NORSOK STANDARD DESIGN OF STEEL STRUCTURES

Transcription

1 NORSOK STANDARD DESIGN OF STEEL STRUCTURES N-004 Rev. 1, December 1998

2 This NORSOK standard is developed by NTS with broad industry participation. Please note that whilst every eort has been made to ensure the accuracy o this standard, neither OLF nor TBL or any o their members will assume liability or any use thereo NTS is responsible or the administration and publication o this standard. Norwegian Technology Standards Institution Oscarsgt. 0, Postbox 707 Majorstua N-0306 Oslo, NORWAY Telephone: Fax: norsok@nts.no Website: Copyrights reserved

3 Rev. 1, December 1998 CONTENTS FOREWORD 5 INTRODUCTION 5 1 SCOPE 7 NORMATIVE REFERENCES 8 3 DEFINITIONS, ABBREVIATIONS AND SYMBOLS Deinitions 9 3. Abbreviations Symbols 10 4 GENERAL PROVISIONS 16 5 STEEL MATERIAL SELECTION AND REQUIREMENTS FOR NON-DESTRUCTIVE TESTING Design class Steel quality level Welding and non-destructive testing 18 6 ULTIMATE LIMIT STATES General 1 6. Ductility 6.3 Tubular members General 6.3. Axial tension Axial compression Bending Shear Hydrostatic pressure Hoop buckling Ring stiener design Material actor Tubular members subjected to combined loads without hydrostatic pressure Axial tension and bending Axial compression and bending Interaction shear and bending moment Interaction shear, bending moment and torsional moment Tubular members subjected to combined loads with hydrostatic pressure Axial tension, bending, and hydrostatic pressure Axial compression, bending, and hydrostatic pressure Tubular joints General Joint classiication Strength o simple joints General Basic resistance Strength actor Q u 40 NORSOK standard Page 1 o 488

4 Rev. 1, December Chord action actor Q Design axial resistance or X and Y joints with joint cans Strength check Overlap joints Ringstiened joints Cast joints Strength o conical transitions General Design stresses Equivalent design axial stress in the cone section Local bending stress at unstiened junctions Hoop stress at unstiened junctions Strength requirements without external hydrostatic pressure Local buckling under axial compression Junction yielding Junction buckling Strength requirements with external hydrostatic pressure Hoop buckling Junction yielding and buckling Ring design General Junction rings without external hydrostatic pressure Junction rings with external hydrostatic pressure Intermediate stiening rings Design o plated structures General Failure modes Deinitions Buckling o plates Lateral loaded plates Buckling o unstiened plates Buckling o unstiened plates under longitudinally uniorm compression Buckling o unstiened plates with variable longitudinal stress Buckling o unstiened plates with transverse compression Buckling o unstiened biaxially loaded plates with shear Stiened plates General Forces in the idealised stiened plate Eective plate width Characteristic buckling strength o stieners Torsional buckling o stieners Interaction ormulas or axial compression and lateral pressure Resistance parameters or stieners Resistance o stieners with predominantly bending Buckling o girders General Girder orces Resistance parameters or girders Eective widths o girder plates 75 NORSOK standard Page o 488

5 Rev. 1, December Torsional buckling o girders Local buckling o stieners, girders and brackets Local buckling o stieners and girders Requirements to web stieners Buckling o brackets Design o cylindrical shells Design against uunstable racture General Determination o maximum allowable deect size 80 7 SERVICEABILITY LIMIT STATES General 8 7. Out o plane delection o plates 8 8 FATIGUE LIMIT STATES General Methods or atigue analysis 83 9 ACCIDENTAL DAMAGE LIMIT STATES REASSESSMENT OF STRUCTURES General Extended atigue lie Material properties Corrosion allowance Foundations Damaged and corroded members General Dented tubular members Axial tension Axial compression Bending Combined loading Corroded members Cracked members and joints General Partially cracked tubular members Tubular joints with cracks Repaired and strengthened members and joints General Grouted tubular members Axial tension Axial compression Bending Combined axial tension and bending Combined axial compression and bending Grouted joints Plates and cylindrical shells with dents and permanent delections Plates with permanent delections Longitudinally stiened cylindrical shells with dents REFERENCES 98 NORSOK standard Page 3 o 488

6 Rev. 1, December COMMENTARY 99 Annex A Design against accidental actions 117 Annex B Buckling strength o shells 179 Annex C Fatigue strength analysis 13 Appendix 1 Classiication o structural details 65 Appendix SCFS or tubular joints 87 Appendix 3 SCFS or cut-outs 99 Annex K Special design provisions or jackets 35 Annex L Special design provisions or ship shaped units 361 Annex M Special design provisions or column stabilized units 411 Annex N Special design provisions or tension leg platorms 455 NORSOK standard Page 4 o 488

7 Errata as per to N-004 Desig o Steel Structures Rev. 1, December 1998 ERRATA TO NORSOK STANDARD DESIGN OF STEEL STRUCTURES, N-004 REV 1, DEC 1998 Updated or misprints as noted per , , and Page 7 (per and ): At the end o paragraph add: Torsional buckling o langed ring stieners may be excluded as a possible ailure mode provided that: 3.5h b Eh 10 + r y below equation 6.5. add N Sd is negative i in tension. Page 30 (per ): add ater equation 6.3: M = M + M provided the same Sd y,sd z,sd variation in M y,sd and M z,sd along the member length. Page 3 ( per and ): equation 6.40 change γ m to γ M. NORSOK Standard Page 1 o 6

8 Errata as per to N-004 Desig o Steel Structures Rev. 1, December 1998 Above equation 6.41, change in the irst inequality cle to he to read: he σ c,sd > 0,5 γ M Page 46 (per ): In equation 6.71 change cj to clj. In the description or cj change to: clj = corresponding tubular or cone characteristic axial local compressive strength. Page 47 (per ): In paragraph change the reerence to the equations in section to equation 6.44 or 6.51 or method A or B respectively. Page 55 (per ): In equation 6.87 change to: σ x,rd =C x y /γ M Page 56 (per ): In equation 6.91 change to σ x,sd σ x,rd ; The ollowing line: where σ c,sd = longitudinal compressive stress( tensile stress to be set equal to zero) should be deleted. Page 60 (per ): Change equation by adding the index l or the parameters λ τ and k l so s 1 y the equation reads: λ τl = t k 35 1 Insert new equation: λ = l y τg t k 35 g l NORSOK Standard Page o 6

9 Errata as per to N-004 Desig o Steel Structures Rev. 1, December 1998 In equation change inequality sign to l<l G in irst line and l>l G or second line. In equation invert the ratio l/s to read s/l or both lines so the equation reads: k l = s = l s l,or l s 4, or l < s Page 64 (per ): In igure 6-17 the correct distance or e is to center o web plate. Page 68 (per ): Add beore equation : qsdl * I NSd z then: 8 Ater equation add: qsdl * I < NSd z then: 8 N N Sd ks,rd N N Sd Rd + N M Sd z s,rd * q Sdl 8 N 1 N Sd E 1, and N N Sd kp,rd + N M Sd z p,rd * q Sd 8 N 1 N Sd E l 1 NORSOK Standard Page 3 o 6

10 Errata as per to N-004 Desig o Steel Structures Rev. 1, December 1998 Page 71 (per ): In the description or n G change the word stieners to: stiener spans Add to the listing o symbols: I s = moment o inertia o stiener and plate with plate width equal to s. Page 93 (per ): Below equation In the explanation to N Sd : Change the wording compression negative to: compression positive. Annex A: Page 138 (per ): Equation A.3.3 exchange: ε cr with ε y and ε y with ε cr. Annex B: Page 00 (per ): In equation B.5,4 change index o parameter r r to r. Page 07 (per ): In the description or l T the parameter t should be changed to h in the square root so the correct description is: l T = or ring stieners: distance (arc length) between tripping brackets l T need not be taken greater than π rh or the analysis or longitudinal stieners: distance between ring rames. NORSOK Standard Page 4 o 6

11 Errata as per to N-004 Desig o Steel Structures Rev. 1, December 1998 Page 08 (per ): The sign o inequality in equation B.5.78 and B.5.83 should be changed rom greater or equal to less or equal Annex C: Page (per ): In the description o the symbols used in equation C..6 change: tre with t re. Page 33 (per ): Equation C..10 is valid or T<t Page 38 (per ): the numbering o paragraph C should be changed to C Page 4 (per ): In Table C.-4 add in the column or Tolerance requirement or Single side and Double side weld with hot spot at surace ( the two lower rows in the table) the ollowing: e min. (0.15t, 4 mm) Page 61 (per ): Insert ater equation C.7.3 the ollowing expression: σ 0 q( σ 0,h) = 1 h (ln n ) 0 Annex K: Table o contents gives wrong page numbers. (per ) NORSOK Standard Page 5 o 6

12 Errata as per to N-004 Desig o Steel Structures Rev. 1, December 1998 Page 330 (per ): The numbering o the Notes to Table K.-1 should be renumbered so b)in line two should be deleted and apply to line 4 Outitting structures.note d) should be changed to c). Starting with I multilegged note d) should apply to note g),note e) apply to h) and ) g) and h) should be deleted. The notes should be: a) Local areas o welds with high utilisation shall be marked with rames showing areas or mandatory NDT when partial NDT are selected. Inspection categories depending on access or in-service inspection and repair. b) Outitting structures are normally o minor importance or the structural saety and integrity. However, in certain cases the operational saety is directly inluenced by the outitting and special assessment is required in design and abrication. A typical example is guides and supports or gas risers. c) I multilegged jacket with corner legs supporting a oundation systems; Upper part o corner legs and inner legs: DC 4, III, B or C Lower part o corner legs: DC, II, A or B d) I multilegged jacket where each leg supporting a oundation system: DC 4, III, B or C e) I one or two pile(s) per leg: DC, II. Pages (per ): Paragraph K.6.1. up to paragraph K6.4 are given wrong item numbers, shall be read as K.6 instead o K.1 Annex L: Table o contents gives wrong page numbers. (per ) Annex M: Table o contents gives wrong page numbers. (per ) Annex N: Table o contents gives wrong page numbers. (per ) NORSOK Standard Page 6 o 6

13 Rev. 1, December 1998 FOREWORD NORSOK (The competitive standing o the Norwegian oshore sector) is the industry initiative to add value, reduce cost and lead-time and eliminate unnecessary activities in oshore ield developments and operations. The NORSOK standards are developed by the Norwegian petroleum industry as a part o the NORSOK initiative and supported by OLF (The Norwegian Oil Industry Association) and TBL (Federation o Norwegian Engineering Industries). NORSOK standards are administered and issued by NTS (Norwegian Technology Standards Institution). The purpose o NORSOK standards is to contribute to meet the NORSOK goals, e.g. by replacing individual oil company speciications and other industry guidelines and documents or use in existing and uture petroleum industry developments. The NORSOK standards make extensive reerences to international standards. Where relevant, the contents o a NORSOK standard will be used to provide input to the international standardisation process. Subject to implementation into international standards, the NORSOK standard will be withdrawn. Annex A, B, C, K, L, M and N are normative parts o this standard. INTRODUCTION This NORSOK standard provides guidelines and requirements or how to design and document oshore steel structures. The standard is intended to ulil NPD Regulations relating to loadbearing structures in the petroleum activities /1/. The design principles ollow the requirements in ISO The standard gives provisions or oshore structures and reerences Norwegian standard NS 347 and NS-ENV Eurocode 3. Either code may be used or design o parts where relevant. NORSOK standard Page 5 o 488

14 Rev. 1, December SCOPE This standard speciies guidelines and requirements or design and documentation o oshore steel structures. The standard is applicable to all type o oshore structures made o steel with a speciied minimum yield strength less or equal to 500 MPa. For steel with higher characteristic yield strength see Chapter 1 Commentary. NORSOK standard Page 6 o 488

15 Rev. 1, December 1998 NORMATIVE REFERENCES The ollowing standards include provisions, which through reerence in this text, constitute provisions o this NORSOK standard. Latest issue o the reerences shall be used unless otherwise agreed. Other recognised standards may be used provided it can be shown that they meet or exceed the requirements o the standards reerenced below. DNV Rules or classiication o ships DNV Rules or planning and executions o marine operations. ISO Oshore structures part 1: General requirements. ISO 3010 Basis or design o structures - seismic action o structures. NORSOK G-001 Soil investigation. NORSOK J-003 Marine operations NORSOK M-001 Materials selection. NORSOK M-101 Structural steel abrication. NORSOK M-10 Material data sheets or structural steel. NORSOK M-1 Cast and orged steel or structural components NORSOK M-501 Surace preparation and protective coating. NORSOK M-503 Cathodic protection. NORSOK N-001 Structural design. NORSOK N-00 Collection o metocean data. NORSOK N-003 Action and action eects. NORSOK N-005 Condition monitoring. NORSOK S-001 Technical saety. NORSOK U-001 Subsea structures and piping systems. NORSOK Z-001 Documentation or operation. NPD Regulations relating to loadbearing structures in the petroleum activities. NS 347 Steel structures. Design rules NS 3481 Soil investigation and geotechnical design or marine structures. NS 18 Weights engineering, terminology. NS 19 Weights engineering, requirements or weight reports. NS 130 Weights engineering, speciication or weighing o major assemblies. NS 131 Weights engineering, speciication or weight data rom suppliers and weighing o bulk and equipment. NS-ENV Eurocode 3: Design o steel structures part 1-1: General rules and rules or buildings Note: The reerence to DNV Rules applies to the technical provisions therein. Any requirement therein or classiication, certiication or third party veriication is not part o this NORSOK standard and may be considered as a separate service. Wherever the terms: agreement, acceptance or consideration etc. appear in the DNV Rules they shall be taken to mean agreement, acceptance or consideration by the Client/Purchaser or any other speciically designated party. Likewise, any statement such as: to be submitted to DNV, shall be taken to mean: to be submitted to Client/Purchaser or any other speciically designated party. NORSOK standard Page 7 o 488

16 Rev. 1, December DEFINITIONS, ABBREVIATIONS AND SYMBOLS 3.1 Deinitions Normative reerences Inormative reerences Shall Should May Can Design Premises Norwegian petroleum activities Operator Petroleum activities Principal Standard Shall mean normative in the application o NORSOK standards. Shall mean inormative in the application o NORSOK standards. Shall is an absolute requirement which shall be ollowed strictly in order to conorm with the standard. Should is a recommendation. Alternative solutions having the same unctionality and quality are acceptable. May indicates a course o action that is permissible within the limits o the standard (a permission). Can-requirements are conditional and indicates a possibility open to the user o the standard. A set o project speciic design data and unctional requirements which are not speciied or are let open in the general standard. Petroleum activities where Norwegian regulations apply. A company or an association which through the granting o a production licence is responsible or the day to day activities carried out in accordance with the licence Oshore drilling, production, treatment and storage o hydrocarbons. A standard with higher priority than other similar standards. Similar standards may be used as supplements, but not as alternatives to the Principal Standard. Recognised classiication society A classiication society with recognised and relevant competence and experience rom the petroleum activities, and established rules and procedures or classiication/certiication o installations used in the petroleum activities. Veriication Examination to conirm that an activity, a product or a service is in accordance with speciied requirements. 3. Abbreviations API American Petroleum Institute. BSI British Standards Institution. DNV Det Norske Veritas. ECCS European Convention or Constructional Steelwork. ISO International Organisation or Standardisation. NPD Norwegian Petroleum Directorate. 3.3 Symbols A cross sectional area, accidental action, parameter, ull area o the brace /chord intersection NORSOK standard Page 8 o 488

17 Rev. 1, December 1998 A c cross sectional area o composite ring section, cracked area o the brace / chord intersection o a tubular joint A Corr corroded part o the cross-section A Crack crack area A e eective area A cross sectional area o lange A G cross-sectional area o girder, cross-sectional area o the grout A R net area o circular part o a dented cylinder A s eective cross sectional area o stiener, gross steel area o a grouted, composite section A w cross sectional area o web B hoop buckling actor C rotational stiness, actor C e critical elastic buckling coeicient C h elastic hoop buckling strength actor C m reduction actor C my, C mz reduction actor corresponding to the member y and z axis respectively C x, C xg, C xs actors C y, C yg, C ys actors C τ, C τg,c τs actors C 0 actor CTOD c characteristic value o crack opening CTOD cd design value o crack opening D outer diameter o chord, cylinder diameter at a conical transition, outside diameter D c diameter to centeroid o composite ring section D e equivalent diameter D j diameter at junction D max maximum measured diameter D min minimum measured diameter D nom nominal diameter D s outer cone diameter E Young s modulus o elasticity, MPa E G modulus o elasticity o the grout E S modulus o elasticity o the steel F AR correction actor or axial resistance and bending resistance o a cracked tubular joint G shear modulus I, I z, I s moment o inertia, moment o inertia o undamaged section I c moment o inertia or ring composite section I ch moment o inertia I ct moment o inertia o composite ring section with external hydrostatic pressure and with eective width o lange I dent moment o inertia o a dented cross-section I e eective moment o inertia I G eective moment o inertia or the grout in a grouted, composite cross section I p polar moment o inertia I po polar moment o inertia = r da where r is measured rom the connection between the stiener and the plate. eective moment o inertia or the steel in a grouted, composite cross section I S NORSOK standard Page 9 o 488

18 Rev. 1, December 1998 I s moment o inertia o web stiener K a actor K Ic characteristic racture toughness (mode I) K Icd design racture toughness L length, distance L 1 distance to irst stiening ring in tubular section L c distance to irst stiening ring in cone section along cone axis L G length o girder L Gk buckling length o girder L GT distance between lateral support o girder L GT0 limiting distance between lateral support o girder L r ring spacing M 1,Sd design bending moment about an axis parallel to the lattened part o a dented tubular section, design end moment M,Sd design bending moment about an axis perpendicular to the lattened part o a dented tubular section, design end moment M crack,rd bending resistance o a cracked tubular joint M dent,rd bending resistance o dented tubular section M g,rd bending resistance o the grouted member M p,rd design bending moment resistance on plate side M pl,rd design plastic bending moment resistance M Rd design bending moment resistance M red,rd reduced design bending moment resistance due to torsional moment M Sd design bending moment M s,rd design bending moment resistance on stiener side M T,Sd design torsional moment M T,Rd design torsional moment resistance M y,rd design in-plane bending moment resistance M y,sd in-plane design bending moment M z,rd design out-o-plane bending moment resistance M z,sd out-o-plane design bending moment N c,rd design axial compressive resistance N can,rd design axial resistance o can N cg,rd axial compression resistance o a grouted, composite member N cl characteristic local buckling resistance N cl characteristic local buckling resistance N cl,rd design local buckling resistance N crack,rd axial resistance o a cracked tubular joint N dent,rd axial resistance o the dented tubular section N E Euler buckling strength N E,dent Euler buckling strength o a dented tubular member, or buckling in-line with the dent N Eg elastic Euler buckling load o a grouted, composite member N Ey,N Ez Euler buckling resistance corresponding to the member y and z axis respectively N ks,rd design stiener induced axial buckling resistance N kp,rd design plate induced axial buckling resistance N Sd design axial orce N t,rd design axial tension resistance N tg,rd axial tension resistance o a grouted, composite section axial yield resistance o a grouted, composite member N ug NORSOK standard Page 10 o 488

