3F0409-04, Attachment B Through E - Crystal River, Unit 3 - License Amendment Request 303, Revision 1, Revision to Final Safety Analysis Report Sections 5.4.3, Structural Design Criteria, and 5.4.5.3, Missile Analysis.
| ML091030168 | |
| Person / Time | |
|---|---|
| Site: | Crystal River  |
| Issue date: | 04/08/2009 |
| From: | Florida Power Corp, Progress Energy Florida |
| To: | Office of Nuclear Reactor Regulation |
| References | |
| 3F0409-04 S07-0037, Rev 1 | |
| Download: ML091030168 (136) | |
Text
PROGRESS ENERGY FLORIDA, INC.
CRYSTAL RIVER UNIT 3 DOCKET Number 50-302 /License Number DPR-72 LICENSE AMENDMENT REQUEST #303, Revision 1 Revision to Final Safety Analysis Report Sections 5.4.3, "Structural Design Criteria," and 5.4.5.3, "Missile Analysis" Attachment B Calculation S07-0037, Revision 1
Systems MX Calc. Sub-Type Priority Code 3 Quality Class S NUCLEAR GENERATION GROUP ANALYSIS I CALCULATION S07-0037 (Calculation #)
Structural Qualification of Auxiliary Building East and South Walls for Tornado Wind and Missile Loading (per AR 00215432)
(Title including structures, systems, components)
[1 BNP UNIT
[CR3 []HNP []RNP [:NES E ALL APPROVAL H--Electronically Annrove d Rev Prepared By Reviewed By . Supervisor Signature ~ Signature NameNaeU Nm Martin McDonald Adam AI-Dabbagh Chris Sward Sargent & Lundy Sargent & Lundy Sargent & Lundy DateDaeDt (For Vendor Calculations)
Vendor Sargent & Lundy LLC Vendor Document No. N/A Owner's Review By C. Glenn Pugh Date 1ýr
Calculation No. S07-0037 Page i Revision 1 List Of Effective Pages Page Rev Page Rev Page Rev Page Rev i 1 ii 1 iii 1 iv 1 v 1 vi 1 vii 1 viii 0 1 0 2 0 3 1 4 0 5 0 6 0 7 0 8 0 9 0 10 0 11 0 12 0 13 0 14 0 15 1 16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 1 Attachments Attach. Number Attach. Number Attach. Number Number of Pages Number of Pages Number of Pages A 0 1 B 0 51 C 0 8 D 0 16 E 0 1 F 0 4 G 1 3 Amendments Rev & No of Rev & No of Rev & No of Rev & No of Letter Pages Letter Pages Letter Pages Letter Pages
Calculation No. S07-0037 Page ii Revision 1 Table Of Contents Page No.
List of Effective Pages ........................................................................................................................ i Ta b le o f C o n te n ts ............................................................................................................................... ii Revision Sum mary ............................................................................................................................. iv Document Indexing Tables ................................................................................................................. iv Record of Lead Review ...................................................................................................................... vi Record of Interdisciplinary Review ..................................................................................................... viii P u rp o s e ............................................................................................................................................. 1 Bo d y o f C a lc u la tio n ............................................................................................................................ 1 1 Me th o d o lo gy ................................................................................................................................. 3 2 De s ig n Inp u ts ............................................................................................................................... 3 3 As s u m ptio n s ................................................................................................................................. 3 4 Detailed Calculations .................................................................................................................... 4 4.1 Ultimate Capacity (Yield-Line Theory) for 3-ft Thick W all ........................................................... 4 4.2 Overall Response to Missile Impact for 3-ft Thick W all ............................................................. 7 4.2.1 Collapse Load for 3-ft Thick W all ............................................................................................ 7 4.2.2 Concrete Properties for 3-ft Thick W all .................................................................................. 8 4.2.3 Elastic Stiffness for 3-ft Thick W all ........................................................................................... 11 4.2.4 Effective Mass for 3-ft Thick W all ............................................................................................. 11 4.2.5 Natural Period of Vibration for 3-ft Thick W all ......................................................................... 12 4.2.6 Im pact Force and Duration of Im pact for 3-ft Thick W all ........................................................ 12 4.2.7 Slab Ductility for 3-ft Thick W all ..................................................... :........................................... 13 4.3 Ultimate Capacity for 2-ft Thick W all ........................................................................................... 16 4.3.1 Ultimate Capacity for Reduced Reinforcement 2-ft Thick W all ................................................ 17 4.3.2 Tornado W ind and Depressurization for 2-ft Thick W all ........................................................... 18 4.3.3 Seism ic Loading for 2-ft Thick W all ......................................................................................... 19 4.4 Overall Response to Missile Im pact for 2-ft Thick W all ............................................................. 20 4.4.1 Ultimate Capacity for 2-ft Thick W all ...................................................................................... 20 4.4.2 Collapse Load for 2-ft Thick W all ............................................................................................ 20 4.4.3 Shear Resistance for 2-ft Thick W all ...................................................................................... 20 4.4.4 Collapse Load for Reduced Reinforcement 2-ft Thick W all .................................................... 21 4.4.5 Concrete Properties for 2-ft Thick W all .................................................................................. 21 4.4.6 Stiffness under Concentrated Load for 2-ft Thick W all ........................................................... 21 4.4.7 Effective Mass for 2-ft Thick W all ........................................................................................... 22 4.4.8 Natural Period of Vibration for 2-ft Thick W all ......................................................................... 22 4.4.9 Impact Force and Duration of Impact for 2-ft Thick W all ......................................................... 22 4.4.10 Slab Ductility for 2-ft Thick W all ............................................................................................. 22 4.4.11 Column Response to Missile Impact .................................................................................... 23 5 R e s u lts ............................................................................................................................................ 24 C o n c lu s io n s ........................................................................................................................................ 24 R efe re n c e s ......................................................................................................................................... 25
Calculation No. S07-0037 Page iii Revision 1 Attachments Tota I Page(s)
A Attachment
Reference:
Impact Force and Duration of Impact Force ............................ 1 B Attachment GT STRUDL ANALYSIS FOR MISSILE LOAD (DESIGN VERIFICATION REVIEW : ALTERNATE CALCULATION METHOD) ................................................... 51 C Attachm ent
Reference:
Yield Line Theory ..................................................................... 8 D Attachment GT STRUDL ANALYSIS FOR 3-FT THICK WALL (DESIGN VERIFICATION REVIEW: ALTERNATE CALCULATION METHOD) ......................... 16 E Attachment LOAD COMBINATION (DESIGN VERIFICATION REVIEW:
ALTERNATE CALCULATION M ETHOD) .................................................................... 1 F Attachment Verify Ultimate Distributed Load Derivation by Yield Line Standard Equations Using W ork Energy Methods ........................................................................ 4 G Attachm ent PCACOLUM N ANALYSIS .......................................................................... 3 Amendments (if applicable) Total Page(s)
A Am endm ent A title ...............................................................................................................
B Am endm ent B title ...............................................................................................................
Calculation No. S07-0037 Page iv Revision 1 Revision Summary Revision Revision Summary
- (Include brief description of revision and a list of EC's and other modifications incorporated into revision) 0 Original Issue in Response to AR 00215432 1 Revised methodology & computations for east wall. Issue in response to RAI for License Amendment Request to Revise FSAR Sections 5.4.3 & 5.4.5.3 Document Indexinq Tables Document Management System Data (For update of PassPort Controlled Document information - Document Service is to delete roll over data only if shown for DELETE in the following tables)
Notes - General Doc Services Text of General Notes Action (Enter ADD, DELETE, or- )
ADD GT-STRUDL, Version 27 analysis software was used in the development of this calculation. Software validation is maintained by Sargent & Lundy.
ADD PCA Column, Version 4.10 analysis software was used in the development of this calculation. Software validation is maintained by Sargent & Lundy.
Reference Numbers - Reference Systems Doc Services System Action (Two letter code for systems affected by results)
(Enter ADD, DELETE, or -)
Reference Numbers - Other References (references to PassPort products)
Doc Services Type Reference Sub Title Action (e.g. AR, (e.g. AR No, EC (AR Assign No, (Enter ADD, EC, WO, No, WO No, etc) WO Task No, DELETE, or-) etc) etc.)
-I-1- -t Legend: ADD = New data record to be added to PassPort; REV = Change revision level of a referenced Controlled Document, DELETE = Existing data record to be deleted; - = Existing PassPort data that is to be retained; Bold Faced column heading = PassPort data label
Calculation No. S07-0037 Page v Revision 1 Input Document References - Controlled Documents with Cross References Doc Services Doc. Type Document Document ID Sheet Doc Minor Ref Action (e.g. CALC, Sub-Type (e.g., Calc No., Dwg. (Dwg. sheet Rev Rev Type (Enter ADD, REV, DWG, NPAS, No., Procedure No) number if (for Calc (for NPAS DELETE, or-) POM, etc) Applicable) Amendments) Docs)
Description Codes (Key Words)
Doc Services Code Action (Codes for Key Words)
(Enter ADD, (To be recorded as document DELETE, or - ) description codes in PassPort)
OutDut Document References (Doc Service is to ooen listed documents and add or delete this Calc as a reference)
Doc Services Document Document Document ID Revision Action Tracking Action Type Sub-Type (e.g., Calc No., Dwg. (AR number or EC number (Enter ADD, (e.g. CALC, DWG, No., Procedure No., that will track revision of DELETE, or - TAG,PROCEDURE, Software name and affected document for the SOFTWARE) version) results of this calculation)
Equipment Database Data (For update of PassPort Equipment Database information)
Equipment Document References Config Mgqt Equipment Equipment Type Relationship to Caic.
Action Tag (includes SFTAPL for (e.g. equipment operation affected by results, (Enter ADD, analysis software) equipment design affected by results, analysis DELETE, or-) software)
- 1- t Legend: ADD = New data record to be added to PassPort; REV = Change revision level of a referenced Controlled Document, DELETE = Existing data record to be deleted; - = Existing PassPort data that is to be retained; Bold Faced column heading = PassPort data label
Calculation No. S07-0037 Page vi Revision 1 Record of Lead Review Document S07-0037 Revision I The signature below of the Lead Reviewer records that:
- the review indicated below has been performed by the Lead Reviewer;
- appropriate reviews were performed and errors/deficiencies (for all reviews performed) have been resolved and these records are included in the design package;
- the review was performed in accordance with EGR-NGGC-0003.
Z Design Verification Review El Engineering Review LI Owner's Review Z Design Review Rii Alternate Calculation E] Qualification Testing ElI Special Engineering Review_________________________
Ej YES F-1 N/A Other Records are attached.
I Adam AI-Dabbagh seld- cc-741e 1,45'66 Civil/Structural Date (print/sign) Discipline I Lead Reviewer Item Deficiency Resolution No.
Incorrect Reference listed for slab stiffness
- 1) calculation on pg 21. Should be reference 12. Updated reference Add information to description of force pulse on Changed description, added diagram depicting page 22. rectangular force pulse.
3). Use conservative dynamic load factor of 2.0 for Changed dynamic load factor to 2.0 column check on page 23.
On page 24, calculate seismic load as an
- 4) equivalent pressure for comparison to tornado Converted seismic load to an equivalent pressure wind loads.
5) 6)
7) 8)
FORM EGR-NGGC-0003-2-10 This form is a QA Record when completed and included with a completed design package. Owner's Reviews may be processed as stand alone QA records when Owner's Review is completed.
Calculation No. S07-0037 Page vii Revision 1 Record of Lead Review Document S07-0037 Revision I The signature below of the Lead Reviewer records that:
- the review indicated below has been performed by the Lead Reviewer;
- appropriate reviews were performed and errors/deficiencies (for all reviews performed) have been resolved and these records are included in the design package;
- the review was performed in accordance with EGR-NGGC-0003.
F- Design Verification Review El Engineering Review Z Owner's Review M] Design Review F1 Alternate Calculation El Qualification Testing El Special Engineering Review El YES RI N/A Other Records are attached.
C. Glenn Pugh 6$~I Civil/Structural Lead Reviewer (priritisign) Discipline Date Item Deficiency Resolution No.
Cover Page- Even though this calculation is
- 1) being prepared under S&L's QA plan, there still Updated cover page needs to be an owner's review. Remove the "N/A" and add my name Revision 0 did not list software, but we should
- 2) have listed GTStrudl. All software should have Added software information to document indexing software name and version listed on the table.
document indexing table.
On Page 17, the clear cover is listed as 3/4" on
- 3) inside face of wall. Drawings indicate that clear Calculated new ductility demand to equal 5.2.
cover is 2" inside and outside.
- 4) On page 19, what is the basis of the leeward Calculated and used windward pressure (0.183 wind pressure of 0.081 ksf. Could not find this. kso in place of 0.081 ksf.
- 5) Is PCA-Column applicable to Safety related PCA column is verified and validated by S&L for applications (see comment 2 above also) all program features.
- 6) Reference 16 should be: Edited reference 6)____ SP-5209, "CR3 Seismic Qualification," Rev. 0 There are no comments on the Record of Lead Review even through there has been some email comments. Add this page as "owner's review" Added comments to the calculation and TOC for Rev. I FORM E-GR-NGGC-0003-2-10 This form is a QA Record when completed and included with a completed design package. Owner's Reviews may be processed as stand alone QA records when Owner's Review is completed.
Calculation No. S07-0037 Page viii Revision 0 Record of Interdisciplinary Reviews PART I - DESIGN ASSUMPTION / INPUT REVIEW: APPLICABLE EI Yes Z No The following organizations have reviewed and concur with the design assumptions and inputs used in this calculation:
Systems Engqineeringq Name Signature Date Operations Name Signature Date Other Name Signature Date PART II - RESULTS REVIEW:
The following organizations are aware of the impact of the results of this calculation (on designs, programs and procedures):
Systems Enqineering FD Yes M NO Name Signature Date Comments:
Operations DYes ZNO Name Signature Date Comments:
Other Name Signature Date Comments:
Other Name Signature Date Comments:
Other Name Signature Date Comments:
Calculation No. S07-0037 Revision 0 Attachment Page 1 Purpose AR 00215432 contains the following problem description:
EXISTING STRUCTURAL CALCULATIONS RELATED TO THE EAST AND SOUTH AUXILIARY BUILDING WALLS DO NOT REFLECT LOADING RELATED TO TORNADO DRIVEN MISSILES. GILBERT AND ASSICIATES CALCULATION 2:01 CONCLUDES WIND LOADING IS ACCEPTABLE BUT DOES NOT INCLUDE THE SPECTRUM OF TORNADO MISSILES DEFINED IN THE FSAR SECTION 5.2.1.2.6.
ADDITIONALLY, THE CALCULATION DID NOT ADDRESS THE TORNADO WIND LOAD COMBINATION (WIND PRESSURE + EXTERNAL PRESSURE DROP) AS DETAILED IN SECTION 5.2.3.2.1.
PRELIMINARY ASSESSMENT OF THE LOADS INDICATES THAT THE BUILDING WILL WITHSTAND THE LOADING WITHOUT FAILURE (SEE ATTRIBUTE 6A). THIS EVALUATION APPLIED A METHODOLOGY NOT CURRENTLY CONTAINED IN THE FSAR AND WILL REQUIRE RECONCILIATION.
This calculation provides the appropriate evaluation to show that both the east and south walls are operable and also determines the walls can be qualified using standard structural analysis techniques. As also stated in the above problem statement these techniques are not currently identified in the existing CR3 design and licensing basis. However, revision to the Design Basis Document and FSAR are being pursued as a follow-up to this calculation.
This calculation will determine the capacity of the Auxiliary Building (South and East walls) to resist the spectrum of tornado missiles in the licensing and design basis. This calculation also determines the capacity of the Auxiliary building walls to resist the wind pressure and depressurization resulting from a tornado.
Body of Calculation From the investigation of AR 00215432 the following loading is applicable to this calculation:
The tornado loads are defined in FSAR Section 5.2.1.2.6 for all Class I structures. The required loads are:
" External wind pressure due to a 300 mph tangential wind velocity. There is no clarification as which direction the wind is on the buildings or what the required design pressure is. The original design basis, Gilbert Calculations (Ref. 4) have calculated a pressure of 297 pounds per square foot (psf) acting on vertical surfaces and -274 psf acting as uplift on windward edge of roofs.
This design pressure is also listed in the Design Basis Document for Major Class I Structures (Tab 1/3), Revision 2, Page 12. The DBD defines this wind pressure as Ww The FSAR defines this wind pressure as Wt.
This calculation will use Wt with a design pressure of 297 psf
" An external pressure drop of 3 psig. As further defined in the DBD this is a 3 psig tornado differential pressure. It is a suction experienced by the outside of the structure corresponding to the drop in atmospheric pressure characteristic of the center vortex of a tornado. The pressure occurs because the structure is relatively airtight and there is little opportunity for contained air to escape and reach equilibrium with the outside. The Gilbert Calculations (Ref. 4) have calculated that this 3 psig pressure drop acts as a 432 psf pressure acting outwards. This design pressure is also listed in the Design Basis Document
Calculation No. S07-0037 Revision 0 Attachment Page 2 for Major Class I Structures (Tab 1/3), Revision 2, Page 12. The DBD defines this outward pressure as Wp. The FSAR defines this outward pressure as Pt This calculation will use Pt with a design pressure of 432 psf The Tornado Missiles to be included in the design of a Class I structure are listed in Section 5.2.1.2.6 of the FSAR. The two main tornado missiles to be designed for include a 14" diameter utility pole and a compact automobile.
The required design kinetic energy's are listed in the FSAR. The Gilbert Calculations use the kinetic energy and various analysis techniques to derive the following design loads:
" Utility Pole= 148 kips on a 14" diameter area
" Compact Auto = 270 kips on a 2.5' x 2.5' area The other missiles listed in Section 5.2.1.2.6 are discounted as being bounded by the utility pole and automobile. The two missiles listed above are also listed in the DBD Design Basis Document for Major Class I Structures (Tab 1/3), Revision 2, Page 12. The DBD defines these missile loads as Win.
The FSAR (Section 5.2.1.2.6) already has determined that a minimum of 2 feet of concrete provides sufficient resistance to the above tornado missile spectrum that no further penetration calculations are required. This calculation applies the loading shown to verify the capacity of the overall wall.
The AR also discussed an apparent discrepancy between the load combinations (using the above tornado loadings) between the FSAR and DBD. The following load combinations will be used for this calculation. These load combinations are a realistic application of the various loads. A follow-up to this calculation will be EC/CMU 68758 to document a change to the DBD and a license amendment request will be filed to request a change to the FSAR for the change in analysis methodology and load combinations.
Abnormal Condition:
C = (D + L + Wt + Pt)
NOTE: Applied to leeward wall. Applies a pressure load from inside towards the outside the building. i.e. suction on the leeward wall; negative moment reinforcement would be on outside face of wall.
Concrete reinforcement is typically installed on both faces of the wall; therefore loading is generic to all walls C =Wm NOTE: Applied to windward wall. Applies a point load from outside towards the inside of the building. i.e. negative moment reinforcement would be on inside face of wall.
Where D = Dead Load (conservatively omitted; combination of D+W < W loading)
L= Live Load (no floor live load)
Wt = Tornado wind load
Calculation No. S07-0037 Revision Attachment Page 3 Pt = Internal pressure due to tornado wind Wm = Tornado missile E' = Maximum Hypothetical Earthquake (Safe Shutdown Earthquake)
- 1. Methodoloqy The following methodologies are applied in this calculation:
" Ultimate strength design per ACI code (see Attachment B and D)
" Yield Line Theory (see Attachment C)
" Strain Energy
" Method of Unit Loads
" Ductility Ratio Evaluation
- 2. Design Inputs 2.1 Design inputs used in this calculation.
" Concrete density = 150 pcf (Ref. 1)
" Poisson's ratio for concrete = 0.17
" Reinforcing steel yield strength, fy = 40 ksi
" Dynamic Increase Factor for Shear = 1.1 (Ref. 13)
" Dynamic Increase Factor for 40 ksi reinforcing steel = 1.2 (Ref. 13)
- 3. Assumptions 3.1 All assumptions in the calculation are directly based on references.
3.2 No engineering judgments were required.
Calculation No. S07-0037 Revision 0 Attachment Page 4
- 4. Detailed Calculations 4.1 DETERMINE THE ULTIMATE LOAD CAPACITY OF THE 3-FT THICK SOUTH AUXILIARY BLDG WALL USING YIELD LINE THEORY FOR SLABS AND VERIFY THAT THE WALL IS ADEQUATE FOR TORNADO WIND + DEPRESSURIZATION Yield line theory offers a simplified analytical method that that can determine the ultimate bending capacity of flat reinforced concrete plates subject to distributed and concentrated loads. Alternately, yield line theory, combined with hinge rotation limits can determine the energy absorption capacity of plates subject to impulsive and impact loads. This method is especially useful in evaluating existing structures that can not be qualified using conservative simplifying analytical assumptions. Typical components analyzed by yield line theory are basemats, floor and roof slabs subject to vertical loads along with walls subject to out of plane loads.
Vertical #7@12" EW (Ea. Face)
Horizontal Edges supported and restrained 7
Capacity =kM, lal Dimensions (b) Top reinforcement (c) Bottom reinforcement Figure 18.9.1 A rectangular two-way slab panel.
Determine moment capacity of reinforcement Concrete compressive strength, f' c = 3 ksi Rebar yield stress, f y = 40 ksi Wall thickness, t = 36 in Rebar cover, c = 2 in Unit width, b= 12 in Flexure ratio, 4= 0.9 Reinforcement in both directions Rebar Direction Location Rebar # - Sp, s (in) "A ( in ) Dia., in. d (in) d ' (in) in a-direction Top [ 7 12 0.6 0.875 33.5625 Bottom 7 12 0.6 0.875 33.5625 in b-direction Top 7 12 0.6 0.875 32.6875 Bottom 7 12 0.6 0.875 32.6875 Unit bending moment for rebar in a-direction (top and bottom)
A's= b'As/s
Calculation No. S07-0037 Revision 0 Attachment Page 5
= 12 *0.60/12
= 0.600 in 2 /in
= fyA's/(0.85f'cb')
= 40"0.600/(0.85"3"12)
= 0.784 in/in M nnx = M npx = OA'ýfy ( d-a/2 )
= 0.9
- 0.600
- 40 * ( 33.563 - 0.784 / 2)
= 716.48 in - kip
= 59.71 ft - kip Bending moment for rebar in b-direction (top and bottom) a= fyA's/(0.85f'cb')
= 40"0.600/(0.85"3*12)
= 0.784 in
.M nny =M npy = ýA 's fy ( d'-a/2 )
= 0.9 *0.600 *40" (32.688- 0.784/2 )
= 697.58 in - kip
= 58.13 ft- kip
.Capacity = ,v Edges supported and resmiained Capacity =M. - Capacity =M" lae Dimensions (M) Top reinforcement (C) Bottom reinforcemrnent Figure 18.9.1 A rectangular two-way slab panel.
Parameters Dimensions Reinforcement a= 79 ft Top capacity, M ,x-= 59.71-, ft - kip / ft b= 24 ft Top capacity, M y = 58.13 ft - kip / ft Bottom capacity, M px = 59.71 ft - kip / ft Bottom capacity, M py = 58.13 ft - kip / ft Determine applicable yield line pattern (Ref. 3, Chapter 18)
Calculate the sum of positive and negative moment in the a-direction divided by the sum of the positive and negative moment reinforcement in the b-direction K rebar --- (M nnx + M npx M nny + M npy)
= (59.71 + 59.71 )/(58.13+58.13)
= 1.027 Calculate the ratio of the squares of a and b dimensions K1a/b a 2/ b 2
= 79A2/24A2
Calculation No. S07-0037 Revision 0 Attachment Page 6
= 10.835 Yield Controlling Pattern Limitation Identity Status Compare the ratio of( M + M 1 npx ) to M nny+ M ny )with the DOES NOT K rebar K a/b ratio a to b . Yield Pattern GOVERN No. 1 will control.
Reinforcement in the "a 2 direction" is less than that for K rebar < Ka/b GOVERNS Y ie ld Pa tte rn No.1 ...............................................
Reinforcement in the "a DOES NOT 3 ' direction" is more than that for K rebar > K a/b 'GOVERN Yield Pattern No.1 Determine the uniform load w , / 0 at the collapse condition Ref. #4 No. Yield Pattern EQN Calculation 1 __,, _ 18.9.3 Wu/0= 12[(Mnnx+Mnpx)/a +(Mnny+Mnpy /bz]
~~~
18.9.9~
e.a ~~ ~~ [-te -..-
i ................................... ~~~~
2 18.9.9ý [D-etfermine x in the following quadratic I equation.
2 S+nny+Mnnpya)X[+ +4b2 innx + M nPx )x-[3a b2(Mnnx +
M npx)] 0 4 *"79 (58.13 + 58.13 )*x A 2+
4"242"(59.71 +59.71 )*x-(b) Yield p'attern No. 2 [ 3 79 24 A2 (59.71 +
59.71 0 EXCEL SOLVER solution or Trial & error solution x= 17.6502 ft 4 *79 (58.13 + 58.13)*
17.6502 2 + 4 *24 2* (59.71
+ 59.71) 17.6502 -[3* 79
- 24 A2 * (59.71 + 59.71 )] = 1.92E-07 2
18.9.11 wu/¢= 6(M nnx+ M npa)/X
= 6 (59.71 + 59.71 )/17.6502 A2
= 2.300 ksf GOVERNS________
3 18.9.14 Determine y in the following quadratic equation.
4b(Mnna+M npa)y 2 +4a 2 (M nny + M npy)y[ 3 b a2 (M ny+
M npy ] 0 (C) yiewpaMm, No. 3 w u/o= 6 ( M ny + M npy )/Y 2 Tornado wind pressure = 0.297 ksf Vacuum pressure = 0.432 ksf Total Tornado Wind Pressure = 0.729 ksf OK < 2.30 ksf
Calculation No. S07-0037 Revision 0 Attachment Page 7 The applied pressure load on the 3-foot thick wall does not exceed the collapse pressure load; therefore, the 3-foot is structurally adequate to withstand tornado wind and depressurization.
4.2 OVERALL RESPONSE TO MISSILE IMPACT The methodology stated in ASCE Manuals and Reports on Eng'g Practice No. 58 "Struct'l Analysis and Design of Nuclear Plant Facilities", Chapter 6, "Design Against Impulse and Impact Loads" will be used for this evaluation (Ref. 8).
4.2.1 CALCULATE COLLAPSE LOAD R m(Per Ref. #8, Table 6.4)
Concentrated collapse load at center of slab with 100% fixity at all sides, Rm = 2t(M ++M + )
where M ,+ = Ultimate positive moment capacity M u. = Ultimate negative moment capacity Since M+ = M _
Let M , = M += M u-Rm 4inM*
Since A= A's M,= O[A'sfy(d-d')]DIF where f y= Re-bar yield strength d= Distance from extreme comoression fiber to centroid of tension reinforcement d'= Distance from extreme compression fiber to centroid of compression reinforcement
= c +d,/2
= 2.000 + 0.875 / 2
= 2.4375 in I)IF= Dynamic increase factor for re-bar. Ref. ASCE Manuals and Reports on Engineering Practice No. 58, "Structural Analysis and Design of Nuclear Plant Facilities", page 317, Table 6.2.
f DIF 40 1.2 60 1.1 DIF = 1.2 Dynamic Increase Factor The dynamic material strength shall be computed by applying a dynamic increase factor that accounts for the increase in material strength due to strain rate effects. The dynamic variation due to increase in strain rate increases the yield stress of steel and compressive strength of concrete. It is common to take credit for the dynamic strength increase.
For reinforced concrete structures subjected to blast effects, response at very high strain rates is often sought. At these high strain rates, the reinforcing bars yield stress can increase by 100%, or more, depending on the grade of steel used. The dynamic increase factor (DIF), i.e. the ratio of the dynamic to static value, is normally reported as function of strain rate. DIF curves for both yield and ultimate strengths have been derived and published in manuals by the Tri-Services, the Defense Special Weapons Agency, the Air Force, and the Department of Energy. Ref. http://www.kcse.com/pdfs/P-98-31_f.pdf In Regulatory Position 10.6, increase in the material strength (i.e., dynamic increase factor, DIF) could be realized only when the material is subjected to very high strain rates of loading, normally associated with impactive loadings. If a structure is found to be responding in a static or semi-static manner to a dynamic loading (i.e., dynamic load factor (DLF) <1.2), the materials of the structure would not undergo very high strain rate that would increase the material strength. Though there is no direct relationship between DLF and DIF, Regulatory Position 10 restricts the use of DIF when the DLF is lower than 1.2.
