24in Concrete Material Model Compressive strength of fc 3 ksi concrete Kent & Park Model Strain at Peak compressive co 0.002 strength Strain at 50% compressive fc strength 3 0.002 psi 3 50u 4.5 u 10 fc | |||
1000 psi Model parameter 0.5 Z 200 50u co Residual compressive strength fc.res fc 0.025 75 psi Steven's Model Young's modulus of concrete Ec 3120ksi Tensile strength of concrete ft 5 fc psi 273.861 psi Strain at cracking ft 5 cr 8.778 u 10 Ec Model parameter that controls M 75mm 0.018 residual db Model parameter that controls 540 3 t 4.005 u 10 softening slope M MATconc( ) min¬fc.res fc ¬1 Z co º1/4º1/4 if co Constitutive model for concrete 2 § 2º fc << ¨ * >> if d 0 | |||
¸ co | |||
¬ co © co ¹ 1/4 Ec if 0 d cr ft ¬( 1 M ) e | |||
t cr º | |||
M1/4 if cr d Attachment A -A Revision 0 | |||
0 Stress (ksi) | |||
MATconc c 2 ksi | |||
4 | |||
3 | |||
0.01 5u 10 0 c | |||
Strain Steel Material Model Yield s trength of steel fy 60ksi Young's modulus of steel Es 29000ksi Yield s train fy 3 y 2.069 u 10 Es Rupture strain sr 0.07 Account for buckling Buckling 1 Put 0 to ignore, put 1 to consider Kashani Model (buckling) | |||
Unbraced length/Diameter LD 15 Slenderness ratio fy p LD 30.509 100MPa Model parameters 1 4.572 p 74.43 65.057 | |||
0.071 p 2 318.4 e 36.495 fy star 3.75 15 ksi LD Attachment A -A Revision 0 | |||
Constitutive model for steel MATsteel ( ) if y | |||
fy if Buckling = 0 | |||
1 2 y y º1/4º | |||
¬star fy star e¬ 1/4 otherwise fy if y d sr 0 if sr d Es otherwise 50 Stress (ksi) | |||
MATsteel s 0 | |||
ksi | |||
50 | |||
0.05 0 0.05 s | |||
Strain Concrete Fibers Width of fibers b 12in Ref. 2, 2ft thick wall Total thickness or height h 24in Number of fibers Conc Num 20 h | |||
Height of fibers Conc H 1.2 in Conc Num Concrete fiber coordinates Conc y for i 1 Conc Num h Conc H ans m ( i 1 ) Conc H i 2 2 ans Concrete fiber strain Conc o for i 1 Conc Num ans m o Conc y i i ans Attachment A -A Revision 0 | |||
Concrete fiber stress Conc o for i 1 Conc Num ans m MATconc Conc o | |||
i i ans Concrete fiber force Conc F o for i 1 Conc Num ans m Conc o b Conc H i i ans Reinforcement/Steel fibers Depth to reinforcement d 20.5in Ref. 2, 2ft thick wall Area of tensile reinforcement 2 As 1in | |||
(#9@12 in.) | |||
Number of reinforcement in row, SteelNum 2 e.g. equal to 2 for tensile and compressive Steely §¨ d | |||
Depth to reinforcement fiber h* | |||
¸ 8.5 in 1 © 2¹ h | |||
Steely d 8.5 in 2 2 Area of reinforcement fiber 2 SteelAs As 1 in 1 | |||
2 SteelAs As 1 in 2 | |||
Steel fiber strain Steel o for i 1 SteelNum ans m o Steely i i ans Steel fiber stress Steel o for i 1 SteelNum ans m MATsteel Steel o | |||
i i ans Steel fiber force SteelF o for i 1 SteelNum ans m Steel o SteelAs i i i ans Attachment A -A Revision 0 | |||
Axial Equilibrium Force o ans1 m 0 for i 1 Conc Num ans1 m ans1 Conc F o | |||
i ans2 m 0 for i 1 SteelNum ans2 m ans2 SteelF o | |||
i ans m ans1 ans2 Moment Equilibrium Moment o ans1 m 0 for i 1 Conc Num ans1 m ans1 1 Conc F o Conc y i i ans2 m 0 for i 1 SteelNum ans2 m ans2 1 SteelF o Steely i i ans m ans1 ans2 Solution Known parameters Axial force P 60kip Iteration Curvature 1 | |||
