129250422-plant-pressure-vessel-training-manual-6-of-6.pdf

KOREA ENGINEERING CONSULTING,INC ASME SEC.VIII, DIV.2, PART 5(STRESS/FATIGUE)PROGRAM : NISA(NISA SOFTWARE, INC. USA) DESIGN & FE ANALYSISVERSION : 15.1 ( Windows 2000 / XP ) PAGE NO. : 6-1

Pressure Vessel Basic Concept ASME 2007 SEC.VIII, DIV.2, PART 5

STRESS/FATIGUE(6권)

(한글번역 및 강도계산)

Korea Engineering Consulting, Inc. Tel) 02-3486-9324/9377, Fax) 02-3486-9325, [email protected], http://www.hkecc.co.kr


==== Contents ===

[1권Book] : Theoretical Strength Calculation & FEA 1.Stress-Strain Curve(Experimental) ............................................................................................ 6 2. Simple Stress(σ) & Strain(ε) Calculation ................................................................................. 8 3. Thin Cylinders & Shells............................................................................................................ 9 4. Thick Cylinders & Shells ........................................................................................................ 16 5. Theories of Elastic Failure ...................................................................................................... 23 6. Torsion Theory........................................................................................................................ 24 7. Basic Lug Calculation ............................................................................................................. 26 8. Basic Skirt Calculation.................................................................................................... 28 ~ 31

8-1. Skirt Stress Calculation.................................................................................................... 31 8-2. Skirt Anchor Bolt Stress Calculation ............................................................................. 32

9. Buckling Equation & Analysis Approach ............................................................................... 32 9-1. Buckling Equation & Analysis Approach........................................................................ 35

10. Circular Flat Plate and Head with Uniform Loading ............................................................ 36 10-1 Roark’s Formulas for Stress & Strain ............................................................................. 38 10-2 ASME Code Sec.VIII, Div.2, Appendix4....................................................................... 40 10-3 Perforated Plate Bending Stress Calculation .................................................................. 44 10-4 Doom Head(Dished/Ellipsoidal/Spherical Heads) under External Calculation.............. 46 10-5 Perforated Plate Bending Stress Calculation(H/E Tubesheet) ........................................ 52

11. Blind Flange with Uniform Loading..................................................................................... 56 12. Internal Components Support Ring under Packing & Pressure Drop Loading............. 58 ~ 62

12-1 Support Ring under Packing & Pressure Drop Loading ................................................. 59 12-2 Intermediate Head Weldment Calculation...................................................................... 63 12-3 Partition Plate Thickness Calculation ............................................................................. 69 12-4 Nozzle Load Application ................................................................................................ 71 12-5 Stress Indices on Nozzle per ASME, Div.2 Para AD-560.7........................................... 74 12-6 Flange Torque Calculation for Sealing Flanges.............................................................. 91 12-7 Bolt Thread Shear/Bending Stress & Nut Length Calculation ....................................... 94 12-8 Girth Flange Calculation................................................................................................. 96 12-9 Buckling(Wrinkling) of Ellipsoidal Head(Internal Pressure) ....................................... 104

12-9-1 Compressive Pressure Calculation Internal Pressure) ........................................... 104 12-9-2 Head Wrinkling Thickness Calculation(ASME Codecase 2261).......................... 110 12-9-3 Stiffening Ring Calculation under External Pressure(ASME UG29) ................... 114 12-9-4 Internal Support Beam Calculation(Pressure Drop + Static Weight) .................... 117

12-10 Linearization of Stress Results and Classification ...................................................... 121 13. ASME Allowable Stress Criteria Concept ...................................................................... 126

14. Vessel Equipment Analysis Approach ................................................................................ 127 14-1. Stress Analysis Approach(based on ASME) ............................................................... 129 14-2. Stress Evaluation Sample 1(based on ASME) ........................................................... 133 14-3. FE Stress/Fatigue Model Sample 2(2D Axisymmetric Solid) ................................... 139 14-4. Stress Analysis Approach(based on ASME) ............................................................... 143 14-5. FE Stress/Fatigue Model Sample 3(3D Shell) ............................................................. 144 14-6. Fatigue Analysis Approach(based on ASME) ............................................................. 147 14-7. Crack/Fracture Analysis Approach(ASME/PD/API) .................................................. 147 14-8. Nozzle Local Stress Analysis....................................................................................... 153 14-9. Agitator Rotating Equipment Analysis ........................................................................ 154


[[2권Book] : Theoretical Strength Calculation & FEA

Appendix ″A″ ................................................................................................................................ 6 ″Additional Vessel/HE Stress Calculation & Information analyzed by NISA″

App 1) 실린더에 외압을 받는 경우 최적두께 계산 ............................................................ 7 App 2) 고온에서 허용응력이 ASME, Sec.II, Part D에 없는 경우 ..................................... 11 App 3) Internal Support Beam의 Bending Stress & Displacement ........................................... 16 App 4) Spread Beam Calculation due to Rigging Condition ...................................................... 18 App 5) Vibration Analysis & Design of Tall Towers ................................................................. 28

1) Sample 1 : Zorrila’s Function..................................................................................... 33 2) Sample 2 : Zorrila’s Function..................................................................................... 35 3) Sample 3 : ASME STS-2006 Code ............................................................................ 38