Calculation No. S07-0037 Revision 0 Attachment Page 8 Ref. RegGuide 1.142 Rev 2 Nov 2001 Mp= 0[A'sfy(d-d')]DlF
= 0.90 * [ 0.0500
- 40000 * ( 33.563 - 2.438 ]
- 1.20
= 67230 in - lb / in Collapse Load Rm 4*3.142*67230
= 844837 lb 4.2.2 DETERMINE CONCRETE PROPERTIES Determine reinforced concrete section properties; use average of cracked and uncracked moment of inertia.
Depth to re-bar, d = t-c,-dd/2 where d s = re-bar diameter
= 0.875 in d= 36.00- 2.00- 0.875/2
= 33.5625 in Average moment of inertia, I a 0.5 ( 1g + I c) Ref. EQN (6.29) page 327 where Ig Gross moment of inertia (uncracked) b t 3 / 12 where b = width of concrete section
= 1 in I=g 1.00*36.00A3/12
= 3888 in 4 /in I = Cracked moment of inertia 3
= Fbd where F= Coefficient of moment of inertia of cracked section Ratio of tensile reinforcement to effective area of concrete in rectangular beam, p = As/bd where A s= Area of tensile reinforcement / spacing
= 0.60/12.00 0.0500 in 2 / in p= 0.0500/( 1.0
- 33.563 )
= 0.00149 Ratio of compr. re-bar to eff.
conc. area, p - = p Ratio p '/ p = 1.0 Elastic modulus of concrete, E , = w 1.533 SQRT (f'c) Ref. ACI Std 318-63 Sect 1102
Calculation No. S07-0037 Revision 0 Attachment Page 9 where w= 150 Ib/ ft 3 (concrete weight)
E c= 150 ^1.5" 33" SQRT (3000)
= 3320561 psi Elastic modulus of steel, E , = 29000000 psi Modulus of elasticity ratio, n = Es/Ec 29000000 / 3320561 8.7 Ratio p n = 0.00149
- 8.7
= 0.0130 1.0 u.
10-C) 0 10-2 10-2 10-1 1.0 Ratio p n Figure15- Coefficient for Moment of Cracked Sections (Source Document 8)
Calculation No. S07-0037 Revision 0 Attachment Page 10 Determine F-coefficient by interpolate for p n and p '/ p Coefficient F p /p P,/ p'/p p,! p'/p=
pn =1.0 p =0.75 =0.50 p =0.25 0 0.02 0.017 0.017 0.017 0.017 0.017 0.0127 0.01 0.01 0.01 0.01 0.01 0.0130 0.0103 0.0103 0.0103 0.0103 0.0103 For p n = 0.0130 and p '/p = 1.0 F= 0.0103 Cracked section moment of inertia, I = F bd 3
= 0.0103 *1.0 *33.563 A3
= 389.3 in 4/ in Alternate solution for cracked section moment of inertia without compression steel B= b(nAs)
= 1 * (8.73" 0.0500)
= 0.437 kd= [SQRT(2dB+ 1)- 1)/B
= [SQRT(2*33.563*0.437+ 1)-1 ]/0.437
= 10.32 Ic= b(kd )2/3+ nAs(d-kd )2
= 1 *( 10.32 ) A2 / 3 + 8.73 *0.0500 (33.56- 10.32 )A2
= 271.4 in 4 /in Ref. US Army Corps of Engineers, "Structures to Resist the Effects of Accidental Explosions", TM 5-1300, July 1965.
In calculating the stiffness of reinforced concrete sections, the moment of inertia must account for cracking of concrete. It is recommended that the average moment of inertia be used which is based on the following expression:
Average moment of inertia, 1a 0.5 (1g + I o)
= 0.5"(3888+389)
= 2139 in 4 / in
Calculation No. S07-0037 Revision 0 Attachment Page _ 1 4.2.3 CALCULATE ELASTIC STIFFNESS OF SLAB (Ref. 8) UNDER CONCENTRATED LOAD Table 8.4 Stillness and resisting values for plates and slabs under concentrated loads Description Resistance Stiffness (a) Simply supported on all four sides with load at center 12E]
1 RR = 2iM , K = aa 2 (l - ,)
b 1.0 .1 1 1 1.6 1,.8 2. 1 3.0 1 .
S 1390
- 0. 0.151 .1624 0,781 0,884 0.1944 0.198YJ.2oiol (b) Fixedsupports on all four sides with load at center a R R, = 21r(Mu +M-) K= a1 20 Iý b ---I I
ba 1.0 1 1.2 1.4 1 1.6 1 .8 1 2.0 a 0-0671 0,0.76 0"0830 0.0854 .0"0864 0.0866 [0.0871 Note: v - Potsson's ratio; r =thickness in inches {nllimeters); E modulus of elasticity, in pounds per square inch (kilopascals); I =moment of inertia per unit width, inches fourth power per Inch (millimeters-fourth power per millimeter);M' = ultimate positive moment capacity, in inches per pound per inch (Millimetes per newton per millimeter);,MAf = ultimate negative moment capacity, in inches per pound per inch (millimeters per newton per tnillivetei).
Compute elastic stiffness of slab under concentrated loads b/a= 79.000 / 24.000
= 3.292
=~ 0.0871 Stiffness, ke= 12 Ecla/[ a 2 (x u 2
)]
where Poisson ratio for concrete, u = 0.17
= 0.15 - 0.25 for concrete [ACI Committee 435 19911 Case(b) ke= 12*3320561*2139/[0.0871 *(12*24)A2*(1_0.17A2)]
= 121469741b/in
= 1.21E+07 lb / in 4.2.4 CALCULATE EFFECTIVE MASS FOR CIRCULAR FAN YIELD LINE PATTERN Compute effective mass of slab For concentrated load, the load factor K L= 1 (Ref. 8, page 355)
Calculation No. S07-0037 Revision 0 Attachment Page 12 (a) (b)
R= 12 ft Ref. 8, page 355 Effective mass of slab, M e = mnRR 2 /6 where m= mass per unit area
= wt/g 2 g= 32.174 ft /sec m= 150*3.00*1*1/32.2
= 13.99 Ib sec 2 /ft 3 0.00809 Ib sec 2 / in 3 Me- 0.00809
- 3.142 * ( 12
- 12 )A 2/6
- 87.9 Ib sec 2 / in 3 4.2.5 NATURAL PERIOD OF VIBRATION ( Ref. 8, pages 355 & 361)
Determine Natural Period of Vibration T= 2ItSQRT(Me/KLke) where KmMt= Me Case (b) T= 2
- 3.142
- SQRT [87.9 /(1.0
- 12146974
= 0.017 4.2.6 IMPACT FORCE ( F j) and DURATION OF IMPACT (t d)
Note: Ref. 8 states that due to significant deformation of the auto, the effects of an impact are based on the impact time history. Methods are given to investigate this time history function; however, the CR-3 DBD for Class 1 Structures and Attachment #2 (page 17, from Gilbert Calc 4.01.1) state that the equivalent static load is 270K and duration of impact is 0.081 sec.
Determine Impact Force F = 270000 lb See Attachment A Determine Duration of Impact Force td = 0.081 sec See Attachment A
Calculation No. S07-0037 Revision 0 Attachment Page 13 4.2.7 DETERMINE SLAB DUCTILITY FOR CIRCULAR FAN FAILURE Ductility Ratio The limits applied to deformation under impulse and impact loads are generally specified in terms of ductility ratios. The allowable ductility ratio is defined as the maximum permissible deflection of a structural system to the deflection at "effective yield" for the system. Recommended values for allowable ductility are given in the following table per Ref. ASCE - Manuals and Reports on Engineering Practice No. 58 "Structural Analysis and Design of Nuclear Plant Facilities" Tb&le064. Allowable ductlilly ratlo$10rimpulse andImpact1load
.M tera .. Ductility Rati(?
Reiriforced concrete:,
nlexur~e (beams*) 0.10
- flexure (slabs) 0.10 <30 compressiio (walls and columns) I,3 sheair(beams and slibi)
-carriedj:by-concriet only i.O
-c#rrid by concrete and stirrups 1.3
-carried completely, bystirrups" 3.0 Structural steel:
beamS (local and lateral buckling prevented) 20 columns (4- <30 and local buckling prevented 5 r
acoluamns members>
30)05j'I axial tension members0-+-
Calculation No. S07-0037 Revision 0 Attachment Page 14 The maximum displacement curve for a rectangular impulse load is used for this calculation.
100 0.1 1.0 /d 40 J4,1,,rOf CT 7T case (b) td/T 0.081 / 0.017 4.7929 CR Rrm/Fi 844837 / 270000 3.1290 > 2.0 ELASTIC RANGE The 3-ft wall is qualified within elastic limits.
Case C T XmCXe (b) 4.7929 2.000 1.000 2.000 1.000 3.129 1.000 Notes:
X m= Maximum displacement under load Xe= Effective yield deflection The maximum permissible deflection is the allowable ductility ratio times the effective yield deflection. The maximum permissible deflection governs peak response in a time history dynamic analysis or strain energy capacity in an energy balance analysis.
Allowable ductility, jt = 0.10/ ( p - pr) < 30
.t = 30 since P= P' SINCE m/
X M X e= 1.000 1i= 30 No overall failure
Calculation No. S07-0037 Revision I Page 15 Using t = 30 and t d = 0.081 sec, an iterative analysis was performed to determine F i.
Iterative Procedure The term F is used to determine C R CR= Rm/Fi The term C R is used to determine X m / X e which is jt Vary F iinput until X m / X e equals 30; therefore, ýt = 30.
F i= 890663 lb F missile / F i = 270000 / 890663
= 0.303
Calculation No. S07-0037 Revision 1 Page 16 4.3 DETERMINE THE ULTIMATE LOAD CAPACITY OF THE 2-FT THICK EAST AUXILIARY BUILDING WALL USING ULTIMATE STRENGTH DESIGN PER ACI 349-97 AND VERIFY THAT THE WALL IS ADEQUATE FOR TORNADO WIND + DEPRESSURIZATION Consistent with Nuclear Regulatory Commision review guidelines in the Standard Review Plan (NUREG-0800, Revision 3 - March 2007), Section 3.8.4, "Other Seismic Category 1 Structures, the east wall of the CR3 Auxiliary Building will be evaluated to the requirements of ACI 349-97, "Code Requirements for Nuclear Safety Related Concrete Structures," as endorsed, and supplemented by regulatory positions, in Revision 2 (November 2001) of Regulatory Guide 1.142, "Safety-Related Concrete Structures for Nuclear Power Plants (Other than Reactor Vessels and Containments)" for all design basis loads and load combinations as described in the FSAR.
The Auxiliary Building east wall is 24" thick and it is reinforced with #6 reinforcing bars at each face and each direction. Design f'c = 3000 psi and design yield strength is 40 ksi.
(Ref. 9 and 10)
Reinforcing Bar Information:
Wall is reinforced with #6 bars @ 12" on both faces in each direction.
db := .750in Diameter of #6 reinforcing bar
. 2 As:= .44-i Cross sectional area of #6 reinforcing bar ft The percent reinforcement on each face, considering gross concrete area, is 0.44 Pwal " 0.44 = 0.0015 = 0.15%
12-24 Appendix C of ACI 349-97 does not specify any requirements for minimum reinforcement so Section 10.5.3 is applied for minimum reinforcement of flexural members which refers to Section 7.12 for structural slabs of uniform thickness. Section 7.12.5 requires that the ratio of reinforcement area be provided at the tension face to gross area of concrete not be less than 0.0018 unless the area of reinforcement provided is at least one-third greater than that required by analysis. The ratio provided in the CR3 Auxiliary Building east wall is 0.0015. In order to satisfy Section 7.12.5 for a lower ratio of reinforcement, the requirements of Appendix C have been checked for a wall with a reduced area of reinforcement which is three-quarters of the actual reinforcement area in the east wall.
3 .2 Steel area to be considered as that required by As - red : -'As 4 As red = 0 -3 3 ft this analysis 349-97 (Ref. to 13)satisfy the7.12.5 Section requirements of ACI fy := 40ksi Es:= 29000ksi
Calculation No. S07-0037 Revision 1 Page 17 Concrete Information:
Section 7.7.1 of ACI 349-97 (Ref. 13) requires a clear cover of 3/4" on the inside face of the wall. However, drawing sections indicate that the clear cover may be 2" on both sides of the Auxiliary Building walls. Conservatively, a clear cover of 2" will be used for both faces of the wall.
r,:= 3000psi Concrete strength cc 2in Concrete clear cover on both faces of wall v := 0.17 Poisson's Ratio for concrete w := 150pcf Concrete weight Modulus of elasticity Ec := E-Tcf l5.33. js pi.p si Ec = 3320561psi (Ref. 13, Section 8.5.1)
Wall section information:
t 2ft Wall thickness b := 12in Unit width of evaluated section lpanel := 24ft Length of the square wall panel considered in analysis Effective depth from either wall face to d := t - cc - db d = 21.25 in average steel layer on opposite face 4.3.1 COMPUTE ULTIMATE MOMENT STRENGTH FOR REDUCED REINFORCEMENT AREA Consider a singly reinforced concrete section with reduced reinforcement area. In order to satisfy the requirements of ACI 349-97 (Ref. 13) Article 7.12.5, the collapse load is calculated with a reduced area of steel to determine the ductility demand of the section crediting only 75% of the provided steel area.
As red" y a.- a = 0.43 in Height of concrete compression stress block 0.85. fc 0.9 Ternsion-controlled section Reduced ultimate moment Wnr -Asred'y. (d - ýMnr = 220.82--f k ft strength of AB east wall
Calculation No. S07-0037 Revision 1 Page 18 4.3.2 CHECK TORNADO WIND PLUS DEPRESSURIZATION Determine the maximum applied moment on the wall due to tornado wind plus depressurization load (Wt + Pt)-
Pt :0.432ksf Tornado 3 psi pressure drop Wt :0.297ksf Tornado wind pressure It is apparent from the development in ASCE Paper 3269 (Ref. 5) that this is the overall wind pressure on the building (i.e. p = 1.3 x 0.002558 x 3002 = 297 psf). For local designs, this should be broken into windward and leeward components with 0.8 and 0.5 shape coefficients, respectively.
WtW 0.18 ksf Windward pressure WtLt WtL= 0. ll ksf Leeward pressure Although windward pressure acts in the opposite direction of the tornado pressure drop, which isa vacuum on the building and thus acts outward on all exterior panels, they will be combined conservatively. Leeward pressure and suction on side walls will be additive with the pressure drop, but will be of lower magnitude than the windward pressure and thus will be enveloped.
q:=. Pt + Wtw q = 0.61 ksf Tornado windward plus pressure drop Table 30 of Reference 15 provides equation for maximum moment calculation of a flat plate under uniform pressure and fixed on all four edges (b/a = 1.0) 2 kip.ft Maximum applied moment Muwind := -0.05 13.q. Ipanel Mu wind = -18.17 ft under tornado wind plus depressurization
.i IMu-winldi ICwind: 4 ICwind = 0.87 < 1.0 OK Mnr Therefore, the AB east wall is acceptable for tornado wind + depressurization loading.
Calculation No. S07-0037 Revision 1 Page 19 4.3.3 CHECK SEISMIC LOADING ON THE WALL PANEL In order to determine wether the tornado wind loads govern the design of the wall for local effects, the local seismic loading will be checked below.
T := 0.022sec First natural period of the wall, calculated on page 22 f = 45.45 Hz Wall frequency T
Using the response spectra in Figure 12A of Reference 16 for Horizontal SSE of the Auxiliary Building at Elevation 143.0', the following wall acceleration is obtained. Since the frequency of the wall is above 33Hz (rigid zone), amplification factor due to higher modes is not required. This acceleration will be multiplied by the weight of the wall per unit area to find an equivalent pressure that can be compared to the wind loading.
aSSE := 0.21 g Acceleration for frequency of 45 Hz and 2% damping (Ref. 16) w-t qeq:= - aSSE qeq = 63.00 psf Equivalent wall pressure under SSE seismic loading g
This equivalent pressure is significantly lower than the 510 psf for the load combination regarding tornado wind plus depressurization. Based on the comparison, tornado wind and missile loading govern the wall design. Therefore, the wall is qualified for SSE loading combination based on the qualification of the higher loading of the wind plus depressurization.
Calculation No. S07-0037 Revision 1 Page 20 4.4 OVERALL RESPONSE TO MISSILE IMPACT The methodology described in References 8, 12 and 14 are used to qualify the wall for the requirements of ACI 349-97 (Ref. 13).
4.4.1 COMPUTE ULTIMATE MOMENT STRENGTH The ultimate moment strength of the east wall with full area of reinforcement considered is required in order to check the shear resistance of the slab per section C.3.6 in ACI 349-97.
Consider a singly reinforced concrete section with actual reinforcement area.
asy a:- a = 0.58 in Height of concrete compression stress block 0.85.fc Mn:= As*fy.(d Mn = 30.74 kip-ft
- 2) ft 4.4.2 COMPUTE COLLAPSE LOAD, Rm DIFf := 1.2 Dynamic Increase Factor for 40 ksi reinforcing steel per Ref. 13, Appendix C M 33.20kip. ft Mu~pos= 4ý.Mn-DIFf Mu-pos = 33.20 ki.ft kipft Mu1 neg := ý.Mn.DIFf Mu neg = 33.20 uneg R,, := 2- TE(M'ijpos + Muineg) Rm = 417kip Reference 12, Table 5.3 4.4.3 CHECK SHEAR RESISTANCE According to ACI 349-97 (Ref. 13), Article C.3.6, the wall resistance to shear must exceed the load capacity of the wall in flexure by at least 20% in order for flexure to control the design.
- v := 0.85 Shear resistance of one edge of psiv 7panefd~psi Vc = 570 kip the wall panel DIFv := 1.1 Dynamic increase factor for concrete shear from Section C.2.1 of Ref. 13 Rv:= DIFvV*C Rv = 627 kip Concentrated Collapse Load Capacity in Shear IC- IC = 1.50 > 1.2 Therefore, the section meets the requirements of Rrn Ref. 13, Article C3.6 to use the ductility ratio prescribed in Article C3.3 of Ref. 13
Calculation No. S07-0037 Revision 1 Page 21 4.4A4 COMPUTE COLLAPSE LOAD, Rmreduced FOR REDUCED REINFORCEMENT AREA DIF:= 1.2 Dynamic Increase Factor for 40 ksi reinforcing steel per Ref. 13, Appendix C R2-reduced :=2DIF. (Mnr + 4iMnr) Rm_reduced = 314kip Ref. 12, Table 5.3 4.4.5 DETERMINE CONCRETE SECTION PROPERTIES FOR REDUCED REINFORCEMENT AREA t3 . 4 I L1 1152in- Gross moment of inertia (uncracked)
Ig 1 2 in As red p As dr p = 0.00129 Ratio of tensile steel to effective concrete area P := P' = 0.00129 Ratio of compression steel to effective concrete area n := -Ec n = 8.73 Modulus of elasticity ratio p'
- 1.00 p
p-n = 0.01130 Use Figure 3.1.10 of Reference 12 to determine coefficient, F, for moment of inertia of cracked sections:
F := 0.011 Coefficient for moment of inertia of cracked section
.4 3
Ic:= Fd ]c = 105.6 in_ Moment of inertia of cracked section in la := 0.5- (1g + I C) .4 la = 628.8 in_ Average moment of inertia in 4.4.6 CALCULATE STIFFNESS OF SLAB UNDER CONCENTRATED LOAD Using Table 5.3 of Ref. 12, Calculate stiffness:
0.0671 Stiffness coefficient for square panel with fixed edges 12"Ec*Ia lb K.-K= 4635723-a .lpanel2.(l -v2) in
Calculation No. S07-0037 Revision 1 Page 22 4.4.7 CALCULATE EFFECTIVE MASS FOR CIRCULAR FAN YIELD PATTERN lpanel R :- - R= 12.00ft Radius of fan yield pattern 2
w-t lb. sec 2 m = 0.00540 .3 Mass per unit area in g.E*
2 lb. sec Effective mass is one-sixth of mass in the circlular Me 6 Me = 58.59 yield line pattern (Ref. 8, Section 6.4.2.1.4) in 4.4.8 NATURAL PERIOD OF VIBRATION T := 2.71. F' T = 0.022 sec First natural period 4.4.9 IMPACT FORCE AND DURATION OF IMPACT The 1 ton automobile load of 270 kips envelopes the utility pole missile load of 148 kips. The resulting missile load is a rectangular force pulse as shown to the right. The impact Fj force and duration of impact are obtained from Reference 4.
Fi := 2700001b td RECTANGULAR FORCE PULSE td := 0.081sec 4.4.10 DETERMINE REQUIRED DUCTILITY RATIO FOR THE SLAB DUE TO IMPULSE td
-- = 3.63 T
Rrn reduced
- Fi = 1.16 a 5.2 Ductility demand (Reference 14, Figure 2.23)
Section C.3.3 of ACI 349-97 (Ref. 13) requires that the permissible ductility ratio be taken as 10 when the area of steel tension reinforcement equals the area of compression reinforcement and flexure controls design.
The calculated ductility demand of 5.2 is well below the limit of 10. This result satisfies the requirement of Section 7.12.5 of ACI 349-97 (Ref. 13), that the area of reinforcement provided on the tension face is at least one third greater than that required by analysis.
Calculation No. S07-0037 Revision 1 Page 23 4.4.11 CHECK COLUMNS FOR MISSILE IMPACT The smallest columns adjacent to any of the wall panels under consideration for missile impact are located on column lines L, M1, N1 , and 01. The governing column on column line 01 is 36" wide by 50.25" deep with 8 - #18 vertical bars and two sets of 2-#4 ties @ 24".
The following loads, used in the original design of this column, were obtained from Section 2.01.55-12 of Reference 4. Conservatively, only the dead load is considered for the combination including tornado missile loading.
DLco1:= 340.6kip Column design dead load (Ref. 4) e := 0.5938ft Column axial load eccentricity (Ref. 4)
Paxial:= DLco0 Paxial = 340.6 kip Column design axial load under dead load me := e.Paxia1 Me = 202.2 kip. ft Column design moment due to eccentricity of dead load The additional moment introduced to the column is calculated by considering the missle impact to occur at the midspan of the column between floors. The ends are assumed fixed by the three foot thick slabs. A dynamic load factor of 2 is conservatively used for the missile impact.
DLF:= 2 Conservative dynamic load factor Mmissile DLF a Mmissile = 1620.0 kip.ft 8
Mco1 : Me+/-+Mm~issile Mco1 = 1822.2 kip. ft PCAcolumn software was used to generate a P-M interaction diagram for the combined loads listed above. The results are attached in Appendix G. The analysis determined that the loading gives a factor of safety of 1.642, or IC = 0.61. Therefore, the columns are OK under tornado missile loading.
Computer Programs Mathcad MathSoft Mathcad Version 11.2a (S&L Program No. 03.7.548-11.2)
PCAColumn PCAColumn Version 3.61 (S&L Program No. 03.7.198-4.10)
These programs (run on PC No. ZD2055) are accessed using the S&L LAN and have been validated per the S&L Software Verification and Validation procedues for the program functions used in this calculation.
Calculation No. S07-0037 Revision 1 Page 24
- 5. Results South Wall:
(1) The South Wall is qualified in accordance with ACI 318-63.
(2) The ultimate strength of the South Wall exceeds the applied tornado wind and pressure drop loads (refer to Alternate Calculation in Attachment D). The load combination, C = D + L + 1.0 Wt + 1.0 Pt is satisfied.
(3) The ultimate strength of the South Wall exceeds the loading from missile impact (refer to Alternate Calculations in Attachment B).
East Wall:
(4) The East Wall is qualified in accordance with ACI 349-97.
(5) The design of the East Wall is governed by tornado wind and missile loading by comparison to SSE loading.
(6) The ultimate strength of the East Wall exceeds the applied tornado wind and pressure drop loads. The load combination, C = D + L + 1.0 Wt + 1.0 Pt is satisfied.
(7) Overall failure of the East Wall will not occur due to missile impact.
Conclusions The south and east walls of the CR3 Auxiliary Building are adequate for loading from the design basis tornado loads and load combinations.
Calculation No. S07-0037 Revision 1 Page 25 References
- 1. FSAR Section 5
- 2. DBD for Major Class I Structures (TAB: 1/3)
- 3. Wang and Salmon, "Reinforced Concrete Design", 4th Edition
- 4. G/C Calc Book 4.01.1 to 4.01.7 and 2.01.55
- 5. ASCE Paper 3269, "Wind Forces on Structures", Vol 126, Part II, 1961
- 6. SER dated 7-5-1974
- 7. DBD for the Containment (TAB: 1/1)
- 8. ASCE Manuals and Reports on Engineering Practice No. 58, "Structural Analysis and Design of Nuclear Plant Facilities"
- 9. Dwg SC-422-019
- 10. Dwg SC-422-021
- 11. ACI Standard 318-63
- 12. ASCE, "Civil Engineering and Nuclear Power, Vol. V: Report of the ASCE Committee on Impactive and Impulsive Loads"
- 13. ACI 349-97, "Code Requirements for Nuclear Safety Related Concrete Structures and Commentary"
- 14. Biggs, "Introduction to Structural Dynamics"
- 15. Timoshenko, "Theory of Plates and Shells", 1940
- 16. SP-5209, "CR-3 Seismic Qualification," Rev. 0
- 17. NUREG-0800, "U.S. Nuclear Regulatory Commission Standard Review Plan," Revision 3, March 2007
- 18. Regulatory Guide 1.142, "Safety-Related Concrete Structures for Nuclear Power Plants (Other than Reactor Vessels and Containments)," Revision 2, November 2001
Calculation No. S07-0037 Revision 0 Attachment A Page Al I i I " j" 7,-A
. C ý. P, , .. ..
b J.
4 A'*.." t,t'/%A;A-'.
4
/ /%l't., )*" ./ .:,~i. 7 -sI a D .JA#,.*. I 7; JA/. ' ~ "~ - . L ~ A ?~A "
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- '7V t" V ,
AP, , ,;.). , C"* /iC t';;-a/ 10 . Y' P',
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, C If f /1. A ,/3 6r
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--r rK .' -- . 7A Z ,-.o ?' /3 ,e' 42, ar Iva.
c-; = .]2...<."
,~ ,/:A.Z L. --; I " ; : : '
rs, e-:,;, ;.<) - 7 2
- r,//-,s<c 4/ho PV.j/..Y -.C ; 4. C ,/ -
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Calculation No. S07-0037 Revision 0 Attachment B Page B1 ATTACHMENT B Description This attachment contains an alternative method to check the Auxiliary Bldg 3-ft South Wall for missile impact only. This alternative method was generated by the Design Verifier.
A GT STRUDL Finite Element Model was generated of the wall and the static impact load of 270 kip was distributed over an impact area of 6' x 6'.
Conclusion The 3-ft thick South Auxiliary Bldg Wall is adequate to resist the missile impact load within the elastic limits.
Finite Element Model for 3' thick South Aux Building Wall 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 19 191 192 193" 19415 196 19 198 199200201 202 20W 20z 205 206 207 208 20921 C211212 213 214 215216 16 16 16516E1167,168 16917 171 172,173 17417517 17-, 178 179 180 181 182 18' 184185 186 187 188 189 13 13 138 139 140 141 142 14 144 145 146 147j 148 14. 15 151 152 153 15 155 15( 15 158 15 160 161 1162 10ý 11 112 1141151111711 811912 1212 12 124 125112 127 1281213 *311321331134135
-98 9 1 10 10 10 '10 1061107108 "8'38 586 87 8889 9091 929394 959 78910 1
'55156 57 158k 6 62 63 64 65 66-67 68 69 7 71 7273 74 75 176 i77 178 79 80181 59- 60 1--- --
28 29 {30 31 T32 33 34 35 36 37 38 394 41 42 43 44 4 484 50 151 52 153 L54 71 9 10 111 3 1 7 18 1920 21 22 23124 2 2 27 81 ".
YJ Lx ,'P 0419
Calculation No. S07-0037 Revision 0 Attachment B Page B2 Finite Element Model for 3' thick South Aux Building Wall Joint Numbers 172 1173 1174 1.75 '176 177 178 179
. +-T m
- I --- *----------------O-------------------------O*--
-f
- I 4--
145 146 ~147 148 151 152
- 118 t
- 125
- 91 192 93 98
---4 64 165 67 68 _69 170 71
ý39 140 13 3 ........
4-! 41 42 :43 44
Calculation No. S07-0037 Revision 0 Attachment B Page B3 Finite Element Model for 3' thick South Aux Building Wall
~ArAy = ~ K/ ~~r4C F~ ]
~Ž 10 L'~I L Z~Lk41 J 18
-2 8. -4. .