0.003 in Solve for strain at centroid Axial strain at centroid (initial xo 0.03 Requires iteration guess) | |||
Axial force equilibrium f ( x) Force( x ) P cent root f xo xo 0.027 Sectional forces Force cent 60 kip Moment cent 48.079 kip ft Attachment A -A Revision 0 | |||
Stress and strain in concrete and steel | |||
§ 0.052 | |||
* Steel fiber stress and strain Rebar Steel cent ¨ 3¸ | |||
© 1.266 u 10 ¹ | |||
§ 60 | |||
* Rebar Steel cent ¨ ¸ ksi | |||
© 36.723 ¹ | |||
§ 60 | |||
* kip SteelF cent ¨ ¸ | |||
© 36.723 ¹ Concretey Conc y Concrete fiber stress and strain Concrete Conc cent | |||
Concrete Conc cent | |||
Rebar Rebar | |||
§¨ * Rebar Maximum compressive strain in 2 1 h 3 max.comp Steely ¸ 9.234 u 10 concrete Steely Steely ©2 1¹ 1 2 1 Attachment A -A Revision 0 | |||
A9. TABLES There are no tables. | |||
A10. FIGURES Figure A1: Schematic representation of fiber section method Figure A2: Moment - curvature diagrams for different axial force Attachment A -A Revision 0 | |||
Figure A3: Moment - curvature diagram considering the effect of including or excluding compressive rebars Attachment A - A Revision 0}} |
Latest revision as of 20:38, 3 February 2020
ML18004A007 | |
Person / Time | |
---|---|
Site: | Seabrook |
Issue date: | 01/02/2018 |
From: | NRC |
To: | Division of Operating Reactor Licensing |
References | |
17-953-02-LA-BD01 | |
Download: ML18004A007 (14) | |
Text
SeabrookLANPEm Resource From: SeabrookLAHearingFile Resource Sent: Tuesday, January 02, 2018 2:42 PM To: SeabrookLANPEm Resource Attachments: 170444-L-001 Rev. 0.pdf 1
Hearing Identifier: Seabrook_LA_NonPublic Email Number: 1341 Mail Envelope Properties (8d5e0168125e4699b25984c1e541eb8d)
Subject:
Sent Date: 1/2/2018 2:41:42 PM Received Date: 1/2/2018 2:41:52 PM From: SeabrookLAHearingFile Resource Created By: SeabrookLAHearingFile.Resource@nrc.gov Recipients:
"SeabrookLANPEm Resource" <SeabrookLANPEm.Resource@nrc.gov>
Tracking Status: None Post Office: HQPWMSMRS01.nrc.gov Files Size Date & Time MESSAGE 3 1/2/2018 2:41:52 PM 170444-L-001 Rev. 0.pdf 619783 Options Priority: Standard Return Notification: No Reply Requested: No Sensitivity: Normal Expiration Date:
Recipients Received:
6 November 2017 Mr. Edward Carley Engineering Supervisor - License Renewal NextEra Energy Seabrook, LLC.
P.O. Box 300, Lafayette Road Seabrook, NH 03874 Project 170444 - License Amendment Request & NRC Review Support, NextEra Energy Seabrook Station, Seabrook, NH Reference - Evaluation of Containment Enclosure Ventilation Area (CEVA),
Calculation 160268-CA-055HY (FP101122), 22 March 2017 Document Number: 170444-L-001
Dear Mr. Carley:
The structural evaluation of the Containment Enclosure Ventilation Area (CEVA), referenced above, showed that its north wall between EL +3 and +19 ft was bowed outward with a maximum out-of-plumbness of 1.25 in., measured during SGH field observation in February 2017. The referenced calculation showed that the wall can move by an additional 25% (reaching to 1.5 in.
at the point of maximum bowing) before conducting a more robust analysis or repairing the wall becomes necessary.