19 Rev. 1, December 1998 N x,rd N x,sd N y,rd N y,sd P Sd Q Q Q g Q u Q yy Q β R R d R k S d S k T T c T n V Rd V Sd W W eg W ep W es W R W tr Z a a i a m a u b b e c d d 0, d 1, d e e e G e S bg c cg ch,rd cj cl design axial resistance in x direction design axial orce in x direction design axial resistance in y direction design axial orce in y direction design lateral orce actor chord action actor chord gap actor strength actor angle correction actor geometric actor, tubular joint geometry actor radius, radius o chord, radius o conical transition design resistance characteristic resistance design action eect characteristic action eect thickness o tubular sections, thickness o chord chord-can thickness nominal chord member thickness design shear resistance design shear orce elastic section modulus eective section modulus on girder lange side eective section modulus on plateside eective section modulus on stienerside elastic section modulus o the circular part o a dented cylinder elastic section modulus o a transormed, composite tubular cross section plastic section modulus stiener length, crack depth, weld throat, actor initial crack depth maximum allowable deect size calculated crack depth at unstable racture plate span measured to centre o support plate, actor, width eective width actor diameter o tubular cross section, brace diameter distance distance rom neutral axis o the cylindrical part o the dented cylinder to the neutral axis o the original, intact cylinder lange eccentricity distance rom centroid o dented grout section to the centroid o the intact grout section distance rom centroid o dented steel section to the centroid o the intact steel section characteristic bending strength o grouted member characteristic axial compressive strength characteristic cube strength o grout design axial compressive strength in the presence o hydrostatic pressure corresponding tubular or cone characteristic compressive strength characteristic local buckling strength NORSOK standard Page 11 o 488

20 Rev. 1, December 1998 cl,rd design local buckling strength, design local buckling strength o undamaged cylinder clc local buckling strength o conical transition cle characteristic elastic local buckling strength cr critical buckling strength d design yield strength E Euler buckling strength Epx, Epy Euler buckling strength corresponding to the member y and z axis respectively Epτ Euler buckling shear strength ET torsional elastic buckling strength Ey, Ez Euler buckling strength corresponding to the member y and z axis respectively h characteristic hoop buckling strength he elastic hoop buckling strength or tubular section hec elastic hoop buckling strength or cone section h,rd design hoop buckling strength k, kx, ky, kp characteristic buckling strength m characteristic bending strength m,rd design bending strength m,red reduced bending strength due to torsional moment mh,rd design bending resistance in the presence o external hydrostatic pressure r characteristic strength T characteristic torsional buckling strength TG characteristic torsional buckling strength or girders th,rd design axial tensile resistance in the presence o external hydrostatic pressure y characteristic yield strength y,b characteristic yield strength o brace y,c characteristic yield strength o chord g gap h height i radius o gyration i e eective radius o gyration k, k g,k l, k σ buckling actor l, l L length, element length l e eective length l l length o longitudinal web stiener l t length o transverse web stiener l T distance between sideways support o stiener m modular ration o E S /E G m q exponent in resistance equation or cracked tubular joints n number o stieners p lateral pressure giving yield in extreme ibre o a continuous stiener p Sd design hydrostatic pressure, design lateral pressure p 0 equivalent lateral pressure q design lateral lineload q Sd design lateral lineload r radius, actor s element width, stiener spacing s e eective width t thickness bracket thickness t b NORSOK standard Page 1 o 488

21 Rev. 1, December 1998 t c t e t t w z p, z t z * α α α β γ γ d γ γ M γ m γ n δ δ δ δ max 0 cone thickness eective thickness o chord and internal pipe o a grouted member lange thickness web thickness distance distance coeicient, angle between cylinder and cone geometrical coeicient, actor exponent in stability equation or dented tubular members circumerential angle o dented / corroded / cracked area o tubular section actor actor material actor to take into account model uncertainties partial actor or actions resulting material actor material actor to take into account uncertainties in material properties material actor to take into account the consequence o ailure dent depth equivalent dent depth the sagging in the inal state relative to the straight line joining the supports. the pre-camber δ1 the variation o the delection o the beam due to the permanent loads immediately ater loading δ the variation o the delection o the beam due to the variable loading plus any time dependent deormations due to the permanent load y 1 out-o-straightness o a dented member, measured perpendicular to the dent (along an axis parallel to the dent) y out-o-straightness o a dented member, measured in-line with the dent (along an axis perpendicular with to the dent) ε actor η hoop buckling actor θ angle θ c the included angle or the compression brace θ t the included angle or the tension brace λ reduced slenderness, column slenderness parameter λ e reduced equivalent slenderness λ G reduced slenderness λ p reduced plate slenderness λ s reduced slenderness, shell slenderness parameter λ T reduced torsional slenderness λ TG reduced torsional slenderness or girders λ τ reduced slenderness µ coeicient, geometric parameter ν Poisson s ratio ξ actor ξ correction actor or axial resistance o the dented tubular section ξ C M correction actor or bending resistance o the dented tubular section NORSOK standard Page 13 o 488

22 Rev. 1, December 1998 ξ δ, ξ m ρ σ a,sd σ ac,sd σ at,sd σ c,sd σ equ,sd σ h,sd σ hc,sd σ hj,sd σ j,sd σ m,sd σ mc,sd σ mlc,sd σ mlt,sd σ mt,sd σ my,sd σ mz,sd σ p,sd σ tot,sd σ q,sd σ x,sd σ y,sd σ y1,sd σ y,sd τ τ ceg, τ cel τ crg, τ crl τ Sd τ T,Sd ψ, ψ x, ψ y actors φ actor empirical actors or characteristic bending strength o grouted member rotational stiness actor design axial stress in member design axial stress including the eect o the hydrostatic capped end axial stress design axial stress in tubular section at junction due to global actions maximum combined design compressive stress, design axial stress in the damaged cylinder equivalent design axial stress within the conical transition design hoop stress due to the external hydrostatic pressure design hoop stress at unstiened tubular-cone junctions due to unbalanced radial line orces net design hoop stress at a tubular cone junction design von Mises equivalent stress design bending stress design bending stress at the section within the cone due to global actions local design bending stress at the cone side o unstiened tubular-cone junctions local design bending stress at the tubular side o unstiened tubular-cone junctions design bending stress in tubular section at junction due to global actions design bending stress due to in-plane bending design bending stress due to out-o-plane bending design hoop stress due to hydrostatic pressure total design stress capped end axial design compression stress due to external hydrostatic pressure design stress in x direction design stress in y direction larger design stress in y direction (tensile stresses taken as negative) smaller design stress in y direction (tensile stresses taken as negative) actor elastic buckling stress critical shear stress design shear stress shear stress due to design torsional moment NORSOK standard Page 14 o 488

23 Rev. 1, December GENERAL PROVISIONS All relevant ailure modes or the structure shall be identiied and it shall be checked that no corresponding limit state is exceeded. In this standard the limit states are grouped into: Serviceability limit states Ultimate limit states Fatigue limit states Accidental limit states For deinition o the groups o limit states, reerence is made to NPD Regulation relating to loadbearing structures in the petroleum activity or ISO The dierent groups o limit states are addressed in designated chapters o this standard. In general, the design needs to be checked or all groups o limit states. The general saety ormat may be expressed as: Sd R d (4.1) where: S d = Sk γ Design action eect R d = R k γm Design resistance S k = Characteristic action eect γ = partial actor or actions R k = Characteristic resistance γ = γ γ γ Resulting material actor M m n d γ m = Material actor to take into account uncertainties in material properties γ n = Material actor to take into account the consequence o ailure γ = Material actor to take into account model uncertainties. d In this standard the values o the resulting material actor are given in the respective chapters. General requirements or structures are given in NORSOK N-001. Determination o actions and action eects shall be according to NORSOK N-003. The steel abrication shall be according to the requirements in NORSOK M-101. NORSOK standard Page 15 o 488

24 Rev. 1, December STEEL MATERIAL SELECTION AND REQUIREMENTS FOR NON-DESTRUCTIVE TESTING 5.1 Design class Selection o steel quality and requirements or inspection o welds shall be based on a systematic classiication o welded joints according to the structural signiicance and complexity o joints. The main criterion or decision o design class (DC) o welded joints is the signiicance with respect to consequences o ailure o the joint. In addition the geometrical complexity o the joint will inluence the DC selection. The selection o joint design class shall be in compliance with Table 5-1 or all permanent structural elements. A similar classiication may also be used or temporary structures. Table 5-1 Classiication o structural joints and components Design Class 1) Joint complexity ) Consequences o ailure DC1 DC High Low Applicable or joints and members where ailure will have substantial consequences 3) and the structure possesses limited residual strength. 4). DC3 DC4 High Low Applicable or joints and members where ailure will be without substantial consequences 3) due to residual strength. 4). DC5 Any Applicable or joints and members where ailure will be without substantial consequences. 3) Notes: 1) Guidance or classiication can be ound in Annex K, L, M and N. ) High joint complexity means joints where the geometry o connected elements and weld type leads to high restraint and to triaxial stress pattern. E.g., typically multiplanar plated connections with ull penetration welds 3) Substantial consequences in this context means that ailure o the joint or member will entail: Danger o loss o human lie; Signiicant pollution; Major inancial consequences. 4) Residual strength means that the structure meets requirements corresponding to the damaged condition in the check or Accidental Damage Limit States, with ailure in the actual joint or component as the deined damage. See Commentary. 5. Steel quality level Selection o steel quality level or a structural component shall normally be based on the most stringent DC o joints involving the component. Through-thickness stresses shall be assessed. The minimum requirements or selection o steel material are ound in Table 5-. Selection o a better steel quality than the minimum required in design shall not lead to more stringent requirements in abrication. NORSOK standard Page 16 o 488

25 Rev. 1, December 1998 The principal standard or speciication o steels is NORSOK M-10, Material data sheets or rolled structural steel. Material selection in compliance with NORSOK M-10 assures toughness and weldability or structures with an operating temperature down to -14 C. Cast and orged steels shall be in accordance with recognised standards. I steels o higher speciied minimum yield strength than 500 MPa or greater thickness than 150 mm are selected, the easibility o such a selection shall be assessed in each case. Traceability o materials shall be in accordance with NORSOK Z-001, Documentation or operation. Table 5- Correlation between design classes and steel quality level Design Class Steel Quality Level I II III IV DC1 X DC (X) X DC3 (X) X DC4 (X) X DC5 X (X) = Selection where the joint strength is based on transerence o tensile stresses in the through thickness direction o the plate. See Commentary. 5.3 Welding and non-destructive testing The required racture toughness level shall be determined at the design stage or joints with plate thickness above 50 mm when steel quality level I and II are selected. The extent o non-destructive examination during abrication o structural joints shall be in compliance with the inspection category. The selection o inspection category or each welded joint shall be in accordance with Table 5-3 and Table 5-4 or joints with low and high atigue utilisation respectively. Welds in joints below 150 m waterdepth should be assumed inaccessible or in-service inspection. The Principal Standard or welder and welding qualiication, welding perormance and nondestructive testing is NORSOK M-101, Structural Steel Fabrication. NORSOK standard Page 17 o 488

26 Rev. 1, December 1998 Table 5-3 Determination o inspection category or details with low atigue utilisation 1). Design Class Type o and level o stress and direction in relation to welded joint. Inspection category ) Welds subjected to high tensile stresses transverse to the weld. 6) A DC1 and DC Welds with moderate tensile stresses transverse to the weld 7) and/or high shear stresses. 3) B Welds with low tensile stresses transverse to the weld and/or moderate shear stress. 8) C 4) Welds subjected to high tensile stresses transverse to the weld. 6) B 3) DC3 and DC4 DC5 Welds with moderate tensile stresses transverse to the weld and/or high shear stresses. 7) C 4) Welds with low tensile stresses transverse to the weld and/or moderate shear stress. 8) D 5) All load bearing connections. D Non load bearing connections. E Notes: 1) Low atigue utilisation means connections with calculated atigue lie longer than 3 times the required atigue lie (Design atigue lie multiplied with the Design Fatigue Factor DFF). ) It is recommended that areas o the welds where stress concentrations occur be marked as mandatory inspection areas or B, C and D categories as applicable. 3) Welds or parts o welds with no access or in-service inspection and repair should be assigned inspection category A. 4) Welds or parts o welds with no access or in-service inspection and repair should be assigned inspection category B. 5) Welds or parts o welds with no access or in-service inspection and repair should be assigned inspection category C. 6) High tensile stresses mean ULS tensile stresses in excess o 0.85 o design stress. 7) Moderate tensile stresses mean ULS tensile stresses between 0.6 and 0.85 o design stress. 8) Low tensile stresses mean ULS tensile stresses less than 0.6 o design stress. NORSOK standard Page 18 o 488

27 Rev. 1, December 1998 Table 5-4 Determination o inspection category or details with high atigue utilisation 1). Design Class Direction o dominating principal stress Inspection category 3) Welds with the direction o the dominating dynamic principal stress transverse to the weld ( between 45 and 135 ) A ) DC1 and DC Welds with the direction o the dominating dynamic principal stress in the direction o the weld ( between -45 and 45 ) B 4) Welds with the direction o the dominating dynamic principal stress transverse to the weld ( between 45 and 135 ) B 4) DC3 and DC4 Welds with the direction o the dominating dynamic principal stress in the direction o the weld ( between -45 and 45 ) C 5) DC5 Welds with the direction o the dominating dynamic principal stress transverse to the weld ( between 45 and 135 ) Welds with the direction o the dominating dynamic principal stress in the direction o the weld ( between -45 and 45 ) D E Notes: 1) High atigue utilisation means connections with calculated atigue lie less than 3 times the required atigue lie (Design atigue lie multiplied with the Design Fatigue Factor DFF). ) Buttwelds with high atigue utilisation and Stress Concentration Factor (SCF) less than 1.3 need stricter NDT acceptance criteria. Such criteria need to be developed in each case. 3) For joints in inspection categories B, C or D, the hot spot regions (regions with highest stress range) at welds or areas o welds o special concern shall be addressed with individual notations as mandatory or selected NDT methods. 4) Welds or parts o welds with no access or in-service inspection and repair should be assigned inspection category A. 5) Welds or parts o welds with no access or in-service inspection and repair should be assigned inspection category B. NORSOK standard Page 19 o 488

28 Rev. 1, December ULTIMATE LIMIT STATES 6.1 General This chapter gives provisions or checking o Ultimate Limit States or typical structural elements used in oshore steel structures, where ordinary building codes lack relevant recommendations. Such elements are tubular members, tubular joints, conical transitions and some load situations or plates and stiened plates. For other types o structural elements NS 347 or NS-ENV (Eurocode 3) apply. The material actor γ Μ is 1.15 or ultimate limit states unless noted otherwise. The material actors according to Table 6-1 shall be used i NS 347 or Eurocode 3 is used or calculation o structural resistance: Table 6-1 Material actors Type o calculation Material actor 1) Value Resistance o Class 1, or 3 cross-sections γ M Resistance o Class 4 cross-sections γ M Resistance o member to buckling γ M Resistance o net section at bolt holes γ M 1.3 Resistance o illet and partial penetration welds γ Mw 1.3 Resistance o bolted connections γ Mb 1.3 1) Symbols according to Eurocode 3 The ultimate strength o structural elements and systems should be evaluated by using a rational, justiiable engineering approach. The structural analysis may be carried out as linear elastic, simpliied rigid plastic, or elastic-plastic analyses. Both irst order or second order analyses may be applied. In all cases, the structural detailing with respect to strength and ductility requirement shall conorm to the assumption made or the analysis. When plastic or elastic-plastic analyses are used or structures exposed to cyclic loading (e.g. wave loads) checks must be carried out to veriy that the structure will shake down without excessive plastic deormations or racture due to repeated yielding. A characteristic or design cyclic load history needs to be deined in such a way that the structural reliability in case o cyclic loading (e.g. storm loading) is not less than the structural reliability or Ultimate Limit States or non-cyclic actions. In case o linear analysis combined with the resistance ormulations set down in this standard, shakedown can be assumed without urther checks. NORSOK standard Page 0 o 488

29 Rev. 1, December Ductility It is a undamental requirement that all ailure modes are suiciently ductile such that the structural behaviour will be in accordance with the anticipated model used or determination o the responses. In general all design procedures, regardless o analysis method, will not capture the true structural behaviour. Ductile ailure modes will allow the structure to redistribute orces in accordance with the presupposed static model. Brittle ailure modes shall thereore be avoided or shall be veriied to have excess resistance compared to ductile modes, and in this way protect the structure rom brittle ailure. The ollowing sources or brittle structural behaviour may need to be considered or a steel structure: 1. Unstable racture caused by a combination o the ollowing actors: brittle material, a design resulting in high local stresses and the possibilities or weld deects.. Structural details where ultimate resistance is reached with plastic deormations only in limited areas, making the global behaviour brittle. E.g. partial butt weld loaded transverse to the weld with ailure in the weld. 3. Shell buckling. 4. Buckling where interaction between local and global buckling modes occur. In general a steel structure will be o adequate ductility i the ollowing is satisied: 1. Material toughness requirements are met, and the design avoids a combination o high local stresses with possibilities o undetected weld deects.. Details are designed to develop a certain plastic delection e.g. partial butt welds subjected to stresses transverse to the weld is designed with excess resistance compared with adjoining plates. 3. Member geometry is selected such that the resistance does not show a sudden drop in capacity when the member is subjected to deormation beyond maximum resistance. (An unstiened shell in cross-section class 4 is an example o a member that may show such an unavourable resistance deormation relationship. For deinition o cross-section class see NS 347 or Eurocode 3). 4. Local and global buckling interaction eects are avoided. 6.3 Tubular members General The structural strength and stability requirements or steel tubular members are speciied in this section. The requirements given in this section apply to unstiened and ring stiened tubulars having a thickness t 6 mm, D/t < 10 and material meeting the general requirements o Section 5 o this standard. In cases where hydrostatic pressure are present, the structural analysis may proceed on the basis that stresses due to the capped-end orces arising rom hydrostatic pressure are either included in or excluded rom the analysis. This aspect is discussed in the Commentary. In the ollowing sub-sections, y and z are used to deine the in-plane and out-o-plane axes o a tubular member, respectively. NORSOK standard Page 1 o 488