~~iN~c7 1Z~ ai*I.
Calculation No. S07-0037 Revision 0 Attachment B Page B4 Finite Element Model for 3' thick South Aux Building Wall
~A TAI ~V2 Li ~G 40 7~;
-?C~
1 -~ 7.66 r22~6~
0.
sýi týNlc,ý ef lt3 Yx
Calculation No. S07-0037 Revision 0 Attachment B Page B5 DESIGN VERIFICATION REVIEW: ALTERNATE CALCULATION METHOD FOR MISSILE LOAD This attachment presents the GT STRUDL analysis for a 3-ft thick flat plate with an impact loading on a 6-ft square area.
As per FSAR Section 5.2.1.2.6, the tornado missile (compact auto) impact area is A= 6.25 ft 2 Equivalent square dimension, S = SQRT (A)
= SQRT (6.25)
= 2.5 ft
= 30 in Conservatively using a 3-ft thick wall and a 45 degree line from periphery of the load to the rebar Face of wall to re-bar, d = 2.75 ft Distributed load dimension, L = S +2 d
= 2.5+2*2.75
= 8.0 ft USE = 6.0 ft 3-ft square element nos. 91, 92, 117 and 118 (see page B17)
Impact force for Compact Auto Missile, F = 270.0 kips See Attachment A Surface load, p , = F/ L2
= 270.0/6 .0 A2 7.5 k/ft 3 (see page B17)
The maximum bending stress occurs at Joint 122 (see page B46). The average nodal bending stress is at the centroid of each element which is tabulated below.
Ref. Ref.
Jt No. M yy AVG M yy Page Jt No. M xx AVG M xx Page 120 -22.3739 B46 176 -10.6514 B49
-28.3610 -17.3808 121 -34.3482 B46 149 -24.1102 B47
-37.6556 -27.65 122 -40.963 B46 122 -31.1898 B46
-37.6556 -27.65 123 -34.3482 -2B46 95 -24.1102 B44
- -17.3808 124 -22.3739 B46 68 -10.6514 B43 MAX -37.7 MAX -27.7 The maximum bending moment due to impact of Automobile Missile is 37.7 ft-kip / ft. Use 37.5 ft-kip / ft.
W MISSILE - 37.5 ft-kip / ft This attachment contains the following application:
- a. The analysis is in accordance with the Ultimate Strength Design presented in the ACI Code; therefore, the Auxiliary Build South Wall is qualified by elastic (linear) analysis.
GT STRUDL 27 - SouthWall missile : -
0 jq Commercial Software Rights Legend Any use, duplication or disclosure of this software by or for the U.S, Government shall be restricted to the terms of a license agreement in accordance with the clause at DFARS 227.7202-3.
This computer software is an unpublished work containing valuable trade secrets owned by the Georgia Tech Research Corporation (GTRC).
No access, use, transfer, duplication or disclosure thereof may be made except under a license agreement executed by GTRC or its authorized representatives and no right, title or interest thereto rA is conveyed or granted herein, notwithstanding receipt or possession hereof. Decompilation of the object code is strictly prohibited. /
Georgia Tech Research Corporation Georgia Institute of Technology Atlanta, Georgia 30332 U.S.A.
Copyright (c) 2003 GTRC ALL RIGHTS RESERVED.
Thu Sep 20 07:56:46 200?
IGTICES/C-NP 2.5.0 MD-NT 2.0, January 1995.
Proprietary to Georgia Tech Research Corporation, U.S.A.
Reading password file D:\GTStrudl\27\password27.pwd C:
5-CI-i-audfile. Command AUDIT file ?ILE0756.aud has been activated.
5.
- G T S T R U D L 0 RELEASE DATE VERSION COMPLETION NO.
June, 2003 27.0 4449
- ACTIVE UNITS - LENGTH WEIGHT ANGLE TEMPERATURE TIME
- ASSUMED TO BE INCH POUND RADIAN FAHRENHEIT SECOND 0
({ 11 > $ --------------------------------------------------------- Ul)
- 2) $ This is the Common Startup Macro; put your company-wide startup commands here. Z
{ >
$ You can edit this file from Tools -- Macros.
( 31 Click "Startup" and then "Edit".
( 41 > $ --------------------------------------------------------- --4
> CINPUT 'T:\Gtstrudl\in\SouthWall missile.txt'
{ 51
> *TITLE 'AB south wall missile'
{ 61
- 7) STRUDL 'FILENAME=AB South wall missile' (D~
- eW*e**
G T S T R U D L
OT STRJDL 27 - SouthWall missile 08:34:23 September 20, 2007 Page 2 44 **
OWNED BY AND PROPRIETARY TO THE GEORGIA TECH RESEARCH CORPORATION
" RELEASE DATE VERSION COMPLETION NO.
" June, 2003 27.0 4449
- 44*44*4*4*4*4*******************
ACTIVE UNITS - LENGTH WEIGHT ANGLE TEMPERATURE TIME
- ASSUMED TO BE INCH POUND RADIAN FAHRENNEIT SECOND 0
{( 8} " TYP plate
{ 9} > UNIT ft LBS DEG 5-
{ 10) > JOI COO
- 11) > generate 27 joints id I 1 x 0.0 INCR 3 0
/ ------- CARTESIAN COORDINATES FREE, GLOBAL--------/
JUINT Y z
0 1 0.000 0.000 0.000 2 3.000 0.000 0.000 3 6.000 0,000 0.000 4 9.000 0.000 0.000 C) 5 12.000 0.000 0.000
"-4 6 15.000 0.000 0.000 7 1B.000 0.000 0.000 8 21.000 0.000 0.000 9 24.000 0.000 0.000 10 27.000 0.000 0.000 I, CD 11 30.000 0.000 0.000 D 12 33.000 0.000 0.000 03 o,3 13 36.000 0.000 0.000 14 39.000 0.000 0.000 Cn 15 42.000 0.000 0.000 "0 CD Co 16 45.000 0.000 0.000 17 48.000 0.000 0.000 18 51.000 0.000 0.000 19 54.000 0.000 0.000 20 57.000 0.000 0.000 21 60.000 0.000 0.000
GT STRUDL. 27 - SouthWall missile 08:'34:23: September 20, w2007 Page .3 22 63.000 0.000 o~O00 0 0 00 23 66.000 0.000 24 69.000 0.000 0.000 25 72.000 0.000 0.000 2E 75.000 0,000 0.000 27 78.000 0.000 0.000 121 > repeat 6 times id incr 27 y incr 3
/-------- CARTESIAN COORDINATES FREE, GLOBAL JOTNT XY z 28 0:000 3.000 0.000 29 3.000 3..000 30 6.000 3.0oo 0.000.
- 32. 9.000 3.000 0.000 32 12.000 3.000 0.000 33 15:000 3.000 0.000 34 18.000 3.000 0.000 35 21.000 3.0000 0.000 36 24.000 3.000 0-000 3.7 27.000 3.000 0.000 3:8 30.000 3.000 0-000 39 33.000 3.000 0.000 C-)
0) 40 36.000 3.000 0.000 0 41 39.000 3.000 0.000 42 42.000 3.000 0.000
'->3i 45.000 3.000 0.000
.44 48.000 3.000 0*.000 0.000 0.000 0
-45 51.0oo 3.000 0.000 0 4 654.000. 3.0010 0.000 z 4.7 57.000 3.000 0.000 48 60.000 3.000 0.00
'49 63.o000 3.000 0.000 50 66.000 3.000 0.000 0 5i G9;000 3.000 52 72.000 3.000 C,,
0.000 53 75.000 3.000 0.000 54 78,000 3.000 0.000 C
- 55. 0.000 6.000 0.000 56 3.000 6.000 0.000 57 6.000 6.000 0.000 0.0.00 58 9.000 6.000o 0.000 0.000 59 12.000 6,000 0.000 -u3*(D 66 15,.000 6.000 0.000 00.000 CD~
- 6. .18-000 6.000 0. O000
.62 21,.000 6,000 63 24A000', 6.000 0.000 T <0 64 27.000 6.000 865 30.006 ý.ooo
- 66. 33.000 6.000 67 36.000 6,000
GT STRUDL 27 SouthWall missile 08:34:23 September 20, 2007 Page 4 68 39.000 6.000 0.000 69 42.000 6. 000 0.000 70 45.000 6.000 0.000 71 48.000 6. 000 0.000 72 51.000 6.000 0,000 73 54.000 6.000 0.000 74 57.000 6.000 0.000 75 60.000 6.000 0.000 76 63.000 6.000 0.000 77 66.000 6.000 0.000 78 69.000 6.000 0.000 79 72.000 6.000 0.000 80 75.000 6.000 0.000 81 78.000 6,000 0.000 82 0.000 9.000 0.000 83 3.000 9.000 0,000 84 6.000 9.000 0.000 85 9.000 9.000 0.000 86 12.000 9.000 0.000 87 15.000 9.000 0.000 88 18.000 9.000 0.000 89 21.000 9.000 0.000 C-)
90 24.000 9.000 0.o00 03 91 27.000 9.000 0.000 92 30.000 9,000 0.000 93 33.000 9.000 0.000 94 36.000 9.000 0.000 95 39.000 9 .000 0.000 96 42.000 9.000 0.000 97 45.000 9.000 0.000 z 98 48.000 9.000 0.000 99 51.000 9.000 0.000 I00 54.000 9.000 0.000 101 57.000 9.000 0.000 {-
102 60.000 9.000 0.000 103 63.000 9.000 0 .000 <
104 66.000 9. 000 0.000 105 69.000 9.000 0.000 D Z3 02 106 72.000 9.000 0.000 107 75.000 9.000 0.000 108 78.000 9,000 0.000 CaC) 109 0.000 12.000 0 .000 110 3.000 12.000 0 .000 CD 111 6.000 12.000 0 .000 112 9.000 12.000 0.000 113 12.000 12.000 0.000 C")
114 15.000 12.000 0.000 115 18.000 12,000 0.000 116 21.000 12.000 0.000 117 24.000 12,000 0.000 118 27.000 12.000 0.000 119 30.000 12.000 0.000
GT STRUDL 27 - SouthWall missile 08:34:23 September 20,_2007 Page 5 120 33.000 12.000 0 .000 121 36,000 12.000 O.O0O 122 39.000 12.000 0.000 123 42.000 12,000 0.000 124 45.000 12.000 0.000 125 48.000 12.000 0.000 126 51.000 12.000 0.000 127 54.000 12.000 0.000 128 57,000 12.000 0 .000 129 60.000 12,000 0 .000 130 63.000 12.000 0 .000 131 66.000 12.000 0.000 132 69.000 12.000 0 .000 133 72 . 000 12.000 0.000 134 75.000 12.000 0.000 135 78.000 12.000 0.000 136 0.000 15.000 0.000 137 3.000 15:000 0.000 138 6.000 15.000 0.000 139 9.000 15. 000 0.000 140 12.000 15.000 0.000 141 15.000 15.000 0,000 142 18.000 15,000 0.000 C) 143 21.000 15.000 0.000 0 144 24.000 15.000 0.000 145 27,000 15.000 0.000 C:
146 30.000 15.000 0.000 147 33,000 15,000 0.000 0 148 36.000 15.000 0.000 149 150 39,000 42,000 15.000 15.000 0.000 0.000 z
c-0 151 45,000 15.000 0.000 152 48.000 15.000 0.000 153 51,000 15.000 0.000 154 54.000 15.000 0.000 155 57.000 15.000 0.000 C) 156 60.000 15.000 0.000 0 157 63.000 15.000 0.000 158 66.000 15.000 0.000 6 159 69. 000 15.000 0.000 CA) o 160 72,000 15.000 0.000 161 75,000 15.000 0 .000 162 78.000 15.000 0 .000 163 0.000 18.000 0.000 -T <
164 3.000 18.000 0 . 000 E3 165 6.000 18.000 0.000 166 9.000 18.000 0.000 167 12.000 18.000 0.000 168 15 .000 18.000 0.000 169 18.000 18.000 0.000 170 21 000 18.000 0.000 171 24.000 18.000 0.000 C)
GTI STRUML 2-7,-Suh llmis e 08.:34:23. September 20, 2o00 Paqe 6 172 27.000 18.000 0.000 30.000 18.000 0.000 173 174 33.000 18.000 0;000 175 36.0oo0 18.000 0.000 176 39;000 18.000 0.0oo 177 42.000 18.000 0.000 178 45.000 18.000 0.000 179 48.000 18.000 0.000 180 51.000 18.000 ýO.000
.0.000 181 54.000 18.000 .0.000 57.000 18.000 183; 0.000
- 60. 000 0.000 184 6*3.000
.18..000, 185 o0,000 0.10001 66.c000 18,6 16.-000 187 72-.000 21. 000 18.0600 188= 0.000
,0.000 75.000 18.000 o.,ob0 218.000 189 78.000 18.000 0.000 0.000 190 0.000 21.000 0.000 191 3.000 21.000 192 6.-000 21.000 0..000 193 9.000 -21.;000 0.000 194 ,12 o000 21.000 0.000 0
195 15.000 21.000 0 .000 196 .18.000 21.000 0.,000 197 21.,000 21.000 0.000 0.000 =3 198 124.000 21.00,0 0.000 0
'99 27.000 21.J00:0 0.000 z 3,0.000 .21'.'000 0.000 20 0 201 33.ý000 2 1. 00,0 0 .000 202 36,.000 21.000 0.000 203 39'. 000 21.000 0.000 cn 204 42.000 21.0'C0 0.000 205 45.. 00o, 21.000 0 . 000 206 48.000 21 ýooo 21.000 0.000 0o 207 51.000 21.000 0.000 208, 54.000 21.000 0 .000 209 57.000 21.000 0.1000
,210 60.000 21,000 63 .000 21.000 0.000 211 212 66.000 21.000 0.000 r,'
213 69.1000 21.000 0.000 0'.4000 CD 214 72 .000 21.000 0.000 21.000 0.000 o 215 75:.000 >
-DD
ý216 78.000 21.000 0.000 2 0:.000 0.000 24-000 0.000
,217 24.000 218. 3 .000 0.000 6.000 24.000 0.000 220 -9.00o 24.*000 12.000 22i 24.000 222' 15.' 000 24.;,000 0.000
ý18. 000 24.000 0.ooo 223
GT STRUDL 27 - SouthWal! missile 08:34:23 September 20, 2007 Page 7 224 21.000 24.000 0.000 225 24.000 24.000 0.000 226 27.000 24.000 0.000 227 30.000 24.000 0.000 228 33.000 24.000 0.000 229 36.000 24.000 0.000 230 39.000 24.000 0.000 231 42.000 24.000 0.000 232 45.000 24.000 0. 000 233 48.000 24.000 0,000 234 51,000 24.000 0.000 235 54.000 24.000 0,000 236 57.000 24 .000 0.000 237 60.000 24.000 0.000 238 63.000 24.000 0.000 239 66.000 24.000 0.000 240 69.000 24.000 0.000 241 72.000 24,000 0.000 242 75.000 24.000 0.000 243 78.000 24.000 0.000 131 >
141 > type plate 151 > generate 26 elements id 1 1 from 1 incr 1 to 2 incr 1 to 29 incr 1 to 28 incr 1 0
/---------------- ELEMENT INCIDENCES-------------------- / a) c-ELEMENT INCIDENCES 0 1 1 2 29 28 2 2 3 30 29 3 3 4 31 30 0
4 4 5 32 31 5 5 6 33 32 0
6 6 7 34 33 7 7 8 35 34 8 8 9 36 35 9 9 10 37 36 10 10 11 38 37 11 11 12 39 38 12 12 13 40 39 0 U) 6 13 13 14 41 40 14 14 15 42 41 c:)
15 15 16 43 42 16 16 17 44 43 17 17 i8 45 44 18 18 19 46 45 CD 19 19 20 47 46 20 20 21 48 47 21 21 22 49 48 22 22 23 50 49 23 23 24 51 50 24 24 25 52 51 25 25 26 53 52 N.)
GT STRUDL 27 - SouthWall missile 08:34:23 September 20, 2007 Page 8 26 26 27 54 53
- 16) > repeat 7 id incr 26 from incr 27 to incr 27
/ ---------------- ELEMENT INCIDENCES------------------
ELEMENT INCIDENCES 27 56 55 28 57 56 29 58 57 30 59 58 31 60 59 32 61 60 33 62 61 34 63 62 35 64 63 36 65 64 37 66 65 38 67 66 39 68 67 40 69 68 41 70 69 42 71 70 C)
O) 43 72 71 44 73 72 0 45 74 73 46 75 74 47 76 75 0 48 77 76 49 78 77 z 50 79 78 51 80 79 0 52 81 8o 53 83 82 54 84 83 C) 55 85 84 6 S6 86 85 C 57 87 86 58 88 87 59 89 88 60 90 89 61 91 90 B -u 62 92 91 63 93 92 nOD 64 94 93 65 95 94 CD-66 96 95 67 97 96 68 98 97 69 99 98 70 100 99 71 101 100
GT STRUDLý 27 - SouthWall missile 08:34:23 September 20, 2007 Page 9 72 74 75 102 101 73 75 76 103 102 74 76 77 104 103 75 77 78 105 104 76 78 79 106 105 77 79 s0 107 106 78 80 81 108 107 79 82 83 110 109 80 83 84 111 110 81 84 85 112 il 82 85 86 113 112 83 86 87 114 113 84 87 88 115 114 85 88 89 116 115 86 89 90 117 116 87 90 91 118 117 88 91 92 119 118 89 92 93 120 119 90 93 94 121 120 91 94 95 122 121 92 95 96 123 122 93 96 97 124 123 94 97 98 125 124 C-)
95 98 99 126 125 96 99 100 127 126 C-,
97 100 101 128 127 0
98 101 102 129 128 99 102 103 130 129 100 103 104 131 130 101 102 104 105 105 106 132 133 131 132 z
103 106 107 134 133 0 104 107 108 135' 134 105 109 110 137 136 106 110 l1l 138 137 C) 107 III 112 139 138 108 112 113 140 139 0
109 113 114 141 140 Cn 110 114 115 142 141 III 115 116 143 142 112 116 117 144 143 113 117 118 145 144 114 I15 118 119 119 120 146 147 145 146 M;
116 120 121 148 147 w 117 121 122 149 148
- CoCD w0 118 122 123 150 149 119 123 124 151 150 120 124 125 152 151 121 125 126 153 152 122 126 127 154 153 123 127 128 155 154
GT STRUML 27 - SouthWal-I missile 08:34:23 September 20, 2007 Page 10 124 128 129 156 185 125 129 130 197 186 126 130 131 158 157 127 131 132 159 158 128 132 133 160 159 129 133 134 161 160 130 134 135 162 161 131 136 137 164 163 132 137 138 165 164 133 138 139 166 165 134 139 140 167 166 135 140 141 168 167 136 141 142 169 168 137 142 143 170 169 138 143 144 171 170 139 144 145 172 171 140 145 146 173 172 141 146 147 174 173 142 147 148 175 174 143 148 149 176 175 144 149 150 177 176 145 150 151 178 177 146 151 152 179 178 C~)
147 152 153 180 179 CD 148 153 154 5-181 180 149 154 155 182 181 150 155 156 183 182 151 156 157 164 183 0 152 157 158 185 184 153 154 158 1S9 159 160 186 187 185 186 z 155 160 161 188 187 0 O
156 161 162 189 188 N
157 163 164 191 190 O 158 164 165 192 191 C',
159 165 166 193 192 160 166 167 194 193 161 167 168 195 194 162 168 169 196 195 ow 163 169 170 197 196 164 170 171 198 197 165 171 172 199 198 166 172 173 200 199 167 173 174 201 200 168 174 175 202 201 (0 CD 169 175 176 203 202 170 176 177 204 203 CD =3 171 177 178 205 204 172 178 179 206 205 173 179 10 207 206 174 175 180 181 181 182 208 209 207 208 w:
cn'
GT STRUDL 27 - Southwall missile 0 8 :34 : 23 September 20, 2007_ Page 11 176 182 183 210 209 177 183 184 211 210 178 184 185 212 211 179 185 186 213 212 180 186 187 214 213 181 187 188 215 214 182 188 189 216 21S 183 190 191 218 217 184 191 192 219 218 185 192 193 220 219 186 193 194 221 220 187 194 195 222 221 188 195 196 223 222 189 196 197 224 223 190 197 198 225 224 191 198 199 226 225 192 199 200 227 226 193 200 201 228 227 194 201 202 229 228 195 202 203 230 229 196 203 204 231 230 197 204 205 232 231 198 205 206 233 232 0 199 206 207 234 233 5-200 207 208 235 234 201 208 209 236 235 =-
202 209 210 237 236 0 203 210 211 238 237 204 211 212 239 238 205 212 213 240 239 z 206 213 214 241 240 0 207 214 215 242 241 208 215 216 243 242
- 17) > oU)
- 18) > status supports I to 27 217 to 243 28 55 82 109 136 163 190 217 - C ow
- 19) > 54 81 108 135 162 189 216 243
- 20) >
- 21) > element properties
- 22) > 1 to 208 type 'SBHQ6' THICKNESS 3.0
- 23) > material concrete all YCD
- 24) > $CONSTANTS
- 25) > $E 3.6E6 ALL CD
- 26) > SDN 0.087 ALL -uB*
- 27) > SPOI 0.2 ALL
- 28) > units ft kips deg 0')
- 29) > $
- 30) > $loading 1 'dead load'
- 31) > Selement loads t
- 32) > $1 to 208 body force global uniform by -0,150 $ (k/ft '3)
- 33) > $
- 34) >
- 35) > loading 2 'missile'
GT STRUDL 27 - SouthWall missile 0B8: 3 4 :23 S*eptember 20, 2007 Page 12 CT STRUOL27missile
- SouthWafl O8~34~23 S~~ptember 20, 2007 Page 12
({ 36) > element loads
( 37) > 91 to 92 117 to 118 surface force global pz -7.5 $ {k/ft**2)
{ 38) >S
{ 39) 5 $
{ 40) > units ft kips deg
- 41) > print structural data
- PROBLEM DATA FROM INTERNAL STORAGE JOB ID - FILENAME JOB TITLE - NONE GIVEN ACTIVE UNITS - LENGTI WEIGHT ANGLE TEMPERATURE TIME FEE, KIP DEG DRGF SEC
- STRUCTURAL DATA***********
JOINT COORDINATES--- STATUS -/
JOINT x y Z CONDITION C-0.000 0.000 0.000 SUPPORT ACTIVE GLOBAL 0.000 GLOBAL 02 2 3.000 0.000 SUPPORT ACTIVE 3 6.000 0.000 0.000 SUPPORT ACTIVE GLOBAL 02 4 9.000 0.000 0.000 SUPPORT ACTIVE GLOBAL 5 12.000 0.000 0.000 SUPPORT ACTIVE GLOBAL 6 15.000 0.000 0.000 SUPPORT ACTIVE GLOBAL z 7 18.000 0.000 0.000 SUPPORT ACTIVE GLOBAL 0 8 21.000 0.000 0.000 SUPPORT ACTIVE GLOBAL GLOBAL 6
9 24.000 0.000 0.000 SUPPORT ACTIVE 27.000 0.000 0.000 SUPPORT ACTIVE GLOBAL 30.000 0.000 0.000 SUPPORT ACTIVE GLOBAL w 12 C:)
33.000 0 .000 0.000 SUPPORT ACTIVE GLOBAL 13 36.000 0 .000 0.000 SUPPORT ACTIVE GLOBAL --4 14 39.000 0 .000 0.000 SUPPORT ACTIVE GLOBAL C 15 42 .000 0.000 0.000 SUPPORT ACTIVE GLOBAL 16 45.000 0.000 0,000 SUPPORT ACTIVE GLOBAL 17 48.000 0.000 0.000 SUPPORT ACTIVE GLOBAL > C.*0 CD 18 51.000 0.000 0.000 SUPPORT ACTIVE GLOBAL 19 54.000 0.000 0.000 SUPPORT ACTIVE GLOBAL 20 57.000 0.000 0.000 SUPPORT ACTIVE GLOBAL D" <
21 60.000 0.000 0.000 SUPPORT ACTIVE GLOBAL 22 63.000 0.000 0.000 SUPPORT ACTIVE GLOBAL - Du02 23 66.000 0.000 0.000 SUPPORT ACTIVE GLOBAL 24 69.000 0.000 0.000 SUPPORT ACTIVE GLOBAL 25 72 .000 0.000 0.000 SUPPORT ACTIVE GLOBAL (0 C:)
26 75.000 0.000 0.000 SUPPORT ACTIVE GLOBAL 27 ?78.000 0.000 0.000 SUPPORT ACTIVE GLOBAL 28 0.000 3.000 0.000 SUPPORT ACTIVE GLOBAL
-4
OT STRUML 27 - Southwall missile 08:34:23 September 20, 2007 Page 13 29 3.000 3.000 0.000 FREE ACTIVE GLOBAL 30 6.000 3.000 0.000 FREE ACTIVE GLOBAL 31 9.000 3.000 0.000 FREE ACTIVE GLOBAL 32 12.000 3.000 0.000 FREE ACTIVE GLOBAL 33 15.000 3.000 0.000 FREE ACTIVE GLOBAL 34 18.000 3.000 0.000 FREE ACTIVE GLOBAL 35 21.000 3.000 0.000 FREE ACTIVE GLOBAL 36 24.000 3.000 0.000 FREE ACTIVE GLOBAL 37 27.000 3.000 0.000 FREE ACTIVE GLOBAL 38 30.000 3.000 0.000 FREE ACTIVE GLOBAL 39 33.000 3.000 0.000 FREE ACTIVE GLOBAL 40 36.000 3,000 0.000 FREE ACTIVE GLOBAL 41 39.000 3.000 0.000 FREE ACTIVE GLOBAL 42 42.000 3.000 0.000 FREE ACTIVE GLOBAL 43 45.000 3.000 0.000 FREE ACTIVE GLOBAL 44 48.000 3.000 0.000 FREE ACTIVE GLOBAL 45 51.000 3.000 0.000 FREE ACTIVE GLOBAL 46 54.000 3.000 0.000 FREE ACTIVE GLOBAL 47 57.000 3.000 0.000 FREE ACTIVE GLOBAL 48 60.000 3.000 0.000 FREE ACTIVE GLOBAL 49 63.000 3.000 0.000 FREE ACTIVE GLOBAL 50 66.000 3.000 0.000 FREE ACTIVE GLOBAL 51 69.000 3.000 0.000" FREE ACTIVE GLOBAL 52 72.000 3.000 0.000 FREE ACTIVE GLOBAL 0 53 75.000 3.000 0.000 FREE ACTIVE GLOBAL 54 78.000 3.000 0.000 SUP PORT ACTIVE GLOBAL 55 0.000 6.000 0.000 SUP PORT ACTIVE GLOBAL 5-O 56 3.000 6.000 0.000 FREE ACTIVE GLOBAL 57 6.000 6.000 0.000 FREE ACTIVE GLOBAL 58 9.000 6.000 0.000 FREE ACTIVE GLOBAL 59 12.000 6.000 0.000 FREE ACTIVE GLOBAL z
60 15.000 6.000 0.000 FREE ACTIVE GLOBAL 0 61 18.000 6.000 0.000 FREE ACTIVE GLOBAL 62 21.000 6.000 0.000 FREE ACTIVE GLOBAL a
63 24.000 6.000 0.000 FREE ACTIVE GLOBAL 64 27.000 6.000 0.000 FREE ACTIVE GLOBAL C.)