The bowing limit of 1.5 in. was calculated conservatively in the referenced calculation by neglecting the compression reinforcement in calculating the moment-curvature behavior of the wall. The limit of bowing is recalculated as shown in Attachment A considering the compression reinforcement in the moment-curvature calculation, and including the effects of upward vertical movement of CEVA. The upward movement of CEVA can impose vertical tension in the north wall of CEVA. Accordingly, moment-curvature relationships are calculated at different levels of tension.
At each level of axial force, a limiting curvature is determined to avoid unacceptable behavior. As explained in Attachment A, the curvature value of 0.003 1/in. corresponds either to the buckling of compression reinforcement (for cases with low level of axial tension) or rupture of tension reinforcement (for cases with high level of axial tension). Conservatively, 90% of this curvature value (0.0027 1/in.) is selected for computing the maximum bowing that the wall can resist.
The computed moment-curvature relationships are assigned to a finite element model of the wall, and nonlinear analyses are performed to determine the lateral displacement at which the curvature of the wall at the point of maximum bowing reaches the limiting curvature. Figure A2 in Attachment A shows that 2 in. of lateral wall deformation induces curvature of 0.0027 1/in. in the wall with a low level of axial force, while the same displacement induces curvature of 0.0023 1/in.
in the wall with a high level of axial tension. Therefore, the wall can resist a lateral bowing of 2 in.
Mr. Edward Carley - Project 170444 6 November 2017 Document No. 170444-L-001 Revision 0 before buckling or rupture of the vertical reinforcement will occur (with 10% margin), and it is recommended that the wall be retrofitted prior to it experiencing 2 in. of bowing.
The site visit report (170444-SVR-01-R0, FP101192-00) for the recent measurements indicates that the wall moved outward since the previous measurements; bulging has increased to 1-7/16 in. Additionally, at a localized area, hammer sounding indicated portions of the concrete cover potentially susceptible to separation, especially at areas with larger horizontal cracks. Therefore, sensitive equipment or processes should be protected against possible falling pieces of concrete cover from this wall before it is retrofitted.
Sincerely yours, Said Bolourchi Michael Mudlock, P.E.
Senior Principal Senior Project Manager NH License No. 14808 I:\BOS\Projects\2017\170444.00-LARS\Workspace\CEVA North Wall\170444-L-001 Rev. 0.docx
PROJECT NO: 170444 DATE: Nov 2017 CLIENT: NextEra Energy Seabrook BY: MR.M.Gargari
SUBJECT:
Evaluation of Additional Displacement for the North Wall of CEVA VERIFIER: I. Baig ATTACHMENT A MOMENT CURVATURE RELATION FOR THE CEVA NORTH WALL A1. REVISION HISTORY Revision 0: Initial document.
A2. OBJECTIVE OF CALCULATION The objective of this calculation is to compute moment-curvature diagrams for the north wall of Containment Enclosure Ventilation Area (CEVA) structure subjected to different tensile force.
A3. RESULTS AND CONCLUSIONS Figure A2 presents moment-curvature diagram for the wall section subjected to different tensile force. As can be seen from the figure, by increasing the magnitude of tensile force, the failure mode changes from compressive rebar buckling to tensile rebar rupture. For all cases, the point of severe damage initiation approximately corresponds to curvature value of 0.003 (1/in.). Accordingly, this point is selected as a limiting curvature and the wall is allowed to deform up to this curvature.
Figure A3 provides a comparison between two cases, one with accounting for the effect of compressive rebars and the other one without considering the compressive rebars. As can be seen from the figure, including the resistance offered by compressive reinforcement does not affect the ultimate capacity noticeably, however, it increases the ductility of a section.