30 Rev. 1, December 1998 The requirements assume the tubular is constructed in accordance with the abrication tolerances given in the NORSOK M-101. The requirements are ormulated or an isolated beam column. This ormulation may also be used to check the resistance o rames and trusses, provided that each member is checked or the member orces and moments combined with a representative eective length. The eective length may in lieu o special analyses be determined according to the requirements given in this chapter. Alternatively the Ultimate Limit States or rames or trusses may be determined on basis o nonlinear analyses taking into account second order eects. The use o these analyses requires that the assumptions made are ulilled and justiied. Tubular members subjected solely to axial tension, axial compression, bending, shear, or hydrostatic pressure should be designed to satisy the strength and stability requirements speciied in Sections 6.3. to Tubular members subjected to combined loads without hydrostatic pressure should be designed to satisy the strength and stability requirements speciied in Section Tubular members subjected to combined loads with hydrostatic pressure should be designed to satisy the strength and stability requirements speciied in Section The equations in this section are not using an unique sign convention. Deinitions are given in each paragraph Axial tension Tubular members subjected to axial tensile loads should be designed to satisy the ollowing condition: N Sd N t,rd = A γ M y (6.1) where N Sd = design axial orce (tension positive) y = characteristic yield strength A = cross sectional area γ M = Axial compression Tubular members subjected to axial compressive loads should be designed to satisy the ollowing condition: N Sd N c,rd = A γ M c (6.) where N Sd = design axial orce (compression positive) c = characteristic axial compressive strength γ M = see section NORSOK standard Page o 488

31 Rev. 1, December 1998 In the absence o hydrostatic pressure the characteristic axial compressive strength or tubular members shall be the smaller o the in-plane or out-o-plane buckling strength determined rom the ollowing equations: c = [ λ ] or λ 1.34 y (6.3) 0.9 c = y or λ > 1.34 λ (6.4) λ = cl E = kl πi cl E (6.5) where cl = characteristic local buckling strength λ = column slenderness parameter E = smaller Euler buckling strength in y or z direction E = Young s modulus o elasticity, MPa k = eective length actor, see Section l = longer unbraced length in y or z direction i = radius o gyration The characteristic local buckling strength should be determined rom: y cl = y or cle (6.6) cl y y = y or > cle cle (6.7) and cle = C e E t D (6.8) where cle = characteristic elastic local buckling strength C e = critical elastic buckling coeicient = 0.3 D = outside diameter t = wall thickness y For cle > the tubular is a class 4 cross section and may behave as a shell. Shell structures may have a brittle structure ailure mode. Reerence is made to section 6.. For class 4 cross sections increased γ M values shall be used according to equation (6.). NORSOK standard Page 3 o 488

32 Rev. 1, December Bending Tubular members subjected to bending loads should be designed to satisy the ollowing condition: M Sd M Rd mw = γ M (6.9) where M Sd = design bending moment m = characteristic bending strength W = elastic section modulus γ M = see section The characteristic bending strength or tubular members should be determined rom: Z yd m = y or W Et (6.10) m D Z Et W y y = y < D Et (6.11) m yd = Et Z W y yd y < 10 Et E (6.1) where W = elastic section modulus 4 4 π [ D (D t) ] = 3 D Z = plastic section modulus = [ D (D t) ] 6 y For > the tubular is a class 4 cross section and may behave as a shell. Shell structures cle may have a brittle structure ailure mode. Reerence is made to section 6.. For class 4 cross sections increased γ M values shall be used according to equation (6.) Shear Tubular members subjected to beam shear orces should be designed to satisy the ollowing condition: V Sd V Rd = A y 3γ M (6.13) NORSOK standard Page 4 o 488

33 Rev. 1, December 1998 where V Sd = design shear orce y = yield strength A = cross sectional area γ M = 1.15 Tubular members subjected to shear rom torsional moment should be designed to satisy the ollowing condition: M T,Sd M T,Rd = D I p y 3γ M (6.14) where M T,Sd = design torsional moment π 4 4 I p = polar moment o inertia = [ D (D t) ] Hydrostatic pressure Hoop buckling 3 Tubular members subjected to external pressure should be designed to satisy the ollowing condition: σ p,sd h,rd = γ σ p, Sd = p Sd D t h M (6.15) (6.16) where h = characteristic hoop buckling strength σ p,sd = design hoop stress due to hydrostatic pressure (compression positive) p Sd = design hydrostatic pressure γ M = see section I out-o-roundness tolerances do not meet the requirements given in NORSOK-M-101, guidance on calculating reduced strength is given in the Commentary. h = y, or >.44 (6.17) he y h he = y or.44 y he > 0.55 y y (6.18) h = he, or 0.55 (6.19) he y The elastic hoop buckling strength, he, is determined rom the ollowing equation: NORSOK standard Page 5 o 488

34 Rev. 1, December 1998 he = C h E t D (6.0) where C h = 0.44 t/d or µ 1.6D/t = 0.44 t/d (D/t) 3 /µ 4 or 0.85D/t µ < 1.6D/t = 0.737/(µ ) or 1.5 µ < 0.85D/t = 0.80 or µ < 1.5 and where the geometric parameter, µ, is deined as: L D µ = and D t L = length o tubular between stiening rings, diaphragms, or end connections Ring stiener design The circumerential stiening ring size may be selected on the ollowing approximate basis: I c = he tl rd 8E (6.1) where I c = required moment o inertia or ring composite section L r = ring spacing D = diameter (See Note or external rings.) Notes: 1. Equation (6.1) assumes that the yield strength o the stiening ring is equal to or greater than that o the tubular.. For external rings, D in equation (6.1) should be taken to the centroid o the composite ring. 3. An eective width o shell equal to 1.1 D t may be assumed as the lange or the composite ring section. 4. Where out-o-roundness in excess o tolerances given in NORSOK-M-101 is permitted, larger stieners may be required. The bending due to out-o-roundness should be specially investigated. Local buckling o ring stieners with langes may be excluded as a possible ailure mode provided that the ollowing requirements are ulilled: h 1.1 t E w y and b t 0.3 E y where NORSOK standard Page 6 o 488

35 Rev. 1, December 1998 h = web height t w = web thickness b = hal the width o lange o T-stieners t = thickness o lange Local buckling o ring stieners without langes may be excluded as a possible ailure mode provided that: h t 0.4 E w y Material actor The material actor, γ M, is given as: γ γ γ M M M = 1.15 = λ = 1.45 s or or 0.5 λ or λ λ s s < 0.5 s > (6.) where λ s = σ y j,sd σ c,sd cle σ + p,sd he (6.3) σ + j, Sd = σ c,sd σ c,sdσ p,sd σ p,sd (6.4) where cle is calculated rom (6.8) and he rom (6.0). σ p,sd is obtained rom (6.16) and σ c,sd = N A Sd + M y,sd + M W z,sd (6.5) Tubular members subjected to combined loads without hydrostatic pressure Axial tension and bending Tubular members subjected to combined axial tension and bending loads should be designed to satisy the ollowing condition at all cross sections along their length: N N Sd t,rd M y,sd M + M Rd z,sd 1.0 (6.6) NORSOK standard Page 7 o 488

36 Rev. 1, December 1998 where M y,sd = design bending moment about member y-axis (in-plane) M z,sd = design bending moment about member z-axis (out-o-plane) N Sd = design axial tensile orce Axial compression and bending Tubular members subjected to combined axial compression and bending should be designed to satisy the ollowing conditions at all cross sections along their length: N N Sd c,rd + 1 M Rd C mym N 1 N y,sd Sd Ey C mzm + N 1 N z,sd Sd Ez (6.7) and N N Sd cl,rd + M y,sd M + M Rd z,sd 1.0 (6.8) where N Sd = design axial compression orce C my, C mz = reduction actors corresponding to the member y and z axes, respectively N Ey, N Ez = Euler buckling strengths corresponding to the member y and z axes, respectively c A Nc,Rd = l l γ design axial local buckling resistance N Ey M π EA = kl i y (6.9) N Ez π EA = kl i z (6.30) k in Equations (6.9) and (6.30) relate to buckling in the y and z directions, respectively. These actors can be determined using a rational analysis that includes joint lexibility and sidesway. In lieu o such a rational analysis, values o eective length actors, k, and moment reduction actors, C m, may be taken rom Table 6-. All lengths are measured centreline to centreline. NORSOK standard Page 8 o 488

37 Rev. 1, December 1998 Table 6- Eective length and moment reduction actors or member strength checking Structural element k (1) C m Superstructure legs - Braced 1.0 (a) - Portal (unbraced) k () (a) Jacket legs and piling - Grouted composite section 1.0 (c) - Ungrouted jacket legs 1.0 (c) - Ungrouted piling between shim points 1.0 (b) Jacket braces - Primary diagonals and horizontals 0.7 (b) or (c) - K-braces (3) 0.7 (c) - Longer segment length o X-braces (3) 0.8 (c) Secondary horizontals 0.7 (c) Notes: 1. C m values or the cases deined in Table 6- are as ollows: (a) 0.85 (b) or members with no transverse loading, C m = M 1,Sd /M,Sd where M 1,Sd /M,Sd is the ratio o smaller to larger moments at the ends o that portion o the member unbraced in the plane o bending under consideration. M 1,Sd /M,Sd is positive when the number is bent in reverse curvature, negative when bent in single curvature. (c) or members with transverse loading, C m = N c,sd /N E, or 0.85, whichever is less, and N E = N Ey or N Ez as appropriate.. Use Eective Length Alignment Chart in Commentary. 3. At least one pair o members raming into the a K- or X-joint must be in tension i the joint is not braced out-oplane. For X-braces, when all members are in compression, the k-actor should be determined using the procedures given in the Commentary. 4. The eective length and C m actors given in Table 6- do not apply to cantilever members and the member ends are assumed to be rotationally restrained in both planes o bending Interaction shear and bending moment Tubular members subjected to beam shear orce and bending moment should be designed to satisy the ollowing condition: M M Sd Rd V Sd 1 or Sd 0. 4 V Rd V V Rd (6.31) M V Sd 1.0 or Sd < 0. 4 M V Rd Rd (6.3) Interaction shear, bending moment and torsional moment Tubular members subjected to beam shear orce, bending moment and torsion should be designed to satisy the ollowing condition: NORSOK standard Page 9 o 488

38 Rev. 1, December 1998 M M Sd Red,Rd V 1 V Sd Rd (6.33) where M Red,Rd = W m,red γ M m,red = τ T,Sd m 1 3 d τ T,Sd = M T,Sd πr t d = y γ M R = radius o tubular member γ M = see section Tubular members subjected to combined loads with hydrostatic pressure The design provisions in this section are divided into two categories. In Method A it is assumed that the capped-end compressive orces due to the external hydrostatic pressure are not included in the structural analysis. Alternatively, the design provisions in Method B assume that such orces are included in the analysis as external nodal orces. Dependent upon the method used in the analysis, the interaction equations in either Method A or Method B should be satisied at all cross sections along their length. It should be noted that the equations in this section are not applicable unless Equation (6.15) is irst satisied. For guidance on signiicance o hydrostatic pressure see Commentary Axial tension, bending, and hydrostatic pressure Tubular members subjected to combined axial tension, bending, and hydrostatic pressure should be designed to satisy the ollowing equations in either Method A or B at all cross sections along their length. Method A (σ a,sd is in tension) In this method, the calculated value o member axial stress, σ a,sd, should not include the eect o the hydrostatic capped-end axial stress. The capped-end axial compression due to external hydrostatic pressure, σ q,sd, can be taken as 0.5σ p, Sd. This implies that, the tubular member takes the entire capped-end orce arising rom external hydrostatic pressure. In reality, the stresses in the member due to this orce depend on the restraint provided by the rest o the structure on the member. The stress computed rom a more rigorous analysis may be substituted or 0.5σ. (a) For σ a,sd σ q,sd (net axial tension condition) p, Sd NORSOK standard Page 30 o 488

39 Rev. 1, December 1998 σ a,sd σ th,rd q,sd + σ my,sd + σ mh, Rd mz,sd 1.0 (6.34) where th, Rd mh, Rd and B = σ σ a,sd = design axial stress that excludes the eect o capped-end axial compression arising rom external hydrostatic pressure (tension positive) σ q,sd = capped-end design axial compression stress due to external hydrostatic pressure 0.5σ ) (compression positive) (= p, Sd σ my,sd = design in plane bending stress σ mz,sd = design out o plane bending stress th,rd = design axial tensile resistance in the presence o external hydrostatic pressure which is given by the ollowing ormula: = γ y M [ mh,rd = = γ m M [ B B η 0.3B] (6.35) design bending resistance in the presence o external hydrostatic pressure which is given by the ollowing ormula: B B η γ M = see section p,sd h,rd, B B] (6.36) (6.37) η = 5 4 h y (6.38) (b) For σ a,sd < σ q,sd (net axial compression condition) σ a,sd σ cl,rd q,sd + σ my,sd + σ mh, Rd mz,sd 1.0 (6.39) = cl,rd γ cl m (6.40) where cl is ound rom equation (6.6) and (6.7). cle when σ c,sd > 0.5 and cle > 0.5 he, the ollowing equation should also be satisied: γ M NORSOK standard Page 31 o 488

40 Rev. 1, December 1998 σ γ c,sd cle M 0.5 γ 0.5 γ he he M M σ + γ p,sd he M 1.0 (6.41) in which σ c, Sd σ m,sd + σ q,sd σ a, Sd = ; σ c,sd should relect the maximum combined compressive stress. M z,sd + M y,sd σ m,sd = W γ M = see section Method B (σ ac,sd is in tension) In this method, the calculated member axial stress, σ ac,sd, includes the eect o the hydrostatic capped-end axial stress. Only the ollowing equation needs to be satisied: σ ac,sd th,rd + σ my,sd + σ mh, Rd mz,sd 1.0 (6.4) where σ ac,sd = design axial stress that includes the eect o the capped-end compression arising rom external hydrostatic pressure (tension positive) Axial compression, bending, and hydrostatic pressure Tubular members subjected to combined compression, bending, and hydrostatic pressure should be proportioned to satisy the ollowing requirements at all cross sections along their length. Method A (σ a,sd is in compression) σ a,sd ch,rd 1 + mh,rd C myσ σ 1 my,sd a,sd Ey C mzσ + σ 1 mz,sd a,sd Ez (6.43) σ a,sd + σ σ q,sd my,sd + σ + cl,rd mh, Rd mz,sd 1.0 (6.44) where σ a,sd = design axial stress that excludes the eect o capped-end axial compression arising rom external hydrostatic pressure (compression positive) NORSOK standard Page 3 o 488

41 Rev. 1, December 1998 Ey π E = kl i y (6.45) Ez π E = kl i z (6.46) ch,rd ch,rd = design axial compression strength in the presence o external hydrostatic pressure which is given by the ollowing ormulas: 1 σ q,sd σ cl q,sd = [ξ + ξ λ ] or γ M cl cl λ < 1.34 σ (1 q,sd cl ) 1 (6.47) and ch,rd = 0.9 cl, λ γ or λ M 1.34 σ (1 q,sd cl ) 1 (6.48) where ξ = 1 0.8λ (6.49) he When σ c,sd > 0.5 and cle > 0.5 he, equation (6.41), in whichσ c, Sd = σ m,sd + σ q,sd + σ a, Sd, should γ also be satisied. M γ M = see section Method B (σ ac,sd is in compression) (a) or σ ac,sd > σ q,sd σ ac,sd σ ch,rd q,sd 1 + mh,rd C σ 1 my σ my,sd σ ac,sd Ey q,sd C + σ 1 mz σ mz,sd σ ac,sd Ez q,sd (6.50) σ ac,sd cl,rd + σ my,sd + σ mh, Rd mz,sd 1.0 (6.51) NORSOK standard Page 33 o 488

42 Rev. 1, December 1998 σ ac,sd = design axial stress that includes the eect o capped-end axial compression arising rom external hydrostatic pressure (compression positive) he cle he When σ c,sd > 0.5 and > 0.5, equation (6.41), in which σ c, Sd = σ m,sd + σ ac, Sd, should also γ M γ M γ M be satisied. (b) or σ ac,sd σ q,sd For σ ac,sd σ q,sd, equation (6.51) should be satisied. he When σ c,sd > 0.5 and γ M γ be satisied. γ M = see section cle he > 0.5, equation (6.41), in which σ c, Sd σ m,sd + σ ac, Sd M γ M =, should also 6.4 Tubular joints General The ollowing provisions apply to the design o tubular joints ormed by the connection o two or more members. Terminology or simple joints is deined in Figure 6-1. Figure 6-1 also gives some design requirements with respect to joint geometry. The gap or simple K-joints should be larger than 50 mm and less than D. NORSOK standard Page 34 o 488

43 Rev. 1, December 1998 Figure 6-1 Detail o simple joint Reductions in secondary (delection induced) bending moments or inelastic relaxation through use o joint elastic stiness may be considered. In certain instances, hydrostatic pressure eects may be signiicant Joint classiication Joint classiication is the process whereby the axial orce in a given brace is subdivided into K, X and Y components o actions, corresponding to the three joint types or which resistance equations exist. Such subdivision normally considers all o the members in one plane at a joint. For purposes o this provision, brace planes within ±15º o each other may be considered as being in a common plane. Each brace in the plane can have a unique classiication that could vary with action condition. The classiication can be a mixture between the above three joint types. Once the breakdown into axial components is established, the resistance o the joint can be estimated using the procedures in Figure 6- provides some simple examples o joint classiication. For a brace to be considered as K- joint classiication, the axial orce in the brace should be balanced to within 10% by orces in other braces in the same plane and on the same side o the joint. For Y-joint classiication, the axial orce in the brace is reacted as beam shear in the chord. For X-joint classiication, the axial orce in the brace is carried through the chord to braces on the opposite side. Additional explanation o joint-classiication is ound in the Commentary NORSOK standard Page 35 o 488