65 30.000 6.000 0.000 FREE ACTIVE GLOBAL 66 33 .000 6.000 0.000 FREE ACTIVE GLOBAL 67 36.000 6.000 0.000 FREE ACTIVE GLOBAL Cl Cl 68 39.000 6.000 0.000 FREE ACTIVE GLOBAL 03 69 42 .000 6.000 0.000 FREE ACTIVE GLOBAL 70 45.000 6.000 0.000 FREE ACTIVE GLOBAL 71 48.000 6.000 0.000 FREE ACTIVE GLOBAL 72 51.000 6.000 0.000 FREE ACTIVE GLOBAL 73 54.000 6.000 0. 000 FREE ACTIVE GLOBAL D
=D-74 57.000 6.000 0.000 FREE ACTIVE GLOBAL 75 60.000 6.000 0.000 FREE ACTIVE GLOBAL co co-76 63 .000 6.000 0.000 FREE ACTIVE GLOBAL 77 66.000 6.000 0.000 FREE ACTIVE GLOBAL 78 69.000 6.000 0.000 FREE ACTIVE GLOBAL 79 72.000 6.000 0.000 FREE ACTIVE GLOBAL 80 75.000 6.000 0.000 FREE ACTIVE GLOBAL 81 78.000 6.000 0.000 SUPPORT ACTIVE GLOBAL 032 82 0.000 9.000 0.000 SUPPORT ACTIVE GLOBAL
GT STRUD 27 - SouthWall missile 08:34:23 September 20, 2007 Page 14 83 3.000 9.000 0.000 FREE ACTIVE GLOBAL 84 6.000 9.000 0.000 FREE ACTIVE GLOBAL 85 9.000 9.000 0.000 FREE ACTIVE GLOBAL 86 12.000 9.000 0.000 FREE ACTIVE GLOBAL 87 15.000 9.000 0.000 FREE ACTIVE GLOBAL 88 18.000 9.000 0.000 FREE ACTIVE GLOBAL 89 21.000 9.000 0.000 FREE ACTIVE GLOBAL 90 24.000 9.000 0.000 FREE ACTIVE GLOBAL 91 27.000 9.000 0.000 FRIEE ACTIVE GLOBAL 92 30.000 9.000 0.000 FREE ACTIVE GLOBAL 93 33.000 9.000 0.000 FREE ACTIVE GLOBAL 94 36.000 9.000 0.000 FREE ACTIVE GLOBAL 95 39.000 9.000 0.000 FREE ACTIVE GLOBAL 96 42.000 9.000 0.000 FREE ACTIVE GLOBAL 97 45.000 9.000 0.000 FREE ACTIVE GLOBAL 98 48.000 9.000 0.000 FREE ACTIVE GLOBAL 99 51.000 9. 000 0.000 FREE ACTIVE GLOBAL 100 54.000 9. 000 0.000 FREE ACTIVE GLOBAL 101 57.000 9. 000 0.000 FREE ACTIVE GLOBAL 102 60.000 9.000 0.000 FREE ACTIVE GLOBAL 103 63.000 9.000 0.000 FREE ACTIVE GLOBAL 104 66.000 9.000 0.000 FREE ACTIVE GLOBAL 105 69.000 9.000 0.000 FREE ACTIVE GLOBAL 106 72.000 9.000 0.000 FREE ACTIVE GLOBAL FREE ACTIVE GLOBAL 0
107 75.000 9.000 0.000 108 78.000 9.000 0.000 SUPPORT ACTIVE GLOBAL 5-109 0.000 12.000 0.000 SUPPORT ACTIVE GLOBAL 110 3.000 12.000 0,000 FREE ACTIVE GLOBAL III 6.000 12.000 0.000 FREE ACTIVE GLOBAL 112 9.000 12.000 0.000 FREE ACTIVE GLOBAL 113 12.000 12.000 0.000 FREE ACTIVE GLOBAL 114 15.000 12.000 0.000 FREE ACTIVE GLOBAL z 115 18.000 12.000 0.000 FREE ACTIVE GLOBAL 0 116 21.000 12.000 0.000 FREE ACTIVE GLOBAL 117 24.000 12.000 0.000 FREE ACTIVE GLOBAL 118 27.000 12.000 0.000 FREE ACTIVE GLOBAL 119 30.000 12.000 0.000 FREE ACTIVE GLOBAL 120 33.000 12.000 0.000 FREE ACTIVE GLOBAL 121 36.000 12.000 0.000 FREE ACTIVE GLOBAL -4 122 39.000 12.000 0.000 FREE ACTIVE GLOBAL LC 123 42 .000 12.000 0.000 FREE ACTIVE GLOBAL c:)
124 45.000 12 .000 0.000 FREE ACTIVE GLOBAL
>-4 125 126 48.000 51.000 12.000 12 000 0.000 0.000 FREE FREE ACTIVE ACTIVE GLOBAL GLOBAL
-o w 127 54.000 12.000 0. 000 FREE ACTIVE GLOBAL 128 57.000 12.000 0.000 FREE ACTIVE GLOBAL 129 60.000 12,000 0.000 FREE ACTIVE GLOBAL 130 63.000 12.000 0.000 FREE ACTIVE GLOBAL 03 C-D<
131 66.000 12.000 0.000 FREE ACTIVE GLOBAL 132 69.000 12.000 0.000 FREE ACTIVE GLOBAL 133 72.000 12.000 0.000 FREE ACTIVE GLOBAL 134 75.000 12.000 0.000 FREE ACTIVE GLOBAL (o 135 78.000 12.000 0.000 SUPPORT ACTIVE GLOBAL 136 0.000 15.000 0.000 SUPPORT ACTIVE GLOBAL
OT STRUDL2 27 - Southwall missile 08:34:23 September 20, 2007 Page 15 137 3.000 15.000 0.000 FREE ACTIVE GLOBAL 138 6.000 15.000 0.000 FREE ACTIVE GLOBAL 139 9.000 15.000 0.000 FREE ACTIVE GLOBAL 140 12.000 15.000 0.000 FREE ACTIVE GLOBAL 141 15.000 15.000 0.000 FREE ACTIVE GLOBAL 142 18,000 15.000 0.000 FREE ACTIVE GLOBAL 143 21.000 15,000 0.000 FREE ACTIVE GLOBAL 144 24.000 15.000 0.000 FREE ACTIVE GLOBAL 145 27.000 15.000 0.000 FREE ACTIVE GLOBAL 146 30.000 15,000 0.000 FREE ACTIVE GLOBAL 147 33.000 15.000 0.000 FREE ACTIVE GLOBAL 148 36.000 15.000 0.000 FREE ACTIVE GLOBAL 149 39.000 15.000 0.000 FREE ACTIVE GLOBAL 150 42 .000 15.000 0.000 FREE ACTIVE GLOBAL 151 45.000 15.000 0.000 FREE ACTIVE GLOBAL 152 48.000 15.000 0.000 FREE ACTIVE GLOBAL 153 51.000 15.000 0.000 FREE ACTIVE GLOBAL 154 54 .000 15.000 0.000 FREE ACTIVE GLOBAL 155 57.000 15.000 0.000 FREE ACTIVE GLOBAL 156 60.000 15.000 0.000 FREE ACTIVE GLOBAL 157 63.000 15.000 0.000 FREE ACTIVE GLOBAL 158 66.000 15.000 0.000 FREE ACTIVE GLOBAL 159 69.000 15.000 0.000 FREE ACTIVE GLOBAL C) 160 72.000 15.000 0.000 FREE ACTIVE GLOBAL 0-00 161 75.000 15.000 0 .000 FREE ACTIVE GLOBAL 162 78.000 15.000 0.000 SUPPORT ACTIVE GLOBAL 163 0.000 18.000 0.000 SUPPORT ACTIVE GLOBAL 0 164 3.000 18.000 0.000 FREE ACTIVE GLOBAL 165 6.000 18.000 0.000 FREE ACTIVE GLOBAL 166 167 9.000 12,000 18.000 18.000 0.000 0.000 FREE FREE ACTIVE ACTIVE GLOBAL GLOBAL z
168 15.000 18.000 0.000 FREE ACTIVE GLOBAL 0 169 18.000 18.000 0.000 FREE ACTIVE GLOBAL o 170 21.000 18.000 0.000 FREE ACTIVE GLOBAL 0
171 24.000 18.000 0.000 FREE ACTIVE GLOBAL 172 27.000 18.000 0.000 FREE ACTIVE GLOBAL U) 173 30.000 18.000 0.000 FREE ACTIVE GLOBAL 4-174 33.000 18.000 0.000 FREE ACTIVE GLOBAL 175 36.000 18.000 0.000 FREE ACTIVE GLOBAL C,)
176 39.000 18.000 0.000 FREE ACTIVE GLOBAL 177 42.000 18.000 0.000 FREE ACTIVE GLOBAL ow 178 45.000 18.000 0.000 FREE ACTIVE GLOBAL 179 48.000 18.000 0.000 FREE ACTIVE GLOBAL 180 51.000 18.000 0.000 FREE ACTIVE GLOBAL C
181 54.000 18.000 0.000 FREE ACTIVE GLOBAL C )CD 182 57.000 18.000 0.000 FREE ACTIVE GLOBAL 183 60.000 18 000 0.000 FREE ACTIVE GLOBAL CD -
184 63.000 18.000 0.000 FREE ACTIVE GLOBAL 185 66.000 18.000 0.000 FREE ACTIVE GLOBAL 186 69.000 18.000 0.000 FREE ACTIVE GLOBAL 0 187 72.000 18.000 0.000 FREE ACTIVE GLOBAL 188 75.000 18.000 0 . 000 FREE ACTIVE GLOBAL 189 78.000 18.000 0.000 SUPPORT ACTIVE GLOBAL 190 0.000 21.000 0.000 SUPPORT ACTIVE GLOBAL
OT STRUDL 27 - SouthWall missile 08:34:23 September 20, 2007 Page 16 191 3.000 21.000 0,000 FREE ACTIVE GLOBAL 192 6.000 21.000 0.000 FREE ACTIVE GLOBAL 193 9.000 21.000 0.000 FREE ACTIVE GLOBAL 194 12.000 21.000 0.000 FREE ACTIVE GLOBAL 195 15.000 21.000 0.000 FREE ACTIVE GLOBAL 196 18.000 21.000 0.000 FREE ACTIVE GLOBAL 197 21.000 21.000 0.000 FREE ACTIVE GLOBAL 198 24.000 21.000 0.000 FREE ACTIVE GLOBAL 199 27.000 21.000 0.000 FREE ACTIVE GLOBAL 200 30.000 21.000 0.000 FREE ACTIVE GLOBAL 201 33.000 21.000 0.000 FREE ACTIVE GLOBAL 202 36.000 21.000 0.000 FREE ACTIVE GLOBAL 203 39.000 21.000 0.000 FREE ACTIVE GLOBAL 204 42.000 21.000 0.000 FREE ACTIVE GLOBAL 205 45.000 21.000 0,000 FREE ACTIVE GLOBAL 206 48.000 21.000 0.000 FREE ACTIVE GLOBAL 207 51.000 21.000 0.000 FREE ACTIVE GLOBAL 208 54.000 21.000 0.000 FREE ACTIVE GLOBAL 209 57.000 21.000 0.000 FREE ACTIVE GLOBAL 210 60.000 21.000 0.000 FREE ACTIVE GLOBAL 211 63.000 21,000 0.000 FREE ACTIVE GLOBAL 212 66.000 21.000 0.000 FREE ACTIVE GLOBAL 213 69.000 21.000 0.000 FREE ACTIVE GLOBAL 0 214 72.000 21.000 0.000 FREE ACTIVE GLOBAL 215 75.000 21.000 0.000 FREE ACTIVE GLOBAL a) 216 78.000 21.000 0.000 SUPPORT ACTIVE GLOBAL 0 217 0.000 24.000 0.000 SUPPORT ACTIVE GLOBAL 218 3.000 24.000 0.000 SUPPORT ACTIVE GLOBAL @-
219 6.000 24.000 0.000 SUPPORT ACTIVE GLOBAL 220 9.000 24.000 0.000 SUPPORT ACTIVE GLOBAL 0 221 12.000 24.000 0.000 SUPPORT ACTIVE GLOBAL O 222 15.000 24.000 0.000 SUPPORT ACTIVE GLOBAL 223 18.000 24.000 0.000 SUPPORT ACTIVE GLOBAL 224 21.000 24.000 0.000 SUPPORT ACTIVE GLOBAL 225 24.000 24.000 0.000 SUPPORT ACTIVE GLOBAL 226 27.000 24.000 0.000 SUPPORT ACTIVE GLOBAL C0 227 30.000 24.000 0.000 SUPPORT ACTIVE GLOBAL CD GLOBAL I*Z 228 33.000 24.000 0.000 SUPPORT ACTIVE 0.000 SUPPORT ACTIVE GLOBAL 1 229 36.000 24.000 220 36.000 24.000 0.000 SUPPORT ACTIVE GLOBAL 39.000 24000 0.000 SUPPORT ACTIVE ACTIVE GLOBAL)
GLOBAL -
230 232 45.000 24.000 0.000 SUPPORT 233 42.000 24.000 0.000 SUPPORT ACTIVE GLOBAL SUPPORT ACTIVE GLOBAL >
232 45.000 24.000 0.000 235 54.000 24.000 0.000 SUPPORT ACTIVE GLOBAL cu 234 57.000 24.000 0.000 SUPPORT ACTIVE GLOBAL 0- CD 237 54.000 24.000 0.000 SUPPORT ACTIVE GLOBAL = <
238 63.000 24.000 0.000 SUPPORT ACTIVE GLOBAL 239 66.000 24.000 0.000 SUPPORT ACTIVE GLOBAL "D 234 69.000 24.000 0.000 SUPPORT ACTIVE GLOBAL 241 62.000 24.000 0.000 SUPPORT ACTIVE GLOBAL 242 76.000 24.000 0.000 SUPPORT ACTIVE GLOBAL r-W 243 78.000 24.000 0.000 SUPPORT ACTIVE GLOBAL 243 78.000 24.000 0.000 SUPPORT ACTIVE GLOBAL
GT STRUDL 27 - SouthWall missile 08:34:23 September 20, 2007 Page 17 ELEMENT INCIDENCES ---------------- - - - - ---
0ELEMENT NODES 1 1 2 29 28 ACTIVE 2 2 3 30 29 ACTIVE 3 3 4 31 30 ACTIVE 4 4 5 32 31 ACTIVE 5 5 6 33 32 ACTIVE 6 6 7 34 33 ACTIVE 7 7 8 35 34 ACTIVE 8 8 9 36 35 ACTIVE 9 9 10 37 36 ACTIVE 10 10 11 38 37 ACTIVE 11 11 12 39 38 ACTIVE 12 12 13 40 39 ACTIVE 13 13 14 41 40 ACTIVE 14 14 15 42 41 ACTIVE 15 15 16 43 42 ACTIVE 16 16 17 44 43 ACTIVE 0 17 17 i8 45 44 ACTIVE 0) 18 18 19 46 45 ACTIVE C-19 19 20 47 46 ACTIVE 20 20 21 48 47 ACTIVE o 21 21 22 49 48 ACTIVE 0 22 22 23 50 49 ACTIVE 23 24 23 24 24 25 51 52 50 51 ACTIVE ACTIVE z
25 25 26 53 52 ACTIVE 0 26 26 27 54 53 ACTIVE 27 28 29 56 55 ACTIVE 29 57 56 0
28 30 ACTIVE 29 30 31 58 57 ACTIVE C-30 31 32 59 58 ACTIVE C
31 32 33 60 59 ACTIVE 32 33 34 61 60 ACTIVE 33 34 35 62 61 ACTIVE 34 35 36 63 62 ACTIVE 35 36 37 64 63 ACTIVE 36 37 38 65 64 ACTIVE 37 38 39 66 65 ACTIVE 38 39 40 67 66 ACTIVE S .-
CD 39 40 41 68 67 ACTIVE 40 41 42 69 68 ACTIVE CD~
41 42 43 70 69 ACTIVE 42 43 44 71 70 ACTIVE 43 44 45 72 71 ACTIVE 44 45 46 73 72 ACTIVE 45 46 47 74 73 ACTIVE 46 47 48 75 74 ACTIVE N)
GT STRUDL 27 - SouthWal! missile 08:34:23 September 20, 2007 Page 18 47 48 49 76 75 ACTIVE 48 49 5O 77 76 ACTIVE 49 5o 51 78 77 ACTIVE 50 51 52 79 78 ACTIVE 51 52 53 80 79 ACTIVE 52 53 54 8l 8o ACTIVE 53 55 56 83 82 ACTIVE 54 56 57 84 83 ACTIVE 55 57 58 85 84 ACTIVE 56 58 59 86 85 ACTIVE 57 59 60 87 86 ACTIVE 58 60 61 88 87 ACTIVE 59 61 62 89 88 ACTIVE 60 62 63 90 89 ACTIVE 61 63 64 91 90 ACTIVE 62 64 65 92 91 ACTIVE 63 65 66 93 92 ACTIVE 64 66 67 94 93 ACTIVE 65 67 68 95 94 ACTIVE 66 68 69 96 95 ACTIVE 67 69 70 97 96 ACTIVE 68 70 71 98 97 ACTIVE 69 71 72 99 98 ACTIVE 70 72 73 100 99 ACTIVE 71 73 74 101 100 ACTIVE 72 74 75 102 101 ACTIVE 0U) 73 75 76 103 102 ACTIVE =3 74 76 77 104 103 ACTIVE z
75 77 78 105 104 ACTIVE 76 78 79 106 105 ACTIVE 77 79 80 107 106 ACTIVE 78 80 81 108 107 ACTIVE 79 82 83 110 109 ACTIVE 8o 83 84 111 110 ACTIVE ACTIVE 0
81 84 85 112 ii1 82 85 86 113 112 ACTIVE 83 86 87 114 113 ACTIVE 84 87 88 i15 114 ACTIVE 85 88 89 116 115 ACTIVE 86 89 90 117 116 ACTIVE 87 90 91 118 117 ACTIVE 88 91 92 119 120 118 119 ACTIVE ACTIVE CD
=30 89 92 93 90 93 94 121 120 ACTIVE =CD 91 94 95 122 121 ACTIVE n 92 95 96 123 122 ACTIVE 93 96 97 124 123 ACTIVE N)03 94 97 98 125 124 ACTIVE w 95 98 99 126 125 ACTIVE 96 99 100 127 126 ACTIVE 97 100 101 128 127 ACTIVE 98 101 102 129 128 ACTIVE 99 102 103 130 129 ACTIVE 100 103 104 131 130 ACTIVE
GT STRUDL 27 - SouthWall missile 08:34:23 September 20, 2007 Page 19 101 104 105 132 131 ACTIVE 102 105 106 133 132 ACTIVE 103 106 107 134 133 ACTIVE 104 107 108 135 134 ACTIVE 105 109 110 137 136 ACTIVE 106 110 111 138 137 ACTIVE 107 ill 112 139 138 ACTIVE 108 112 113 140 139 ACTIVE 109 113 114 141 140 ACTIVE 110 114 115 142 141 ACTIVE ill 115 116 143 142 ACTIVE 112 116 117 144 143 ACTIVE 113 117 118 145 144 ACTIVE 114 118 119 146 145 ACTIVE 115 119 120 147 146 ACTIVE 116 120 121 148 147 ACTIVE 117 121 122 149 148 ACTIVE 118 122 123 150 149 ACTIVE 119 123 124 151 150 ACTIVE 120 124 125 152 151 ACTIVE 121 125 126 153 152 ACTIVE 122 126 127 154 153 ACTIVE 123 127 128 155 154 ACTIVE 124 128 129 156 155 ACTIVE 0 125 129 130 157 156 ACTIVE 0) 126 130 131 158 157 ACTIVE e-127 131 132 159 158 ACTIVE C 128 132 133 160 159 ACTIVE 129 133 134 161 160 ACTIVE 0 130 134 135 162 161 ACTIVE 131 136 137 164 163 ACTIVE z
132 137 138 165 164 ACTIVE 133 138 139 166 165 ACTIVE 0 134 139 140 167 166 ACTIVE 135 140 141 168 167 ACTIVE 136 141 142 169 168 ACTIVE 137 142 143 170 169 ACTIVE (D) 138 143 144 171 170 ACTIVE 139 144 145 172 171 ACTIVE 140 145 146 173 172 ACTIVE 141 146 147 174. 173 ACTIVE 142 147 148 175 174 ACTIVE 143 148 149 176 175 ACTIVE >-
144 149 150 177 176 ACTIVE 145 150 151 178 177 ACTIVE 146 151 152 179 178 ACTIVE a, 2(D 147 152 153 180 179 ACTIVE o( <
148 153 154 181 180 ACTIVE 3 cn 149 154 155 182 181 ACTIVE 150 151 155 156 156 157 183 184 182 183 ACTIVE ACTIVE (Da CD W0 152 157 158 185 184 ACTIVE 153 158 159 186 185 ACTIVE 154 159 160 187 186 ACTIVE co
GT STRUDL 27 - SouthWall missile 08:34:23 September 20, 2007 Page 20 155 160 161 188 187 ACTIVE 156 161 162 189 188 ACTIVE 157 163 164 191 190 ACTIVE 158 164 165 192 191 ACTIVE 159 165 166 193 192 ACTIVE 160 166 167 194 193 ACTIVE 161 167 168 195 194 ACTIVE 162 168 169 196 195 ACTIVE 163 169 170 197 196 ACTIVE 164 170 171 198 197 ACTIVE 165 171 172 199 198 ACTIVE 166 172 173 200 199 ACTIVE 167 173 174 201 200 ACTIVE 168 174 175 202 201 ACTIVE 169 175 176 203 202 ACTIVE 170 176 177 204 203 ACTIVE 171 177 178 205 204 ACTIVE 172 178 179 206 205 ACTIVE 173 179 180 207 206 ACTIVE 174 180 181 208 207 ACTIVE 175 181 182 209 208 ACTIVE 176 182 183 210 209 ACTIVE 177 183 184 211 210 ACTIVE 178 184 185 212 211 ACTIVE w
C-)
179 185 186 213 212 ACTIVE 02 180 186 187 214 213 ACTIVE 181 187 188 215 214 ACTIVE 5--t 182 188 189 216 215 ACTIVE 183 190 191 218 217 ACTIVE 184 191 192 219 218 ACTIVE 185 192 193 220 219 ACTIVE z 186 193 194 221 220 ACTIVE 0 187 194 195 222 221 ACTIVE 188 195 196 223 222 ACTIVE 189 196 197 224 223 ACTIVE 190 197 198 225 224 ACTIVE 191 198 199 226 225 ACTIVE 0 192 199 200 227 226 ACTIVE 4 193 200 201 228 227 ACTIVE 6 194 201 202 229 228 ACTIVE 195 202 203 230 229 ACTIVE 196 203 204 231 230 ACTIVE S0) 197 204 205 232 231 ACTIVE 198 205 206 233 232 ACTIVE > -4 199 206 207 234 233 ACTIVE w; 200 207 208 235 234 ACTIVE
£0 201 208 209 236 235 ACTIVE 202 209 210 237 236 ACTIVE oCD CD Dl 203 210 211 238 237 ACTIVE 204 211 212 239 238 ACTIVE 205 212 213 240 239 ACTIVE 206 213 214 241 240 ACTIVE 207 214 215 242 241 ACTIVE 208 215 216 243 242 ACTIVE cn
GT STRUDL 27 - SouthWall missile 08:34:23 September 20, 2007__Pa~ge 21 ELEMENT PROPERTIES --------- - - --- OF THE CABLE ELEMENT ARE LENGTH AND AX -)-------
-THE PROPERTIES OELEMENT TYPE THICKNESS CURVATURES OR AX - / / -------------- THERMAL EXPANSION COEFFICIENTS -
OR LENGTH KE K2 K12 CAX CAY CAZ CSXY CSXZ CSYZ 1 SBHQ6 3.000 2 SBHQ6 3.000 3 SBHQ6 3.000 4 SBHQ6 3.000 5 SBHQ6 3.000 6 SBHQ6 3.000 7 SBHQ6 3.000 8 5BHQ6 3.000 9 SBHQ6 3.000 10 SBHQ6 3.000 11 SBHQ6 3.000 12 SBHQ6 3.000 13 SBHQ6 3.000 14 SBNQ6 3.000 15 SBHQ6 3.000 16 SBHQ6 3.000 17 SBHQ6 3.000 18 SBHQ6 3.000 19 SBHQ6 3.000 c-20 SBHQ6 3.000 21 SBHQ6 3.000 22 SBHQ6 3.000 23 SBHQ6 3.000 0 24 SBHQ6 3.000 25 SBHQ6 3.000 z 26 SBHQ6 3.000 0 27 SBHQG 3.000 28 SBHQ6 3.000 O 29 SBHQ6 3.000 30 SBHQ6 3.000 31 SBHQ6 3.000 C')
32 SBHQ6 3.000 33 SBHQ6 3.000 34 SBHQ6 3.000 35 SBHQ6 3.000 0 36 SBHQ8 3.000 >
3.000
- 00 37 SBHQ6 38 SBHQ6 3.000 39 SBHQ6 3.000 40 SBHQ6 3.000 J- <D 41 SBHQ6 3.000 (Da 42 SBHQ6 3.000 43 SBHQ6 3.000 CD Dl 44 SBHQ6 3.000 45 SBHQ6 3.000 46 SBHQ6 3.000 47 SBHQ6 3.000 NJ C M2W
GT STRUDL 27 - SouthWall missile 08:34123 September 20, 2007 Page 22 48 SBHQ6 3.000 49 SBHQ6 3.000 50 SBHQ6 3.000 51 SBHQ6 3.000 52 SBHQ6 3.000 53 SBHQ6 3.000 54 SBHQ6 3.000 55 SBHQ6 3,000 56 SBHQ6 3.000 57 SBHQ6 3.000 58 SB14Q6 3.000 59 SBHQ6 3.000 60 SBHQ6 3.000 61 SBHQ6 3.000 62 SBHQ6 3.000 63 SBHQ6 3.000 64 SBHQ6 3.000 65 SBHQ6 3.000 66 SBHQ6 3.000 67 SBHQ6 3.000 68 SBHQ6 3 .000 69 SBHQ6 3.000 70 SBHQG 3.000 71 SBHQ6 3.000 72 SBHQG 3.000 73 SBEQ6 3.000 74 SBHQ6 3.000 :3 75 SBHQ6 3 .000 76 SBHQ6 3.000 0 77 SBHQ6 3 .000 78 SBHQ6 3 .000 SBHQ6 z 79 3 .000 0 80 SBHQ6 3.000 82 SBE06 3.000 82 SBHQ6 3.000 SBHQ6 0 83 3.000 84 SBHQ6 3.000 C')
85 SBHQ6 3.000 86 SB14Q6 3.000 87 SB3HQ6 3.000 88 SBHQ6 3.000 CA-89 SBHQ6 3.000 90 SBHQ6 3.000 C)
SBHQ6 3.000 (A) 92 SBHQ6 3.000 93 SBHQ6 3 .000 94 SBHQ6 3.000 95 SBHQ6 3 .000 96 SBHQ6 3.000 97 SBHQ6 3 .000 98 SBHQ6 3.000 co~
99 SBHQ6 3 .000 100 SBHQ6 3.000 101 SBHQ6 3.000 NMWDOC N
missile 08:34:23 September 20, 2007 Page 23 GT STRUDL 27 - SouthWal!
102 SBHQG 3.000 103 SBHQ6 3 .000 104 SBHQG 3.000 105 SBHQ6 3 .000 106 SBHQ6 3 .000 107 SBHQ6 3 .000 108 SBHQ6 3.000 109 SBHQ6 3 .000 110 SBHQ6 3 .000 ill SBHQ6 3.000 112 SBHQ6 3.000 113 SBHQ6 3.000 114 SBHQ6 3.000 115 SRHQ6 3,000 116 SBHQ6 3.000 117 SBHQ6 3.000 118 SBHQ6 3.000 119 SBHQ6 3.000 120 SBHQ6 3.000 121 SBHQ6 3.000 122 SBHQ6 3.000 123 SBHQ6 3.000 124 SBHQ6 3.000 SEFQE SB.HQ6 125 3.000 126 SEH06
$BM4Q6 3.000 C-)
SBHQ6 3.000 0
127 128 SBHqQ6 3.000 129 SBHiQ6 3.000 130 SBHQ6 3.000 0 131 SB3HQG 3.000 132 SBHQ6 3.000 133 SBHQ6 3.000 134 SBHQ6 3 .000 135 SBKQ6 555Q6 3 .000 136 SBHQG SB506 3.000 137 SBI-Q6 3.000 0 138 SBHQ6 3.000 139 SBHQ6 3.000 (,3:
140 SBHQ6 3,000 CA, 141 SBHQ6 3.000 142 SBHQ6 3.000 143 SBHQ6 3.000 -0 0-144 SBI-Q6 3.000 C)
SBEQ6 145 3.000 CA)
S0HQ6 146 SBHQ6 3 .000 147 3.000 SBHQ6 148 SBHQ6 3.000 MCDn 149 SBHQ6 3.000 150 SBHQG 3.000 151 SBQ06 3.000 (c 152 3.000 SBHQ6 153 3 .000 154 3.000 155 3.000
08:34:23 September 20, 2007 Page 24 GT STRUDL 27 - SouthWail missile 156 SBHQ6 3.000 157 SBHQ6 3.000 158 SBHQ6 3,000 159 SBHQ6 3.000 160 SBHQ6 3.000 161 SBHQ6 3 .000 162 SBHQ6 3.000 163 SBHQ6 3.000 164 SBHQ6 3.000 165 SBHQ6 3.000 166 SR14Q6 3.000 167 SBHQ6 3.000 168 SBHQ6 3.000 169 SBHQ6 3.000 170 SBHQ6 3.000 171 SBHQ6 3.000 172 SBHQ6 3.000 173 SBHQ6 3.000 174 SBHQ6 3.000 175 SBHQ6 3,000 176 SBHQ6 3.000 177 SBHQ6 3.000 178 SBHQ6 3 .000 179 SBHQ6 3 .000 0 180 SBHQ6 3 .000 181 SBHQ6 3 000 182 SBHQ6 3 .000 183 SBHQ6 3 .000 184 S9610 3 .000 185 SBHQ6 3 .000 (-
186 SB0Q6 3 .000 z 0
187 SBHQ6 3.000 0 188 SBHQ6 3.000 N
189 SBHQ6 3.000 SBHQ6 3.000 0 190 191 SBQ6 3.000 C) 192 SBHQ6 3.000 193 SBHQ6 3.000 194 SBHQ6 SBHQ6 3.000 3.000 o
195 196 SBHQ6 3.000 > 4 197 SBHQ6 3.000 198 SBHQ6 3.000 M XU 199 SBQ6 3 .000 200 SBHQ6 3 .000 201 SBHQ6 3 .000 ,-,.