A4. DESIGN DATA / CRITERIA See Section 4 of the calculation main body (160268-CA-05 Rev.0).
A5. ASSUMPTIONS A5.1 Justified assumptions There are no justified assumptions.
A5.2 Unverified assumptions There are no unverified assumptions.
Attachment A -A Revision 0
A6. METHODOLOGY To calculate the moment-curvature diagrams, sectional analysis based on fiber section method for integrating over the cross section is used. In this method, the cross section is discretized into fibers (or layers subjected to unidirectional bending), and an appropriate material model is assigned to each fiber.
Figure A1 demonstrates a typical fiber section discretization. In this study, each section is discretized into 20 fibers/layers. The concrete material is represented by Kent and Park [A5] model in compression and Stevens exponential softening model in tension [A3]. Reinforcing steel bars are modeled using elastic perfectly plastic material with strain cutoff of 0.007 in tension and accounting for inelastic buckling model of Kashani et al. [A4] in compression.
Moment-curvature diagrams are then calculated for axial tension of 0, 10, 30 and 60 kips. Each point is derived by selecting an axial force, and then changing curvature value and calculating the moment. Figure A2 presents the computed moment-curvature diagrams.
An additional study is conducted to show the effect of including or excluding compressive reinforcement.
The study shows accounting for the effect of compressive rebars increases the ductility of a member as presented in Figure A3; therefore, the member can accommodate more displacement.
A7. REFERENCES
[A1] Simpson Gumpertz & Heger Inc., Evaluation of Containment Enclosure Ventilation Area, 160268-CD-05 Rev. 1, Waltham, MA, Mar. 2017.
[A2] United Engineers & Constructors Inc., Seabrook Station Structural Design Drawings.
[A3] Yuan Lu, and Marios Panagiotou. "Three-dimensional cyclic beam-truss model for nonplanar reinforced concrete walls." Journal of Structural Engineering, 2013, 140(3): 04013071.
[A4] Mohammad M. Kashani, Laura N. Lowes, Adam J. Crewe, Nicholas A. Alexander, Phenomenological hysteretic model for corroded reinforcing bars including inelastic buckling and low-cycle fatigue degradation, Computer and Structures, 156 (1), 58-71, 2015.
[A5] Dudley. C. Kent, and Robert Park, Flexural members with confined concrete, ASCE Journal of Structural Division, 97 (ST7), 1969-1990, 1971.
Attachment A -A Revision 0
A8. COMPUTATION Geometry Rebar diameter db 1.128in Reinforcement ratio 2 2 1 in 3
6.944 u 10 12in 24in Concrete Material Model Compressive strength of fc 3 ksi concrete Kent & Park Model Strain at Peak compressive co 0.002 strength Strain at 50% compressive fc strength 3 0.002 psi 3 50u 4.5 u 10 fc
1000 psi Model parameter 0.5 Z 200 50u co Residual compressive strength fc.res fc 0.025 75 psi Steven's Model Young's modulus of concrete Ec 3120ksi Tensile strength of concrete ft 5 fc psi 273.861 psi Strain at cracking ft 5 cr 8.778 u 10 Ec Model parameter that controls M 75mm 0.018 residual db Model parameter that controls 540 3 t 4.005 u 10 softening slope M MATconc( ) min¬fc.res fc ¬1 Z co º1/4º1/4 if co Constitutive model for concrete 2 § 2º fc << ¨ * >> if d 0
¸ co
¬ co © co ¹ 1/4 Ec if 0 d cr ft ¬( 1 M ) e