App 6) Seismic Spectrum Analysis(UBC/ASCE/IBC Code) ..................................................... 50 App 7) Tubesheet Stress Analysis............................................................................................... 57 App 8) Conical Section Calculation under Nozzle Load ............................................................ 66 App 9) Theoretical procedures of Expansion Bellows Calculation ............................................ 68 App 10) Expansion Bellows Stress & Fatigue Calculation......................................................... 83 App 11) Seismic Responses Spectrum Analysis....................................................................... 100 App 12) Reaction Load on Multi-Saddle Supports ................................................................... 106 App 13) Stress Linerization Analysis........................................................................................ 110 App 14) Imperfection Shape on Equipments ............................................................................ 160 App 15) Spring Constants Calculation(Perforated Plate).......................................................... 172 App 16) Thickness & Deflection Calculation of Impingement................................................. 178


[3권Book] : Theoretical Strength Calculation & FEA

Appendix ″B″ ................................................................................................................................ 6 ″Additional Vessel/HE Stress Calculation & Information analyzed by NISA″

App 1) Stability Check for Girth Flange/Bolt under Erection Conditions.................................... 7 App 2) Stability Check for Girth Flange/Bolt under Erection Conditions.................................. 17 App 3) Stability Check for Tube/Header Pipe under Thermal Expansion.................................. 22 App 4) Wind Guide Design for Bending Moment due to Wind Load ........................................ 25 App 5) Knee Brace Support Buckling Stability Analysis ........................................................... 32 App 6) Saddle Bending Checking under Sea Motion Load ........................................................ 42 App 7) Tube to Tubesheet Joint Welding Checking & Fatigue .................................................. 54 App 8) High Temp Creep Damage Procedure & Calculation..................................................... 59 App 9) Bending/Buckling Checking of Spread Beam under Erection........................................ 73 App 10) Bending Checking of Circular Plate subjected to Fluid Load....................................... 81 App 11) Tubesheet Calculation(Miller’s Method) .................................................................... 85 App 12) Thickness Calculation under External Pressure ............................................................ 93 App 12-1) Cylinder Thickness Calculation under External Pressure.......................................... 96 App 12-2) Spherical Thickness Calculation under External Pressure....................................... 103 App 12-3) Cylinder Thickness with Stiffener under External Pressure .................................... 107 App 13) Heating Up Force(Air/Saturated Water) in Isolated Space......................................... 120 App 14) App 14) Main Shell Thickness Calculation(ASME Code 2006 & 2007) ................. 138


[4권Book] : FEA(Finite Element Analysis) Theoretical Course

Appendix ″C″ ................................................................................................................................ 4 ″Finite Element Theoretical & Analysis by NISA″ Theoretical Course ″A″

1. 유한요소법(Finite Element Method)의 개념.....................................................1-1

2. 유한요소법의 단계별 적용..........................................................................2-1

3. 요소의 형상 함수.....................................................................................3-1

4. 요소 형상 및 특징 ...................................................................................4-1

5. 요소의 생성기법 및 결과 분석 방법 .............................................................5-1

Theoretical Course ″B″ 1-1. 선형용수철 요소(Linear Spring Element).....................................................1-1

1-2. 축 방향 보 요소(Axial Bar Element) ..........................................................2-1

1-3. 굽힘 보 요소(Bending Beam Element).......................................................3-1

1-4. 평면 구조 요소(Plane Frame Element) .......................................................4-1

1-5. 평면 격자 요소(Plane Lattice Element) ......................................................5-1

1-6. 평면 요소(Plane Element).......................................................................6-1

Theoretical Course ″C″ [예제1] 스프링 계로 이루어진 구조의 유한요소해석 ........................................... C-1

[예제2] 트러스(Truss) 구조물의 유한요소해석................................................... C-2

[예제3] 빕(Beam) 구조물의 유한요소해석 ........................................................ C-3

[5권Book] : Crack Propagation & Facture Mechanics

Appendix ″D″ ................................................................................................................................ 7 1. Crack Propagation ..................................................................................................................... 7

1.1 Theoretical Descriptions ..................................................................................................... 7 1) Paris Law .......................................................................................................................... 7

2) Forman Law...................................................................................................................... 8 3) Elber Law.......................................................................................................................... 9 4) Walker Law..................................................................................................................... 10

2. Fracture Mechanics ................................................................................................................. 37 2.1 Theoretical Descriptions ................................................................................................... 37

2.2 Stress Intensity Calculation..........................................................................................80 ~ 228


[6권Book] : ASME 2007, Div.2 Part 5(응력 및 피로분석) 번역 및 강도계산

Part 5( Design by Analysis Requirement) 5.1 General Requirements ..............................................................................................................9 5.2 Protection Against Plastic Collapse .......................................................................................13 5.3 Protection Against Local Failure............................................................................................25 5.4 Protection Against Collapse Form Buckling..........................................................................28 5.5 Protection Against Failure From Cyclic Loading ..................................................................31 5.6 Supplemental Requirements for Stress Classification in Nozzle Necks ................................63 5.7 Supplemental Requirements for Bolts....................................................................................65 5.8 Supplemental Requirements for Perforated Plates .................................................................67 5.9 Supplemental Requirements for Layered Vessels..................................................................67