202 SBHQ6 3.000 203 SBHQG 3.000 CD D 204 SBHQ6 3.000 205 SBHQ6 3.000 206 SBHQ6 3.000 207 SBHQ6 3.000 208 SBHQ6 3.000 co
GT STRUDI, 27 - SouthWall missile 08:34:23 September 20, 2007 Page J 25 GT STRUEL 27 - SouLhMall missile 08:34:23 Sentember 20. 2007 Pacie 25 MEMBER CONSTANTS------------------------ - - - -- - - - - -/ ---
0CONSTANT STANDARD VALUE DOMAIIN VALUE MEMBER LIST E 0 S58400E+06 ALL G 0.207360E+06 ALL DENSITY 0.149990E+00 ALL CTE 0,55000.E-05 ALL BETA 0.000000E+00 ALL POISSON 0.170000E+00 ALL DAMP STI 0.OOQ00E+00 ALL DAMP INE 0.OOOOOOE+00 ALL C)
CO CURVED ELEMENT DATA --------------------------------------------------------------------------------------------------------------- / 0 z:
CURVED ELEMENT SPECIFICATIONS ---------------------------------------------------------------------------------------------------- / 0 ELEMENT TYPE SPECIFICATIONS /--------------------------------------------------
- NO SHAPE DATA FOUND FOR MEMBER LIST SPECIFIED 0f)
C:
CD 0CD CURVED ELEMENT PROPERTIES -------------------------------------------------------------------------------------------------------- /
ELEMENT TYPE PROPERTIES ------------------------------------------------------------------------------
CD5 CURVED ELEMENT END CONDITIONS --------------------------------------------------------------------------------------------------- / CD=
ELEMENT TYPE ECCENTRICITIES-- -------------------------------------------------------------------------
START END x Y Z X Y Z c:)
C:
rri S'RUrmr 2~7 - cnoit-¶Wnll missile 08:34:23 September 20, 2007 Pagre 26
- END OF DATA FROM INTERNAL STORAGE *
- 42) > STIFFNESS ANALYSIS BANDWIDTH INFORPMATION BEFORE RENUMBERING.
THE MAXIMUM BANDWIDTH IS 26 AND OCCURS AT JOINT 57 THE AVERAGE BANDWIDTH IS 22 .389 THE STANDARD DEVIATION OF THE BANDWIDTH IS 8 .750 31.139 BANDWIDTH INFORMATION AFTER RENUMBERING. C) 5)
THE MAXIMUM BANDWIDTH IS 8 AND OCCURS AT JOINT 57 THE AVERAGE BANDWIDTH IS 7.577 THE STANDARD DEVIATION OF THE BANDWIDTH IS 1.416 0 8 .993 zc-)
TIME FOR CONSISTENCY CHECKS FOR 208 MEMBERS 0.01 SECONDS TIME FOR BANDWIDTH REDUCTION 0.02 SECONDS N TIME TO GENERATE 208 ELEMENT STIF. MATRICES 0.17 SECONDS 0 TIME TO PROCESS 4 MEMBER LOADS 0.00 SECONDS Co TIME TO ASSEMBLE'THE STIFFNESS MATRIX 0.06 SECONDS TIME TO PROCESS 243 JOINTS 0.00 SECONDS TIME TO SOLVE WITH 25 PARTITIONS 0.10 SECONDS w TIME TO PROCESS 243 JOINT DISPLACEMENTS 0.00 SECONDS TIME TO PROCESS 208 ELEMENT STRESSES 0.03 SECONDS >4 TIME TO PROCESS 208 ELEMENT REACTIONS 0.03 SECONDS CDa TIME FOR STATICS CHECK 0.00 SECONDS <
{ 43) > $
{ 44) > LOAD LIST ALL
- 45) > OUTPUT DEC 3 m3 1 46) > OUTPUT BY loading Cw CD,. C .
{ 47) > LIST REA ALL 1
- RESULTS OF LATEST ANALYSES*
08:34:23 September 20, 2007 Page 27 GT STRUDL 27 - SouthWall missile 08:34:23 Semtember 20. 2007 PaGe 27 OT STEUDL 27 - SouthWalJ. missile PROBLEM - FILENAME TITLE - NONE GIVEN ACTIVE UNITS FEET KIP DEG DEGF SEC
--- LOADING - 2 missile RESULTANT---------OI-------OADS----S--------T--
RESULTANT JOINT LOADS SUPPORTS JOINT /----------------- FORCE- / --- -- - -- - -- - -- - - MOME NT -- S/
/
X FORCE Y FORCE Z FORCE X MOMENT Y MOMENT Z MOMENT 1 GLOBAL 0.000 0.000 0 .034 0.009 -0.009 0.000 2 GLOBAL 0.000 0.000 -0.012 -0.093 -0.009 0.000 3 GLOBAL 0.000 0.000 -0.163 -0.293 0.010 0.000 4 GLOBAL 0.000 0.000 -0.342 -0.373 0,097 0.000 GLOBAL 0. 000 0.000 -0.557 -0.089 0.285 0.000 6 0.635 0.000 0 GLOBAL 0. 000 0.000 -0.786 0.987 7 GLOBAL 0 , 000 0.000 -0.937 3.601 1.234 0.000 8 GLOBAL 0.000 0.000 -0.780 8.952 2.174 0.000 9 GLOBAL 0.000 0.000 0.169 18.775 3.497 0.000 10 GLOBAL 0.000 0.000 2.779 35.138 5.062 0.000 11 GLOBAL 0.000 0.000 8.249 59.432 6.335 0.000 12 GLOBAL 0.000 0.000 17.177 89.790 6.309 0.000 0.000 27.116 117,673 4.075 0.000 .--
13 GLOBAL 0.000 14 GLOBAL 0.000 0.000 31.741 129.408 0.000 0.000 CD 15 GLOBAL 0.000 0.000 27.116 117.673 -4.075 0.000 16 GLOBAL 0.000 0.000 17.177 89.790 -6.309 0.000 17 GLOBAL 0.000 0.000 8.249 59.432 -6.335 0.000 18 GLOBAL 0.000 0.000 2.779 35.138 -5.062 0.000 19 GLOBAL 0.000 0.000 0. 169 18.775 -3.497 0.000 20 GLOBAL 0.000 0.000 -0.780 8.952 -2.174 0.000 21 GLOBAL 0.000 0.000 -0.937 3.601 -1.234 0.000 CD 0.000 -0.786 0.987 -0.635 0.000 C-22 GLOBAL 0.000 23 GLOBAL 0.000 0.000 -0.557 -0.089 -0.285 0.000 24 GLOBAL 0.000 0.000 -0.342 -0.373 -0.097 0.000 25 GLOBAL 0.000 0.000 -0.163 -0.293 -0.010 0.000 0.000 0 26 GLOBAL 0.000 0.000 -0.012 -0.093 0.009 27 GLOBAL 0.000 0.000 0.034 0.009 0.009 0.000 CD-28 GLOBAL 0.000 0.000 -0.008 0.012 0.087 0.000
-0.087 0.000 (D 54 GLOBAL 0.000 0.000 -0.008 0.012 55 GLOBAL 0.000 0.000 -0.101 0. 017 0.252 0.000 81 GLOBAL 0.000 0,000 -0.101 0.017 -0.252 0.000 82 GLOBAL 0.000 0.000 -0.136 0.008 0.341 0.000 108 GLOBAL 0.000 0.000 -0.136 0.008 -0.341 0.000 -o 109 GLOBAL 0.000 0.000 -0 .143 0.000 0.365 0.000 135 GLOBAL 0.000 0,000 -0.143 0.000 -0.365 0.000
GT STRUDL 27 - SouthWall missile 08:34:23 September 20, 2007 Page 28 136 GLOBAL 0 . 000 0,000 -0,136 -0.008 0.341 0.000 162 GLOBAL 0 .000 0.000 -0.136 -0.008 -0.341 0.000 163 GLOBAL 0 .000 0.000 -0.101 -0.017 0.252 0.000 189 GLOBAL 0 .000 0.000 -0.101 -0,017 -0.252 0.000 190 GLOBAL 0.000 0,000 -0.008 -0.012 0.087 0.000 216 GLOBAL 0.000 0 .000 -0.008 -0.012 -0.087 0.000 217 GLOBAL 0.000 0 ,0 00 0.034 -0.009 -0.009 0.000 218 GLOBAL 0.000 0,000 -0.012 0.093 -0.009 0.000 219 GLOBAL 0.000 0 .000 -0.163 0.293 0.010 0.000 220 GLOBAL 0.000 0.000 -0.342 0.373 0.097 0.000 221 GLOBAL 0.000 0 .000 -0.557 0.089 0.285 0,000 222 GLOBAL 0.000 0,000 -0.786 -0.987 0.635 0.000 223 GLOBAL 0.000 0.000 -0.937 -3.601 1.234 0.000 224 GLOBAL 0.000 0.000 -0.780 -8.952 2.174 0.000 225 GLOBAL 0.000 0,000 0.169 -18.775 3.497 0.000 226 GLOBAL 0.000 0,000 2.779 -35.138 5.062 0.000 227 GLOBAL 0.000 0.000 8.249 -59.432 6.33S 0.000 228 GLOBAL 0.000 0.000 17.177 -89,790 6.309 0.000 229 GLOBAL 0.000 0,000 27.116 -117.673 4.075 0.000 230 GLOBAL 0.000 0.000 31.741 -129.408 0.000 0.000 231 GLOBAL 0.000 0,000 27.116 -117.673 -4.075 0.000 232 GLOBAL 0.000 0.000 17.177 -89.790 -6.309 0.000 233 GLOBAL 0.000 0.000 8.249 -59.432 -6,335 0.000 234 GLOBAL 0.000 0.000 2.779 -35.138 -5.062 0.000 235 GLOBAL 0 .000 0.000 0.169 -18.775 -3.497 0.000 0 236 GLOBAL 0 .000 0.000 -0.760 -8.952 -2.174 0.000 c) 5-237 GLOBAL 0 .000 0,000 -0.937 -3.601 -1.234 0.000 238 GLOBAL 0.000 0.000 -0.786 -0.987 -0.635 0.000 239 GLOBAL 0 .000 0,000 -0,557 0.089 -0.285 0.000 240 GLOBAL 0.000 0.000 -0.342 0.373 -0.097 0.000 D 241 242 GLOBAL GLOBAL 0.000 0.000 0.000 0.000
-0.163
-0.012 0.293 0.093
-0.010 0.009 0.000 0.000 z0 243 GLOBAL 0.000 0.000 0.034 -0.009 0.009 0.000 co 48} > LIST DISP ALL
- RESULTS OF LATEST ANALYSES*
C)
PROBLEM - FILENAME TITLE - NONE GIVEN CD CD ACTIVE UNITS FEET KIP DEG DEGF SEC CD :3 =3
-. -. - - LO.. I .G.-. .2 . . . . . . . . . . . . . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
--- LOADING - 2 missile co2
08:34:23 Se*tem er 20 2007 Page 29 GT STRUDL 27 - SouthWall missile *74.9.~ 0sr~t~bsr 70 7007 0s~s 25 27 GT STRUDL - SourhWall missiTh RESULTANT JOINT DISPLACEMENTS SUPPORTS JOINT /---------- - DISPLACEMENT // -----------------ROTATION-------------------/
X DISP. Y DISP. Z DISP. X ROT. Y ROT. Z ROT.
1 GLOBAL 0,000 0.000 0.000 0 .000 0.000 0.000 2 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 3 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 4 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 5 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 6 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.O0O 7 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 8 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 9 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 10 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 11 GLOBAL 0.000 0.000 0.000 0.000 0 .000 0.000 12 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 13 GLOBAL 0 . 000 0.000 0.000 0.000 0..000 0.000 14 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 15 GLOBAL 0,000 0.000 0.000 0.000 0,000 0.000 16 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 17 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 18 GLOBAL 0 .000 0.000 0.000 0.000 0.000 0.000 19 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0
20 GLOBAL 0.000 0.000 0.000 0.000 21 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 22 GLOBAL 0.000 0.000 0,000 0.000 0.000 0.000 23 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 24 GLOBAL 0.000 0.000 O.OO0 0.000 0.000 0.000 cn 25 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 z 26 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 0 27 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 28 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 54 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 55 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 ow 81 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 82 GLOBAL 0.000 0.000 0,000 0.000 0.000 0.000 108 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 00 109 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 135 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 136 GLOBAL 0.000 0.000 0.o000 0.000 0.000 0.000 c:)
162 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 163 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 189 GLOBAL 0.000 0.000 0.000 0,000 0.000 0.000 190 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 -o3 c.
216 217 GLOBAL GLOBAL 0.000 0.000 0.000 0.000 0,000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 Co ° 218 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 219 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 220 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 221 GLOBAL 0.000 0.000 0.000 0.000 0 .000 0.000 222 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000
08:34:23 September 20, 2007 Page 30 GT STRUDL 27 - Southwall missile 223 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 224 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 225 GLOBAL 0.000 0.000 0.000 0.000 0.000 0,000 226 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 227 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 228 GLOBAL 0.000 0,000 0 .000 0.000 0.000 0.000 229 GLOBAL 0 .000 0.000 0,000 0.000 0.000 0.000 230 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 231 GLOBAL 0.000 0 000 0.000 0,000 0.000 0.000 232 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 233 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 234 GLOBAL 0.000 0.000 0.000 0.000 0.000 0,000 235 GLOBAL 0.000 0.000 0.000 0 .000 0.000 0.000 236 GLOBAL 0.000 0,000 0.000 0.000 0.000 0.000 237 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 238 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 239 GLOBAL 0.000 0 .000 0.000 0.000 0.000 0.000 240 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 241 GLOBAL 0,000 0.000 0.000 0.000 0.000 0.000 242 GLOBAL 0.000 0 .000 0.000 0.000 0.000 0,000 243 GLOBAL 0.000 0 .000 0.000 0.000 0.000 0.000 RFEE JOINTS 0 RESULTANT JOINT DISPLACEMENTS z-
-- ~ROTATION-------------------/
JOINT DISPLACEMENT- --------------- .--------------
X DISP. Y DISP. Z DISP. X ROT. Y ROT. Z ROT.
0 29 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 O 30 GLOBAL 0 .000 0.000 0.000 0.000 0.000 0.000 0t-31 GLOBAL 0.000 0.000 0.000 0.000 0.000 0,000 32 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 33 GLOBAL 0.000 0.000 0.000 0,000 0.000 0.000 0 34 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 35 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 36 GLOBAL 0,000 0.000 0.000 -0.001 0.000 0.000 o 37 GLOBAL 0.000 0.000 0.000 -0.001 0.000 0.000 CD 38 GLOBAL 0.000 0.000 0.000 -0.002 0.000 0.000 39 GLOBAL 0.000 0.000 0.000 -0.003 0.001 0.000 >-4 40 GLOBAL 0.000 0.000 0.000 -0,004 0.000 0.000 41 GLOBAL 0.000 0.000 0.000 -0.004 0.000 0.000 42 GLOBAL 0.000 0.000 0.000 -0.004 0.000 0.000 ma ;a; 43 GLOBAL 0.000 0.000 0,000 -0.003 -0.001 0.000 ,-u-
=0CD 44 GLOBAL 0.000 0.000 0.000 -0.002 0.000 0.000 45 GLOBAL 0.000 0 .000 0.000 -0.001 0.000 0.000 46 GLOBAL 0.000 0 .000 0.000 -0.001 0.000 0.000 47 GLOBAL 0 .000 0 .000 0.000 0.000 0.000 0.000 48 GLOBAL 0 .000 0.000 0.000 0.000 0.000 0.000 49 GLOBAL 0.000 0 .000 0.000 0.000 0.000 0.000 CD~
50 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 51 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 52 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 53 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000
08:34:23 September 20, 2007 Page 31 GT STRUL 27 - Southwall missile 56 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 57 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 58 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 59 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 60 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 61 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 62 GLOBAL 0.000 0.000 0.000 -0.001 0.000 0.000 63 GLOBAL 0.000 0.000 0.000 -0.001 0.001 0.000 64 GLOBAL 0.000 0.000 0.000 -0.002 0.001 0.000 65 GLOBAL 0.000 0.000 0.000 -0.003 0.002 0.000 66 GLOBAL 0.000 0.000 0.000 -0.004 0.002 0.000 67 GLOBAL 0.000 0.000 0.000 -0.005 0.001 0.000 68 GLOBAL 0.000 0.000 0.000 -0.006 0.000 0.000 69 GLOBAL 0.000 0.000 0.000 -0.005 -0.001 0.000 70 GLOBAL 0.000 0.000 0.000 -0.004 -0.002 0.000 71 GLOBAL 0.000 0.000 0.000 -0.003 -0.002 0.000 72 GLOBAL 0.000 0.000 0.000 -0.002 -0.001 0.000 73 GLOBAL 0.000 0.000 0.000 -0.001 -0.001 0.000 74 GLOBAL 0.000 0.000 0.000 -0.001 0.00O 0.000 75 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 76 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 77 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 78 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 79 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 80 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0 83 GLOBAL 84 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 0-85 86 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 87 88 GLOBAL GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 zo 0.000 0.000 0.000 0.000 0.001 0.000 89 GLOBAL 0.000 O 0.000 0.000 -0.001 0.001 90 GLOBAL 0.000 GLOBAL 0.000 0.000 0.000 -0.001 0.002 0.000 91 GLOBAL 0.000 0.000 0.000 -0.002 0.003 0.000 92 93 GLOBAL 0.000 0.000 0.000 -0.003 0.003 0.000 0.001 -0.004 0.002 0.000 09 94 GLOBAL 0.000 0.000
-0.005 0.000 0.000 U) 95 GLOBAL 0.000 0.000 -0.001 C)
-0.001 -0.004 -0.002 0.000 96 GLOBAL 0.000 0.000 0.000 0.000 0.000 -0.003 -0.003 0.000 0 97 GLOBAL 0.000 -0.002 -0.003 0.000 0 98 GLOBAL 0.000 0.000 99 GLOBAL 0.000 0.000 0.000 -0.001 -0.002 0.000 0.000 -0.001 -0.002 0.000 -4 100 GLOBAL 0.000 0.000 0.000 -0.001 0.000 >
101 GLOBAL 0.000 0.000 0.000 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 102 103 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 -0 .
0.000 0.000 <
0.000 0.000 0.000 0.000 104 105 GLOBAL GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 Q) 3 Fn 0.000 0.000 0.000 0.000 ) CD 106 GLOBAL 0.000 0.000 107 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 110 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 110 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 112 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 0o 0.000 0.000 0.000 0.000 0.000 0.000 113 GLOBAL
SouthWal1 mi~1l~ 08:34 23 Se tember 20 2007 Pa e 32 OT STRUOL 27 -
GT S7RUDL 27 - SouthWall missile 114 GLOBAL 0. 000 0.000 0.000 0.000 0.000 0.000 115 GLOBAL 0. 000 0 000 0.000 0.000 0.001 0.000 116 GLOBAL 0. 000 0.000 0 000 0.000 0.001 0.000 117 GLOBAL 0.000 0.000 0.000 0.000 0.002 0.000 118 GLOBAL 0-000 0.000 0.000 0.000 0.002 0.000 119 GLOBAL 0.000 0.000 0.000 0.000 0.003 0.000 120 GLOBAL 0.000 0.000 -0.001 0.000 0.004 0.000 121 GLOBAL 0.000 0.000 -0.001 0.000 0.003 0.000 122 GLOBAL 0.000 0 .000 -0.001 0.000 0.000 0.000 123 GLOBAL 0.000 0 .000 -0.001 0.000 -0.003 0.000 124 GLOBAL 0.000 0.000 -0.001 0.000 -0.004 0.000 125 GLOBAL 0.000 0.000 0.000 0.000 -0.003 0.000 126 GLOBAL 0.000 0.000 0.000 0,000 -0.002 0.000 127 GLOBAL 0.000 0,000 0.000 0.000 -0.002 0.000 128 GLOBAL 0.000 0.000 0.000 0.000 -0.001 0.000 129 GLOBAL 0.000 0 . 000 0.000 0.000 -0.001 0.000 130 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 131 GLOBAL 0.000 0 .000 0.000 0.000 0.000 0.000 132 GLOBAL 0. 000 0.000 0.000 0.000 0.000 0.000 133 GLOBAL 0. 000 0.000 0.000 0.000 0.000 0.000 134 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 137 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 138 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 139 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 140 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 141 142 GLOBAL GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0,000 0.000
~0 143 GLOBAL 0.000 0.000 0 .000 0.000 0.001 0.000 144 GLOBAL 0.000 0.000 0.000 0.001 0.001 0.000 0 145 GLOBAL 0,000 0.000 0 .000 0.001 0.002 0.000 146 GLOBAL 0.000 0.000 0.000 0.002 0.003 0.000 z 147 GLOBAL 0.000 0 .000 0.000 0.003 0,003 0.000 0 148 GLOBAL 0.000 0 .000 -0.001 0.004 0.002 0.000 149 GLOBAL 0.000 0.000 -0.001 0.005 0.000 0.000 150 GLOBAL 0,000 0.000 -0.001 0.004 -0.002 0.000 151 GLOBAL 0.000 0.000 0.000 0,003 -0.003 0.000 152 GLOBAL 0.000 0.000 0.000 0.002 -0.003 0.000 153 GLOBAL 0.000 0.000 0.000 0.001 -0.002 0.000 154 GLOBAL 0.000 0.000 0.000 0.001 -0.001 0.000 155 GLOBAL 0.000 0.000 0.000 0.000 -0,001 0.000 0 156 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 157 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 158 GLOBAL 0.000 0. 000 0.000 0.000 0.000 0.000 C'D 159 GLOBAL 0.000 0 .000 0.000 0.000 0.000 0.000 -- 4 160 GLOBAL 0,000 0.000 0.000 0.000 0.000 0.000 0
- 161 GLOBAL 0.000 0 . 000 0.000 0.000 0.000 0.000 164 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 165 GLOBAL 0.000 0.000 0.000 0.000 0.000 0,000 166 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 <
167 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 N 168 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 169 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 170 GLOBAL 0.000 0.000 0.000 0.001 0.000 0.000 171 GLOBAL 0.000 0.000 0.000 0.001 0.001 0.000
08:34:23 September 20, 2007 Page 33 GT STRUDL 27 - SouthWall missile 172 GLOBAL 0.000 0.000 0.000 0.002 0.001 0.000 173 GLOBAL 0.000 0.000 0.000 0.003 0.002 0.000 174 GLOBAL 0.000 0.000 0.000 0.004 0.002 0.000 175 GLOBAL 0.000 0.000 0.000 0.005 0.001 0.000 176 GLOBAL 0.000 0.000 0.000 0.006 0.000 0.000 177 GLOBAL 0.000 0.000 0.000 0.005 -0.001 0.000 178 GLOBAL 0.000 0.000 0.000 0.004 -0.002 0.000 179 GLOBAL 0.000 0.000 0.000 0.003 -0.002 0.000 180 GLOBAL 0.000 0.000 0.000 0.002 -0.001 0.000 181 GLOBAL 0.000 0.000 0.000 0.001 -0.001 0.000 182 GLOBAL 0.000 0.000 0.000 0.001 0.000 0.000 183 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 184 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 185 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 186 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 187 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 188 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 191 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 192 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 193 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 194 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 195 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 196 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 Q 197 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 0) 198 GLOBAL 0.000 0.000 0.000 0.001 0.000 0.000 199 GLOBAL 0.000 0.000 0.000 0.001 0.000 0.000 200 GLOBAL 0.000 0.000 0.000 0.002 0.000 0.000 201 GLOBAL 0.000 0.000 0.000 0.003 0.001 0.000 0 202 GLOBAL 0.000 0.000 0.000 0.004 0.000 0.000 -D 203 GLOBAL 0.000 0.000 0.000 0.004 0.000 0.000 Z 204 GLOBAL 0.000 0.000 0.000 0.004 0.000 0.000 0 205 GLOBAL 0.000 0.000 0.000 0.003 -0.001 0.000 200 GLOBAL 0.000 0.000 0.000 0.002 0.000 0.000 207 GLOBAL 0.000 0.000 0.000 0.001 0.000 0.000 208 GLOBAL 0.000 0.000 0.000 0.001 0.000 0.000 U) 209 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 210 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 211 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0 212 GLOBAL 213 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 4 214 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 215 GLOBAL 0.000 0.000 0.000 0.000 0.000 0.000 1 49} 5 calculate average resultants at mid surf =- <
-***ELEMENT LIST MISSING - ALL ASSUMED -0 CD O C) O
- RESULTS OF LATEST ANALYSES*
0*
GT STRUDL 27 - SouthWall missile 08:34:23 September 20, 2007 Page 34 PROBLEM - FILENAME TITLE - NONE GIVEN ACTIVE UNITS FEET KIP DEG DEGF SEC LOADING - 2 missile AVERAGE RESULTANTS (MEMBRANE/BENDING)
JOINT NUMBER OF ELEMENTS NXX/ uYY/ NXY/
USED IN AVERAGING MXX MYY MXY VXX VYY 1 1 0.000000E+00 0.000000E+00 0.00000OE+00
- 0. 19979E-01 0.121160E-01 0.940850E-02 -0.18214BE-01 -0.178596E-01 0.000000E+00 0.000000E+00 0.0000D0E+00 C)
-0.244988E-02 -0.301279E-01 -0.287135E-02 -0.231931E-01 0.688708E-02 2 0.000000E+00 0.000000E+00 0.000000E+00
=-
-0.268305E-01 -0.979648E-01 -0.455018E-02 -0.138652E-01 0.442638E-01 0
2 0.000000E+00 0.0000OOE+00 0.000000E+00
-0.490043E-01 -0.127826E+/-00 -0.i18801E-01 0.416223E-01 0.875596E-01 z 0
2 0.000000E+00 0.000000E+00 0.OOOOOOE+00
-0.626140E-01 -0.383581E-01 -0.267432E-01 0.168932E+00 0.131848E÷00 2 0000000E+00 0.OOOOOOE+00 0.00000OE+00
-0.510768E-01 0.310897E+00 -0.527506E-01 0.416779E+00 0.163392E+00 CD, 2 0.000000E+00 0.000000E+00 0.O00000E+00 6 0.204290E-01 0.116549E+01 -0.941022E-01 0.858205E+00 0.146084E+00 2 0.000000E+00 0.000000E+00 0.00O000E+00 0.217861E+00 0.292357E+01 -0.153456E+00 0.158155E+01 0.343938E-02 2 0.OOOOOOE+00 0.000000E+00 0.00000CE+O0 0.655636E+00 0.616536E+/-0l -0.226516E+00 0.265272E+01 -0,406212E+00 3 C 0.000000E+00 0.000000E+00 0.000000E+00 0(73 10 0.151279E+01 0.115952E+02 -0.292106E+00 0.401029E+01 -0.130997E+01 0.000000E+00 0.000000E+0O 0.000000E+00 (.0 0.301378E+01 0.197192E+02 -0.304626E+00 0,525815E+01 -0.298423E+01
GT STRUM 27 - SouthWall missile CT~~~~~~~~ SSUD 27 ~
- otwl ~ islell~~l0:42 Cn.~hr 20 2007 Parr e 3 12 2 0.000000E+00 0.000000E+00 0.000000E+00 0.525148E+01 0.2996638+02 -0.222792E+00 0.548704E+01 -0.551501E+01 13 2 o.000000E+00 0.000000E+00 0.000000E+00 0.767681E+01 0.394507E+02 -0.906053E-01 0.368062E+01 -0.822759E+01 14 2 0.000000E+00 0.000,000E+00 0.000000E+00 0.880520E+01 0.434584E+02 0.000000E+00 0.000000E+00 -0.947411E+01 15 0.000000E+00 0.00000D2+00 0.000000E+00 0.767681E+01 0.394507E+02 0.906053E-01 -0.368062E+01 -0.822759E+01 16 0.000000E+00 0.000000E+00 0.000000E+00 0.525146E+01 0.2996'63E+02 0.222792E+00 -0.548704E+01 -0.551501E+01 17 2 0.000000E+00 0.000000E+00 0.000000E+00 0.301378E+01 0.197192E+02 0.304626E+00 -0.525815E+01 -0.298423E+01 18 0.000000E+00 0.000000E+00 0.000000E+00 0.151279E+01 0.115952E+02 0.292106E+00 -0.401029E+01 -0.130997E+01 . ......