44 Rev. 1, December 1998 Figure 6- Classiication o simple joints NORSOK standard Page 36 o 488

45 Rev. 1, December Strength o simple joints General The validity range or application o the practice deined in is as ollows: 0. β γ θ 90 g 0.6 (or K joints) D The above geometry parameters are deined in Figure 6-3 to Figure 6-6. d β = d D t γ = D T T Θ τ = t T D crown crown saddle L L α = D Figure 6-3 Deinition o geometrical parameters or T- or Y-joints d β = d D t γ = D T T Θ D τ = t T L α = D Figure 6-4 Deinition o geometrical parameters or X-joints NORSOK standard Page 37 o 488

46 Rev. 1, December 1998 da β A = d A D β B = d B D BRACE A d B t A t B BRACE B τ A = t A T τ B = t B T T Θ A g Θ B D γ = D T ζ = g D Figure 6-5 Deinition o geometrical parameters or K-joints d A d B d C β A = d A D β B = d B D β C = d C D A t B B C t A t C τ A = t A T τ B = t B T τ C = t C T T Θ A g Θ AB B g BC Θ C D g ζ AB AB = D g ζ BC BC = D γ = D T Figure 6-6 Deinition o geometrical parameters or KT-joints Basic resistance Tubular joints without overlap o principal braces and having no gussets, diaphragms, grout, or stieners should be designed using the ollowing guidelines. The characteristic resistances or simple tubular joints are deined as ollows: N M Rd Rd yt = Q γ sinθ M M u Q yt d = Q uq γ sinθ (6.5) (6.53) Where NORSOK standard Page 38 o 488

47 Rev. 1, December 1998 N Rd = the joint design axial resistance M Rd = the joint design bending moment resistance y = the yield strength o the chord member at the joint γ M = 1.15 For joints with joint cans, N Rd shall not exceed the resistance limits deined in For braces with axial orces with a classiication that is a mixture o K, Y and X joints, a weighted average o N Rd based on the portion o each in the total action is used to calculate the resistance Strength actor Q u Q u varies with the joint and action type, as given in Table 6-3. Table 6-3 Values or Q u Joint Classiication Brace action Axial Tension Axial Compression In-plane Bending K ( β ) Q β Q gq ( β ) Q Q yy β gqyy Y X β 30 ( ) β γ β Qβ β or β 0.9 (.8 14β ) Qβ + ( β - 0.9)( 17γ 0) or β > β γ β γ Out-o-plane bending 3.γ 3.γ 3.γ 0.5β 0.5β 0.5β The ollowing notes apply to Table 6-3: (a) Q β is a geometric actor deined by: Q β 0.3 = or β > 0.6 β ( β ) Q β = 1.0 or β 0.6 (b) Q g is a gap actor deined by: Q g 0.5 g g = 1.9 or.0,but Q g 1. 0 D T Qg 65φγ g or T 0.5 = where φ = t T y,b y,c y,b = yield strength o brace y,c = yield strength o chord NORSOK standard Page 39 o 488

48 Rev. 1, December 1998 Q g = linear interpolated value between the limiting values o the above expressions or g.0.0 T (b) Q yy is an angle correction actor deined by: Q yy = 1.0 when θ t 4θ 90 c Q yy θ c θ t = 00 when θ t > 4θ 90 c with θ c and θ t reerring to the included angle or the compression and tension brace, respectively Chord action actor Q Q is a design actor to account or the presence o actored actions in the chord. Q = 1.0 λ c A (6.54) Where: λ = or brace axial orce in equation (6.5) = or brace in-plane bending moment in equation (6.53) = 0.01 or brace out-o-plane bending moment in equation (6.53) c = 14 or Y and K joints = 5 or X joints The parameter A is deined as ollows: A σ σ my,sd + σ + m a,sd = y mz,sd (6.55) where: σ a,sd = design axial stress in chord σ my,sd = design in-plane bending stress in chord σ mz,sd = design out-o-plane bending stress in chord y = yield strength m = characteristic bending strength or the chord determined rom equation (6.10)- (6.1) The chord thickness at the joint should be used in the above calculations. The highest value o A or the chord on either side o the brace intersection should be used in Equation (6.54). Apart rom X joints with β > 0.9, Q may be set to unity i the magnitude o the chord axial tension stress is greater than the maximum combined stress due to chord moments. NORSOK standard Page 40 o 488

49 Rev. 1, December Design axial resistance or X and Y joints with joint cans For Y and X joints with axial orce and where a joint can is speciied, the joint design resistance should be calculated as ollows: N Rd = r + T T c n ( 1- r) N can, Rd (6.56) where N can,rd = N Rd rom Equation (6.5) based on chord can geometric and material properties T n = nominal chord member thickness T c = chord can thickness r = L/D or joints with β 0.9 L = β + ( 1 β ) 10 9 or joints with β > 0.9 D L = the least distance between crown and edge o chord can, excluding taper In no case shall r be taken as greater than unity Strength check Joint resistance shall satisy the ollowing interaction equation or axial orce and/or bending moments in the brace: N N Sd Rd M + M y,sd y,rd M + M z,sd z,rd 1 (6.57) where: N Sd = design axial orce in the brace member N Rd = the joint design axial resistance M y,sd = design in-plane bending moment in the brace member M z,sd = design out-o-plane bending moment in the brace member M y,rd = design in-plane bending resistance M z,rd = design out-o-plane bending resistance Overlap joints Braces that overlap in- or out-o-plane at the chord member orm overlap joints. Joints that have in-plane overlap involving two or more braces may be designed on the ollowing basis: NORSOK standard Page 41 o 488

50 Rev. 1, December 1998 a) For brace axial orce conditions that are essentially balanced (within 10%), the individual brace intersection resistance may be calculated using the guidelines in However, or the overlapping brace, the resistance should be limited to that o an Y joint with the controlling through brace properties (eective yield and geometry) assumed to represent the chord and the included angle between the braces representing θ. In instances o extreme overlap, shear parallel to the chord ace is a potential ailure mode and should be checked. b) The above assumption o K joint behaviour applies only to the portion o axial orce that is balanced. Any residual portion o an individual brace orce that is not balanced should be treated as Y or X orces (see 6.4.). c) I all or some o the axial orces in the relevant braces have the same sign, the combined orce representing the portion o orce that has the same sign should be used to check the through brace intersection resistance. d) For in-plane bending moments that are essentially balanced (equal and opposite), the resistance can be taken as the simple joint resistance or an individual brace (Equation (6.53)). I the brace moments have the same orientation, the combined moment should be used to check the through brace intersection resistance. As or axial orces, the overlapping brace should also be checked on the basis o the chord having through brace properties. e) Out-o-plane moments generally have the same orientation. The combined moment should be used to check the through brace intersection resistance. The moment in the overlapping brace should also be checked on the basis o the chord having through brace properties. ) The relevant joint axial or moment resistance shall be limited to the individual brace axial and moment resistance, respectively (see ). g) The Q and brace action interaction expressions associated with simple joints may be used or overlapping joints. The simple joint guidelines covering mixed classiication may be ollowed in assessing utilisation values. Joints with out-o-plane overlap may be assessed on the same general basis as in-plane overlapping joints, except that axial orce resistance should normally revert to that or Y joints Ringstiened joints Design resistance o ringstiened joints shall be determined by use o recognised engineering methods. Such methods can be elastic analyses, plastic analyses or linear or non-linear inite element analyses. See Commentary Cast joints Cast joints are deined as joints ormed using a casting process. They can be o any geometry and o variable wall thickness. The design o a cast joint requires calibrated FE analyses. An acceptable design approach or strength is to limit the stresses ound by linear elastic analyses to the design strength using γ M appropriate yield criteria. Elastic peak stresses may be reduced ollowing similar design principles as described in Commentary to y NORSOK standard Page 4 o 488

51 Rev. 1, December Strength o conical transitions General The provisions given in this section are or the design o concentric cone rusta between tubular sections. They may also be applied to conical transitions at brace ends, where the junction provisions apply only to the brace-end transition away rom the joint Design stresses Equivalent design axial stress in the cone section. The equivalent design axial stress (meridional stress) at any section within the conical transition can be determined by the ollowing equation: σ equ,sd σ = ac,sd + σ cosα mc,sd (6.58) σ ac,sd = π(d s NSd t cosα)t c c (6.59) σ mc,sd = π 4 (D s M t c Sd cosα) t c (6.60) where σ equ,sd = equivalent design axial stress within the conical transition σ ac,sd = design axial stress at the section within the cone due to global actions σ mc,sd = design bending stress at the section within the cone due to global actions D s = outer cone diameter at the section under consideration t c = cone thickness α = the slope angle o the cone (see Figure 6-7) N Sd and M Sd are the design axial orce and design bending moment at the section under consideration. σ ac,sd and σ mc,sd should be calculated at the junctions o the cone sides. NORSOK standard Page 43 o 488

52 Rev. 1, December 1998 CL. CL. t 0.5D L 1 b e L c t c α α Figure 6-7 Cone geometry Local bending stress at unstiened junctions In lieu o a detailed analysis, the local bending stress at each side o unstiened tubular-cone junctions can be estimated by the ollowing equations: 0.6t D j(t + t c ) σ mlt,sd = ( σ at,sd + σ t 0.6t D j(t + t c ) σ mlc, Sd = ( σ at,sd + σ t c mt,sd mt,sd )tanα )tanα (6.61) (6.6) where σ mlt,sd = local design bending stress at the tubular side o unstiened tubular-cone junction σ mlc,sd = local design bending stress at the cone side o unstiened tubular-cone junction D j = cylinder diameter at junction t = tubular member wall thickness σ at,sd = design axial stress in tubular section at junction due to global actions σ mt,sd = design bending stress in tubular section at junction due to global actions Hoop stress at unstiened junctions The design hoop stress at unstiened tubular-cone junctions due to unbalanced radial line orces may be estimated rom: NORSOK standard Page 44 o 488

53 Rev. 1, December 1998 D j σ hc, Sd = 0.45 ( σ at,sd + σ mt, Sd )tanα t (6.63) At the smaller-diameter junction, the hoop stress is tensile (or compressive) when (σ at,sd + σ mt,sd ) is tensile (or compressive). Similarly, the hoop stress at the larger-diameter junction is tensile (or compressive) when (σ at,sd + σ mt,sd ) is compressive (or tensile) Strength requirements without external hydrostatic pressure Local buckling under axial compression For local buckling under combined axial compression and bending, the ollowing equation should be satisied at all sections within the conical transition. σ equ,sd γ clc M (6.64) where clc = local buckling strength o conical transition For conical transitions with slope angle α < 30, clc can be determined using (6.6) to (6.8) with an equivalent diameter, D e, at the section under consideration. D e = Ds cosα (6.65) For conical transitions o constant wall thickness, it would be conservative to use the diameter at the larger end o the cone as D s in Eq. (6.65) Junction yielding Yielding at a junction o a cone should be checked on both tubular and cone sides. This section only applies when the hoop stress, σ hc,sd, is tensile. For net axial tension, that is, when σ tot,sd is tensile, σ tot,sd + σ hc,sd σ hc,sd σ tot,sd γ y M (6.66) For net axial compression, that is, when σ tot,sd is compression, σ tot,sd + σ hc,sd + σ hc,sd σ tot,sd γ y M (6.67) where NORSOK standard Page 45 o 488

54 Rev. 1, December 1998 σ tot,sd = σ + σ + σ or checking stresses on the tubular side o the junction at, Sd mt,sd mlt, Sd σ ac,sd + σ mc,sd = + σ mlc, Sd or checking stresses on the cone side o the junction cosα y = corresponding tubular or cone yield strength Junction buckling. This section only applies when the hoop stress, σ hc,sd, is compressive. In the equations, σ hc,sd denotes the positive absolute value o the hoop compression. For net axial tension, that is, when σ tot,sd is tensile, a η + b + ν a b 1.0 (6.68) where σ a = γ σ b = γ tot,sd y M hc,sd h M (6.69) (6.70) and ν is Poisson s ratio o 0.3 and η is deined in Equation (6.38) For net axial compression, that is, when σ tot,sd is compressive, σ tot,sd γ cj M (6.71) and σ hc,sd γ h M (6.7) where cj = corresponding tubular or cone characteristic axial compressive strength h can be determined using equations (6.17) to (6.19) with he = 0.80E(t/D j ) and corresponding y Strength requirements with external hydrostatic pressure Hoop buckling Unstiened conical transitions, or cone segments between stiening rings with slope angle α < 30, may be designed or hoop collapse by consideration o an equivalent tubular using the equations in NORSOK standard Page 46 o 488

55 Rev. 1, December 1998 Sect The eective diameter is D/cosα, where D is the diameter at the larger end o the cone segment. The equivalent design axial stress should be used to represent the axial stress in the design. The length o the cone should be the slant height o the cone or the distance between the adjacent rings or ring stiened cone transition Junction yielding and buckling The net design hoop stress at a tubular-cone junction is given by the algebraic sum o σ hc,sd and σ h,sd, that is σ = σ + σ hj, Sd hc,sd h,sd (6.73) where σ h,sd = design hoop stress due to the external hydrostatic pressure, see eq. (6.16) When σ hj,sd is tensile, the equations in Sect should be satisied by using σ hj,sd instead o σ hc,sd. When σ hj,sd is compressive, the equations in Sect should be satisied by using σ hj,sd instead o σ hc,sd Ring design General A tubular-cone junction that does not satisy the above criteria may be strengthened either by increasing the tubular and cone thicknesses at the junction, or by providing a stiening ring at the junction Junction rings without external hydrostatic pressure I stiening rings are required, the section properties should be chosen to satisy both the ollowing requirements: A c = td y j ( σ + σ a,sd m, Sd )tanα (6.74) I c = td D j 8E c ( σ + σ a,sd m, Sd )tanα (6.75) where σ a,sd = larger o σ at,sd and σ ac,sd. σ m,sd = larger o σ mt,sd and σ mc,sd. D c = diameter to centroid o composite ring section. See Note 4 in section A c = cross-sectional area o composite ring section I c = moment o inertia o composite ring section In computing A c and I c, the eective width o shell wall acting as a lange or the composite ring section may be computed rom: NORSOK standard Page 47 o 488

56 Rev. 1, December 1998 b e = 0.55( D jt + D t j c ) (6.76) Notes: 1. For internal rings, D j should be used instead o D c in Equation (6.75).. For external rings, D j in equations (6.73) and (6.74) should be taken to the centroid o the composite ring Junction rings with external hydrostatic pressure Circumerential stiening rings required at the tubular-cone junctions should be designed such that the moment o inertia o the composite ring section is equal to or greater than the sum o Equations (6.75) and (6.78): I I + I ct c ch (6.77) where hec Ich he D j = tl1 16E t clc + cos α (6.78) where I ct = moment o inertia o composite ring section with external hydrostatic pressure and with eective width o lange computed rom Equation (6.76) D j = diameter o tubular at junction. See Note 4 o section L c = distance to irst stiening ring in cone section along cone axis 113. L 1 = distance to irst stiening ring in tubular section 113. he = elastic hoop buckling strength or tubular hec = he or cone section treated as an equivalent tubular D e = larger o equivalent diameters at the junctions Notes: 1. A junction ring is not required or hydrostatic collapse i Equation (6.15) is satisied with he computed using C h equal to 0.44 (cosα) (t/d j ) in Equation (6.0), where D j is the tubular diameter at the junction.. For external rings, D j in Equation (6.77) should be taken to the centroid o the composite ring, except in the calculation o L 1. 3 D j t 3 De t Intermediate stiening rings I required, circumerential stiening rings within cone transitions may be designed using Equation (6.1) with an equivalent diameter equal to D s /cosα, where D s is the cone diameter at the section under consideration, t is the cone thickness, L is the average distance to adjacent rings along the cone axis and he is the average o the elastic hoop buckling strength values computed or the two adjacent bays. NORSOK standard Page 48 o 488

57 Rev. 1, December Design o plated structures General Failure modes Section 6.6 addresses ailure modes or unstiened and stiened plates, which are not covered by member design checks. The ailure modes are: Yielding o plates in bending due to lateral load Buckling o slender plates (high span to thickness ratio) due to in-plane compressive stresses Buckling o plates due to concentrated loads (patch loads) Buckling o stiened plates with biaxial in-plane membrane stress and lateral load Material actor γ M =1.15 or design o plates Deinitions Figure 6-8 Stiened plate panel The terms used in this standard or checking o plates are shown in Figure 6-8. The plate panel may be web or lange o a beam, or a part o a box girder, a pontoon, a hull or an integrated plated deck. NORSOK standard Page 49 o 488

58 . Design o Steel Structures N-004 Rev. 1, December Buckling o plates Buckling checks o unstiened plates in compression shall be made according to the eective width method. The reduction in plate resistance or in-plane compressive orces is expressed by a reduced (the eective) width o the plate which is multiplied with the design yield stress to obtain the resistance. (See Figure 6-9). Real stress distribution Eective stress distribution S S e S Figure 6-9 Eective width concept Buckling o plates should be checked according to the requirements given in either Eurocode 3 or NS 347 or the requirements given in this standard. Guidance on which standard to be used is given in Table 6-4. NORSOK standard Page 50 o 488

59 Rev. 1, December 1998 Table 6-4 Reerence table or buckling checks o plate panels Description Load Sketch Code reerence Unstiened plate Longitudinal compression σ x,sd - t - σ x,sd S Limiting value s < l Buckling check not s necessary i 4 ε t l Unstiened plate Transverse compression - t - y,sd σ S s < l Buckling check not s necessary i 5.4ε t Unstiened plate Combined longitudinal and transverse compression l - t - σ y,sd y,sd σ σ x,sd S s < l Buckling check not s necessary i 5.4ε t Unstiened plate Combined longitudinal and transverse compression and shear l y,sd x,sd -ts s < l Buckling check not s necessary i 5.4ε t Sd Unstiened plate Pure bending and shear s - t - τ Sd σ x,sd NS 347 or Eurocode 3 s < l Buckling check not s necessary i 69ε t l ε = 35/ y NORSOK standard Page 51 o 488

60 Rev. 1, December 1998 Description Load Sketch Code reerence Unstiened plate Concentrated loads NS 347 or Eurocode 3 Limiting value Unstiened plate Uniorm lateral load and in-plane normal and shear stresses τ Sd σ y,sd s - t - σ x,sd PSd 6.6. and s < l Buckling check not s necessary i 5.4ε t Flange outstand Longitudinal compression l NS 347 or Eurocode 3 Buckling check o lange outstand not necessary i b t 15ε Transverse stiened plate panel Bending moment and shear τ Sd σ x,sd NS 347 or Eurocode 3 S - t - l Longitudinal stiened plate panel Longitudinal and transverse compression combined with shear and lateral load S τ Sd σ y,sd - t - σ x,sd PSd ε = 35/ y l NORSOK standard Page 5 o 488