Annex 5.A(Linearization of Stress Results for Stress Classification) 5.A.1 Scope ..................................................................................................................................95 5.A.3 Selection of Stress Classification Lines .............................................................................97 5.A.4 Stress Integration Method ..................................................................................................99 5.A.5 Structural Stress Method based on Nodal Forces.............................................................102

Annex 5.B(Histogram Development and Cycle Counting for Fatigue Analysis) 5.B.1 General .............................................................................................................................119 5.B.2 Definition..........................................................................................................................119 5.B.3 Histogram Development...................................................................................................120 5.B.4 Cycle Counting using the Railflow Method .....................................................................120

Annex 5.C(Alternating Plasticity Adjustment Factors and Effective --- Fatigue Analysis) 5.C.1 General .............................................................................................................................127 5.C.2 Effective Alternating Stress for Elastic Fatigue Analysis ................................................127

Sample Strength Calculation for Reactor Main Shell/Hemi-Head/Nozzle Opening, Local Stress/Girth Flange,,,, ..........................137 ~ 237 Internal Support Ring Calculation.....................................................................................138~ 242


PART 5

DESIGN BY ANALYSIS REQUIRMENTS

″해석 설계 기법″


5.1 General Requirements

5.1.1 Scope

5.1.1.1 Design-by-analysis 방법론의 분류의 적용을 위한 디자인 요건은 Part 5에 기술되어 있다. 응력 보고서로부터 결과를 인용하는 세부 디자인 절차는 Plastic Collapse, Local Failure, Buckling과 Cyclic Loading의 요소를 평가하기 위하여 제공되었다. 추가적인 요건은 Bolts, Perforated Plates와 Layered Vessels의 보고서를 위하여 제공되었다. 절차 또한 실험 응력 보고서로부터 결과를 인용하는 디자인과 기계적 균열 평가를 위하여 제공되었다.

5.1.1.2 Design-by-analysis 필요 조건은 밑에 열거된 failure modes에 대비하는 protection에 의하여 구성되었다. 요소들은 각각의 Applicable failure mode에 대하여 평가 되어야 할 것이다. 만약 다중의 평가 절차가 Failure mode을 위해 제공되었다면, 요소 디자인에 자격을 주기 위해 이 절차들 중에 하나는 반드시 만족되어야 한다.

a) The Scope of this Division의 이내 모든 Pressure Vessels은, 사이즈와 압력에 상관없이, 이 부분의 요건에 의해서 overpressure에 대비되는 Protection과 함께 제공되어야 한다.

b) Protection Against Plastic Collapse – 이 필수 조건들은 두께와 요소의 configuration 가 Design-by Analysis규정의 의해 재정된 모든 요소들에게 적용된다.

c) Protection Against Local Failure – 이 조건들은 두께와 요소의 configuration 가 Design-by Analysis규정의 의해 재정된 모든 요소들에게 적용된다. 만약 요소 디자인이 Part 4 (i.e. component wall Thickness and weld Detail per paragraph 4.2)에 의한 거라면 Local strain Limit Criterion의 값을 구할 필요는 없다.

d) Protection Against Collapse From Buckling - 이 필수 조건들은 두께와 요소의 configuration 가 Design-by Analysis규정의 의해 재정된 모든 요소들과 compressive stress field의 applied loads result에 적용이 된다.


e) Protection Against Failure From Cyclic Loading - 이 필수 조건들은 두께와 요소의 configuration 가 Design-by Analysis규정의 의해 재정된 모든 요소들에게 적용되고 applied loads는 순환한다. 결과적으로, 이 요건들은 두께와 사이즈가 Design-by Analysis규정의 의해 재정된 Cyclic Loading의 요소를 qualify 하기 위하여 사용 될 수도 있다.

5.1.1.3 Part5의 Design-by-Analysis 절차는 오직 디자인 온도에서 평가된 Annex 3.A 의Allowable stress가 time-independent properties에 의해 운영되거나 만약 specific design procedure에 기록되지 않았다면 사용되어야 한다. 만약 디자인 온도에서 평가된 Annex 3.A 의Allowable stress가 time-independent properties에 의해 운영되고 Fatigue Screening criteria of Paragraph 5.5.2.2가 만족이 되었다면, paragraph 5.2.2, 5.3.2, 5.6, 5.7.1, 5.7.2와 5.8에 있는 Elastic Stress Analysis Procedures는 사용될 것이다.


5.1.2 Numerical Analysis 5.1.2.1 Part5의 Design-by-analysis procedures는 detailed stress analysis 의

component로부터 얻어진 results의 use에 의하였다. Loading condition에 의존한 temperature distribution을 결정하기 위한 thermal analysis와 resulting thermal stresses는 요구될 것이다.

5.1.2.2 절차는 Plastic Collapse, Local Failure, Buckling과 Cyclic Loading에 대비하는 protection을 결정하기 위한 Performing Stress Analyses를 위하여 제공되었다. 이러한 절차들은 development of loading conditions, selection of material properties, post processing of results와 component의 suitability를 결정하기 위한 acceptance criteria까지의 comparison과 함께 consistent result를 구하기 위한 필요한 detail들을 제공한다.