19 0.000000E+00 0.000000E+00 0.O00000E+00 0.655636E+00 0.616536E+01 0.226516E+00 -0,265272E+01 -0.406212E+00 r7 T7&
20 0.000000E+00 0.000000E+00 0.000000E+00 0.217861E+00 0.292357E+01 0.153456E+00 -0.158155E+01 0.343938E-02 21 2 0.000000E+00 0.000000E+00 0.000000E+00 0.204290E-01 0.116549E+01 0.941022E-01 -0.858205E+00 0.146064E+00 22 2 0.000000E+00 0.000000E+00 0.000000E+00 IC- C)
-0.510768E-01 0.310897E+00 0.527506E-01 0.416779E+00 0.163392E+00 CD 23 2 0.000000E+00 0.000000E+00 0.000000E+00 C)
-0.626140E-01 -0.383581E-01 0.267432E-01 -0.168932E+00 0.131848E+00 w
24 2 0.000000E+00 0.000000E+00 0.000000E+00
-0.490043E-01 -0.127826E+00 0.118801E-01 -0.416223E-01 0.875596E-01 25 0.000000E+00 0.000000E+00 0.000000E+00
-0.268305E-01 -0.979648E-01 0.455018E-02 0.138652E-01 0,442638E-01 0CD 26 0.000000E+00 0.000000E+00 0.000000E+00 3&-4
-0.244988E-02 -0.301279E-01 0.287135E-02 0.23193!E-01 0.688708E-02 27 0.000000E+00 0.000000E+00 0.000000+E00 0.119979E-01 0.121160E-01 -0.940880E-02 0.182148E-01 -0.178596E-01 CD a,
Co CD0 28 0.000000E+00 0.0000002+00 0. 00000E+00 CD
-0.289654E-01 -0.261273E-02 -0.263598E-02 0.665964E-02 -0.220775E-01 29 0.000000E+00 0.000000E+00 0.000000E+00
-0.821133E-02 -0.6128042-02 -0.236812E-01 0.113474E-01 0.763798E-02 CD
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i * -'-* 7-., \ *1 J - -
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171 0.000000E+00 0.000000E+00 0.000000E+00 =0 C 0.757017n+00 Co <
0,254108E+01 0.700264E-01 -0.348085E+01 0.148241E+00 172 0.000000E+00 O.000008E+00 0.00O000E+00 0.300569E+01 -0.343724E+00 -0,524980E+01 -0,751829E-01 0.152057E+01 CDW 173 0.000000E+00 0.000000E+00 0.0000000E+00 0.242844E+01 -0.I02481E+01 -0.719261E+01 -0.563708E+00 0.278156E÷01 oo
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> C) 186 4 0.000000E+00 0.000000E+00 0.000000E+00 -.4 0.193901E+00 0.861106E-01 0.970929E-01 -0.585315E-01 -0.285531E-01 6 CA) 187 0.000000E+00 0.000000E+00 0.000000E+00 0.771214E-01 0.425428E-01 0.916738E-02 -0.383241E-01 -0.178143E-01 188 0.000000E+00 0.000000E+00 0.000000E+00
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-0.197526:-02 0.927535E-02 -0.170809E-01 -0.312382E-01 7-u*r <
189 0.000000E+00 0.000000E+00 0.0O0000E+00 C) o
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-0.821133E-02 -0.612804E-02 0.236812E-01 0.113474E-01 -0.763798E-02
GT STRUDL 27 - SouthWall missile 08:34:23 September 20 2007 Page 45 0624 23 Sentember 20. 7007 Pace 45 GT STRUVL 27 - SouthWall missile 192 4 0.000000E+00 0.000000E+00 0.000000E+00 0.197693E-01 0.107949E-01 0.117030E-01 0.230642E-01 -0.342043E-01 193 4 O.000000E+00 0.000000E+00 0.000000E+00 0.624721R-01 0.690125E-01 -0.461409E-01 0.450592E-01 -0.637937E-01 194 4 0.000000E+00 0.000000E+00 0.000000E+00 0.144713E+00 0.221297E+00 -0.174606E+00 0.859148E-01 -0.866183E-01 195 0.000000R+00 0.000000E+00 0.000000E+00 0.296303E+00 0.547699E+00 -0.422631E+00 0.151771E+00 -0.857350E-01 196 0.000000E+00 0.0000002+00 0.000000E+00 0.553854E+00 0.116749E+01 -0.862009E+00 0.246883E+00 -0.234384E-01 197 0.000000E+00 0.000000E+00 0.000000E+00 0,952900E+00 0.224233E+01 -0,158065E+01 0.366753E+00 0.172259E+00 198 0.OOOOOOE+00 0.000000E+00 0.0000002E00 0.150019E+01 0.396021E+01 -0.265107E+01 0.4858312+00 0.624323E+00 199 0.000000E+00 0.0000002+00 0.000000E+00 0+210582E+01 0.648175E+01 -0.404287E+01 0.543921E+00 0.151551E+01 C) 200 0.000000E+00 0.000000E+00 0.000000E+00 0.246581E+01 0.983728E+01 -0.543422E+01 0.456561E+00 0.305373E+01 03 201 0.000000E+00 0,000000E+00 0-000000E+00 Z) 0.205654E+01 0.137531E+02 -0.594038E+01 0.208398E+00 0.530361E+01 202 4 0.000000E+00 0.846737E+00 0.000000E+00 0.172676E+02 0.000000E+00
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20, 2007 Page ae4 46 2,20 GT STRUDL 27 - SouthWall missile 210 0.000000E+00 0.000000E+00 0.000000E+00 0.553854E+00 0.1167495+01 0.862009E200 -0.246883E+00 -0.234384E-01 211 4 0.000000E+00 0.000000E+00 0.000000E+00 0.296303E+00 0.547699E+00 0.422631E+00 -0.1517715+00 -0.857350E-01 212 4 0.000000E+00 0.000000E+00 0.000000E+00 0.144713E+00 0.221297E+00 0.174606E+00 -0.859148E-01 -0.866183R-01 213 4 0.000000E+00 0.000000E+00 0.OOOOOOE+00 0.624721E-01 0.690125E-01 0.461409E-01 -0.450592E-01 -0.637937E-01 214 4 0.000000E+00 0.000000E+00 0.000000E+00 0.1976932-01 0.107949E-01 -0.117030E-01 -0.230642E-01 -0.342043E-01 215 0.000000E+00 0.000000E+00 0.0D0000E+00
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218 0.000000E+00 0.000000E+00 0.000000E+00 C-)
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222 2 0,000000E+00 0.000000E+00 0.000000E+00
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08:34:23 September 20, 2007 Page Pae4 47 CT SRUD27 Soth~al msil CT SRUO 27 Soth~alms:
ile083:3 Spebr2, 07 228 0.000000E+00 0.000000E+00 0.0000008+00 0.525148E+01 0.299663E+02 0.222792E+00 0.548704E+01 0.551501E+01 229 0.000000E+00 0.000000E+00 O.000000E+00 0.767681E+01 0.394507E+02 0.906053E-01 0.368062E+01 0.822759E+01 230 2 0.000000E+00 0.000000E+00 0.000000E+00 0.880520E+01 0.434584E+02 0. 000000+00 0.000000E+00 0.947411E+01 231 2 0.00000OE+00 0.000000E+00 0.000000E+00 0.7676818+01 0.394507B+02 -0.906053E-01 -0.368062E+01 0.822759E+01 232 2 0.000000E+00 0.000000E+00 0.000000E+00 0.525148E+01 0.299663E+02 -0,222792R+00 -0.548704E+01 0.551501E+01 233 2 0. 000000E00 0.000000E+00 0.O000000S+00 0.301378E+01 0.197192E+02 -0.3046268+00 -0.525815E+01 0.298423E+01 234 0.000000E+00 0.000000E+00 0.000000E+00 0.151279E+01 0.115952E802 -0.292106E+00 -0.401029E+01 0.130997E+01 235 0.000000E+00 0.00000OE00 0.000000E+00 0.655636E+00 0.616536E+01 -0.226516E+00 -0.265272E+01 0.406212E+00 C-)
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0.119979E-01 0.121160E-01 0.940850E-02 0.182148E-01 0.178596E-01 (D
- MAXIMUM AND MINIMUM
SUMMARY
OF ABOVE RESULTS ***
- RESULT + MAXIMUM JOINT
- MINIMUM JOINT
- 01
- 03 Ca
08:34:23 September 20, 2007 Page 48 GT STRFUDL 27 - SouthWall missile W
NXX 0.000000E+00 1 0.000000E+00 1 1
NYY
- 0.000000E+00 1 0.000000E+00 0.000O00E+00 1 NXY 0. 00000E+00 14 W m
MXX 0.880520E+01 14 -0.311898E+02 122 MYY 0.434584E+02 -0.409630E+02 122 MX'? 0.846784E+01 66 -0.846784E+01 70 VXX 0.924844E+01 123 -0.924844E+01 121 W
W Vyy 0.110850E+02 149 -0.110850E+02 95
- 50) > plot plane
- 51) >
{ 52} >
- 53) >
1 54) > $$
1 55) >
561 > FINISH
- STRUD-L MESSAGE PL.31 - SCOPE ENVIRONMENT ENDED,
- 57) > GTMENU GT STREJDL is initializing GTMenu. Before returning to this window, you must End your GTMenu session.
c-0 Z
0 cn 0
co C-A 00 cyioo
- D
Calculation No. S07-0037 Revision 0 Attachment C Page C1 ATTACHMENT C REFERENCE Reinforced Concrete Design, 4th Edition, Chu-Kai Wang & Charles G. Salmon 18.9 YIELD LINE ANALYSIS OF RECTANGULAR TWO-WAY SLABS A typical rectangular two-way slab panel shown in Fig. 18.9.1 has two-way reinforcement within the panel near the bottom face providing positive moment nominal strengths M,,, and M,.,, and it also has*two-way reinforce-ment along the edges near the top face providing negative moment nominal strengths M,,, and M,,,; these strengtbs are Paer unit width of slab. The uniform load to give the collapse condition based on the yield line theory may be determined in terms of the sides a and b, and the absolute values of Map M,, M,,,.n, and M,,anr Edges supported and restrained I tl-'-~I b-Capacity Capacity U=e.
lal Dimensions (b) Tdp reinforcement (c) Bottom reinforcement Figure 18.9.1 A rectangular two-way slab panel.
Yield Line Pattern. "T1ree possible yield line patterns are shown in Fig.
18.9.2.,'There is no unknown position in yield line pattern No. 1 of Fig.
18.9.2(a); consequently the nodal forces V need not be predetermined and their value is dictated by statics alone. The unknowns x and yin yield line patterns Nos. 2 and 3 of Figs. 18.9.2(b) and (c) must be determined by means of differential calculus in the virtual work method; but for the equi-librium method, in this particular case the nodal forces to define the yield lines are all zero because the moment strengths under a set of three inter-secting yield lines are identical.
Analysis for Yield Pattern No. 1. Assuming a vertical deflectioni of A at the-intersection of the diagonal yield lines in Fig. 18.9.3, the deflection at the centroids of the four triangles A-B-C-D is A./I. The work done at the V
V+
V
- 18) Yield pattern No. 1 (VI Yield pattern No, 2 (c) Yield pattern No, 3 Figure 15.9.2 Yield line patterns for a rectangular two-way slab panel.
Calculation No. S07-0037 Revision 0 Attachment C Page C2 I I
+
Figure 18.9.3 Analysis for yield pattern No. 1.
collapse condition by tihe uniform load is the product of the total load on the entire panel and A/3; thus W - -h() (18.9rz.1)
The work done by the yield moments on the boundaries of all four slab segments is, referring to Fig. 18.9.3, W=2(,,, 1 M~~2A()i 2(M,,, 26Rb L(S (18.9.2)
Equating Eq. (18.9.1) to Eq. (18.9.2) and solving for w,,,
= 12 +)M. +/-A (18,9.3)
Taling moments about the lower edge of slab segment A in Fig. 18.9.3, 2()a) (}) -t- V = (M, + M,1Q(a) (18.9.4)
Taking moments about the left edge of slab segment D in Fig. 18.9.3,
- 6) (M2,6 + M,.)(b) .,- v (18.9,5)
Eliminating V between Eqs. (18.9.4) and (18.9,5) and solving for wck, the same expression for w,,/4 as Eq. (18.9.3) is obtained.
Analysis for Yield Paftern No. 2. Assuming a vertical deflection of A at the two points of intersection of the yield lines in Fig, 18.9.4, the work done at the collapse .condition by the uniform load on the, entire panel is W = 2WD + 2WA, + 4W,
=+ 2Q)(a - 2x)()4) 2 2
= (#3ab - 26x) (896 The tnrl done by the yield moments on the boundaries of all four slab
Calculation No. S07-0037 Revision 0 Attachment C Page C3 746 Yield Line Theory of Slabs
.*- *--- *0a- _______
= 26-A j *.
bX s Mpy-ff. /VI Figuat 18.9.4 Analysis for yield pattern No. 2.
segments is, referring to Fig. 18.9.4, W =2(M~ny + M,,,)(a) (Lb) + 2(M,.~ + M~)b (j)~19.9.7)
Equating Eq. (18.9.6) to Eq. (18,9.7) and solving for wl/,
W
_12[1M(M?=
1 + M + ;, M_,
+
quadratic equxationi MrM) 2ar(Mv'> +
Saitilg to zero the derivative of Eq. (18.9.8) with respect to x gives the quadratic equation in x, 4a(M°A + M.>)x9 + 4hN(M,,,,r + 4,,,Jx - [3ab"(M,,, + M0, 1)1 - 0 .
L... " (18.9,9)
Taking molments about the lower edge of slab segment A in Fig. 18.9.4,
+ *N" - 2x) Q) = . + Ms)(o)
=S,24a(M,,_, + M+/-.
$ 2b~x + bt (a - 2x).
Taking moments about the left edge of slab segment D in Fig. 18.9.4,_
Q,__x)= 6(M.,, + M,,.)b)
Equating Eq. (18.9.10) to Eq. (18.9.11) gives the same quadratic equation in I as Eq. (18.9.9),
The conditon for x = a/2 in Eq, (18.9,9) can be shown to be M,4 + M, =apy P 1..g a"+Mforz1 (18. ii.12) which means that if the sum of positive and negative moment reinforcement
Calculation No. S07-0037 Revision 0 Attachment C Page C4 t,9 Yield Una Anals*sis of ReclangularTwo-WaySlabe 747 The condition for x < a/2 in Eq. (18,9.9) can be shown to be M- form (<89.13)
M"~ + M~v, 2 which means that in order for yield pattern No. 2 to prevail, the reinforce-ment in the a direction is less than. that for yield pattern No. 1 to control.
Analysis for Yield Pattern No. 3. By interchanging the subscripts z and y as well as the quantities a and b in Eqs. (18.9.8), (18.9.9), (18.9,10), and (18.9.11), the following equations applicable to yield line pattern No. 3'are obtained. The quadratic equation in y (Fig. 18.9.2) is 4b(Mn.n + M Jy2t + 4a2 M.,w + MN,)y - [3ba2 (M,*v. + MW,)]= 0 (18.9.1}4)
Three expressions for wJ4 in terms of y are w!!5_ 12[aNMmy t.Mnpy + 2by(MA.S + M,,PjJ
. a2 (3by - 2y)(
w~_24b(M..~ M,)(1.916
- a'y + 3a2 (b - 2y) w~_6(M,, + (18.9.17 The condition for y < b/2 in Eq. (18,9,14) can be shown to be 4 , 4 +MbI> a M1 <. b ( M 9 . 18 )
ltlI rk~y+
p.g h which means that in order for yield pattern No. 3 to prevail, the reinforce-ment in the a direction is more than that for yield pattern No. I to control.
EXAMPLE 18.9.1 Determine the controlling yielh line pattern and the corresponding collapse condition uniform load fir a reetangullar two-way slab panel with dimensions as shown in Fig. 18.9.5(a). The slab- has re-infbrcement in the top near' the edges and in the bottom within the panel.
Obtain solutions for the following three cases:
- 1. M." + M",= 6.25 ft-kips/ft MnMV + MM = 4 ft-kips/ft 2, M,,., + MV. = 2 f-kips/ft MiN, + M,, = 4 ft.-kips/ft 3
. M,, + M,,, = Sft-kips/ft MA + M = 4f t-kips/ft Solution: (a) Case 1. The applicable yield line pattern may be determined by comparing the ratio of(M . + M,.) to (, . ) with the ratio of 11 ir. W$ Tv. +MO i
Calculation No. S07-0037 Revision 0 Attachment C Page C5 7418 Yield Line Theory of SWaXs M"P per it (c) Bottom reinfor-ement 4a) Dimensions (b) Top reiniorrcement
+ M.,, - 2.00 ft-k/ft M,,, + M,,,, 8.00 ft-k/ft 44 M.., + W,,,, - .25 ft-k/ft M. +Mp, 4.00 ft-k/ft
'*÷Ml,, = 4.0 ft'k/ft M,,~ +M,,,p = 4.00 ft-k/ft (e) Case 2 (f) .Case 3 (dý Caw I ol Example 18.9,1.
FIgure 18,9.5 Rectangular two-way ,lab a to that in direction b per foot Since the ratio of reinforcement in direction yield pattern is shown in Fig.
slab width is equal to the ratio of a' to bY, the 189.5(d). Then fr-om Eq. (18,9.3),
IV,_,[2Mazr\ a+ MnPx KI.M, + MnylVI 12( aM, + b2FM
\2 + = 0.240 f
+ Mý,,) is, in this case, (b) Case 2. The ratio of (M2., + M,,A,) to (My,,
+ M.p) 2 =~y . < 1 .5625 (M= + 4 18,9.5(e). The quadratic equation The yield line pattern is as showti in Fig.
(18.9.9) is used to solve for x.
4 + 4bNMý,,, +4 - b(M,,,,,,, - A,,..) =+
= 0 4(25)(4)x2 + 4(400)(2)x - 3(25M(400)(2)
X2 + 8z - 150 =0 V-=16 4 = 8.884 ft
Calculation No. S07-0037 Revision 0 Attachment C Page C6 IUJU L.cMf l I1,1gi tF rt*w .qwwulw .Jbr F (18.9.11); the fat that it is so serves as a check on the ,...nerical compu-tation.
12(b(Mns +M 4 > + Ze r(M,,, +i-y) 4, b(Sax -Mi9 12(400(2) + 2(2V{8.884)(4)] 0.152 k-400f3(255(8.884) - 2(8.884)*}
o,=, = 24a(M..v++/-
4' V2x + 3Sia - 2x) 24(M5(4) 0 5 i 2(400)(8.884) + 3(400)[25 - 2(8.884)] 0.152k (3-w _6(M,. ." M+Q 6(2)
_, - ____=__ 8 = 0 152 ksfa 4,(8,884? C (c) Case 3, The ratio of (M,, + M.1) to (M.U + Mv,) is, in this case, t 4 ba2 (M~++- M",v)
(MInV 2> 1-5%25 The yield line pattern is as shown in Fig. 18.9,5(o. The quadratic equation (18.914) is used to solve for y.
4b(M,.,, + M,7.,~)t + 4a2(M.~, + Md,,O)y - 3ba2 (M~~A- ,,,)=
4(20)(&)V 4 4-6256(4)y - 3(20)(625)(4) = 0 8 Y2 + 125y - 1875 =0 y = 9.375 ft The same uniform load wc/!o is obtained from Eqs. (18.9.15), (18.9.16), or (18.9.17); the fact that it is so serves as a cheek on the numerical compu-tation.
w M_ 2a 2(M.,,t + Mý~ + 200"'.jm + l"'4.
- a2(Sbv - 2V2) 12([62(4) + 2(20)(9, 375(8)] . ksf
.273 62513(2o)(9.375) - 2(9,375)'1 w,__ =24b(Mn. + May) 4, 2a'j+3a2 (b-2y) 24(20(8) 273 kf 2(625)(9.375) + 3(625)12 - 2(9.317)i w~ _6( I +IM "d 6(4 = 0.273 k4f 4 (S.37512 18.10 CORNER EFFECTS WNRECTANGULAR SLABS In Sec. 18.4 on method of yield line analysis, it has been stated that there d-r~
ika nnn ý na J wihIn insr nakflprt isp in UddiŽ1' case lalndnns
Calculation No. S07-0037 Revision 0 Attachment C Page C7 750 Yield( C wry of Stabs to all possible yield line patterns must be sought and the one giving the smallest collapse load would actually happen and thus should be used in design. Although the three typical yield line patterns for a rectangular two-way slab panel have been shown in Fig. 18.9.2 and their analysis has been completely treated in Sec. 18.9, it can be demonstrated that the corner yield patterns 4-5-6 shown itt Fig, I8. I0.1-in one-to-one correspondence to yield patterns 1-2--5 of Fig. 18.9.2-inay indeed give a smaller collapse load and therefore control. These comer. patterns are complicated to ana-lyze, either by virtual work method or by equilibrium method. For instance, there are three unknowns E-F-G for the yield line positions; then once the expression for w.1 0 is obtained from the virtual work equation as a function of three independent variables, the partial derivative ofw./#0 with respect to each of the three unknown variables can be equated to zero. In the equilibrium method the same set of equations for the positions of poiný E-F--G may be obtained by inserting the predetermined zero or n6nzero nodal forces and applying the moment equation of equilibrium to each of the slab segments.
C G F F F (a) Yield pattern No, 4 (b} Yield pattern No. 5 fe Yield pattern No. 8 Figure 18.1O., Comer yield patterns for a rectangular two-way slab panel.
An analysis [5] of a square slab with equal reinforcenrient in the x and y directions will show that the corner yield pattern No. 4 of Fig. 18.10.2(b)
[see also Fig. 18.10. 1(a)J results in iv,,j/ = 22(Mf + Mb,)I/a2 whereas the regular yield pattern of Fig. 18.10.2(a) indicates wJ/ = 24(M,, + M,,)/a 2.
M.,4and M,, are the nominal moment strengths per unit slab width for the negative moment and positive moment regions, respeclively, in each direc-tion, and a is the side of the square. Thus the corner pattern is more critical by approximately (24 - 22)/24 = 8.3%. It may be proper then to discount the results of a regular yield pattern analysis as made in Se. 8.9 for most rectangular slabs by 8 to 10% for reason of corner dIfe's.
It may be pointed out that the yield line'EF in Fig. 18.10.2(b) is a negative moment yidld line; thus when there is no-negative reinforcement, the moment strength along EF is zero. In this case the crack or yield line Etv will not form if the corner A is not held down because the corner would simply lift up. ACI-13.4.6 requires the-provision of special reinforcement at exterior corners in both top and bottom of the slab, for a distance in each direction from the comer equal to one-fifth. the longer span. The use of
-- - t.......
............ L---j .IL.. ... i-*.-.. , &r .n' . j.a*'Iko' nrntL~'l f"
Calculation No. S07-0037 Revision 0 Attachment C Page C8 18.11 Application of Y'eld Line Analysib to Speciel Cases 751
=!.221}. 4 M,,P)
D 40 a2 C K
a A
A F P 0
=.a fa) Regular yield pattern (b) Cornieyerd pattem Figure 18.10.2 Square slab panel with equal reinforcement in.two directions.
18.11 APPLICATION OF YIELD LINE ANALYSIS TO SPECIAL CASES The yield line theory of slabs, as has been developed and illustrated in the preceding sections, is particularly suitable for special cases involving irreg-ular shapes or irregular boundary conditions. Prerequisite to the analysis of these,cases is the picturing of an applicable yield line pattern. The governing concept here is that rigid body plane rotations of slab segments separated at yield lines are possible under compatible deflection conditions, To this end the following guides may be provided:
- 1. Yield lines end at a slab boundary.
2, A yield line (or its prolongation) between two slab segments passes through the intersection of the axes of rotation of the two adjacent.
slab segments.
- 3. The axes of rotation lie along lines of supports or pass over column supports.
In addition to those already described, two other yield line patterns to further illustrate the use of the above guides are shown in Fig. 18.11.1.
Special Case. Shown in Fig. 1.8. 11. 2 is a rectangular slab simply supported at three edges and free at the upper edge. The posidve moment reinforce-ment parallel to the a dimension provides a nominal moment strength of Mr, per unit of the b distance; and the positive moment reinforcement parallel to the b dimension provides strength M,,, 2 per unit of the a distance.
Two possible yield patterns are shown in Figs. 18.11.2(c) .aad (d); the un-4 Icncnur ic 'r n iLAn mitam M. I -nA a 4. __4-M.. -44 A.L 0
Calculation No. S07-0037 Revision 0 Attachment D Page D1 ATTACHMENT D GT STRUDL ANALYSIS FOR 3-FT THICK WALL - DESIGN VERIFICATION REVIEW: ALTERNATE CALCULATION METHOD This attachment presents the GT STRUDL analysis for an L-shape frame structure with a 3-ft thick wall and 3-ft thick floor slab. Wind loads are applied in different directions and the worst case load combination is determined based on the maximum bending moment in the wall.
The maximum bending stress at Joint 3 due to various wind load combinations are tabulated below.
Load T MZ Ref.
Case Load Combination ft-kip / ft Page 1 DL+LL -6.88 D7 2 DL -4.76 D8 3 Ww 11.02 D8 33 WL -0.53 D8 4 P T -8.63 D8 5 DL+LL+Ww(+y,+x)+PT -4.48 D8 55 DL+LL+WL (+y,-x)+PT -16.03 D8 6 DL+Ww (+y,+x)+PT -2.37 D8 66 DL+WL (+y,-x)+PT -13.92 D8 7 DL+LL+Ww (+y,+x) 4.14 D8 77 DL+LL+WL -7.40 D8 8 DL+Ww 6.26 D8 88 DL+WL -5.29 D8 MAX I -16.03 DL = Dead load of structure LL = Live load Ww = Windward wind loads based on the tornado WL= Leeward wind loads based on the tornado P T= Pressure load based on an external pressure drop of 3 psig between inside and outside of the building
+y = interior surface of slab
+x = exterior surface of wall
-x = interior surface of wall The maximum bending moment due to DL + LL + W LEEWARD + P T, Max M is 16.03 ft-kip / ft.
This attachment contains the following applications:
- a. The analysis is in accordance with the Ultimate Strength Design presented in the ACI Code; therefore, the Auxiliary Building South Wall is qualified by elastic (linear) analysis.
- b. The wind loads for uplift on the roof and suction on the leeward wall are addressed in this attachment.
Calculation No. S07-0037 Revision 0 Attachment D Page D2 The area of tension reinforcement equals the area of compression reinforcement.
A = A's p= p ACI Std 318-63 Sect 1600 Therefore, the calculated ultimate moment is per ACI Std 318-63 EQN (16-1) which neglects the effects of compression steel.