61 Rev. 1, December 1998 NORSOK standard Page 53 o Lateral loaded plates. For plates subjected to lateral pressure, either alone or in combination with in-plane stresses, the stresses may be checked by the ollowing ormula: + x y M y Sd ψ s ψ s t γ 4.0 p l (6.79) where p Sd = design lateral pressure y Sd y x,sd y j,sd y τ 3 σ σ 1 ψ = (6.80) y Sd y y,sd y j,sd x τ 3 σ σ 1 ψ = (6.81) Sd y,sd x,sd y,sd x,sd Sd j, 3τ σ σ σ σ σ + + = This ormula or the design o a plate subjected to lateral pressure is based on yield-line theory, and accounts or the reduction o the moment resistance along the yield-line due to applied in-plane stresses. The reduced resistance is calculated based on von Mises equivalent stress. It is emphasized that the ormulation is based on a yield pattern assuming yield lines along all our edges, and will give uncertain results or cases where yield-lines can not be developed along all edges. Furthermore, since the ormula does not take account o second-order eects, plates subjected to compressive stresses shall also ulill the requirements o

62 Rev. 1, December Buckling o unstiened plates Buckling o unstiened plates under longitudinally uniorm compression σ x,sd σ x,sd - t - s Figure 6-10 Plate with longitudinal compression l The buckling resistance o an unstiened plate under longitudinal compression stress may be ound rom: N x,rd = t C x s γ y M (6.8) where C x = 1 when λ p (6.83) C x ( λ 0.) p = when λ p > λ p Where λ p is the plate slenderness given by: (6.84) λ y p = = cr s 0.55 t y E (6.85) In which s = plate width t = plate thickness cr = critical plate buckling strength The resistance o the plate is satisactory when: N x, Sd = t s σ x,sd N x,rd (6.86) NORSOK standard Page 54 o 488

63 Rev. 1, December Buckling o unstiened plates with variable longitudinal stress The buckling resistance o an unstiened plate with variable longitudinal stress may be ound rom: N x,rd = t C x s γ y M (6.87) where C x = 1 when λ p (6.88) C x ( λ 0.) p = when λ p > λ p Where λ p is the plate slenderness given by: (6.89) λ p = y cr = s t 1 8.4ε k σ (6.90) In which s = plate width t = plate thickness cr = critical plate buckling strength ε = 35 y k σ = ψ or 0 ψ ψ+9.78ψ or 1 ψ < (1-ψ) or ψ < 1 x,sd σ σ x,sd - t - s ψσ x,sd l x,sd ψσ Figure 6-11 Plate with variable longitudinal stress The resistance o the plate is satisactory when: NORSOK standard Page 55 o 488

64 Rev. 1, December 1998 N = x, Sd t σ c,sdds N x,rd (6.91) where σ c,sd = longitudinal compressive stress (tensile stresses to be set equal to zero) Buckling o unstiened plates with transverse compression σy,sd - t - s Figure 6-1 Plate with transverse compression l σ y,sd The buckling resistance o a plate under transverse compression orce may be ound rom: N y,rd = t C y l γ y M (6.9) where C y C s s = x l l λ p, but C y 1. 0 (6.93) In which C x is ound in (6.83) or (6.84) λ p is ound in (6.85) l = plate length s = plate width The resistance o the plate is satisactory when: N y, Sd = σ y,sd t l N y,rd (6.94) In case o linear variable stress the check can be done by use o an uniormly distributed stress equal the design stress value at a distance 0.5s rom the most stressed end o the plate. NORSOK standard Page 56 o 488

65 Rev. 1, December s - t - s σ y,sd Figure 6-13 Linear variable stress in the transverse direction l Buckling o unstiened biaxially loaded plates with shear y,sd x,sd -ts Sd Figure 6-14 Biaxially loaded plate with shear a. Biaxially loaded plate with shear The buckling resistance o an unstiened plate subjected to longitudinal compression, transverse compression or tension and shear may be ound rom: N x,rd = t C x C y C τ s γ y M (6.95) NORSOK standard Page 57 o 488

66 Rev. 1, December 1998 where C x is ound rom (6.83) or (6.84) I the plate is subjected to transverse compression, C y may be ound rom: C y = σ 1 y,sd ky (6.96) where ky s = y C x l l s λ p, but ky y (6.97) I the plate is subjected to transverse tension, may C y be ound rom: 1 σ y,sd σ y,sd C y = 4 3 +, C y 1.0 y y (6.98) Tensile stresses are deined as negative. C τ is ound rom (6.119) The resistance o the plate is satisactory i: N x, Sd = t s σ x,sd N x,rd (6.99) b. plates with transverse compression and shear: The buckling resistance o an unstiened plate under transverse compression and shear may be ound rom: N y,rd = t Cy Cτ l γ y M (6.100) where C y is ound rom (6.93) C τ is ound rom (6.119) The resistance o the plate is satisactory i: N y, Sd = σ y,sd t l N y,rd (6.101) NORSOK standard Page 58 o 488

67 Rev. 1, December Stiened plates General This chapter deals with stieners in plate ields subjected to axial stress in two directions, shear stress and lateral load. There are dierent ormulaes or stieners being continuous or connected to rames with their ull moment strengths and simple supported (sniped) stieners. Examples o stiened plates are shown in Figure 6-8. The stiener cross section need to ulill class 3 requirement according to Eurocode 3 or NS 347. For shear leg eects see Commentary. The plate between stieners will normally be checked implicit by the check o the stiener since plate buckling is accounted or by the eective width method. However, in case o small or zero σ x,sd stresses it is necessary to check that σ y,sd is less than plate resistance according to equation (6.94). For slender stiened plates it may be considered to neglect the load carrying resistance in the direction transverse to the stiener and assum σ y,sd stresses carried solely by the girder. In this case eective girder lange is determined by disregarding stieners and the stiener with plate can be checked with neglecting σ y,sd stresses. (Method in ). N Sd = ( x,sd, Sd) N σ τ τ Sd σ y, Sd q =q Sd (p p ) Sd, o σ x,sd p Sd σ y1,sd N Sd STIFFENED PLATE BEAM COLUMN Figure 6-15 Strut model NORSOK standard Page 59 o 488

68 Rev. 1, December Forces in the idealised stiened plate Stiened plates subjected to combined orces, see Figure 6-15, are to be designed to resist a equivalent axial orce deined by: ( A + st) Cτ st NSd = σ x,sd s + Sd (6.10) where A s = cross sectional area o stiener s = distance between stieners t = plate thickness σ x,sd = axial stress in plate and stiener with compressive stresses as positive where s C Q = 7 5 l τ Sd τ τ crl crg or τ Sd > τ crg (6.103) C = 0 or τ Sd < τ crg (6.104) Q = λ 0., but not less than 0 and not greater that 1.0 λ = y E, where E is taken rom (6.13) τ crg = critical shear stress or the plate with the stieners removed, according to (6.105) τ crl = critical shear stress or the plate panel between two stieners, according to (6.105) τ cr = = λ τ y, y, or λ or λ τ τ 1 > 1 (6.105) λ τ = s t 1 k y 35 (6.106) where k = k g when calculating τ crg and k = kl when calculating τ crl and k k g l l = L l = 5.34 L l = 5.34 s G l = s + G +,or l L 4, or 4, or,or l s l < s l < L G G (6.107) (6.108) NORSOK standard Page 60 o 488

69 Rev. 1, December 1998 L G = Girder length s = stiener spacing, see Figure 6-8 The lateral line load should be taken as: = ( p p )s qsd Sd + 0 (6.109) p 0 shall be applied in the direction o the external pressure p Sd. For situations where p Sd is less than p 0 the stiener need to be checked or p 0 applied in both directions (i.e. at plate side and stiener side). p Sd = design lateral pressure s = stiener spacing ( ψ) C0 y1, Sd p = + i ψ > -1.5 (6.110) 0 σ p 0 = 0 i ψ -1.5 (6.111) where 0.8 y l C0 = 0.4 ψ = σ σ y,sd y1,sd ( 1+ n) E s h t, but not less than t 0.0 s (6.11) σ y1,sd = larger design stress in the transverse direction, with tensile stresses taken as negative σ y,sd = smaller design transverse stress, with tensile stresses taken as negative n = numbers o stieners in the plate h = web height o the stiener Eective plate width The eective plate width or a continuous stiener subjected to longitudinal and transverse stress and shear is ound rom: s e s = C xs C ys C τs (6.113) The reduction actor in the longitudinal direction, C xs, is ound rom: C xs = λ p 0., λ p i λ p > (6.114) = 1.0, i λ p where NORSOK standard Page 61 o 488

70 Rev. 1, December 1998 λ p = s 0.55 t y E (6.115) and the reduction actor or compression stresses in the transverse direction, C ys, is ound rom: C ys = σ 1 y,sd ky (6.116) where ky s C = y xs + l l s λ p, but ky y (6.117) In case o linear variable stress, σ y,sd may be ound at a distance 0.5s rom the most stressed end o the plate. The reduction actor or tension stresses in the transverse direction, C ys, is ound rom: 1 σ y,sd σ y,sd C ys = 4 3 +, C ys 1.0 y y (6.118) Tensile stresses are deined as negative. The reduction actor or shear is ound rom: C τs = τ 1 3 Sd y (6.119) In the case o varying stiener spacing, s, or unequal thickness in the adjoining plate panels, the eective widths, s e, and the applied orce, N x,sd, should be calculated individually or both side o the stiener using the geometry o the adjacent plates. See also Figure Figure 6-16 Eective widths or varying stiener spacing NORSOK standard Page 6 o 488

71 Rev. 1, December Characteristic buckling strength o stieners The characteristic buckling strength or stieners may be ound rom: k = 1 i λ 0. r (6.10) k r ( 1+ µ + λ ) µ + λ 1+ 4λ = i λ > 0. λ (6.11) In which λ = r E (6.1) E i = π E l e k (6.13) zp µ = ( λ 0.) i or check at plate side e ( λ 0.) z t µ = i or check at stiener side e (6.14) (6.15) where r = y or check at plate side r = y or check at stiener side i λ T 0.6 r = T or check at stiener side i λ T > 0.6, T may be ound in section λ T = see equation (6.19) l k may be ound rom (6.16) i e = Ie Ae eective radius o gyration I e eective moment o inertia A e eective area z p, z t is deined in Figure 6-17 NORSOK standard Page 63 o 488

72 Rev. 1, December 1998 Figure 6-17 Deinition o cross-section parameters or stieners or girders Torsional buckling o stieners The torsional buckling strength may be ound rom: T = 1.0 i λ T 0.6 y (6.16) T y ( 1+ μ + λ ) 1+ μ + λt T 4λT = i λ T > 0.6 λt (6.17) where μ = 0.35 λ = T ( λ 0.6 ) y ET T Generally ET may be ound rom: ET GI = β I po t Eh I + π I s z polt (6.18) (6.19) (6.130) For T- and L-stieners ET may be ound rom: NORSOK standard Page 64 o 488

73 Rev. 1, December 1998 ET t A W + A t W = β A + 3A W t G h W π EI z + A W + A 3 l T (6.131) I z = 1 1 A b + e A A 1+ A W (6.13) β = 1.0, or may alternatively or stocky plates be calculated as per equation (6.133) or s l A = cross sectional area o lange A W = cross sectional area o web G = shear modulus I po = polar moment o inertia = r da where r is measured rom the connection between the stiener and the plate. I t = stiener torsional moment o inertia (St. Venant torsion). I z = moment o inertia o the stieners neutral axis normal to the plane o the plate. b = lange width e = lange eccentricity, see ig Figure 6-17 h = web height h s = distance rom stiener toe (connection between stiener and plate) to the shear centre o the stiener. l T = distance between sideways supports o stiener, distance between tripping brackets (torsional buckling length). t = plate thickness t = thickness o lange t W = thickness o web 3C + 0. β = C + 0. (6.133) C = h s where t t w 3 ( 1 η) (6.134) σ j,sd η = η 1.0 kp σ + j, Sd = σ x,sd + σ y,sd σ x,sdσ y,sd 3τSd (6.135) (6.136) kp = y 1+ λ 4 e (6.137) NORSOK standard Page 65 o 488

74 Rev. 1, December 1998 λ e = σ y j,sd σ x,sd Epx c σ + y,sd Epy c τ + Sd Epτ 1 c c (6.138) c = s l (6.139) Epx Epy Epτ = 3.6E = 0.9E = 5.0E t s t s t s (6.140) (6.141) (6.14) σ x,sd and y, Sd σ should be set to zero i in tension Interaction ormulas or axial compression and lateral pressure a. Continuous stieners For continuous stieners the ollowing our interaction equations need to be ullilled in case o lateral pressure on plate side: N N Sd ks,rd M + M 1,Sd s,rd * NSd z 1 N Sd 1 N E (6.143) N N Sd kp,rd N N Sd Rd + M M 1,Sd p,rd * NSd z 1 N Sd 1 N E (6.144) N N Sd ks,rd N N Sd Rd M + M,Sd s,rd * + NSd z 1 N Sd 1 N E (6.145) N N Sd kp,rd M + M,Sd p,rd * + NSd z 1 N Sd 1 N E (6.146) NORSOK standard Page 66 o 488

75 Rev. 1, December 1998 The ollowing our interaction equations need to be ulilled in case o lateral pressure on stiener side: N N Sd ks,rd N N Sd Rd M + M 1,Sd s,rd * + NSd z 1 N Sd 1 N E (6.147) N N N N Sd kp,rd Sd ks,rd M + M M + M 1,Sd p,rd,sd s,rd * + NSd z 1 N Sd 1 N E * NSd z 1 N Sd 1 N E (6.148) (6.149) N N Sd kp,rd N N Sd Rd M + M,Sd p,rd * NSd z 1 N Sd 1 N E (6.150) Resistance parameters see or stiener and or girders. M 1,Sd = q Sdl 1 or continuous stieners with equal spans and equal lateral pressure in all spans = absolute value o the actual largest support moment or continuous stieners with unequal spans and/or unequal lateral pressure in adjacent spans M,Sd = q Sdl 4 or continuous stieners with equal spans and equal lateral pressure in all spans = absolute value o the actual largest ield moment or continuous stieners with unequal spans and/or unequal lateral pressure in adjacent spans q Sd is given in equation (6.109) l = span length z * is the distance rom the neutral axis o the eective section to the working point o the axial orce. z * may be optimised so that the resistance rom equations (6.143) to (6.146) or (6.147) to (6.150) is maximised. The value o z * is taken positive towards the plate. The simpliication z * = 0 is always allowed. b. Simple supported stiener (sniped stiener): Lateral pressure on plate side: NORSOK standard Page 67 o 488

76 Rev. 1, December 1998 N N Sd ks,rd N N Sd Rd + qsdl 8 M s,rd + N Sd N 1 N z Sd E * 1 (6.151) N N Sd kp,rd qsdl 8 + M p,rd + N Sd N 1 N z Sd E * 1 (6.15) Lateral pressure on stiener side: N N Sd ks,rd + qsdl 8 M s,rd N Sd N 1 N z Sd E * 1 (6.153) N N Sd kp,rd N N Sd Rd qsdl 8 + M p,rd N Sd N 1 N z Sd E * 1 (6.154) q Sd is given in equation (6.109) l = span length z * is the distance rom the neutral axis o the eective section to the working point o the axial orce, which or a sniped stiener will be in the centre o the plate. The value o z * is taken positive towards the plate Resistance parameters or stieners The ollowing resistance parameters are used in the interaction equations or stieners. N = A Rd e γ y M (6.155) A e = (A s +s e t), eective area o stiener and plate N = A ks,rd e γ k M (6.156) where k is calculated rom section using (6.15). NORSOK standard Page 68 o 488

77 Rev. 1, December 1998 N = A kp,rd e γ k M (6.157) where k is calculated rom section using (6.14). A s = cross sectional area o stiener s e = eective width, see M = W s,rd es γ r M where r is ound rom section M = W p,rd ep γ y M (6.158) (6.159) W ep = W es = I z I z e p e t, eective elastic section modulus on plate side, see Figure 6-17, eective elastic section modulus on stiener side, see Figure 6-17 N E = π EA lk i e e (6.160) where i = e I A e e (6.161) For a continuous stiener the buckling length may be calculated rom the ollowing equation: l k p l p = Sd (6.16) where p Sd is design lateral pressure and p is the lateral pressure giving yield in extreme ibre at support. p 1W = l γ y M 1 s (6.163) W = the smaller o W ep and W es l = span length NORSOK standard Page 69 o 488

78 Rev. 1, December 1998 In case o varying lateral pressure, p Sd in equation (6.16) is to be taken as the minimum o the value in the adjoining spans. For simple supported stiener l k = l Resistance o stieners with predominantly bending I the stiener is within section class 1 and the axial orce N Sd is less than the smaller o 0.1 N ks,rd and 0.1 N kp,rd the resistance may be ound rom: M M Sd pl,rd where 1 (6.164) M pl,rd = design plastic moment resistance Buckling o girders General Checking o girders is similar to the check or stieners o stiened plates in equation (6.143) to (6.150) or (6.151) to (6.154) or continuous or sniped girders, respectively. Forces shall be calculated according to section and cross section properties according to Girder resistances should be ound rom Torsional buckling o girders may be assessed according to Girder orces The axial orce should be taken as: N + ( t ) y, Sd = σ y,sd l AG (6.165) The lateral lineload should be taken as: q = ( p + p )l Sd Sd 0 (6.166) where p Sd = design lateral pressure p 0 = equivalent lateral pressure A G = cross sectional area o girder The calculation o the additional equivalent lateral pressure due to longitudinal compression stresses and shear shall be calculated as ollows: For compression in the x-direction: NORSOK standard Page 70 o 488