5.1.2.3 Stress analysis method, 요소의 modeling과 validation of analysis의 권장은 제공되지 않았다. 이러한 디자인 공정의 양상이 중요하고 analysis에서 고려되어야 하는 동안, approaches와 design processes의 변화성 때문에 subject의 detailed treatment는 제공되지 않는다. 그러나, 모든 결과의 validation을 포함하고 있는 정확한 Stress analysis는 design의 한 부분으로 제공 되어야 한다.

5.1.2.4 Stress Analysis에서 사용될 다음의 재료 속성들은 Part 3에 나오는 Data와 Material models를 사용하여 결정되어야 한다.

a) Physical Properties – Young’s Modulus, 열팽창 coefficient, 열전도율, 열확산성, 밀도, Poisson’s ratio

b) Strength Parameters – Allowable Stress, Minimum Specified yield strength, minimum specified tensile strength

c) Monotonic Stress-Strain Curve – elastic perfectly plastic과 elastic-plastic true stress-strain curve with strain hardening

d) Cyclic Stress-Strain Curve – Stabilized true Stress-Strain 도량 곡선


5.1.3 Loading Conditions

5.1.3.1 component 상의 모든 applicable applied 하중은 design-by-analysis를 실행할 때 고려되어야 한다. 추가적 하중은 applicable load cases의 형태에서 applied pressure과 더불어 고려되어야 한다. 만약 load case가 시간에 따라 변한다면, loading histogram은 각각의 specific load의 time variation을 보여주기 위하여 전개되어야 된다. Load Case의 정의는 User’s Design Specification에 포함 되어야 한다. 추가적인 하중과 design에서 고려되어야 하는 loading conditions의 개요는 table 5.1에 보여지고 잇다.

5.1.3.2 Load case combinations는 Analysis에서 고려되어야 된다. 전형적인 load descriptions는 table 5.2에 제공되어 있다. Elastic analysis, limit load analysis와 elastic plastic analysis를 위한 Load case combinations는 table 5.3, 5.3와 5.4에 각각 보여지고 있다. Pressure term, P를 포함하는 Load cases를 계산하는 중에, 압력이 0이 되는 현상을 고려해야 된다. Applicable load case combinations는 User’s Design Specification에 명시된 다른 combinations과 더불어 고려되어야 된다.

5.1.3.3 만약 어떠한 하중이라도 시간과 함께 변화한다면, loading histogram은 각각의 specific load의 time variation을 표기하기 위하여 전개되어야 한다. Loading histogram은 모든 significant operating temperatures, pressures, supplemental loads와 the corresponding cycles나 모든 요소들에 작용된 significant events에 대한 time periods들을 포함 하여야 한다. 다음에 설명하는 것들은 loading histogram을 전개할 때 고려되어야 한다.

a) operation 수명 동안 각각의 event와 상기된 cycles의 수량, 이러한 events은 start-ups를 포합하여야 한다, normal operation, upset conditions와 shutdowns.

b) Histogram을 창작할 때, assessment에 사용될 history는 operation의 anticipated sequence에 기반을 두어야 한다. 그것이 가능하지 않거나 operation의 actual sequence에 기초를 둔 histogram을 전개하기에 실용적이지 않을 때, histogram은 값이 실제 시행에 머무르도록 쓰일 수 있다. 만약 그렇지 않다면, cyclic evaluation은 모든 가능한 loading의 combinations을 고려해야 한다.


c) 압력, 온도, 질량, support displacement와 nozzle reaction loadings처럼 추가적 하중처럼 applicable loadings

d) Time history 동안의 Applied loadings 사이의 관계

5.2 Protection Against Plastic Collapse

5.2.1 Overview

5.2.1.1 three alternative analysis methods는 protection against plastic collapse를 계산하기 위하여 제공되었다. 이러한 analysis methodologies의 간결한 서술은 밑에 제공되어있다.

a) Elastic Stress Analysis Method - 응력들은 Elastic analysis를 이용하여 계산되고, categories들로 분류되고, plastic collapse가 일어나지 않게 보수적으로 제정된 allowable values에 제한되어 있다.

b) Limit-Load Method – 요소의 제한 하중까지의 밑의 bound를 단정하기 위해서 계산이 실행되었다. Components에 있는 Allowable load들은 gross plastic deformations (plastic collapse)의 onset이 발생하지 않게 design factor을 limit load까지 적용하는 것에 의해서 제정 되었다.

c) Elastic-Plastic Stress Analysis Method – collapse load는 applied loading과 components의 deformation characteristics를 고려하는 elastic-plastic analysis로부터 유도되었다.

5.2.1.2 complex geometry와/또는 complex loading과 함께 components를 위해서, stresses의 categorization은 significant knowledge와 judgment를 요구한다. 이는 특히 3-D stress fields에서는 사실이다. 각각의 Paragraphs 5.2.3과 5.2.4에 있는 elastic-plastic analysis methods와 limit load의 application은 categorization process가 ambiguous results를 만드는 케이스에서 권장된다.