t cr º
M1/4 if cr d Attachment A -A Revision 0
0 Stress (ksi)
MATconc c 2 ksi
4
3
0.01 5u 10 0 c
Strain Steel Material Model Yield s trength of steel fy 60ksi Young's modulus of steel Es 29000ksi Yield s train fy 3 y 2.069 u 10 Es Rupture strain sr 0.07 Account for buckling Buckling 1 Put 0 to ignore, put 1 to consider Kashani Model (buckling)
Unbraced length/Diameter LD 15 Slenderness ratio fy p LD 30.509 100MPa Model parameters 1 4.572 p 74.43 65.057
0.071 p 2 318.4 e 36.495 fy star 3.75 15 ksi LD Attachment A -A Revision 0
Constitutive model for steel MATsteel ( ) if y
fy if Buckling = 0
1 2 y y º1/4º
¬star fy star e¬ 1/4 otherwise fy if y d sr 0 if sr d Es otherwise 50 Stress (ksi)
MATsteel s 0
ksi
50
0.05 0 0.05 s
Strain Concrete Fibers Width of fibers b 12in Ref. 2, 2ft thick wall Total thickness or height h 24in Number of fibers Conc Num 20 h
Height of fibers Conc H 1.2 in Conc Num Concrete fiber coordinates Conc y for i 1 Conc Num h Conc H ans m ( i 1 ) Conc H i 2 2 ans Concrete fiber strain Conc o for i 1 Conc Num ans m o Conc y i i ans Attachment A -A Revision 0
Concrete fiber stress Conc o for i 1 Conc Num ans m MATconc Conc o
i i ans Concrete fiber force Conc F o for i 1 Conc Num ans m Conc o b Conc H i i ans Reinforcement/Steel fibers Depth to reinforcement d 20.5in Ref. 2, 2ft thick wall Area of tensile reinforcement 2 As 1in
(#9@12 in.)
Number of reinforcement in row, SteelNum 2 e.g. equal to 2 for tensile and compressive Steely §¨ d
Depth to reinforcement fiber h*
¸ 8.5 in 1 © 2¹ h
Steely d 8.5 in 2 2 Area of reinforcement fiber 2 SteelAs As 1 in 1
2 SteelAs As 1 in 2
Steel fiber strain Steel o for i 1 SteelNum ans m o Steely i i ans Steel fiber stress Steel o for i 1 SteelNum ans m MATsteel Steel o
i i ans Steel fiber force SteelF o for i 1 SteelNum ans m Steel o SteelAs i i i ans Attachment A -A Revision 0
Axial Equilibrium Force o ans1 m 0 for i 1 Conc Num ans1 m ans1 Conc F o
i ans2 m 0 for i 1 SteelNum ans2 m ans2 SteelF o
i ans m ans1 ans2 Moment Equilibrium Moment o ans1 m 0 for i 1 Conc Num ans1 m ans1 1 Conc F o Conc y i i ans2 m 0 for i 1 SteelNum ans2 m ans2 1 SteelF o Steely i i ans m ans1 ans2 Solution Known parameters Axial force P 60kip Iteration Curvature 1
0.003 in Solve for strain at centroid Axial strain at centroid (initial xo 0.03 Requires iteration guess)
Axial force equilibrium f ( x) Force( x ) P cent root f xo xo 0.027 Sectional forces Force cent 60 kip Moment cent 48.079 kip ft Attachment A -A Revision 0
Stress and strain in concrete and steel
§ 0.052
- Steel fiber stress and strain Rebar Steel cent ¨ 3¸
© 1.266 u 10 ¹
§ 60
- Rebar Steel cent ¨ ¸ ksi
© 36.723 ¹
§ 60
- kip SteelF cent ¨ ¸
© 36.723 ¹ Concretey Conc y Concrete fiber stress and strain Concrete Conc cent
Concrete Conc cent
Rebar Rebar
§¨ * Rebar Maximum compressive strain in 2 1 h 3 max.comp Steely ¸ 9.234 u 10 concrete Steely Steely ©2 1¹ 1 2 1 Attachment A -A Revision 0
A9. TABLES There are no tables.
A10. FIGURES Figure A1: Schematic representation of fiber section method Figure A2: Moment - curvature diagrams for different axial force Attachment A -A Revision 0
Figure A3: Moment - curvature diagram considering the effect of including or excluding compressive rebars Attachment A - A Revision 0