Re-bar data:
Yield strength, f y= 40 ksi Ref. Dwg SC-422-019 Re-bar size # = 7 Re-bar spacing each way = 12 in Concrete cover, c c = 2 in Ref. Dwg SC-422-021 Sect 64-64 Parameters Area of compression re-bar, A's = 0.6 in 2 Top cover, d'= 2.0 + 0.875 + 0.875 / 2 3.3125 in Top to tensile re-bar, d = t - c c - re-bar - re-bar / 2 12
- 3.00 - 2.00 - 0.875 - 0.875 / 2 32.688 in Beam width, b = 12 in M.= O[A'sfy(d-d')
where 0= 0.9 Compressive strength, f' c = 3000 psi Ref. Dwg SC-422-019 Area of compression re-bar, A's = 0.6 in 2 Ultimate design resisting moment, M , = ý [ A s f y ( d - a / 2 )] EQN (16-1) where a= Asfy/0.85f'b
= 0.60
- 40000 /(0.85
- 3000
- 12.0) 0.784 M,= 0.90"[0.60"40000*(32.688-1.176/2)]
= 697579 in - lb
= 58132 ft-lb GT STRUDL RESULTS For 36-in. thick wall, the worst load case combination (load case no. 55) is DL+ LL+WLEEWARD+ PT, Max M= -16.03 ft-kip / ft
< 58.13 ft-kip/ft OK Worst possible load combination is load case 3 with missile loading W W + W MISSILE - 11.02 + 37.5 (See Attachment B for W MISSILE) 48.5 ft-kip / ft
< 58.13 ft-kip/ft OK
C*T STRUDL 27 - !*BWALLI .14: f0:44* sept'fmber '20, 2007,_,page-I GT .STsRlL 27 - ABWAIJ 4l0:6SpLbe 0 0d aA Commercial Software Rights Legend Any use, duplication or disclosure of this software by or for the UJ.S.
~i1 Government 'shll be restricted to the terms of a license agreement in accordance with the clause at DFARS 227.7202-3.
This canputer-software is an unpublished work containing valuable trade sec*r t owned by the Georgia Tech Research Corporation (OTRC)..
1No access, use; transfer, duplication or disclosure thereof may be made except uddr a- license agreement executed by GTRC or, its and nd right, 'title or interest theret6 authri zeýdr e-r is coriveyed 6r4+A eentazivds ited herein,, n6twtthstanding receipt or possession hereof,.' Ded Ipilation tfthe- object code is strictly prhhibited;
'6 /
Georgia Tech Research Corporation.
Georgia Ihsttitute of Technology Atlanta,, Georgia. 3*0332:
Copyright, (c) 2003 GTRC U.S.A.
12 4 ALL RIGHTS RESERVED.
- Thu Sep 20 14.:01:05,2007 0C0)
IGTICES/C-NP 2.5 0.:MDANT 2.0, January 1995. 7 0 Proprietary toGeorgia Tech Research Corporation, U.S.A.
z Reading password file D:\GTStrudl\2?7\password27.pwd 0 CI-i-audfile, Command AUDIT file FILE140*.aud has been activated.
G T S -T-R U U: L.
RELEASE DATE VERSION COMPLETION NO.
June, .20 013 27.0 4449 t
- *-ACTIVE UNITS - LENGTH WEIGHT ANGLE TEMPERATURE TIME ASSUMED TOA'BE INCH POUND RADIAN FAHRENHEIT SECOND C Cn
- 1) > $,. 7 ....
21 >1 $ This is the. Cn'mson Startup Macro; put your company-wide startup commands here. C
- 3) 2 $ You can edit this file from Tools -- Macros. Click "Startup" and then- "Edit".
- 4) >- $5------------------ -- ----. ---. -. -- -- --- -. --- --
- 5) >' CINPUT 'T:\C-tstrudl\in\ABWALLl.tx:t' 6:) 2 "TITLE 'abwall' STRUDL *'FILENAHE=CHECK'AB Wall' -0 CD CD 5
.* **. iý** *;,* *** * * * ***
C:)
G T S T R U D L
GTSTRUDL 27 - ABWALLI 14:10:45 September 20, 2007 Page 2 OWNED BY AND PROPRIETARY TO THE GEORGIA TECH RESEARCH CORPORATION
- RELEASE DATE VERSION COMPLETrON Nc.
June, 2303 27.0 4449
- ACTIVE UNITS - LENGTH WEIGHT ANiLE TEMPERATURE TIME
- ASSUMED TO BE IN7H POUND RADIAN FAOIR.EM{EIT SECOID 81 > TYP space frame
- 9) > UNIT f- LES DEC Ic) > JOI COO II} > 0,0 G.0 0,0 c-212 > 2 0.0 6.0 13i > 3 0.0 12.0 14,} > 4 0.0 16.0 0.0 24.0 0
- 15) > 5
- 16) > 6 5.0 24.0
- 18) > 8 1.0 024.0 z
o
- 19) > 9 2010 24.0 c.)
2C) > i0 25.0 24.0
- 21) > 11 30.0 24.0 s
- 22) >
231 > ger.e.ate 10 memb id I incr 1 from I 4fncr 1 to 2 incr I
/ ----------------- MEMBER INCIDER1C.S------------------. CA)
MEMBER INCIDENCES 1 2 2 2 3 3 3 4 0 4 S CD 5 6 -uBN 2J-<
6 .7 7 7 CD 8 8 CD =
9 9 10
- -P.,
0 .
GT STRUDL 27 - ABWALLI t' 'U' ' ' 14:10:46 September .20_, 2007 Pa'*e3.
,*--"T 10 10 .1
- 24) ,> unit in lbs
> Mjemprop prismatic 26.) >: 1 to 10 ax 432 ay 360 az 360 ix 20736 iy 5.184 iz 46656 28), ~L~)L)
> material, concrete members 1 to 10 30): >S
'31) 321 '0 units ft lbs 33.)
- 34) > loading 1 "dead load + LL'
- 35) >.member loads
- 36) > 5 to 10 force y global uniform -650 $ 3 x 150 + 200psf. LL
- 38) '>$
- 39) > loading 2 'dead, load'
- 40) >-member loads
- 41) > 5to l0 force y global uniform -450 $ 3 x 150
- 42) i>
.43)
,> loading 3 'tornado wind )+y,+x '
> member loads C-)
L 45), > '1to 4 force x global uniform 297
~49" 5-0
~5)} > 5 to 10 force y global uniform 184
>5 ="
40) 54)'1 > loading 33 'tornado wind '+y,-x)'
51 ) > member loads 52), > 1 to 4 force x global uniform -81 Cl 531 > 5 0 force y global uniform 184 1to M 55).. 0
- 56) .> loading 4 'vacuum' 6 57). > meffber' loads" 0 581, >. to 4 force x global uniform -432 > CD 59). >5 to -10 force v global uniform 432 -u 60' 62)
-4 63}) > STIFFNESS ANALYSIS C)
D <CD BANDWIDTH INFORMATION BEFORE RENUMBERING.
CD THE MAXýIMUMBANDWIDTH IS 1 AND OCCURS AT JOINT 3 THE AVERAGE BANDWIDTH IS 0.889 THE JTANDARDJ DEVIATION OF THE BANDWIDTH IS 0.314 1.203 Ca,
14:10:46 September 20. .2007 .Pao.4 GT ST UD 27 -* W AL . .... *... .
0BANDWIDTH REDUCTION HAS FAILED TO PRODUCE A BETTER NUMBERING.
ORIGINAL NUMBERING WMLL BE USED.
TIME FOR CONSISTENCY CHECKS FOR 10 MEMBERS 0.00 SECONDS TIME 'FOR.BANDWIDTH REDUCTION 0.00 SECONDS TIME TO GENERATE 1 .ELEMENT STIF. MATRICES 0o.o SECONDS TIME TO PROCESS 42 MEMBER LOADS 0.00 SECONDS TIME TO ASSEMBLE THE STIFFNESS MATRIX SECONDS TIME TO PROCESS 11 JOINTS 0.00 SECONDS TIME TO SOLVE WITH '2 PARTITIONS 01.00 SECONDS TIME TO PROCESS 11 JOINT DISPLACEMENTS 0.00 SECONDS TIME 'TO PRO CESS 10: ELEMENT DISTORTIONS 0.00 SECONDS TIME FOR STATICS CHECK 0.00 SECONDS j 64) >
1 65) '> create load comb 5 'DL + LL + Torna do wind (+y,+x) + pressure drop' sj pec 1 1.0 3 1.0 4 !.0 1 66] > create load comb 55 'DL + LL + Torna do wind (+y,-x) + pressure drop' s' oec .1 1.0 33 1. 4 1.0
- 67) > cieate load comb 6 'DL + Tornado wi]nd (+y,+x) + pressure drop' spec 2 2.0 3 1.-0 4 1.0 t 6B) .> create load comb 66 'DL + Tornado wijnd (+y,-x) + pressure dropý- spec_2 1.0 33 1.0 4 1.0 69)1-> create load comb 7 'DL + LL + Torna do wind (+y,+x)' spec 1 I 1 3 1 0
.A 70) .> create load comb .77 'DL + LL + Tornacdo wind (+-y,-x)' spec 1 1.0 33 1:0
{ 71) > create load comb 8 'DL + Tornado wi]nd ý+y,+x)' spec 2 1.0 3 1.0 721 > create load comb 88 'DL + Tornado wil n-d (+y,-x)' spec 2 1.0 33 3 10 f 73)
{ 74)},.>
{ 75) .> $ C) j76}> LOAD LIST ALL 0 f 771 > OUTPuT LsC 3
( 76i > OUTPUT BY member j 79);Ž LIST forces REA ALL =3
-RESULTS OF LATEST ANALYSES* z 0
0 PROBLEM - FILENAME TITLE - NONE GIVEN C')
ACTIVE UNITS FEET. LB DEG DEGF SEC -4 (D
CD MEMBER FORCES -u MEMBER LOADING JOINT /------------------- FORCE ---------------------- / - --- . --- MOMENT------ --- CD AXIAL SHEAR-Y SHEAR-Z TORSIONAL BENDING-Y BENDING-z 8614.876 -1612.101 0 000 0.000 01.000 ý0..000 `124,68'.596 2 -8614 .876 1612.101 0.000 0.60,o 275§1598 Coo a)
CT .STRUI)L 27 - ABWALLI 14l10:46 :Septe&bei,,20, 2'007 Page 5
.5964.145 -1116.070 0,000 0..00 -8632.105
-5964.145 1116.070 0: 000 0.000 193.s.ý684
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-2138.800 -2759.694 0.000 0.- 000 -192 .A-25 33 -2520.456 .- 657.836 0.000 0.000 G.000 -1534..1078 171.836 0.000 O.666 0.000 -954-.940 2520.456.
4 -6161.757 -4870.893 0.000 0,00 0. 000 6161.757 "2278.693 0.1000 o.oooo 0-. 000, 30.045 0.000 S 314 ;319 -1941.300 0,000 -9 091-.618 a-.000
-314.319 1131.300 0-.000
- 0 000 0-000 -126.182,
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'0.000 67.337 4062 .831 0.000 ,888.997,
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-6,4"8
- 0. 000 -28885.495 66 -2718.,069 -6644.799 :0 000: 0 A000 2718.069 3566.799 0.000 -I:7 49.301 0...000o 7 6476.076 2929.592 0.00o .0..000 o..0ooo .9627.. 693 0:000 00-.000
.000 2603.8631
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-3825.345 -1643.624 0.000 <0.,00o
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- 88. 3443 .688 -1773.906 0.000 0.000
ý.0. 60~0 0.000 ý10166-.183
-3443.688 1287.906 0.000 980.744
.0. b00 0 1 2 8614.876 -1612.101 0.000 <0. b00 0-000 -2795.988-3 -8614.876 1612.101 0,000 0. 000 -6876.620 5-2 2 5964.145 -ii16.070 0.000 .0.000 u1935.684 03
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,33 2 -2520.456 -171.836 0.000. o.600
. 000 o..ooo 954.940 z 3 2520.456. -314.164 0.000 0.06o 0.000 *527.958 0 4- 2 -6161.757 -2278.893 0.0oo0 0O. 000 0.000 2730'.045 6161.757 -313 .107 0.0001 0.000 0.000 -864,7o02
- 5. 2 314.319 -1131.300 o.0o0 0.000 126. 182 0.000, O0.000 O0.00oo 55 3
2
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-67.337 321.300
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0.000 0.000 6, 2 -2336.413 -635.269 0.000 o.0o00 986-.486 3 2336.413 -174.731 0.000 -2368.101 C) 66 .2 -2718".069 -3566.799 0.000 0.000 1749.301 2718.069 488..799 0.000 ..0..000.
0.000 --13 916 .096
~-4 7 2 0.000 0.000
.o. 00o. 0'.000 -2603.863 6476.076 1147.592 3
-6476.076 634,408 0.000 0.000
- o. ooo 4143. 418 77 2 0.000 0 6094.420 -1783.938 0,000 0.000 0.000 -1841 .048 3 3
-6094.420 1297.938 0.000 0.006 -7404.577 77 2 3825.345 1643.624 0.000 &'1743.559 a
3 2 -3825.345 138 .376 0.000 0.000
<6259.-301. (a CD 5
'88 2 0,000 0.600 CD 3443.688 -1287.906 0.000 0.000 0 .000 -98 0.744
.3. -3443.688 891. 906 S.o000 0.000 -5.5,288.695 3 1 3, 8614 .876' -1612.101 0.000 0.000 0.000 6876.,620 4 -8614.876 1612.101 0.000 0.000 -16549.. 228 o ,..
14:10:.46 September 20, 2007 Page 6 CT STRirDL 27 - ABSWALLI 2:, 3 -1116 070 0.000 .0.000 0 .000 4760..737 59864-145 "1116.070 *0.000 0.900 -1145'7.158 4 -5954.145 0:.000 0.000 -11:020.038
-2138.800 977.694' 0.'000 0.000 0.6000 11540, 201
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- . 3 0.000 0.600 i483 .484 314 .319 -321.300 0.000 4 0.000 0.0600 0.:oo -3981.786
-314.319 -488.700 55 0-0060 o.0oo0 16031..97
-67.337 -984.831 .. 000 4 67.337 -2093.169. 0.000 o.obb 0.060 -12706.962 174.731 0.000 0.000 2368.101
-2336.413 d.ooo 0:'000 0.000 1110.284 66 3 2336.413 -984 .731 0d.6000 13916..096
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-6094.420 811.938 0.0,00
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-3825.345 0 .~000, 0:.'000 0 .000 5288,.695 88 3 -801,906 3443.688 0.000 0'.:000:
0:000.
4 315,906 0.000 0..0900 -:8642,133
-3443.688 DO
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- '*****.******* 4 (DZc-PROBLEM - FILENAME TITLE - NONE GIVEN ACTIVE ,UNITS FEET ýLB DEG DEGF SEC
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Calculation No. S07-0037 Revision 0 Attachment E Page El ATTACHMENT E LOAD COMBINATION - DESIGN VERIFICATION REVIEW: ALTERNATE CALCULATION METHOD The load combination used in Calc section 4.1 [C = (1.0 + 0.05)D + 1.OWt + 1.OPt] is specifically for containment design and does not apply to "Other Class I Structures". This combination is tabulated in the FSAR Section 5.2.3.2.1 together with other accident load combinations (including accident temperature and pressure) for design of the RB. Note that tornado missile is not included in any of these load combinations. Page 13 of 48 of the Containment DBD states that consideration of tornado missile was not included in the design load combinations (for containment) due to analysis at TMI for aircraft impact. FSAR section 5.4 contains design requirements for "Other Class I Structures and Systems" (other than containment). The following pertinent information can be found in this section:
- a. Section 5.4.1.2 states that for tornado loads including missiles refer to Section 5.2.1.2.6. This section identifies the loads but not the load combinations.
- b. Section 5.4.3 states that the design is based on ACI 3 18-63 "Ultimate Strength Design" for tornado, earthquake and missile.
- c. Section 5.4.3.2.2 states that the AB has been designed to withstand short term tornado loadings, including tornado generated missiles. Structural design is in accordance with ACI 318-63 "Ultimate Strength Design".
- d. Section 5.4.5.3 states that the structural design for tornado generated missiles including the wood pole and 2000# auto are per the ultimate strength provisions of ACI 318-63.
Note that ACI 318-63 does not directly address tornado wind loads or tornado generated missiles. This code does apply a load factor of 1.25 when checking wind loads. Also note that G/C generally applied a load factor of 1.25 to both tornado wind and missile loads. However, the SER dated July 5, 1974 Section 3.3 "Wind and Tornado Design Criteria" specifically states that for tornado loads on concrete structures a load factor of 1.0 is to be used.
It has also been noted that GIC calculations generally combine tornado missile with tornado wind.
My interpretation/recommendation:
I believe the intent of the FSAR and SER is that missile load is evaluated separately from wind. Also that the LF of 1.25 is not required. Based on this interpretation the following load cases should be valid but must be confirmed.
C = DL + LL + Ww + Wp C = DL + LL + Ww C=Wm Ww = Tornado wind Wp = tornado depressurization Wm = tornado missile
Calculation No. S07-0037 Revision 0 Attachment F Page F1 ATTACHMENT F VERIFY ULTIMATE UNIFORM DISTRIBUTED LOAD DERIVES BY YIELD LINE STANDARD EQUATIONS USING WORK ENERGY METHODS Strain energy is the mechanical energy stored up in stressed material. Stress within the elastic limit is implied; therefore, the strain energy is equal to the work done by the external forces in producing the stress and is recoverable. Ref. Roark 5 th Edition, page 11.
Aceoluý:A V2-
- p\.
Determine ultimate load w
- that can be carried by the wall.
Concrete compressive strength, f' c = 3000 psi Steel yield stress, f y = 40 ksi Slab thickness, t = 24 in Slab width, S x = 24 ft Slab height, S y = 24 ft Slab unit width, b = 12 in Re-bar cover, c c = 2 in Reinforcement in both directions Direction Location Re-bar # Spacing As(in Dia., in X - Top 6 12 0.44 0.75 Bottom 6 12 0.44 0.75 Y Top 6 12 0.44 0.75
!Bottom 6 12 0.44 0.75 Effective depth in x-direction, d x = t-cc-Dia/2
= 24- 2.000- 0.750 / 2
= 21.625 in Effective depth in y-direction, d y = t-cc-Dia-Dia/2 dI
= 24 - 2.000 - 0.750 - 0.750 / 2
= 20.875 in
= 0.9 For X-direction d x = dx 21.625 in For X-direction d y = dy 20.875 in
Calculation No. S07-0037 Revision 0 Attachment F Page F2 0.85 f C= 85 PCab T~ ~ , .8fT d d-d' d-4/
Calculation of the moments per unit length in both directions Positive bending moment in X-direction z
Fig. .2Positiv'e bending inoment.if;X direction Top re-bar spacing, s ,t = 12 in Bottom re-bar spacing, s xb = 12 in Re-bar area, A s, = 0.44 in 2 As= ( 12 /Sxb)AS
= (12/12)'0.4
= 0.44 in 2 a= fyAs/(0.85f'cb)
= 40000" 0.44 (0.85 3000" 12)
= 0.575 in m ux, pos= pAsfy(dx-a/2)
= 0.9" 0.440" 40.0" (21.6- 0.575/ 2
= 337.98 in - kip
= 28.17 ft- kip Negqative bendingq moment in X-direction z
x FMg. 3 Negativebending moment inXdirction.
A,= (12/sxt)A
= (12/12)*0.4
= 0.44 in 2 a= fyAs/(0.85f' b)
= 40000" 0.44 /(0.85" 3000" 12)
= 0.575 in
Calculation No. S07-0037 Revision 0 Attachment F Page F3 m ux,neg= 0Asfy(dx-a/2)
= 0.9"0.44"40.0"(21.6-0.575/2)
= 337.98 in - kip
= 28.17 ft - kip Positive bending moment in Y-direction z
x 11g. 4 Positive'bending moment in Y'direction Top re-bar spacing, s yt = 12 in Bottom re-bar spacing, s yb = 12 in Re-bar area, A y = 0.44 in 2 2
A 11= /sxb)As
= (12/12)'0.4 0.44 in 2 a= fYAs/(0.85f'cb)
= 40000" 0.44 /(0.85" 3000" 12 0.575 in m uy, pos= A sf y( dy -a /2)
= 0.9 *0.440
- 40.0 *(20.9- 0.575/ 2)
= 326.10 in - kip
= 27.18 ft - kip Negative bending moment in Y-direction y
Figý 5 Negative bending momeht in X direction As= (12/ syt )A s
= (12112)*0.4
= 0.44 in 2 a= fyAs/(0.85f'ob)
= 40000 0.44 /(0.85" 3000" 12)
= 0.575 in m uy, neg 0.9
- 0.44
- 40.0 * ( 20.9 - 0.575 / 2) 326.10 in - kip 27.18 ft - kip
Calculation No. S07-0037 Revision 0 Attachment F Page F4 Segment Location M,, L 0 Value Remark A +Mu 28.27*24/12= 56.34 (1)
-M (Support) 56.34 B +Mu 28.27*24/12= 56.34 (1)
-M (Support) 56.34 C +MU 27.18 24/12= 54.36 (1)
- M u (Support) 54.36 D +MU 27.18
- 24 / 12= 54.36 (1)
- M u (Support) 54.36 Z M u L E= 442.8 Note: (1) Moment varies along yield lines. Values used are conservative.
YP = 2*(w*24 *12* 1 /2)2* 1 /3
= 192 w By conservation of energy the sum of internal and external work must be zero and this will make it possible to calculate the failure load of the construction.
EP6= YMuLO 192 w = 442.8 w= 442.8/192
= 2.306 ksf CHECKS OK
STRUCTUREPOINT - pcaColumn v4.10 (TM) Page 1 Licensed to: Sargent & Lundy Engineers. License ID: 54143-1013717-4-2801B-21AB0 04/01/09 D: \PROJECTS\CRYSTAL RIVER\YIELD LINE ANALYSIS\Column Check\Column.col 05:12 PM Calculation No. S07-0037 Revision 1 Attachment G Page G1 00000 00 00 00 00 0000000 00000 00000 00 00000 00 00 00 00000000 0000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 0000000 00 00 00 00 00 00 00 00 00 00 00 00 0000000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00000 00 00 00000 00000 00000 00000 00 00 00 00 00 (TM) pcaColumn v4.10 (TM)
Computer program for the Strength Design of Reinforced Concrete Sections Copyright © 1988-2008, STRUCTUREPOINT, LLC.
All rights reserved Licensee stated above acknowledges that STRUCTUREPOINT (SP) is not and cannot be responsible for either the accuracy or adequacy of the material supplied as input for processing by the pcaColumn computer program. Furthermore). SP neither makes any warranty expressed nor implied with respect to the correctness of the output prepared by the pcaColumn program. Although SP has endeavored to produce pcaColumn error free the program is not and cannot be certified infallible. The final and only responsibility for analysis, design and engineering documents is the licensees. Accordingly, SP disclaims all responsibility in contract, negligence or other tort for any analysis, design or engineering documents prepared in connection with the use of the pcaColumn program.
STRUCTUREPOINT - pcaColumn v4.10 (TM) Page 2 Licensed to: Sargent & Lundy Engineers. License ID: 54143-1013717-4-2801B-21ABO 04/01/09 D:\PROJECTS\CRYSTAL RIVER\YIELD LINE ANALYSIS\Column Check\Column.c6l 05:12 PM Calculation No. S07-0037 Revision 1 General Information: Attachment G Page G2 File Name: D:\PROJECTS\CRYSTAL RIVER\YIELD LINE ANALYSIS\Column Check\Column.col Project: CR3 AB East Wall Column: 01 Engineer: MWM Code: ACI 318-02 Units: English Run Option: Investigation Slenderness: Not considered Run Axis: X-axis Column Type: Structural Material Properties:
f'c = 3 ksi fy 40 ksi Ec = 3320.56 ksi Es 29000 ksi Ultimate strain = 0.003 in/in Betal = 0.85 Section:
Rectangular: Width = 36 in Depth = 50.25 in Gross section area, Ag 1809 in^2 Ix = 380653 in^4 Iy = 195372 in^4 Xo = 0 in Yo = 0 in Reinforcement:
Bar Set: ASTM A615 Size Diam (in) Area (in^2) Size Diam (in) Area (in^2) Size Diam (in) Area (in^2)
- 3 0.38 0.11 # 4 0.50 0.20 # 5 0.63 0.31
- 6 0.75 0.44 # 7 0.88 0.60 # 8 1.00 0.79
- 9 1.13 1.00 # 10 1.27 1.27 # 11 1.41 1.56
- 14 1.69 2.25 # 18 2.26 4.00 Confinement: Tied; #3 ties with #10 bars, #4 with larger bars.
phi(a) = 0.8, phi(b) = 0.9, phi(c) = 0.65 Layout: Rectangular Pattern: Sides Different (Cover to longitudinal reinforcement)
Total steel area: As = 32.00 in^2 at rho = 1.77%
Top Bottom Left Right Bars 4 #18 4 #18 0 #18 0 #18 Cover (in) 2 2 2 2 Factored Loads and Moments with Corresponding Capacities:
Pu Mux fMnx fMn/Mu N.A. depth epst Phi No. kip k-ft k-ft in 1 340.60 1822.25 2760.23 1.515 5.64 0.02208 0.900
- End of output ***
0 0 0 0 Y
+x 0 0 0 0 36 x 50.25 in Code: ACI 318-02 Units: English Run axis: About X-axis Run option: Investigation Slenderness: Not considered -4000 Column type: Structural Bars: ASTM A615 Date: 04/01/09 Time: 17:12:32
-1500 pcaColumn v4.10. Licensed to: Sargent & Lundy Engineers. License ID: 54143-1013717-4-2801B-21ABO File: D:\PROJECTS\CRYSTAL RIVER\YIELD LINE ANALYSIS\ColumnCheck\Column.col Project: CR3 AB East Wall Column: 01 Engineer: MWM fc = 3 ksi fy = 40 ksi Ag= 1809 inA2 8#1 8 bars Ec = 3321 ksi Es = 29000 ksi As = 32.00 inA2 rho = 1.77%
fc = 2.55 ksi Xo 0.00 in. Ix = 380653 inA4 e_u = 0.003 in/in Yo = 0.00 in ly = 195372 inA4 Betal = 0.85 Min clear spacing = 7.66 in Cleair cover = 2.00 in Confinement: Tied phi(a) = 0.8, phi(b) = 0.9, phi(c) = 0.65
PROGRESS ENERGY FLORIDA, INC.
CRYSTAL RIVER UNIT 3 DOCKET Number 50-302 /License Number DPR-72 LICENSE AMENDMENT REQUEST #303, Revision 1 Revision to Final Safety Analysis Report Sections 5.4.3, "Structural Design Criteria," and 5.4.5.3, "Missile Analysis" Attachment C Description of Proposed Change, Background, Technical Analysis, Determination of No Significant Hazards Considerations, and the Environmental Assessment
U. S. Nuclear Regulatory Commission Attachment C 3F0409-04 Page 1 of 6 Description of Proposed Change, Background, Technical Analysis, Determination of No Significant Hazards Consideration, and the Environmental Assessment 1.0 Description of Proposed Chance The proposed License Amendment Request (LAR) will revise the Crystal River Unit 3 (CR-3)
Final Safety Analysis Report (FSAR) Sections 5.4.3 and 5.4.5.3 to include a statement regarding the design of the east wall of the CR-3 Auxiliary Building.
Verbatim FSAR Section 5.4.3 currently states that the design of Class 1 structures is based on American Concrete Institute (ACI) standard ACI 318-63, "Working Stress Design," for normal operating conditions, and "Ultimate Strength Design" for tornado, earthquake, and missile impact conditions. FSAR Section 5.4.5.3, states that for Class 1 structures, the structural design shall be checked by the ultimate strength provisions of ACI 318-63. These sections are being revised to read:
(5.4.3) This design has been based on ACI 318-63 "Working Stress Design" for normal operating conditions and "Ultimate Stress Design" for tornado, earthquake, and missile impact conditions, except for the east wall of the Auxiliary Building, which has been based on ACI 349-97, "Code Requirementsfor Nuclear Safety Related Concrete Structures."
(5.4.3.1) Same as Section 5.2.3.1 a, b, c, and e, and AC1 349-97.
(5.4.3.2.2) The structural design is in accordance with ACI 318-63, "Ultimate Strength Design,"
except for the east wall of the Auxiliary building, which has been based on ACI 349-97.
(5.4.5.3) The orientation of the pole to give the most critical load is end-on. For this condition, standard column formulas indicate that the pole will elastically buckle at a loading of 148 kips, which is considerably smaller than the crushing strength of either the pole or the concrete. The structural design was then checked by the ultimate strength provisions of ACI 318-63 for capacity to withstand this load, exceptfor the east wall of the Auxiliary Building, which has been based on ACI 349-9 7.
The analysis for the automobile is based on the approach used in Reference 40, which has been verified + 20% in tests conducted by Dr. T. J. Hirsh of the Texas Transportation Institute at Texas A&M University, and by tests indicated in the Reference. This approach was extrapolated for the case of a 2,000 lb automobile traveling at 150 mph. Although the variation of deceleration is sinusoidal, due to the scatter of the test results the analysis was based on maximum deceleration to develop a maximum force applied to the structure. The structural design was then checked by the ultimate strength provisions of ACI 318-63 for capacity to withstand this automobile load, except for the east wall of the Auxiliary Building, which has been based on ACI 349-97.