5.2.1.3 Heavy-wall(R/t≤4) pressure containing components를 위한 Structural integrity를 설명하기 위한 Stress classification procedures과 조합된 Elastic stress analysis는 non-conservative results를 초래할 수도 있고, 특히 structural discontinuities에서는, 권장되지 않는다. non conservatism의 이유는 the nonlinear stress distributions 과 같이 있는 빽빽한 벽 파트가 the implicit linear stress distribution utilized in the stress categorization and classification procedure에 의해서


정확하게 나타나지 않는다. 만약 yielding이 일어난다면 응력 분포의 misrepresentation은 강화된다. 예를 들어, calculated peak stresses가 예상 값을 넘고 벽 두께의 5%보다 많은 thickness dimension만큼을 넘은 케이스에서는, elastic analysis가 non-conservative 결과를 줄 수도 있다. 이런 케이스에서는, paragraph 5.2.3 또는 5.2.4에 나오는 elastic-plastic stress analysis procedures가 사용되어야 한다.

5.2.1.4 Paragraph 5.2.2에 기술된 Elastic stress analysis에 기반을 둔 Structural evaluation procedures는 plastic collapse에 대비되는 protection의 근사값을 제공한다. Component의 plastic collapse에 대비되는 protection의 더 정확한 어림 값은 한도와 plastic collapse load를 전개하기 위한 elastic-plastic stress analysis를 사용하여 얻어질 수 있다. General membrane equivalent stress에서의 limits, local membrane equivalent stress와 paragraph 5.2.2의 primary membrane plus primary bending equivalent stress는 collapse의 prevention을 limits analysis의 principles에 의해 단정된 것처럼 신중하게 보증하는 레벨에서 배열되었다. 만약 paragraph 5.2.3 또는 paragraph 5.2.4의 requirements가 만족되었다면, 이러한 limits들은 만족될 필요가 없다.


SAMPLE STRENGTH CALCULATION

ASME 2007, DIV.2


tuse_thead 98.0mm:=Used Thickness of Hemi-Head w/o LiningTop Head

tuse_bhead 100.0mm:=Used Thickness of Hemi-Head w/o LiningBottom Head

ttol_shell 0.3mm:=Mill Tolerence of Main Shell

tuse_shell 173.0mm:=Used Thickness of Main Shell

Pex 1.049kgf

cm2=

Pex 0.1029N

mm2:=External Pressure(F.V)

Pin_top 123kgf

cm2=

Pin_top 12.06218N

mm2:=Internal Pressure acting on Top Head

Pin_bot 123.996kgf

cm2=

Pin_bot 12.15985N

mm2:=Internal Presure acting on Bottom Head

including Liquid+Catalyst

Pin 123.973kgf

cm2=

Pin 12.1576N

mm2:=Internal Pressure including Liquid+Catalyst

based on Bottom Shell Section

Tde 440.0:=Design Temperature

Did_wo 4.21 103× mm=Did_wo Did 2 Ca⋅+:=

Ca 5.0mm:=Corrosion allowance(Alloy Lining Thickness)

Did 4200.0mm:=Inside diamter based on Alloy Lining of main shell

1) Basic Input Data

1. SHELL THICKNESS CALCULATIOB(INTERNAL PRESSURE)


metal insulation lining iquid nozzle packing tray s. Total WeightTop Head 19490.63 1240.33 1130.47 4738.3 26599.71 26599.71Cylinder 243607.2 7154.97 6792.57 51101.2 2615.8 234051.5 915.3 546238.51 572838.2Bottom 20836.69 1237.44 1125.73 20561.2 1373.7 44105.93 0 89240.62 662078.8Skirt 1 3164.170 3218.990 0.000 0.000 6383.16 668462Skirt 2 8226.390 8369.390 0.000 0.000 16595.78 685057.8Skirt 3 7119 7242.68 0 0 14361.68 699419.5Base 2643.08 0 0 0 2643.08 702062.5

305087.2 9048.77 71662.4 8727.7 278157.4 915.3 702062.54

Weight Total Summary for Vertical Load(kg)

E 1.0:=Weld Joint Efficient

Ltl 13100.0mm:=Length of Top T.L to Bottom T.L

tmin_thead 88.2mm=tmin_thead tuse_thead tform_r⋅:=

Top Head Minimum Thickness

tmin_bhead 90mm=tmin_bhead tuse_bhead tform_r⋅:=

Bottom Head Minimum Thickness

tform_r 0.9:=Head Forming Ratio(10%)

Did_th 4287.0mm:=Inside Diameter of Hemi Heads in Div.2, Table 4.2.5Detail 4, Joint Type 1, Joint Category A,B(Top Head)

Did_bh 4283.0mm:=Inside Diameter of Hemi Heads in Div.2, Table 4.2.5Detail 4, Joint Type 1, Joint Category A,B(Bottom Head)


Weight/Wind/Seismic Load Input(Refer to Chapter 8. for Wind/Seismic)based on results of Compress Program RunningSeismic Load shall be used in this calculation due to higher than wind load