79 Rev. 1, December 1998 A 0.4 t + p + s E l h 1 LG s s y LG 0 = x,sd CτSd ( σ ), (6.167) A t + But not less than 0.0 s ( σ + Cτ ) l s x,sd Sd where C is ound rom equation (6.103) or (6.104) with τ crg = critical shear stress o panel with girders removed, calculated rom eq. (6.105) with λ τ taken as below τ crl = critical shear stress o panel between girders calculated rom eq. (6.105) with λτ taken as below λ τ = 0.6y τce with τ cel = E t Is tl s τ ceg = τcel 4( n ) G + 1 n G the largest number o stieners o equally loaded girders to each side o the girder under consideration h = web height o girder A s = cross sectional area o stiener L G = girder span s = stiener spacing For linear variation o σ x,sd, the maximum value within 0.5L G to each side o the midpoint o the span may be used. τ Sd should correspond to the average shear low over the panel. For tension in the x-direction: p A 0.4 t + s s y LG 0 = CτSd s h 1 L G E l (6.168) Resistance parameters or girders The resistance o girders may be determined by the interaction ormulas in section using the below resistances. NORSOK standard Page 71 o 488

80 Rev. 1, December 1998 N Rd = ( A + l t) G e γ y M (6.169) N ks,rd = ( A + l t) G e γ k M (6.170) Where k is calculated rom section using µ according to (6.15). N kp,rd = ( A + l t) G e γ k M (6.171) Where k is calculated rom section using µ according to (6.14). where: r = y or check at plate side r = y or check at girder lange side i λ TG 0.6 r = TG or check at girder lange side i λ TG > 0.6 s,rd E ie = π E L Gk (6.17) L Gk = buckling length o girder equal L G unless urther evaluations are made TG may be ound in equation (6.187) and λ TG may be ound in equation (6.188). A G = cross sectional area o girder l e = eective width o girder plate, see M = W eg γ r M where r is ound rom above or check at girder lange side. M = W p,rd ep γ y M (6.173) (6.174) W ep = W eg = I z I z e p e t, eective elastic section modulus on plate side, see Figure 6-17, eective elastic section modulus on girder lange side, see Figure 6-17 N E π EA = LGk ie e (6.175) where NORSOK standard Page 7 o 488

81 Rev. 1, December 1998 i = e I A e e (6.176) Eective widths o girder plates The eective width or the plate o the girder is taken equal to: le l = C xg C yg C τg (6.177) For the determination o the eective width the designer is given two options denoted method 1 and method. These methods are described in the ollowing: Method 1. Calculation o the girder by assuming the stiened plate is eective against transverse compression (σ y ) stresses. In this method the eective width may be ound rom: C xg = σ 1 x,sd kx (6.178) where: = C kx xs y (6.179) C xs is ound rom (6.114). I the σ y stress in the girder is in tension due to the combined girder axial orce and bending moment over the total span o the girder, C yg may be ound rom: C yg = l L G L 4 l G, C yg 1 (6.180) I the σ y stress in the plate is partly or complete in compression C yg may be ound rom: C yg s C s , C λ yg 1 p = xs + l l (6.181) C τg = τ 1 3 Sd y (6.18) λ p may be ound rom equation (6.115). NORSOK standard Page 73 o 488

82 Rev. 1, December 1998 Method. Calculation o the girder by assuming the stiened plate is not eective against transverse compression σ y stresses. In this case the plate and stiener can be checked with σ y stresses equal to zero. In method the eective width or the girder has to be calculated as i the stiener was removed that means: C xg = σ 1 x,sd y (6.183) Where σ x,sd is based on total plate and stiener area in x-direction. C yg λ = G = 1.0, 0., λ G i i λ λ G G > (6.184) where λ G l = 0.55 t y E (6.185) C τg = τ 1 3 Sd y (6.186) Torsional buckling o girders The torsional buckling strength or girders may be calculated according to section taking: TG = A π EI A w + 3 z L GT (6.187) λ TG = y TG (6.188) where L GT = distance between lateral supports A, A w = cross sectional area o lange and web o girder NORSOK standard Page 74 o 488

83 Rev. 1, December 1998 I z = moment o inertia o girder (exclusive o plate lange) about the neutral axis perpendicular to the plate Torsional buckling need not to be considered i tripping brackets are provided so that the laterally unsupported length L GT, does not exceed the value L GT0 deined by: L b GT0 = C EA A w y A + 3 (6.189) where b = lange width C = 0.55 or symmetric langes 1.10 or one sided langes Tripping brackets are to be designed or a lateral orce P Sd, which may be taken equal to (see Figure 6-18): P Sd = 0.0σ y,sd A A + 3 w (6.190) σ y,sd = compressive stress in the ree lange PSd A 1/3 Aw Tripping bracket Figure 6-18 Deinitions or tripping brackets Local buckling o stieners, girders and brackets Local buckling o stieners and girders The methodology given in is only valid or webs and langes that satisy the requirements to class 3 in Eurocode 3 or NS 347. NORSOK standard Page 75 o 488

84 Rev. 1, December Requirements to web stieners In lieu o more reined analysis such as in 6.6.4, web stieners should satisy the ollowing requirements: Transverse web stieners: I s > 0.3l s t t W l s t y.5 s lt E I s = moment o inertia o web stiener with ull web plate lange s l t = length o transverse web stiener s = distance between transverse web stieners (6.191) lt s Figure 6-19 Deinitions or transverse web stieners Longitudinal web stiener: I 0.5l ( A st ) E s > l s + W y (6.19) I s = moment o inertia o web stiener with ull web plate lange s. A s = cross sectional area o web stiener exclusive web plating. l l = length o longitudinal web stiener s = distance between longitudinal web stieners s ll Figure 6-0 Deinitions or longitudinal web stieners NORSOK standard Page 76 o 488

85 Rev. 1, December Buckling o brackets Brackets are to be stiened in such a way that: d 0.7t 0 b E y (6.193) d 1.65t 1 b E y (6.194) d 1.35t b E y (6.195) t b = plate thickness o bracket. Stieners as required in (6.194) to (6.195) may be designed in accordance with See Figure 6-1 or deinitions. Figure 6-1 Deinitions or brackets 6.7 Design o cylindrical shells Unstiened and ringstiened cylindrical shells subjected to axial orce, bending moment and hydrostatic pressure may be designed according to 6.3. For more reined analysis o cylindrical shells or cylindrical shells with other stiening geometry or loading, Annex B should be used. The susceptibility to less avourable post-critical behaviour associated with more slender geometry and more and /or larger stress components may be expressed through the reduced slenderness parameter, λ, which is deined in Annex B. The resulting material actor or design o shell structures is given as γ M = 1.15 or λ s < 0.5 (6.196) γ M = λ s or 0.5 λ s 1.0 γ M = 1.45 or λ s > 1.0 NORSOK standard Page 77 o 488

86 Rev. 1, December 1998 λ s is deined in Annex B. 6.8 Design against unstable racture General Normally brittle racture in oshore structures is avoided by selecting materials according to section 5 and with only acceptable deects present in the structure ater abrication. Unstable racture may occur under unavourable combinations o geometry, racture toughness, welding deects and stress levels. The risk o unstable racture is generally greatest with large material thickness where the state o deormation is plane strain. For normal steel qualities, this typically implies a material thickness in excess o mm, but this is dependent on the actors: geometry, racture toughness, weld deects and stress level. See reerence /8/ or guidance on the use o racture mechanics. I relevant racture toughness data is lacking, material testing should be perormed Determination o maximum allowable deect size The design stress shall be determined with load coeicients given in the Regulations. The maximum applied tensile stress, accounting also or possible stress concentrations, shall be considered when calculating the tolerable deect size. Relevant residual stresses shall be included in the evaluation. Normally, a structure is designed based on the principle that plastic hinges may develop without giving rise to unstable racture. In such case, the design nominal stress or unstable racture shall not be less than the yield stress o the member. The characteristic racture toughness, K Ic,(or, alternatively K c, J c, J Ic, CTOD c ), shall be determined as the lower 5% ractile o the test results. The design racture toughness shall be calculated rom the ollowing ormula: K K Icd = γ Ic M (6.197) where γ M γ M = 1.15 or members where ailure will be without substantial consequences = 1.4 or members with substantial consequences Notes: 1. Substantial consequences in this context means that ailure o the joint will entail: Danger o loss o human lie; Signiicant polution; Major inancial consequences.. Without substantial consequences is understood ailure where it can be demonstrated that the structure satisy the requirement to damaged condition according to the Accidental Limit States with ailure in the actual joint as the deined damage. The design values o the J-integral and CTOD shall be determined with a saety level corresponding to that used to determine the design racture toughness. For example, the design CTOD is ound rom the ollowing ormula: NORSOK standard Page 78 o 488

87 Rev. 1, December 1998 CTOD CTOD cd = γ M c (6.198) The maximum deect size likely to remain undetected (a i ) shall be established, based on an evaluation o the inspection method, access or inspection during abrication, abrication method, and the thickness and geometry o the structure,. When determining the value o a i consideration shall be given to the capabilities o the inspection method to detect, localise, and size the deect. The maximum allowable deect size ( a m ), shall be calculated on the basis o the total stress (or corresponding strains) and the design racture toughness. It shall be shown that a i < a m. For a structure subjected to atigue loading, the crack growth may be calculated by racture mechanics. The initial deect size shall be taken as a i. The inal crack size, a u, shall be determined with the atigue load applied over the expected lie time. It shall be veriied that a u < a m. NORSOK standard Page 79 o 488

88 Rev. 1, December SERVICEABILITY LIMIT STATES 7.1 General General requirements or the serviceability limit states are given in NORSOK N-001. Shear lag eects need to be considered or beams with wide langes. Normally reduced eective width o slender plates due to buckling need not to be included. 7. Out o plane delection o plates Check o serviceability limit states or slender plates related to out o plane delection may normally be omitted i the smallest span o the plate is less than 150 times the plate thickness. See Commentary to NORSOK standard Page 80 o 488

89 Rev. 1, December FATIGUE LIMIT STATES 8.1 General In this standard, requirements are given in relation to atigue analyses based on atigue tests and racture mechanics. Reerence is made to Annex C or more details with respect to atigue design. The aim o atigue design is to ensure that the structure has an adequate atigue lie. Calculated atigue lives can also orm the basis or eicient inspection programmes during abrication and the operational lie o the structure. The design atigue lie or the structure components should be based on the structure service lie speciied by the operator. I no structure service lie is speciied by the operator, a service lie o 15 years shall be used. A short design atigue lie will imply shorter inspection intervals. To ensure that the structure will ulil the intended unction, a atigue assessment, supported where appropriate by a detailed atigue analysis should be carried out or each individual member which is subjected to atigue loading. It should be noted that any element or member o the structure, every welded joint and attachment, or other orm o stress concentration, is potentially a source o atigue cracking and should be individually considered. The number o load cycles shall be multiplied with the appropriate actor in Table 8-1 beore the atigue analysis is perormed. Table 8-1 Design atigue actors Classiication o structural components based on damage consequence Access or inspection and repair No access or Accessible in the splash Below splash zone zone Above splash zone Substantial consequences 10 3 Without substantial 3 1 consequences Substantial consequences in this context means that ailure o the joint will entail: Danger o loss o human lie; Signiicant pollution; Major inancial consequences. Without substantial consequences is understood ailure where it can be demonstrated that the structure satisy the requirement to damaged condition according to the Accidental Limit States with ailure in the actual joint as the deined damage. Welds in joints below 150 m waterdepth should be assumed inaccessible or in-service inspection. In project phases where it is possible to increase atigue lie by modiication o structural details, grinding o welds should not be assumed to provide a measurable increase in the atigue lie. 8. Methods or atigue analysis The atigue analysis should be based on S-N data, determined by atigue testing o the considered welded detail, and the linear damage hypothesis. When appropriate, the atigue analysis may NORSOK standard Page 81 o 488

90 Rev. 1, December 1998 alternatively be based on racture mechanics. I the atigue lie estimate based on atigue tests is short or a component where a ailure may lead to substantial consequences, a more accurate investigation considering a larger portion o the structure, or a racture mechanics analysis, should be perormed. For calculations based on racture mechanics, it should be documented that the inservice inspection accommodate a suicient time interval between time o crack detection and the time o unstable racture. See also chapter 6.8. Reerence is made to Annex C or more details. All signiicant stress ranges, which contribute to atigue damage in the structure, should be considered. The long term distribution o stress ranges may be ound by deterministic or spectral analysis. Dynamic eects shall be duly accounted or when establishing the stress history. NORSOK standard Page 8 o 488

91 Rev. 1, December ACCIDENTAL DAMAGE LIMIT STATES The structure shall be checked or all Accidental Damage Limit States (ALS) or the design accidental actions deined in the risk analysis. The structure shall according to NORSOK N-001 be checked in two steps: a) Resistance o the structure against design accidental actions b) Post accident resistance o the structure against environmental actions. Should only be checked i the resistance is reduced by structural damage caused by the design accidental actions The overall objective o design against accidental actions is to achieve a system where the main saety unctions are not impaired by the design accidental actions. In general the ailure criteria to be considered, should also be deined in the risk analyses. (See Commentary) The design against accidental actions may be done by direct calculation o the eects imposed by the actions on the structure, or indirectly, by design o the structure as tolerable to accidents. Examples o the latter is compartmentation o loating units which provides suicient integrity to survive certain collision scenarios without urther calculations. The inherent uncertainty o the requency and magnitude o the accidental loads, as well as the approximate nature o the methods or determination o accidental action eects, shall be recognised. It is thereore essential to apply sound engineering judgement and pragmatic evaluations in the design. I non-linear, dynamic inite elements analysis is applied, it shall be veriied that all behavioural eects and local ailure modes (e.g. strain rate, local buckling, joint overloading, joint racture) are accounted or implicitly by the modelling adopted, or else subjected to explicit evaluation. Typical accidental actions are: Impact rom ship collisions Impact rom dropped objects Fire Explosions The dierent types o accidental actions require dierent methods and analyses to assess the structural resistance. Design recommendations or the most common types o accidental actions are given in Annex A. The material actor or accidental limit state γ M = 1.0 NORSOK standard Page 83 o 488

92 Rev. 1, December REASSESSMENT OF STRUCTURES 10.1 General An existing structure shall undergo an integrity assessment to demonstrate itness or purpose i one or more o the ollowing conditions exists: Extension o service lie beyond the originally calculated design lie Damage or deterioration to a primary structural component Change o use that violates the original design or previous integrity assessment basis Departure orm the original basis o design: Increased loading on the structure Inadequate deck height Assessment o existing structures should be based on the most recent inormation o the structure. Material properties may be revised rom design values to as built values. Foundation data may be updated according to indings during installation and data rom adjacent structures (i applicable). Load data should be revised according to latest met-ocean data and the current layout o the structure. The water depth should be revised according to measured installation data and later scour and settlements. The integrity o structural elements and systems should be evaluated by using a rational, deensible engineering approach. The consequence o minor events or minor structural changes may in most case be suiciently evaluated by comparison with existing engineering documentation or the structure in question. I this ails to provide the required documentation, additional analyses will be required using either conventional design-level checks or non-linear second-order analysis methods. 10. Extended atigue lie An extended lie is considered to be acceptable and within normal design criteria i the calculated atigue lie is longer than the total design lie times the Fatigue Design Factor. Otherwise an extended lie may be based on results rom perormed inspections throughout the prior service lie. Such an evaluation should be based on: calculated crack growth crack growth characteristics; i.e. crack length/depth as unction o time/number o cycles (this depends on type o joint, type o loading, stress range, and possibility or redistribution o stress) reliability o inspection method used elapsed time rom last inspection perormed. It is recommended to use Eddy current or Magnetic Particle Inspection or inspection o surace cracks starting at hot spots. Even i cracks are not ound it might in some situations be recommended to perorm a light grinding at the hot spot area to remove undercuts and increase the reliability o the inspection. Detected cracks may be ground and inspected again to document that they are removed. The remaining lie o such a repair should be assessed in each case; but provided that less than one third the thickness is removed locally by grinding a considerable atigue lie may still be documented depending on type o joint and loading conditions. NORSOK standard Page 84 o 488

93 Rev. 1, December Material properties The yield strength should be taken as the minimum guaranteed yield strength given in material certiicates or the steel used in the structure, provided such certiicates exist. Alternatively, material tests may be used to establish the characteristic as built yield strength. Due consideration must be given to the inherent variability in the data. The determination o a characteristic value shall be in accordance with the evaluation procedure given in NS ENV , Annex Z. The material actor γ M is 1.15 unless otherwise determined by separate structural reliability studies Corrosion allowance The presence o local or overall corrosion should be taken into account in determining the properties o corroded members o structural components. Strength assessment shall be based on net sections, reduced or corrosion allowance Foundations Foundation data should be updated according to inormation gained during installation o the structure and rom supplementary inormation rom adjacent installations. Pile resistance should primarily be estimated on the basis o static design procedures. I suicient data are available it may be appropriate to adjust the design soil strength due to loading rate eects and cyclic load eects. I pile-driving records are available, the design inormation should be updated according to additional inormation with respect to location and thickness o soil layers. One dimensional wave equation based methods may be used to estimate soil resistance to driving and iner a revised estimate o as-installed resistance. The load carrying eect o mud-mats and horizontal mudline members should not be considered in the integrity assessment Damaged and corroded members General The ultimate strength o damaged members should be evaluated by using a rational, justiiable engineering approach. Alternatively, the strength o damaged members may be determined by reined analyses. Corroded or damaged members and joints should be modelled to represent the actual corroded or damaged properties. Strengthened or repaired members and joints should be modelled to represent the actual strengthened or repaired properties. NORSOK standard Page 85 o 488

94 Rev. 1, December Dented tubular members Axial tension Dented tubular members subjected to axial tension loads should be assessed to satisy the ollowing condition y A 0 NSd N dent,t,rd = γ M where N Sd = design axial orce N dent,t,rd = design axial tension capacity o the dented section A 0 = cross-sectional area o the undamaged section y = characteristic yield strength o steel γ M = resistance actor Axial compression (10.1) Dented tubular members subjected to axial compressive loads should be assessed to satisy the ollowing condition N N = Sd dent,c,rd N γ dent,c M (10.) N dent,c = ( λ 0.9 ξ λ d d C ) ξ A y C A 0 y 0,, or λ or λ d d 1.34 > 1.34 where N dent,c,rd = design axial compressive capacity o the dented section N dent,c = characteristic axial compressive capacity o dented member λ = reduced slenderness o dented member, which may be calculated as d λ 0 N dent,c C = = λ 0 N E, dent ξ M ξ = reduced slenderness o undamaged member δ δ ξ C = exp( 0.08 ) or < 10 t t δ δ ξ M = exp ( 0.06 ) or < 10 t t δ = dent depth t = wall thickness = resistance actor γ M (10.3) (10.4) (10.5) NORSOK standard Page 86 o 488