U. S. Nuclear Regulatory Commission Attachment C 3F0409-04 Page 2 of 6 2.0 Background The CR-3 Auxiliary Building, excluding the steel roof support, is a Class 1 structure. As described in the CR-3 FSAR, a Class 1 structure is a structure whose failure might cause or increase the severity of a Loss of Coolant Accident (LOCA) or result in an uncontrolled release of radioactivity. Class 1 structures are also vital to the safe shutdown and isolation of the reactor. CR-3 Class 1 structures, including the Auxiliary Building, contain and protect safety-related equipment.
The loads used in the design of these Class 1 structures have been determined based on operating and accident requirements, as specified below, :in addition to regular loads as required by applicable codes:
Loads During Normal Operation
" Dead load
" Live load
" Wind load
" Equipment loads
Abnormal Loads
" Tornado loads
" Maximum Hypothetical Earthquake (MHE)
The tornado loading includes tornado generated missiles. Tornado design requirements are:
- a. Tangential wind velocity of 300 miles per hour (mph)
- b. An external pressure drop of 3 pounds per square inch gauge (psig)
- c. Missile equivalent to a utility pole 35 feet long, 14 inches in diameter, density of 50 pounds per cubic foot, and traveling at 150 mph
- d. Missile equivalent to a one ton automobile traveling at 150 mph. (Limiting design basis missile)
The CR-3 FSAR summarizes Class 1 structural design criteria in Section 5.4.3, "...design has been based on ACI 318-63, "Working Stress Design," for normal operating conditions, and "Ultimate Stress Design," for tornado, earthquake, and missile impact conditions."
Upon review of the original design basis structural calculations for the east and south Auxiliary Building walls, it was discovered that calculations were not performed to reflect loading related to tornado driven missiles or tornado wind load combinations as described in the FSAR. An investigation and an assessment of the operability of the east and south walls of the Auxiliary Building were completed. The south wall was qualified using the methods described in the FSAR (ACI 318-63). Calculations indicate the east wall is operable and does not pose a nuclear safety risk.
Calculations to qualify the east wall were performed using the Yield Line Theory methodology.
Application of the Yield Line Theory methodology to qualify the east wall is based on meeting
U. S. Nuclear Regulatory Commission Attachment C 3F0409-04 Page 3 of 6 the requirements of ACI 349-97, "Code Requirements for Nuclear Safety Related Concrete Structures," and is contrary to the FSAR Section 5.4.3 and 5.4.5 statement that, "The design has been based on ACI 318-63." Therefore, a revision to the FSAR is required.
The Yield Line Theory methodology has been used as an acceptable methodology for internal missiles inside the Reactor Building at CR-3. FSAR Section 5.2.4.1.3 documents the application of this methodology. Additionally, a letter from the NRC to Florida Power Corporation, dated September 1, 1973, discusses the use of the Yield Line Theory methodology as an acceptable technique for determining the failure capacity of concrete structures for a High Energy Line Break in Category 1 structures outside containment.
3.0 Technical Analysis The proposed amendment will revise FSAR described methodology for determining ultimate yield strength of the east wall of the CR-3 Auxiliary Building. The design basis structural design criteria described in the FSAR for Class 1 structures is that of ACI 318-63. Upon review of the original design basis calculations for the Auxiliary Building, it was discovered that calculations were not performed on the east or south wall that reflect loading related to tornado driven missiles or tornado wind load combinations as described in the FSAR.
The east wall of the Auxiliary Building is approximately 2 feet thick, constructed of reinforced concrete. FSAR Section 5.2.1.2.6, "Tornado Load," has determined that a minimum of two feet of concrete provides sufficient resistance to the postulated missile spectrum and no additional penetration calculations are required.
Calculation S07-0037, Revision 1, (Attachment B) was performed to confirm that the east wall of the Auxiliary Building is OPERABLE. The calculation also qualifies the wall to the FSAR described postulated tornado driven missile and wind loads using standard structural analysis techniques.
Calculations were performed to qualify the east wall using methods of ACI 318-63 as described in the FSAR. These calculations were not successful. The stresses on the wall due to tornado wind pressure and missiles are not within the allowable limits of ACI 318-63. However, the east wall can be qualified utilizing the Yield Line Theory methodology. The Yield Line Theory methodology is one of the methods discussed in ACI 349-97.
The guidelines of Standard Review Plan (NUREG-0800, Revision 2 - March 2007) Section 3.8.4, "Other Seismic Category 1 Structures," provide direction that the design and analysis of Category 1 buildings be in accordance with ACI 349-97. A review of the requirements of ACI 349-97 was performed to verify that the east wall of the Auxiliary Building would satisfy the applicable design requirements due to the amount of reinforcement in the wall.
Appendix C of ACI 349-97 does not specify any requirements for minimum reinforcement so Section 10.5.3 is applied for minimum reinforcement of flexural members which refers to Section 7.12 for structural slabs of uniform thickness. Section 7.12.5 requires that the ratio of reinforcement area provided at the tension face to gross area of concrete not be less than 0.0018 unless the area of reinforcement provided is at least one-third greater than that required by analysis. The ratio provided in the CR-3 Auxiliary Building east wall is 0.0015. In order to satisfy Section 7.12.5 for a lower ratio of reinforcement, the requirements of Appendix C have
U. S. Nuclear Regulatory Commission Attachment C 3F0409-04 Page 4 of 6 been checked for a wall with a reduced area of reinforcement which is three-quarters of the actual reinforcement area in the east wall. The result satisfies the requirement of ACI 349-97, Section 7.12.5, in that the area of reinforcement provided on the tension face is at least one third greater than required by analysis. The shear capacity of the east wall has been reviewed to ensure that the wall meets the requirements of Section C.3.6 for flexure to control the design.
The collapse load due to tornado missiles used to calculate ductility demand was determined by using a circular fan yield pattern based on the Yield Line Theory methodology. This analysis assumes fixed boundary conditions at the ends of the wall panel. The two-foot thick wall is bounded by three-foot thick slabs on the top and bottom, and three-foot wide by four-foot deep columns on each side. These members provide enough rigidity to assume fixed boundary conditions. The columns have also been checked to withstand the missile impact loads.
The governing loads for the Auxiliary Building east wall are the tornado wind plus depressurization and the tornado missile. The tornado wind plus depressurization load is qualified against the ultimate moment strength of the wall with reduced reinforcement area. The tornado missile loading is governed by the one ton automobile. The resulting missile load is a rectangular force pulse with duration of 0.081 seconds.
Structural Calculation S07-0037, Revision 1, (Attachment B) was performed using the Yield Line Theory methodology and concludes that the ultimate strength of the Auxiliary Building east wall exceeds the applied tornado and pressure drop loads and no overall failure for the walls will occur due to missile impact.
4.0 No Significant Hazard Consideration Determination The proposed License Amendment Request (LAR) #303, Revision 1, will revise the Crystal River Unit 3 (CR-3) Final Safety Analysis Report (FSAR) Sections 5.4.3, "Structural Design Criteria," and 5.4.5.3, "Missile Analysis." The proposed amendment will revise the analysis utilized to qualify specific portions of Class 1 structures.
- 1. Does not involve a significant increase in the probabilityor consequences of an accident previously evaluated The proposed LAR will revise the methodology used to qualify the east wall of the CR-3 Auxiliary Building for all expected and postulated loads including tornado wind and missile loading. The Yield Line Theory methodology is an industry standard that is used for the design and analysis of concrete slabs and is applied to CR-3 in accordance with American Concrete Institute (ACI) 349-97, "Code Requirements for Nuclear Safety Related Concrete Structures." A change in the methodology of an analysis used to verify qualification of an existing structure will not have any impact on the probability of accidents previously evaluated.
The analysis performed demonstrates that the CR-3 Auxiliary Building east wall will remain structurally intact following the worst case loadings assumed in the calculation. Therefore, this proposed change does not involve a significant increase in the probability or consequences previously evaluated.
U. S. Nuclear Regulatory Commission Attachment C 3F0409-04 Page 5 of 6 2, Does not create the probability of a new or different type of accidentfrom any accident previously evaluated.
The function of the CR-3 Auxiliary Building wall is to house and protect the equipment that is important to safety from damage during normal operation, transients, and design basis accidents.
The use of ACI 349-97 for qualifying the east wall of the CR-3 Auxiliary Building has no impact on the capability of the structure. A calculation that uses the Yield Line Theory methodology demonstrated that the structure meets required design criteria. This ensures that the wall is capable of performing its design basis function without alteration or compensatory actions of any kind. No changes to any plant system, structure, or component (SSC) are proposed. No changes to any plant operating practices, procedures, computer firmware/software will occur.
Therefore, the proposed change will not create the possibility of new or different type of accident from any previously evaluated.
- 3. Does not involve a significantreduction in the margin of safety.
The design basis of the plant requires structures to be capable of withstanding normal and accident loads including those from a design basis tornado. The requirements of ACI 349-97, as applied in an approved plant calculation, demonstrated that the east wall of the CR-3 Auxiliary Building is capable of performing its design function. There is a slight reduction in conservatism between the method used for the remaining Class 1 structures, ACI 318-63 and ACI 349-97, but the calculation performed validates the requirement that the east wall of the Auxiliary Building will protect the important to safety systems, structures, and components located in proximity to the wall from damage.
Therefore, the proposed change does not involve a significant reduction in the margin of safety.
Based on the above, Florida Power Corporation concludes that the proposed amendment presents no significant hazards consideration under the standards set forth in 10 CFR 50.92(c) and, accordingly, a finding of "no significant hazards consideration" is justified.
5.0 Applicable Regulatory Regquirements/Criteria The proposed amendment is not a risk-informed change. The operation of the system will be the same as is currently considered in the CR-3 Probabilistic Risk Analysis. Requirements in 10 CFR 50, Appendix A, "General Design Criteria," do not directly apply to CR-3 since CR-3 was licensed prior to the General Design Criteria. However, there is a similarity to some of the criteria that CR-3 was licensed to, and of these, Criteria, 1, 2, and 40 are applicable as referenced in the CR-3 FSAR.
Criterion 1, "Quality Standards," requires systems, structures and components used in the prevention of accidents or mitigating the effects of an accident to be constructed according to quality standards. The Yield Line Theory methodology is an industry standard used in verifying that the design of the east wall of the Auxiliary Building assures its design function is satisfied.
The calculation performed to demonstrate adequacy of the Auxiliary Building east wall is performed using this methodology, and is applicable for use in this application under ACI 349-97, "Code Requirements for Nuclear Safety Related Concrete Structures."
U. S. Nuclear Regulatory Commission Attachment C 3F0409-04 Page 6 of 6 Criterion 2, "Performance Standards," requires systems, structures, and components to be designed, fabricated, and erected in accordance to performance standards that will enable the facility to withstand, without loss of the capability to protect the public, additional forces that may be imposed by natural forces such as earthquakes, tornados, flooding, etc. ACI 318-63 is one such performance standard. ACI 349-97 is another performance standard that provides for similar design and construction techniques and methodologies that will assure protection to the public from failures of structures that could allow the release of radioactive materials. The Yield Line Theory methodology is applicable for use at CR-3 under the provisions of ACI 349-97.
Criterion 40, "Missile Protection," requires protection of engineered safeguard equipment from the effects of internal and externally generated missiles. Inherent in this requirement is the protection afforded by the external walls of the building that houses the equipment. The calculation performed on the east wall of the Auxiliary Building, satisfying the requirements of ACI 349-97, demonstrates that the Auxiliary Building east wall will successfully perform this function against all required loading combinations.
6.0 Environmental Impact Evaluation 10 CFR 51.22 (c)(9) provides criteria for identification of licensing and regulatory actions eligible for categorical exclusion from performing an environmental assessment. A proposed amendment to an operating license for a facility requires no environmental assessment if operation of the facility in accordance with the proposed amendment would not:
(i) Involve a significant hazards consideration, (ii) Result in a significant change in the types or significant increase in the amounts of any effluents that may be released offsite, and (iii) Result in a significant increase in individual or cumulative occupational radiation exposure.
FPC has reviewed proposed License Amendment Request #303, Revision 1, and concludes it meets the eligibility criteria for categorical exclusion set forth in 10 CFR 51.22(c)(9). Pursuant to 10 CFR 51.22(c), no environmental impact statement or environmental assessment needs be prepared in connection with this request.
PROGRESS ENERGY FLORIDA, INC.
CRYSTAL RIVER UNIT 3 DOCKET Number 50-302 /License Number DPR-72 LICENSE AMENDMENT REQUEST #303, Revision 1 Revision to Final Safety Analysis Report Sections 5.4.3, "Structural Design Criteria," and 5.4.5.3, "Missile Analysis" Attachment D Proposed Revised Final Safety Analysis Report Pages Strikeout and Shadowed Text Format
FINAL SAFETY ANALYSIS REPORT Revision: 31.2 Florida Power A Progress Energy Company CONTAINMENT SYSTEM & OTHER Chapter: 5 SPECIAL STRUCTURES Page: 55 of 92 5.4 OTHER CLASS I STRUCTURES AND SYSTEMS Other Class I structures are listed in Section 5.1.1.1. With the exception of the Dedicated Emergency Feedwater Tank Enclosure and the Diesel Driven Emergency Feedwater Pump Enclosure, other Class I structures are designed as discussed in Sections 5.4.1 through 5.4.3. Design of the Dedicated Emergency Feedwater Tank Enclosure is discussed in Section 5.4.6. Design of the Diesel Driven Emergency Feedwater Pump Enclosure is discussed in section 5.4.7.
5.4.1 STRUCTURAL DESIGN PARAMETERS The loads used in design of these other Class I structures have been determined based on operating and accident requirements, as specified below, in addition to regular loads as required by applicable codes.
5.4.1.1 Loads During Normal Operation The loads due to normal operating conditions are:
- a. Dead load
- b. Live load
- c. Wind load
- d. Equipment loads
- e. Design Basis Earthquake (DBE), see Section 5.2.1.2.9a 5.4.1.2 Abnormal Loads (Protection of Safeguards)
These Class I structures which protect Class I Systems and equipment have been designed for such incidents as:
- a. Tornado loads, see Section 5.2.1.2.6.
- c. Tornado missiles, see Section 5.2.1.2.6.
- d. Maximum Hypothetical Earthquake (MHE), see Section 5.1.2.1.
5.4.2 MATERIALS AND SPECIFICATIONS The material and specifications for these other Class I structures are similar to those detailed in Section 5.2.2, except for the concrete which has a minimum compressive strength of 3,000 psi in 28 days (see Section 5.2.2.1).
5.4.3 STRUCTURAL DESIGN CRITERIA This design has been based on ACI 318-63 "Working Stress Design" for normal operating conditions, and "Ultimate Strength Design" for tornado, earthquake, and missile impact conditions! except for the east wall of the Auxiliaryj
ýBiilding, which has been based on ACI 349-97, "Code Requirements for Nuclear Safety Related Concrete Strucures.'i 5.4.3.1 Codes Same as Section 5.2.3.1 a, b, c, and el, and-ACI 349-971.
Revision: 31.2 FINAL SAFETY ANALYSIS REPORT Florida Power Chapter: 5 AProgress Energy Company CONTAINMENT SYSTEM & OTHER Page:
SPECIAL STRUCTURES Page: 56 of 92 5.4.3.2 Loads The design has been based upon normal operating loads, earthquake loads, and accident loads as described in Sections 5.4.1.1 and 5.4.1.2.
5.4.3.2.1 At Normal Operating Conditions The stresses in the concrete and reinforcing steel resulting from combinations of those loads listed in Section 5.4.1.1 are in accordance with ACI 318-63, "Working Stress Design."
5.4.3.2.2 Abnormal Loads The other Class I structures have been designed to withstand short term tornado loadings, including tornado generated missiles where such structures house systems and components whose failure would result in an inability to safely shutdown and isolate the reactor. Structures that are so designed include the following:
- a. Control building.
- b. Auxiliary building, excluding the steel roof support structure.
The concrete portion of the auxiliary building which houses Class I items is designed for tornado generated missiles. The spent fuel pool and new fuel vault have been evaluated for tornado generated missiles by calculation S06-0010.
The roof was designed considering seismic loads but the roof will not act as a barrier against a tornado missile.
- c. Diesel generator building, including the radiator exhaust air deflector wall and its support structure (EGX-2).
The deflector wall is missile resistant, not missile proof. Structural failure (collapse) of the wall will not occur, but it is not designed to prevent local deformation of the structure or puncture of the wall (Ref 68).
- d. NSSS intake pump structure.
- e. Intermediate building.
- f. Exterior safety related piping and component missile shields.
The tornado design requirements are described in Section 5.2.1.2.6.
The structural design is in accordance with ACI 318-63, "Ultimate Strength Design7 ," except for the east wall of thd LAuxiliary Building, which has been based on ACI 349-97, "Code Requirements for Nuclear Safety Related Concrete Structures.,'
5.4.3.2.3 Turbine Report A vulnerability analysis of the plant design was made to determine what changes would have to be made in the event a turbine-missile could be produced. The basic criteria for this analysis was that plant shutdown and security could not be jeopardized by a turbine-missile strike. Moreover, the consequences of a strike could not cause or result in an uncontrolled release of excessive amounts of radioactivity. On this basis, those systems, structures, and
Revision: 31.2 FINAL SAFETY ANALYSIS REPORT Florida Power AProgress Energy Company CONTAINMENT SYSTEM & OTHER Chapter:
5 SPECIAL STRUCTURES Page: 72 of 92 A detailed stress analysis of the internals under accident conditions is discussed in Babcock & Wilcox Topical Report BAW-10008.
Equipment such as safety features valves, tanks, and heat exchangers were stress analyzed using the equivalent static load method. The analysis includes evaluation of the equipment for normal and abnormal conditions. Seismic shock and vibration tests have been conducted on a valve operator which is typical of the valves used in the Engineered Safeguards (ES) Systems. The valve operator was tested at a 5.3g shock level at 35 cps with no discrepancies observed. A scan from 5 cps to 35 cps was made and no critical resonant frequencies were noted. The valve operator was shock and vibration tested in each of three different axes in a 2 minute "on" - 1 minute "off' cycle for a total of 3 times per axis. The unit was then electrically operated to the full-open and full-closed position, and all torque switches and limit switches functioned properly. All electrical and mechanical devices on the operator functioned properly.
The RCP motors have been dynamically tested by the supplier under operational conditions in a test loop. The tests demonstrated that the pump motor would operate satisfactorily under the worst anticipated vibratory loadings resulting from full flow conditions for Crystal River Unit 3. The natural frequency of the RCP and motor (above 25 cps) is appreciably above the fundamental seismic response spectra (10 cps) of the reactor coolant loop. The pump motors are capable of withstanding the calculated design earthquake loading with unaffected operational capability.
5.4.5.3 Missile Analysis The missile loading requirements for Class I structures are as in Section 5.4.3.2.3 for main steam turbine missiles, and as in Section 5.2.1.2.6 for tornado missiles.
The orientation of the pole to give the most critical load is end-on. For this condition, standard column formulas indicate that the pole will elastically buckle at a loading of 148 kips, which is considerably smaller than the crushing strength of either the pole or the concrete. The structural design was then checked by the ultimate strength provisions of ACI 318-63 for capacity to withstand this pole loadxce t for the east wall of the Auxiliary Bdilding-[
Which has been based on ACI 349-971 The analysis for the automobile is based on the approach used in Reference 40, which has been verified +20% in tests conducted by Dr. T. J. Hirsh of the Texas Transportation Institute at Texas A&M University, and by tests indicated in the Reference. This approach was extrapolated for the case of a 2,000 lb automobile traveling at 150 mph. Although the variation of deceleration is sinusoidal, due to the scatter of the test results the analysis was based on maximum deceleration to develop a maximum force applied to the structure. The structural design was then checked by the ultimate strength provisions of ACI 318-63 for capacity to withstand this automobile load except east wall of the Auxiliary Buildi, which has been based-on ACI 347]
Missile analysis based on Standard Review Plan 3.5.1.4 (Ref 49) guidelines was used for the Emergency Feedwater Tank Enclosure and the Diesel Driven Emergency Feedwater Pump Enclosure. See sections 5.4.6 and 5.4.7 for more information.
5.4.5.4 Seismic Design and Review of Class I (Seismic) Components and Equipment The seismic input, including any necessary feedback from structural and system dynamic analyses, were specified to the vendors of purchased Class I (seismic) components and equipment. Independent engineering review was made within the respective departments by persons other than the original Design Engineer.
PROGRESS ENERGY FLORIDA, INC.
CRYSTAL RIVER UNIT 3 DOCKET Number 50-302 /License Number DPR-72 LICENSE AMENDMENT REQUEST #303, Revision 1 Revision to Final Safety Analysis Report Sections 5.4.3, "Structural Design Criteria," and 5.4.5.3, "Missile Analysis" Attachment E Proposed Revised Final Safety Analysis Report Pages Revision Bar Format
-4 FINAL SAFETY ANALYSIS REPORT Revision: 31.2 Florida Power AProgress EnergyCompany CONTAINMENT SYSTEM & OTHER Chapter:
5 SPECIAL STRUCTURES Page: 55 of 92 5.4 OTHER CLASS I STRUCTURES AND SYSTEMS Other Class I structures are listed in Section 5.1.1.1. With the exception of the Dedicated Emergency Feedwater Tank Enclosure and the Diesel Driven Emergency Feedwater Pump Enclosure, other Class I structures are designed as discussed in Sections 5.4.1 through 5.4.3. Design of the Dedicated Emergency Feedwater Tank Enclosure is discussed in Section 5.4.6. Design of the Diesel Driven Emergency Feedwater Pump Enclosure is discussed in section 5.4.7.
5.4.1 STRUCTURAL DESIGN PARAMETERS The loads used in design of these other Class I structures have been determined based on operating and accident requirements, as specified below, in addition to regular loads as required by applicable codes.
5.4.1.1 Loads During Normal Operation The loads due to normal operating conditions are:
- a. Dead load
- b. Live load
- c. Wind load
- d. Equipment loads
- e. Design Basis Earthquake (DBE), see Section 5.2.1.2.9a 5.4.1.2 Abnormal Loads (Protection of Safeguards)
These Class I structures which protect Class I Systems and equipment have been designed for such incidents as:
- a. Tornado loads, see Section 5.2.1.2.6.
- c. Tornado missiles, see Section 5.2.1.2.6.
- d. Maximum Hypothetical Earthquake (MHE), see Section 5.1.2.1.
5.4.2 MATERIALS AND SPECIFICATIONS The material and specifications for these other Class I structures are similar to those detailed in Section 5.2.2, except for the concrete which has a minimum compressive strength of 3,000 psi in 28 days (see Section 5.2.2.1).
5.4.3 STRUCTURAL DESIGN CRITERIA This design has been based on ACI 318-63 "Working Stress Design" for normal operating conditions, and "Ultimate Strength Design" for tornado, earthquake, and missile impact conditions, except for the east wall of the Auxiliary Building, which has been based on ACI 349-97, "Code Requirements for Nuclear Safety Related Concrete Structures."
5.4.3.1 Codes Same as Section 5.2.3.1 a, b, c, and e, and ACI 349-97.
Revision: 31.2 FINAL SAFETY ANALYSIS REPORT AProgress Energy Company CONTAINMENT SYSTEM & OTHER Chapter: 5 SPECIAL STRUCTURES Page: 56 of 92 5.4.3.2 Loads The design has been based upon normal operating loads, earthquake loads, and accident loads as described in Sections 5.4.1.1 and 5.4.1.2.
5.4.3.2.1 At Normal Operating Conditions The stresses in the concrete and reinforcing steel resulting from combinations of those loads listed in Section 5.4.1.1 are in accordance with ACI 318-63, "Working Stress Design."
5.4.3.2.2 Abnormal Loads The other Class I structures have been designed to withstand short term tornado loadings, including tornado generated missiles where such structures house systems and components whose failure would result in an inability to safely shutdown and isolate the reactor. Structures that are so designed include the following:
- a. Control building.
- b. Auxiliary building, excluding the steel roof support structure.
The concrete portion of the auxiliary building which houses Class I items is designed for tornado generated missiles. The spent fuel pool and new fuel vault have been evaluated for tornado generated missiles by calculation S06-0010.
The roof was designed considering seismic loads but the roof will not act as a barrier against a tornado missile.
- c. Diesel generator building, including the radiator exhaust air deflector wall and its support structure (EGX-2).
The deflector wall is missile resistant, not missile proof. Structural failure (collapse) of the wall will not occur, but it is not designed to prevent local deformation of the structure or puncture of the wall (Ref 68).
- d. NSSS intake pump structure.
- e. Intermediate building.
- f. Exterior safety related piping and component missile shields.
The tornado design requirements are described in Section 5.2.1.2.6.
The structural design is in accordance with ACI 318-63, "Ultimate Strength Design," except for the east wall of the Auxiliary Building, which has been based on ACI 349-97, "Code Requirements for Nuclear Safety Related Concrete Structures."
5.4.3.2.3 Turbine Report A vulnerability analysis of the plant design was made to determine what changes would have to be made in the event a turbine-missile could be produced. The basic criteria for this analysis was that plant shutdown and security could not be jeopardized by a turbine-missile strike. Moreover, the consequences of a strike could not cause or result in an uncontrolled release of excessive amounts of radioactivity. On this basis, those systems, structures, and
31.2 i Power FFlorida oFINAL SAFETY ANALYSIS REPORT Revision:
5 AProgress Energy Company CONTAINMENT SYSTEM & OTHER Chapter:
SPECIAL STRUCTURES Page: 72 of 92 A detailed stress analysis of the internals under accident conditions is discussed in Babcock & Wilcox Topical Report BAW- 10008.
Equipment such as safety features valves, tanks, and heat exchangers were stress analyzed using the equivalent static load method. The analysis includes evaluation of the equipment for normal and abnormal conditions. Seismic shock and vibration tests have been conducted on a valve operator which is typical of the valves used in the Engineered Safeguards (ES) Systems. The valve operator was tested at a 5.3g shock level at 35 cps with no discrepancies observed. A scan from 5 cps to 35 cps was made and no critical resonant frequencies were noted. The valve operator was shock and vibration tested in each of three different axes in a 2 minute "on" - 1 minute "off' cycle for a total of 3 times per axis. The unit was then electrically operated to the full-open and full-closed position, and all torque switches and limit switches functioned properly. All electrical and mechanical devices on the operator functioned properly.
The RCP motors have been dynamically tested by the supplier under operational conditions in a test loop. The tests demonstrated that the pump motor would operate satisfactorily under the worst anticipated vibratory loadings resulting from full flow conditions for Crystal River Unit 3. The natural frequency of the RCP and motor (above 25 cps) is appreciably above the fundamental seismic response spectra (10 cps) of the reactor coolant loop. The pump motors are capable of withstanding the calculated design earthquake loading with unaffected operational capability.
5.4.5.3 Missile Analysis The missile loading requirements for Class I structures are as in Section 5.4.3.2.3 for main steam turbine missiles, and as in Section 5.2.1.2.6 for tornado missiles.
The orientation of the pole to give the most critical load is end-on. For this condition, standard column formulas indicate that the pole will elastically buckle at a loading of 148 kips, which is considerably smaller than the crushing strength of either the pole or the concrete. The structural design was then checked by the ultimate strength provisions of ACI 318-63 for capacity to withstand this pole load, except for the east wall of the Auxiliary Building, which has been based on ACI 349-97.
The analysis for the automobile is based on the approach used in Reference 40, which has been verified +20% in tests conducted by Dr. T. J. Hirsh of the Texas Transportation Institute at Texas A&M University, and by tests indicated in the Reference. This approach was extrapolated for the case of a 2,000 lb automobile traveling at 150 mph. Although the variation of deceleration is sinusoidal, due to the scatter of the test results the analysis was based on maximum deceleration to develop a maximum force applied to the structure. The structural design was then checked by the ultimate strength provisions of ACI 318-63 for capacity to withstand this automobile load, except for the east wall of the Auxiliary Building, which has been based on ACI 349-97.
Missile analysis based on Standard Review Plan 3.5.1.4 (Ref 49) guidelines was used for the Emergency Feedwater Tank Enclosure and the Diesel Driven Emergency Feedwater Pump Enclosure. See sections 5.4.6 and 5.4.7 for more information.
5.4.5.4 Seismic Design and Review of Class I (Seismic) Components and Equipment The seismic input, including any necessary feedback from structural and system dynamic analyses, were specified to the vendors of purchased Class I (seismic) components and equipment. Independent engineering review was made within the respective departments by persons other than the original Design Engineer.