Compressive Axial Weight Focre acting at the pointof consideration

Wver

26599.710

572838.20

668462.00

685057.80

699419.50

702062.50

⎛⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎠

kg:= Fver Wver g⋅:= Fver

2.609 105×

5.618 106×

6.555 106×

6.718 106×

6.859 106×

6.885 106×

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎠

N=

Bending Moment Focre acting at the point of consideration

Mben

4320.8800

380109.11

380120.70

425575.94

555199.11

667901.60

⎛⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎠

kg m⋅:= M Mben g⋅:= M

4.237 107×

3.728 109×

3.728 109×

4.173 109×

5.445 109×

6.55 109×

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎠

N mm⋅=

Torsion Moment Focre acting at the pointof consideration

Mtor

00000

00000

00000

00000

00000

00000

⎛⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎠

kg m⋅:= Mt Mtor g⋅:= Mt

0

0

0

0

0

0

⎛⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎠

N mm⋅=


Shear Focre acting at the point

Vshe

4121.750

57076.77

57077.34

62321.15

62860.31

63040.03

⎛⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎠

kg:= V Vshe g⋅:= V

4.042 104×

5.597 105×

5.597 105×

6.112 105×

6.164 105×

6.182 105×

⎛⎜⎜⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎟⎟⎠

N=

Angle of Force acting at the point of consideration θ 0deg:=

Angle measured around circumferential from Shear Force φ 90deg:=

Density of Hydrotest Water ρhydro 1000.0kg

m3:=

Hydrostatic Head

Hhydro Ltl Did+:= Hhydro 1.73 104× mm=


Ey 1.844 106×kgf

cm2=

Ey 180800.0N

mm2:=Elastic Modulus of Main Shell at Design Temp

Sy_hydro 3.161 103×kgf

cm2=

Sy_hydro 310.0N

mm2:=Yield Strength of Main Shell at Test Temp

Sy_516 1.489 103×kgf

cm2=

Sy_516 146.0N

mm2:=Yield Strength of Skirt Support(SA516-60)

at Design temp as Critical Conditions

Sy 2.386 103×kgf

cm2=

Sy 234.0N

mm2:=Yield Strength of Main Shell/Top Skirt Support

at Design Temp

Ku 2.1:=Coefficient of End ConnectionFree & Fixed(Skirt Support)

Lu 1.602 104× mm=Lu 2 Did_bh tuse_bhead tform_r⋅+( ) 13⋅ Ltl+:=

Assume an Unsupported Total Length[2007,Div.2,4.4.17 Figures,(a)]

Ltl 13100.0mm:=Length of Top T.L to Bottom T.L

ST 2.111 103×kgf

cm2=

ST 207.0N

mm2:=Allowable stress of main shell(at ambient)

Sn 1.238 103×kgf

cm2=

Sn 121.4N

mm2:=Allowable stress of Pipe Neck(Top/Bot Nozzles)

Connection Pipe/Elbow Pipe(SA234-WP22)

Sm7 1.587 103×kgf

cm2=

Sm7 155.6N

mm2:=Allowable stress of main shell(at 440 deg C)

425 degC=158.0MPa, 450 degC=154.0, 440 deg C=155.6MPa

2007 Sec.II, Part D, Table 5A(METRIC UNIT)

2) Allowable Stress in ASME 2007 Div.2 Code


Did_skirt 4.499 103× mm=Did_skirt Dm_sk 2tskirt−:=

I.D of Skirt Support(Corroded I.D)

Dod_skirt 4.556 103× mm=Dod_skirt Dm_sk:=

O.D of Skirt Support

Dm_sk 4.556 103× mm=Dm_sk Did_wo 2tuse_shell+:=

Outside Diameter of Main Body Shell

tskirt 28.4mm=tskirt tuse_skirt Cca_skirt−:=

Thickness of Skirt Support

Cca_skirt 1.6mm:=Corrosion Allowance of Skirt Support

tuse_skirt 30.0mm:=Used Thcikness of Skirt Support

Fic_bskirt 818.832kgf

cm2=

Fic_bskirt 80.3N

mm2=Fic_bskirt 0.55 Sy_516⋅:=

Allowable Buckling Stress(Bottom Skirt Part)In order to get critical design factor, FS=2.0 shall beused in this calculation using(Fic<0.55Sy)

Fic_tskirt 1.312 103×kgf

cm2=

Fic_tskirt 128.7N

mm2=Fic_tskirt 0.55 Sy⋅:=

Allowable Buckling Stress(Top Skirt Part)In order to get critical design factor, FS=2.0 shall beused in this calculation using (Fic< 0.55Sy)

Fic_shell 2.231 103×kgf

cm2=

Fic_shell 218.825N

mm2:=Allowable Buckling Stress(Main Shell)

Input value from 4.4.5.1 c) step 3 External pressurecalculation para in this calculation sheet


Length of Skirt Support assumed as Full Length Lu_skirt 5850.0mm:=

Yield Strength of Skirt Support(SA-516 60)at Design Temp as Critical Conditions

Sy_516 146.0N

mm2:=

Sy_516 1.489 103×kgf

cm2=

Elastic Modulus of Main Shell(SA516-60)at Design Temp

Ey_516 163800.0N

mm2:=

Ey_516 1.67 106×kgf

cm2=

Coefficient whose values is establishedfor an unbraced skirt support vessel

Cm 1.0:=


3) Thickness Calculation

Inside Diameter w/o Weld Overlay

Did_wo Did 2.Ca+:= Did_wo 4.21 103× mm=

Thickness Calculation[(2007, Div.2, 4.3.3, 4.3.3.1/(4.31 equation)]

t7_shellDid_wo

2exp

PinSm7 E⋅

⎛⎜⎝

⎞⎟⎠

1−⎛⎜⎝

⎞⎟⎠

⋅ ttol_shell+:= t7_shell 171.367mm=

Thickness Evaluation

ts_check "No Acceptable Thickness-Redesign" t7_shell tuse_shell>if

"Acceptable Thickness" otherwise

:=

ts_check "Acceptable Thickness"=


4) Combined Load Checking

(1) Combined Loading Calculation(2007, Div.2, 4.3.3.2/4.3.10/4.3.10.2 paragraph)

a) Step 1(calculation membrane stress)