95 Rev. 1, December Bending Dented tubular members subjected to bending loads should be assessed to satisy the ollowing condition M Sd M dent,rd ξ M M = M Rd Rd i the dented area acts in compression otherwise (10.6) where M Sd = design bending moment M dent,rd = design bending capacity o dented section M Rd = design bending capacity o undamaged sections, as given in Section Combined loading Dented tubular members under combined loading should be assessed to satisy the ollowing condition: N N Sd dent,c,rd + NSd Δy N (1 N Sd E,dent + C m1 ) M M 1,Sd dent,rd α + NSd Δy1 + CmM NSd (1 ) M Rd N E,Sd 1, N in compression (10.7) N N Sd dent,t,rd + M M 1,Sd dent,rd α M + M,Sd Rd 1, N in tension where α = δ 3 D i the dented area acts in compression otherwise (10.8) N Sd = design axial orce on the dented section M 1,Sd = design bending moment about an axis parallel to the dent M,Sd = design bending moment about an axis perpendicular to the dent N E,dent = Euler buckling strength o the dented section, or buckling in-line with the dent = E I dent π ( k l ) k = eective length actor, as deined in Table 6- I dent = moment o inertia o the dented cross-section, which may be calculated as = ξ M I I = moment o inertia o undamaged section y 1 = member out-o-straightness perpendicular to the dent y = member out-o-straightness in-line with the dent C m1,c m = moment reduction actor, as deined in Table 6- NORSOK standard Page 87 o 488

96 Rev. 1, December 1998 δ 1 1 Figure 10-1 Deinition o axes or dented section Corroded members In lieu o reined analyses, the strength o uniormly corroded members can be assessed by assuming a uniorm thickness loss or the entire member. The reduced thickness should be consistent with the average material loss due to corrosion. The member with the reduced thickness can then be evaluated as an undamaged member. In lieu o reined analyses, the strength o members with severe localised corrosion can be assessed by treating the corroded part o the cross-section as non-eective, and using the provisions given or dented tubulars (Section 10.6.). An equivalent dent depth can be estimated rom (10.9), and the resulting resistance calculated rom (10.7). δ D 1 A = (1 cosπ A Corr ) (10.9) where δ = equivalent dent depth D = tube diameter A Corr = corroded part o the cross-section A = ull cross section area For atigue sensitive conditions, a atigue evaluation o the corroded member should also be considered Cracked members and joints General Welded connections containing cracks may be assessed by racture mechanics such as given by /8/. NORSOK standard Page 88 o 488

97 Rev. 1, December Partially cracked tubular members In lieu o reined analyses, partially cracked members with the cracked area loaded in compression can be treated in a similar manner to the one discussed or dented tubulars (Section 10.6.). An equivalent dent depth can be estimated rom (10.10), and the resulting resistance calculated rom (10.7). δ D 1 A = (1 cosπ A Crack ) (10.10) where δ = equivalent dent depth D = tube diameter A Crack = crack area A = ull cross section area Partially cracked members with the cracked area loaded in tension should be subject to a racture mechanics assessment considering tearing mode o ailure and ductile crack growth. For atigue sensitive conditions, a atigue evaluation o the cracked member should also be considered Tubular joints with cracks The static strength o a cracked tubular joint can be calculated by reducing the joint resistances or a corresponding uncracked geometry taken rom Section 6.4.3, with an appropriate reduction actor accounting or the reduced ligament area /1/. The reduced strength is given by N M crack,rd crack,rd = F AR = F AR N Rd M Rd (10.11) where N crack,rd = axial resistance o the cracked joint M crack,rd = bending resistance o cracked joint N Rd and M Rd are given in Section 6.4. F AR = ( 1 A A C ) 1 Q β m q (10.1) A C = cracked area o the brace / chord intersection A = ull area o the brace /chord intersection Q β = tubular joint geometry actor, given in Section m q = 0 or part-thickness cracks For tubular joints containing through-thickness cracks, validated correction actors are limited. Guidance on available data are listed in the Commentary. Post-peak behaviour and ductility o cracked tubular joints should be subjected to separate assessment in each case. NORSOK standard Page 89 o 488

98 Rev. 1, December Repaired and strengthened members and joints General The ultimate strength o repaired members and joints should be evaluated by using a rational, and justiiable engineering approach. Alternatively, the strength o repaired members and joints may be determined by reined analyses Grouted tubular members The resistance o grouted tubular members, with and without dents, may be determined according to the ollowing paragraphs Axial tension The resistance o grouted tubular members under axial tension should be assessed to satisy the ollowing condition: y A S NSd N tg,rd = γ M (10.13) where N Sd = design axial orce on the grouted section N tg,rd = design axial tension resistance o the grouted, composite section A S = gross steel area = πdt y = characteristic yield strength o steel γ M = material actor Axial compression The resistance o grouted tubular members under axial compression should be assessed to satisy the ollowing condition: N N = Sd cg,rd N γ cg M (10.14) N cg = ( λ 0.9 N λ g g ug ) N ug,, or λ or λ g g 1.34 > 1.34 (10.15) λ = g N N ug Eg (10.16) where N Sd = design axial orce on the grouted section N cg,rd = design axial compression resistance o the grouted member NORSOK standard Page 90 o 488

99 Rev. 1, December 1998 N ug = axial yield resistance o the composite cross-section = A S y A G cg (10.17) N Eg = elastic Euler buckling load o the grouted member = ESIS + 0.8E GIG π ( k l ) (10.18) cg = characteristic cube strength o grout A S = cross-sectional area o the steel = πdt, or intact sections (10.19) α sinα πdt ( 1 ), or dented sections π A G = cross-sectional area o the grout = D π 4 D (10.0) π, or intact sections 4 α 1 sinα (1 + ), or dented sections π π I S = eective moment o inertia o steel cross section 3 D t α sinα sinα cos α = π 1 ASeS 8 + π π π (10.1) I G = eective moment o inertia o grout cross section = 4 D α sin4α π 1 AGeG 64 + π 4π (10.) E S = modulus o elasticity o the steel E G = modulus o elasticity o the grout m = modular ration o E S /E G 18, in lieu o actual data e S = distance rom centroid o dented steel section to the centroid o the intact steel section = D t sinα (1 cosα) A S (10.3) e G = distance rom centroid o dented grout section to the centroid o the intact grout section = (D sinαi 1A α = δ cos 1 (1 ) D δ = dent depth D = tube diameter G 3 (10.4) NORSOK standard Page 91 o 488

100 Rev. 1, December Bending The resistance o ully grouted tubular members subject to bending loads should be assessed to satisy the ollowing condition: M Sd M g,rd = W tr γ M bg (10.5) where M Sd = design bending moment or the grouted section M g,rd = design bending resistance o the grouted member W tr = elastic section modulus o the transormed, composite section I ( I S + ) D m (10.6) m = modular ration o E S /E G 18, in lieu o actual data bg = characteristic bending strength o grouted member = 4 ξ ξ (1 y δ + ) π 100 (10.7) ξ δ = δ δ D D (10.8) ξ m = 5.5 ξ δ 0.6 cg y D t 0.66 cg = characteristic cube strength o grout (10.9) Combined axial tension and bending In lieu o reined analyses, the resistance o ully grouted tubulars in combined tension and bending may be assessed by Equation (6.6) by neglecting the eect o the grout, or by Equation (10.5) i the maximum stress due to tension is small compared to the that o the bending component Combined axial compression and bending The resistance o ully grouted tubular members under combined axial compression and bending should be assessed to satisy the ollowing condition: N N Sd cg,rd MSd + T1 M g,rd M M Sd g,rd M + T M 1 Sd g,rd 1, or, or N N N N Sd cg,rd Sd cg,rd < K K K K 1 1 (10.30) where N Sd = design axial orce on the grouted section, compression negative NORSOK standard Page 9 o 488

101 Rev. 1, December 1998 N cg,rd = design axial compression resistance o the grouted member M Sd = design bending moment or the grouted section M g,rd = design bending resistance o the grouted member T = K 3 4 K T 1 = K 1 T K1 K 1 = λ g, or λg 1.34 N cg = 0.9 N, or λ g > 1.34 ug λ g K = (β 1) (1.8 γ) 100λ g K 0, 0 K K 0 50 (.1 β) K 3 = (0.5β + 0.4) (γ 0.5) K 30 + λ g 3 1+ λ g K 0 = 0.9γ K 30 = 0.04 γ 15 0 γ = t 0.67 A g ( cg + C1 y ) D N ug β = 1, provided no end moments apply, otherwise it is the ratio o the smaller to the larger end moment C 1 = 4 φε 1+ φ + φ φ = k 0.0 (5 l ) D 0 γ = k 0.5 (5 l ) D 0 k = eective length actor, as deined in Table 6- l = length o member Grouted joints For grouted joints that are otherwise simple in coniguration, the simple joint provisions deined in Section may be used with the ollowing additions: a) The Q U values in Table 6-3 should be replaced with values pertinent or grouted sections. See Commentary. Classiication and joint can derating may be disregarded or ully grouted joints. The adopted Q U values should not be less than those or simple joints. b) For brace compression loading, the joint resistance will normally be limited by the squash or local buckling resistance o the brace. This brace resistance should thereore be used in the joint interaction expressions given by Equation (6.57). c) For brace tension loading, the Q U value can be established rom consideration o the shear pullout resistance o the chord plug. NORSOK standard Page 93 o 488

102 Rev. 1, December 1998 d) For brace moment loading, the Q U value section can be established rom consideration o the shear pullout resistance o the portion o the chord plug subjected to tension, taking into account the shit in the axis o rotation o the brace. e) Tension and moment resistances shall not exceed the brace resistances. ) For double-skin joints, the ailure may also occur by chord ovalisation. The ovalisation resistance can estimated by substituting the ollowing eective thickness into the simple joint equations: t e = t + t p (10.31) where t e t t p = eective thickness o chord and internal pipe = wall thickness o chord = wall thickness o internal member t e should be used in place o t in the simple joint equations, including the γ term. The Q calculation, however, should be based on t. It is presumed that calculation o Q has already accounted or load sharing between the chord and the inner member, such that urther consideration o the eect o grout on this term is unnecessary Plates and cylindrical shells with dents and permanent delections Plates with permanent delections The residual strength o moderately distorted plates loaded by longitudinal compression can be assessed by an eective width approach /9/ where the eective width is given by s ered s = C xs 0.39 (1 λ p δ ) t, δ λ t p < 0.55 (10.3) in which C xs is ound rom (6.83) or (6.84) λp is ound rom (6.85) s = plate width between stieners s ered = eective width o plate with permanent delections t = plate thickness δ = maximum permanent distortion The resistance o the plate is given by (6.8) s ered can also be used to check stiened plates loaded by longitudinal compression by substituting C xs with s ered in (6.113). s Longitudinally stiened cylindrical shells with dents The compressive strength o longitudinally stiened cylindrical shells with dents may be assessed by an eective section approach, assuming the dented area ineective /10/. The stress becomes NORSOK standard Page 94 o 488

103 Rev. 1, December 1998 critical when the total stress in the damaged zone becomes equal to the stress or an undamaged cylinder σ c,sd cl,rd 1 + A R e W R A A R 1 (10.33) where σ c,sd = design axial stress in the damaged cylinder cl,rd = design local buckling resistance o undamaged cylinder A R = net area o circular part o the cylinder (total minus dented area) α = A ( 1 ) π A = gross area o the undamaged cylinder δ α = cos 1 (1 ) D e = distance rom neutral axis o the cylindrical part o the dented cylinder to the neutral axis o the original, intact cylinder D sinα = π α W R = elastic section modulus o the circular part o the dented cylinder 1 sin α π α sinα = W π α δ e π (1 + ) D D W = elastic section modulus o the intact cylinder NORSOK standard Page 95 o 488

104 Rev. 1, December REFERENCES /1/ Regulations relating to loadbearing structures etc. Issued by the Norwegian Petroleum Directorate 7 February 199. // Odland, J.: Improvements in design Methodology or Stiened and Unstiened Cylindrical Structures. BOSS 88. Proceedings o the International Conerence on behaviour o Oshore Structures. Trondheim, June /3/ Frieze, P.A., Hsu, T. M., Loh, J. T. and Lotsberg, I.: Background to Drat ISO Provisions on Intact and Damaged Members. BOSS, Delt, /4/ Smith, C. S., Kirkwood, W. and Swan, J. W.: Buckling Strength and Post-Collapse Behaviour o Tubular Bracing Members Including Damage Eects. Procs. nd International Conerence on the Behaviour o Oshore Structures, BOSS 1979, London, August /5/ Livesley, R. K.: The Application o an Electronic Digital Computer to Some Problems o Structural Analysis. The Structural Engineer, January /6/ American Institute o Steel Construction (AISC), Manual o Steel Construction Load and Resistance Factor Design, Vol. 1, nd ed., 1994 /7/ Boardman, H. C.: Stresses at Junctions o Two Right Cone Frustums with a Common Axis,The Water Tower, Chicage Bridge and Iron Company, March /8/ PD Guidance on methods or assessing the acceptability o laws in usion welded structures. BSI (New revision 1998). /9/ Faulkner, D.: Design Against Collapse or Marine Structures, Advances in Marine Technology, Trondheim, 1979 /10/ Dow, R.S. and Smith, C.S.: Eects o Localised Imperections on Compressive Strength o Long Rectangular plates, Journal o Constructional steel Research, vol. 4, pp , 1984 /11/ ULTIGUIDE. DNV, SINTEF, BOMEL. Best Practice Guidelines or Use o Non-linear Analysis Methods in Documentation o Ultimate Limit States or Jacket Type Oshore Structures. /1/ A. Stacey, J.V. Sharp, N.W. Nichols. "Static Strength Assessment o Cracked Tubular Joints", OMAE, Florence /13/ ISO Fixed Steel Structures, Drat, NORSOK standard Page 96 o 488

105 Rev. 1, December COMMENTARY This Commentary provides additional guidance and background to selected clauses o the standard. The Commentary is an inormative part o this standard. Comm. 1 Scope In general the provisions o this standard are developed, tested and calibrated or steel with traditional stress/strain relations. Design o structures made rom steel material with higher yield strength may require additional or dierent design checks due to, among other the ollowing eects: usually a higher yield to tensile strength ratio implying less strain hardening, larger elastic delection beore reaching resistance limit, which is important where second order eects play a role, usually reduced weld overmatch leading to increased risk o ailure in weld material, and reduced maximum elongation. Comm. 4 General Provisions The notation R k and S k must be read as indicative or a resulting characteristic resistance and action eect respectively. In the general case the design resistance, R d, will be a unction o several parameters where the material parameter y should be divided by γ M, and S d will be derived as a summation o dierent characteristic actions multiplied with dierent partial coeicients. The groups o limit states, applied in this standard, are deined according to ISO part 1. In contrast, Eurocode 3 and most national building codes are treating limit states associated with ailure due to accidental loads or atigue as ultimate limit states. Whilst atigue and ailure rom accidental loads are characteristically similar to ultimate limit states, it is convenient to distinguish between them due to dierent load actors or ULS, FLS and ALS. FLS and ALS may thereore be regarded as subgroups o ULS. Comm. 5.1 Design class The check or damaged condition according to the Accidental Damage Limit States (ALS) imply that the structure with damage is checked or all characteristic actions, but with all saety actors set to unity. With regard to material selection the associated damage is brittle ailure or lamellar tearing. I the structure subjected to one such ailure is still capable o resisting the characteristic loads, the joint or component should be designated DC 3 or DC 4. As an example one can consider a system o 4 cantilever beams linked by a transverse beam at their ree ends. A material ailure at the supports in one o the beams will only reduce the resistance with 5%. (Assuming suicient strength in the transverse beam). Since the structure without damage need to be checked with partial saety actors according to Ultimate Limit States, such a system will prove to satisy ALS, and design class DC 3 or DC 4 dependent upon complexity will apply. A similar system o only two cantilever beams will normally not ullill the ALS criterion to damage condition and DC 1 or DC will apply. NORSOK standard Page 97 o 488

106 Rev. 1, December 1998 Comm. 5. Steel quality level Steel materials selected in accordance with the tabled steel quality level (SQL) and as per Material Data Sheet (MDS) in NORSOK M-10 are assured to be o the same weldability within each SQL group, irrelevant o the actual material thickness or yield strength chosen. Requirements or SQL I are more severe than those or SQL II. This is achieved through the dierent optional requirements stated in each MDS or each SQL. The achievement o balanced weldability is reached mainly by two means: Requirement to higher energy absorption at toughness testing or yield strength above 400 MPa. Lowering the test temperature or qualiication testing, relecting the dierences between SQL II and I and stepwise increases in material thickness. For high strength material o 40 MPa and above, the MDS's assume the same minimum yield strength irrelevant o material thickness o plates. This is normally achieved through adjustments in chemical composition, but without jeopardising the required weldability. Improved properties in the trough thickness direction (SQL I) should be speciied or steel materials where ailure due to lamellar tearing will mean signiicant loss o resistance. Alternatively the plate can be tested ater welding to check that lamellar tearing has not taken place. Comm. 6 Ultimate Limit States Comm. 6.1 General Eurocode 3 uses the ollowing deinition o Ultimate Limit States: "Ultimate limit states are those associated with collapse, or with other orms o structural ailure which may endanger the saety o people. States prior to structural collapse which, or simplicity, are considered in place o the collapse itsel are also classiied and treated as ultimate limit states". For structures designed according to this standard structural ailures which will imply signiicant pollution or major inancial concequences should be considered in addition to human saety. All steel structures behave more or less non-linear when loaded to their ultimate limit. The ormulae or design resistance in this standard or similar codes and standards are thereore developed on the basis that permanent deormation may take place. Traditionally, oshore structures are analysed by linear methods to determine the internal distribution o orces and moments, and the resistances o the cross-sections are checked according to design resistances ound in design codes. The design ormulae oten require deormations well into the in-elastic range in order to mobilise the prescribed resistances. However, no urther checks are considered necessary as long as the internal orces and moments are determined by linear methods. When non-linear analysis methods are used, additional checks o ductility and repeated yielding, are to be perormed. The check or repeated yielding is only necessary in case o cyclic loading e.g. wave loads. The check or ductility requires that all sections subjected to deormation into the in-elastic range should deorm without loss o the assumed load-bearing resistance. Such loss o resistance can be due to racture, instability o cross-sectional parts or member buckling. The design codes give little NORSOK standard Page 98 o 488