Dod Did_wo 2 tuse_shell⋅+:= Dod 4.556 103× mm=

Equation(4.3.32)

σθmPin

E lnDod

Did_wo

⎛⎜⎝

⎞⎟⎠

⋅

:= σθm 153.928N

mm2=

σθm 1.57 103×kgf

cm2=

Equation(4.3.33)

σsm1E

PinDid_wo

2

Dod2 Did_wo

2−⋅ 4

Fver

π Dod2 Did_wo

2−( )⋅⋅+

32 M⋅ Dod⋅ cos θ( )⋅

π Dod4 Did_wo

4−( )⋅+

⎡⎢⎢⎣

⎤⎥⎥⎦

⋅:=

σsm

71.172

74.886

75.279

75.525

76.089

76.54

⎛⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎠

N

mm2=

Equation(4.3.34)

τ16 Mt⋅ Dod⋅

π Dod4 Did_wo

4−( )⋅:= τ

0

0

0

0

0

0

⎛⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎠

Pa=


σcheck "Acceptable Thickness for Main Body Shell"=

σcheck "No Acceptable Thickness & Re-design" max σeq( ) Sm7>if

"Acceptable Thickness for Main Body Shell" otherwise

:=

σeq

128.345

128.143

128.128

128.119

128.101

128.088

⎛⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎠

N

mm2=σeq

1

2σ1 σ2−( )2

σ2 σ3−( )2+ σ3 σ1−( )2

+⎡⎣

⎤⎦

0.5⋅:=

Equation(4.3.44)

c) Step 3(Von-mises streess calculation)

(3) Equivalent Von-mises Stress Calculation for limitation and safety creitera

σ3 6.079N

mm2=σ3 0.5 Pin( )⋅:=

Equation(4.3.43)

σ2

71.172

74.886

75.279

75.525

76.089

76.54

⎛⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎠

N

mm2=σ2 0.5 σθm σsm+ σθm σsm−( )2 4 τ2⋅+−⎡

⎣⎤⎦⋅:=

Equation(4.3.42)

σ1

153.928

153.928

153.928

153.928

153.928

153.928

⎛⎜⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎟⎠

N

mm2=σ1 0.5 σθm σsm+ σθm σsm−( )2 4 τ

2⋅++⎡

⎣⎤⎦⋅:=

Equation(4.3.31)

b) Step 2(1st/2nd/3rd pricipal stress calculation)

(2) Calculation for the principal stresses


5) Axial Compressive Stress Checking

Main Shell Buckling Evaluation

(1) Compressive Stress Checking[2007, Div.2, 4.4.12.2, b)]

Design Factor

Equation(4.4.1 thru 4.4.3)

FS 2.0 Fic_shell 0.55 Sy⋅≤if

2.407 0.741Fic_shell

Sy

⎛⎜⎝

⎞⎟⎠

⋅− 0.55 Sy⋅ Fic_shell< Sy<if

1.667 otherwise

:=

FS 1.714=

Radius of Gyration

Equation(4.4.123)

rg 0.25 Dod2 Did_wo

2+⋅:= rg 1.551 103× mm=

A. Axial Compressive Stress(Local Buckling, λc<0.15)

Equation(4.4.61 thru 4.4.64)

Fxa1SyFS

Dodtuse_shell

135.0≤if

466 Sy⋅

FS 331Dod

tuse_shell+

⎛⎜⎝

⎞⎟⎠

⋅

135Dod

tuse_shell< 600<if

0.5 Sy⋅

FS600

Dodtuse_shell

< 2000≤if

:=

Fxa1 136.518N

mm2=

Fxa1 1.392 103×kgf

cm2=


Sy 233.0N

mm2:=Allowable yield strength of support ring

(design temperaature 440 deg C)

Tring 150.0mm:=Thickness of support ring

Wb 170.0mm:=Beam width acting on support ring(sheet no. 22)

E 180800.0N

mm2:=Elastic modulus at design temp(440 deg C)

υ 0.3:=Poisson ratio

Rt_ring 2.015 103× mm=Rt_ring Rt_in Bring−:=

Inside radius of support ring

Bring 90.00mm:=Support ring width

Rt_in 2.105 103× mm=Rt_in Rin Tlay+:=

Total inside radius of main shell

Tlay 5.0mm:=Thickness of weld overlay

Rin 2100.0mm:=Shell inside radius

1. CATALYST SUPPORT GRID SUPPORT RING

[INTERNAL SUPPORT RING CALCULATION] "WEIGHT LOAD DUE TO PRESSURE DROP+VERTICAL WEIGHT"


wmax 4.733 103×N

mm=wmax

Fmaxn Wb⋅

:=

Fmax 1.609 106× N=Fmax max F1N F2N, F3N,( ):=

Maximum load among above load

w3 2.853 103×N

mm=w3

F3Nn Wb⋅

:=

F3N 9.699 105× N=F3N F3:=

F3 98898.0kgf:=Maximum reaction load among suppot beams164079kg, 136856 kg, 98898 kg(sheet no. 9)

w2 3.947 103×N

mm=w2

F2Nn Wb⋅

:=

F2N 1.342 106× N=F2N F2:=

F2 136856kgf:=Maximum reaction load among suppot beams164079kg, 136856 kg, 98898 kg(sheet no. 9)

w1 4.733 103×N

mm=w1

F1Nn Wb⋅

:=

F1N 1.609 106× N=F1N F1:=

F1 164079.0kgf:=Maximum reaction load among suppot beams164079kg, 136856 kg, 98898 kg(sheet no. 9)

n 2:=No. reaction point

Unit load acting on support ring(assumed as loading subject to edge of support ring

2. LOAD CALCULATION


3. PROPERTY CONSTANT CALCULATION (BASED ON ROARK's FORMULA FOR STRESS/STRAIN, 7TH, P461/CASE 1e)

C11 υ+

2

Rt_ringRt_in

⋅ lnRt_in

Rt_ring

⎛⎜⎝

⎞⎟⎠

⋅1 υ−

4

Rt_inRt_ring

Rt_ringRt_in

−⎛⎜⎝

⎞⎟⎠

⋅+:=

C1 0.042=

C412

1 υ+( )Rt_ringRt_in

⋅ 1 υ−( )Rt_in

Rt_ring⋅+

⎡⎢⎣

⎤⎥⎦

⋅:= C4 0.988=

C712

1 υ2

−( )⋅Rt_in

Rt_ring

Rt_ringRt_in

−⎛⎜⎝

⎞⎟⎠

⋅:= C7 0.04=

L3Rt_ring4 Rt_in⋅

Rt_ringRt_in

⎛⎜⎝

⎞⎟⎠

2

1+⎡⎢⎢⎣

⎤⎥⎥⎦

lnRt_in

Rt_ring

⎛⎜⎝

⎞⎟⎠

⋅Rt_ringRt_in

⎛⎜⎝

⎞⎟⎠

2

+ 1−⎡⎢⎢⎣

⎤⎥⎥⎦

⋅:=

L3 1.274 10 5−×=

L6Rt_ring4 Rt_in⋅

Rt_ringRt_in

⎛⎜⎝

⎞⎟⎠

2

1− 2 lnRt_in

Rt_ring

⎛⎜⎝

⎞⎟⎠

⋅+⎡⎢⎢⎣

⎤⎥⎥⎦

⋅:= L6 8.878 10 4−×=

L9Rt_ringRt_in

1 υ+

2ln

Rt_inRt_ring

⎛⎜⎝

⎞⎟⎠

⋅1 υ−

41

Rt_ringRt_in

⎛⎜⎝

⎞⎟⎠

2

−⎡⎢⎢⎣

⎤⎥⎥⎦

⋅+⎡⎢⎢⎣

⎤⎥⎥⎦

⋅:= L9 0.041=


4. BENDING STRESS CALCULATION

Plate constant calculation

DE Tring

3⋅

12 1 υ2

−( )⋅:= D 5.588 1010× N mm⋅=

Moment calculation

M wmaxRt_in⋅ L9C7 L6⋅

C4−

⎛⎜⎝

⎞⎟⎠

⋅:= M 4.101 105× N=

Bending stress

σb6 M⋅

Tring2

:= σb 109.372N

mm2=

Allowable bending stress checking(66% Sy)

σb_check "Problem & Re-design" σb 0.66 Sy⋅>if

"No problem under maximum load" otherwise

:=

σb_check "No problem under maximum load"=


σs_check "No problem under maximum load"=

σs_check "Problem & Re-design" Ss 0.4 Sy⋅>if

"No problem under maximum load" otherwise

:=

Allowable shear stress checking(40% Sy)

Ss 30.201N

mm2=Ss

QTring

:=

Maximum shear stress on unit ring

Q 4.53 103×N

mm=Q

wmaxRt_ring⋅

Rt_in:=

Unit shear force(force per unit of circumferential length)

6. SHEAR STRESS CALCULATION

σmax_check "No problme under maximum load"=

σmax_check "Problem & Re-design" δmax2 Rt_in⋅( )

1000>if

"No problme under maximum load" otherwise

:=

Allowable deflection checking(0.1% ID)

δmax 0.02mm=δmaxwmaxRt_in

3⋅

D

C1 L6⋅

C4L3−

⎛⎜⎝

⎞⎟⎠

⋅:=

Maximum Deflection under maximum load

5. DEFLECTION CALCULATION

Korea Engineering Consulting., Inc.

Tel. (02) 3486-9324, 9377 Fax. (02) 3486-9325

Rm.3F, Seonggyun Building, 1359-13, Seocho-Dong, Seocho-Gu, Seoul, Korea137-863 서울특별시 서초구 서초동 1359-13 성균빌딩 3층 e-mail : [email protected]

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