107 Rev. 1, December 1998 guidance on this issue, with exception or stability o cross-sectional parts in yield hinges, which will normally be covered by requirement to cross-sectional class 1. See e.g. Eurocode 3. The check against repeated yielding is oten reerred to as the check that the structure can achieve a stable state called shakedown. In the general case it is necessary to deine a characteristic cycling load and to use this load with appropriate partial saety actors. It should be checked that yielding only take place in the irst ew loading cycles and that later load repetitions only cause responses in the linear range. Alternatively a low cycle atigue check can be perormed and substitute the check or shakedown. I non-linear analyses are applied, it shall be checked that the analysis tool and the modelling adopted represent the non-linear behaviour o all structural elements that may contribute to the ailure mechanism with suicient accuracy (See Ultiguide /11/). Stiness, resistance and post ultimate behaviour (i applicable) should be represented, including local ailure modes such as local buckling, joint overload, joint racture etc. Use o non-linear analysis methods may result in more structural elements being governed by the requirements to the Serviceability Limit State and additional SLS requirements may be needed compared with design using linear methods. The ollowing simpliications are valid or design with respect to the ultimate limit states, provided that ductile ailure modes can be assumed: built in stresses rom abrication and erection may be neglected when abrication requirements according to NORSOK M-101 are met, stresses rom dierential temperature under normal conditions e.g. sun heating may be neglected, and the analytical static model need not in detail represent the real structure e.g. secondary (delection induced) moments may be neglected or trusses. Comm. 6. Ductility Steel structures behave generally ductile when loaded to their limits. The established design practise is based on this behaviour, which is beneicial both with respect to the design and perormance o the structure. For a ductile structure, signiicant delections may occur beore ailure and thus give a collapse warning. Ductile structures also have larger energy absorption capabilities against impact loads. The possibility or the structure to redistribute stresses lessens the need or an accurate stress calculation during design as the structure may redistribute orces and moments to be in accordance with the assumed static model. This is the basis or use o linear analyses or ULS checks even or structures, which behave signiicantly non-linear when approaching their ultimate limit states. Comm General This section has been developed speciically or circular tubular shapes that are typical o oshore platorm construction. The types o tubulars covered include abricated roll-bent tubulars with a longitudinal weld seam, hot-inished seamless pipes, and ERW pipes that have undergone some types o post-weld heat treatment or normalisation to relieve residual stresses. Relie o the residual stresses is necessary to remove the rounded stress-strain characteristic that requently arises rom the ERW orm o manuacture. The recommendations in this section are basically in accordance with drat or ISO , /13/. NORSOK standard Page 99 o 488

108 Rev. 1, December 1998 Comm Axial compression Tubular members subjected to axial compression are subject to ailure due to either material yielding, overall column buckling, local buckling, or a combination o these ailure modes. The characteristic equation or column buckling is a unction o λ, a normalised orm o column slenderness parameter given by ( cl / E ) 0.5 ; where cl is the local buckling strength o the cross-section and E is the Euler buckling strength or a perect column. For members with two or more dierent cross sections, the ollowing steps can be used to determined the resistance: Determine the elastic buckling load, N E, or the complete member, taking into account the end restraints and variable cross-section properties. In most cases, the eective length actor o the member needs to be determined. The design compressive resistance, N cr,rd, is given by N N N N = cl cl c,rd γ M E or N N cl E < 1.34 (1.1) N c,rd 0.9 N γ E cl = or M N N E (1.) in which N cl = smallest characteristic local axial compressive strength o all the cross sections = cl A cl = as given by Equation (6.6) or (6.7) A = cross-sectional area In design analysis, a member with variable cross sections can be modelled with several prismatic elements. For each prismatic element, added length and/or input eective length actor are used to ensure that the design compressive resistance is correctly determined. The theoretical value o C x or an ideal tubular is 0.6. However, a reduced value o C x = 0.3 is recommended or use in Equation (6.8) to account or the eect o initial geometric imperections within tolerance limits given in NORSOK M-101. A reduced value o C x = 0.3 is also implicit in the limits or y / cle given in Equations (6.6) or (6.7). Short tubular members subjected to axial compression will ail either by material yielding or local buckling, depending on the diameter-to-thickness (D/t) ratio. Tubular members with low D/t ratios are generally not subject to local buckling under axial compression and can be designed on the basis o material yielding, i.e., the local buckling stress may be considered equal to the yield strength. However, as the D/t ratio increases, the elastic local buckling strength decreases, and the tubular should be checked or local buckling. Unstiened thin-walled tubular subjected to axial compression and bending are prone to sudden ailures at loads well below the theoretical buckling loads predicted by classical small-delection shell theory. There is a sudden drop in load-carrying resistance upon buckling o such members. The post-buckling reserve strength o tubular members is small, in contrast to the post-buckling behaviour o lat plates in compression, which usually continue to carry substantial load ater local NORSOK standard Page 100 o 488

109 Rev. 1, December 1998 buckling. For this reason, there is a need or more conservatism in the deinition o buckling load or tubulars than or most other structural elements. The large scatter in test data also necessitates a relatively conservative design procedure. The large scatter in test data is partly caused by initial imperections generated by abrication. Other actors o inluence are boundary conditions and builtin residual stresses (Re. /3/ and /4/). Some experimental evidence indicates that inelastic local buckling may be less sensitive to initial imperections and residual stresses than elastic local buckling (Re. /3/). Thereore, in order to achieve a robust design, it is recommended to select member geometry such that local buckling due to axial orces is avoided. The characteristic equations are developed by screening test data and establishing the curve at 95% success at the 50% conidence level, which satisies the ollowing conditions: 1) it has a plateau o material characteristic yield strength over the range 0 y / cle 0.17, ) it has the general orm o Equation (6.7), 3) it converges to the elastic critical buckling curve with increasing member slenderness ratio, and 4) the dierence between the mean minus standard deviations o test data and the developed equations is minimum. The local buckling data base contains 38 acceptable tests perormed by several dierent investigators (Re. /3/). A comparison between test data and the characteristic local buckling strength equation, Equations (6.6) to (6.8) was made. The developed equations have the bias o 1.065, the standard deviation o 0.073, and the coeicient o variation o The elastic local buckling stress ormula recommended in Equation (6.8) represent one-hal o the theoretical local buckling stress computed using classical small-delection theory. This reduction accounts or the detrimental eect o geometric imperections. Based on the test data shown in /3/, this reduction is considered to be conservative or tubulars with t 6 mm and D/t < 10. Oshore platorm members typically all within these dimensional limits. For thinner tubulars and tubulars with higher D/t ratios, larger imperection reduction actors may be required, re. Annex B. The local buckling database limits the applicability o the nominal strength equations to D/t<10 and t 6mm. Annex B provides guidance or the design o tubular members beyond these dimensional limits. Comm Hoop buckling Unstiened tubular members under external hydrostatic pressure are subject to elastic or inelastic local buckling o the shell wall between the restraints. Once initiated, the collapse will tend to latten the member rom one end to the other. Ring-stiened members are subject to local buckling o the shell wall between rings. The shell buckles between the rings, while the rings remain essentially circular. However, the rings may rotate or warp out o their plane. Ring-stiened tubular members are also subject to general instability, which occurs when the rings and shell wall buckle simultaneously at the critical load. It is desirable to provide rings with suicient residual strength to prevent general instability. Reerence is made to Annex B, buckling strength o shells. For tubular members satisying the maximum out-o-roundness tolerance o 1 percent, the hoop buckling strength is given by Eqs. (6.17) to (6.19). For ring-stiened members, Eqs. (6.17) to (6.19) NORSOK standard Page 101 o 488

110 Rev. 1, December 1998 gives the hoop buckling strength o the shell wall between the rings. To account or the possible 1 percent out-o roundness, the elastic hoop buckling stress is taken as 0.8 o the theoretical value calculated using classical small delection theory. That is, C h =0.44t/D, whereas the theoretical C h =0.55t/D. In addition, the remaining C h values are lower bound estimates. For members with out-o-roundness greater than 1 %, but less than 3 %, a reduced elastic hoop buckling strength, he, should be determined (Re. /3/). The characteristic hoop buckling strength, h, is then determined using the reduced he. Reduced he = he α 0.8 in which α = geometric imperection actor D max D min = D D D max 0.01 D min nom nom = out-o-roundness (%) where D max and D min are the maximum and minimum o any measured diameter at a cross section and D nom the nominal diameter. Comm Ring stiener design The ormula recommended or determining the moment o inertia o stiening rings, Equation (6.1), provides suicient strength to resist buckling o the ring and shell even ater the shell has buckled between stieners. It is assumed that the shell oers no support ater buckling and transers all its orces to the eective stiener section. The stiener ring is designed as an isolated ring that buckles into two waves (n=) at a collapse pressure 0 percent higher than the strength o the shell. The eect o ring stieners on increased axial resistance or large diameter/thickness ratios is not accounted or in this section. Reerence is made to Annex B or guidance on this. Comm Tubular members subjected to combined loads without hydrostatic pressure This section describes the background o the design requirements in Section 6.3.8, which covers unstiened and ring-stiened cylindrical shell instability mode interactions when subjected to combined axial and bending loads without hydrostatic pressure In this section and Section 6.3.9, the designer should include the second order rame moment or P- eect in the bending stresses, when it is signiicant. The P- eect may be signiicant in the design o unbraced deck legs, piles, and laterally lexible structures. Comm Axial tension and bending This section provides a resistance check or components under combined axial tensile load and bending. The interaction equation is modiied compared with the present drat to ISO /13/ as the term or axial load is rised in the power o NORSOK standard Page 10 o 488

111 Rev. 1, December 1998 Comm Axial compression and bending This section provides an overall beam-column stability check, Equation (6.7), and strength check, Equation (6.8), or components under combined axial compression orce and bending. Use o φ-unctions (Livesley Re. /5/) implies that exact solutions are obtained or the considered buckling problem. General eective buckling lengths have been derived using the φ-unctions incorporating end lexibility o the members. The results or an X-brace with our equal-length members are shown in Figure 1-1 to Figure 1-3 as a unction o the load distribution in the system Q/P and o the end rotational stiness. P is the maximum compression orce. The non-dimensional parameter ρ is given as: CL ρ = EI where C is the local rotational stiness at a node (accounting or local joint stiness and stiness o the other members going into the joint) and I is the moment o inertia o the tubular member. Normally L reers to center-line-to-center-line distances between nodes. The results in Figure 1- indicates or realistic end conditions (ρ > 3) or single braces, i.e., when Q/P = 1, a k-actor less than 0.8 is acceptable provided end joint lexibilities are not lost as the braces become ully loaded. Experimental results relating to rames seem to conirm that 0.7 is acceptable. For X-braces where the magnitude o the tension brace load is at least 50% o the magnitude o the compression brace load, i.e., when Q/P < -0.5, and the joints remain eective, k = 0.45 times the length L is supported by these results, whilst 0.4 seems justiied based on experimental evidence. Figure 1- and Figure 1-3 provide eective length actors or X-braces when the longer segment is equal to 0.6 times the brace length and 0.7 times the brace length, respectively. To estimate the eective length o a unbraced column, such as superstructure legs, the use o the alignment chart in Figure 1-4 provides a airly rapid method or determining adequate k-values. For cantilever tubular members, an independent and rational analysis is required in the determination o appropriate eective length actors. Such analysis shall take ull account o all large delection (P- ) eects. For a cantilever tubular member, C m =1.0. The use o the moment reduction actor (C m ) in the combined interaction equations, such as Eq. (6.7), is to obtain an equivalent moment that is less conservative. The C m values recommended in Table 6- are similar to those recommended in Re. /6/. NORSOK standard Page 103 o 488

112 Rev. 1, December 1998 Figure 1-1 Eective length actors or a X-brace with equal brace lengths NORSOK standard Page 104 o 488

113 Rev. 1, December 1998 Figure 1- Eective length actors or a X-brace with the shorter segment equal to 0.4 times the brace length NORSOK standard Page 105 o 488

114 Rev. 1, December 1998 Figure 1-3 Eective length actors or a X-brace with the shorter segment equal to 0.3 times the brace length NORSOK standard Page 106 o 488

115 Rev. 1, December 1998 Figure 1-4 Alignment chart or eective length o columns in continuous rames Comm Tubular members subjected to combined loads with hydrostatic pressure This section provides strength design interaction equations or the cases in which a tubular member is subjected to axial tension or compression, and/or bending combined with external hydrostatic pressure. Some guidance on signiicance o hydrostatic pressure may be ound rom Figure 1-5 or a given water depth and diameter/thickness ratio. NORSOK standard Page 107 o 488

116 Rev. 1, December Waterdepth (m) % 5 % 10 % 100 % Diameter/thickness Figure 1-5 Reduction in bending resistance o members due to external pressure, (γ M γ = 1.5, y = 350 MPa) The design equations are categorised into two design approaches, Methods A and B. The main purpose o providing two methods is to acilitate tubular member design by the two common analyses used by designers. Either design method is acceptable. In the limit when the hydrostatic pressure is zero, the design equations in this section reduce to those given in Sect In both methods the hoop compression is not explicitly included in the analysis, but its eect on member design is considered within the design interaction equations. For both design methods, the hoop collapse design check stipulated in Sect must be satisied irst. Method A should be used when the capped-end axial compression due to external hydrostatic pressure is not explicitly included in the analysis, but its eect is accounted or while computing the member utilisation ratio. Method B should be used when the capped-end axial compression due to external hydrostatic pressure is included explicitly in the analysis as nodal loads. The explicit application o the cappedend axial compression in the analysis allows or a more precise redistribution o the capped-end load based on the relative stinesses o the braces at a node. The two methods are not identical. However, since redistribution o the capped-end axial compression in Method B is minimal because o similar brace sizes at a node, the dierence between the two methods should be small. Comm Axial tension, bending, and hydrostatic pressure Method A (σ a,sd is in tension) The actual member axial stress, or the net axial stress, is estimated by subtracting the ull cappedend axial compression rom the calculated axial tension, σ a,sd. The net axial tensile stress, (σ a,sd - σ q,sd ), is then used in Eq. (6.34), which is a linear tension-bending interaction equation. There are NORSOK standard Page 108 o 488

117 Rev. 1, December 1998 mainly three eects due to the presence o external hydrostatic pressure: 1) a reduction o the axial tension due to the presence o a capped-end axial compression, ) a reduction o the axial tensile strength, th,rd, caused by the hoop compression, and 3) a reduction o the bending strength, mh,rd, caused by the hoop compression. As demonstrated in Re. /3/, the axial tension-hydrostatic pressure interaction is similar to the bending-hydrostatic pressure interaction. The reduced axial tensile and bending strengths, as given by Eqs. (6.35) and (6.36), were derived rom the ollowing ultimate-strength interaction equations: combined axial tension and hydrostatic pressure: σ a,sd d σ + p,sd h,rd η σ + ν p,sd h,rd σ a,sd d = 1.0 = d γ y M (1.3) σ m,sd m,rd σ + p,sd h,rd η σ + ν p,sd h,rd σ m,sd m, Rd = 1.0 = m,rd γ m M (1.4) To obtain the axial tensile and bending strengths rom the above two equations, the σ a,sd and σ m,sd terms are represented by th and mh, respectively, which are given by the positive roots o the quadratic equations. When the calculated axial tensile stress is greater than or equal to the capped-end axial compression, that is, σ a,sd σ q,sd, the member is subjected to net axial tension. For this case, the member yield strength, y, is not replaced by a local buckling axial strength. When the calculated axial tensile stress is less than the capped-end axial compression, that is, σ a,sd < σ q,sd, the member is subjected to net axial compression and to a quasi-hydrostatic pressure condition. (A member is subjected to a pure hydrostatic pressure condition when the net axial compressive stress is equal to the capped-end axial stress, that is, σ a,sd = 0.) Under this condition there is no member instability. Hence or this case, in which σ a,sd σ q,sd, the cross-sectional yield criterion (Eq. (6.39)) and the cross-sectional elastic buckling criterion (Eq. (6.41)) need to be satisied. Method B (σ ac,sd is in tension) In this method the member net axial stress is the calculated value, σ ac,sd, since the eect o the capped-end axial compression is explicitly included in the design analysis. Thereore, the calculated axial tensile stress, σ ac,sd, can be used directly in the cross-sectional strength check, as given in Eq. (6.4). Comm Axial compression, bending, and hydrostatic pressure Method A (σ a,sd is in compression) The capped-end axial compression due to hydrostatic pressure does not cause buckling o a member under combined external compression and hydrostatic pressure. The major contribution o the capped-end axial compression is earlier yielding o the member in the presence o residual stresses NORSOK standard Page 109 o 488

118 Rev. 1, December 1998 and additional external axial compression. The earlier yielding in turn results in a lower column buckling strength or the member, as given in Eq. (6.47). When there is no hydrostatic pressure, that is, σ q,sd = 0, Eq. (6.47) reduces to the in-air case, Eq. (6.3). It is incorrect to estimate the reduced column buckling strength by subtracting the capped-end axial compression rom the in-air buckling strength calculated by Eq. (6.3). This approach assumes that the capped-end axial compression can cause buckling and actually the reduced strength can be negative or cases where the capped-end axial compression is greater than the in-air buckling strength. For the stability check (Eq. (6.43)), the calculated axial compression, σ a,sd, which is the additional external axial compression, is used. The eect o the capped-end axial compression is captured in the buckling strength, ch,rd, which is derived or hydrostatic conditions. For strength or crosssectional yield check (Eq. (6.44)), the net axial compression o the member is used. In addition, the cross-section elastic buckling criterion (Eq. (6.41)) need to be satisied. Method B (σ ac,sd is in compression) In this method the calculated axial stress, σ ac,sd, is the net axial compressive stress o the member since the capped-end axial compression is included in the design analysis. For the stability check (Eq. (6.50)), the axial compression to be used with the equation is the component that is in additional to the pure hydrostatic pressure condition. Thereore, the capped-end axial compression is subtracted rom the net axial compressive stress in Eq. (6.50). For the strength check (Eq. (6.51)), the net axial compressive stress is used. When the calculated axial compressive stress is less than the capped-end axial compression, the member is under a quasi-hydrostatic pressure condition. That is, the net axial compression is less than the capped-end axial compression due to pure hydrostatic pressure. Under this loading, the member can not buckle as a beam-column. O course, hoop collapse is still a limit state. For this case, in which σ ac,sd σ q,sd, only the yield criterion o Eq. (6.51) needs to be satisied. Comm 6.4 Tubular joints Reasonable alternative methods to the requirements in this standard may be used or the design o joints. Test data and analytical techniques may be used as a basis or design, provided that it is demonstrated that the resistance o such joints can be reliably estimated. The recommendations presented here have been derived rom a consideration o the characteristic strength o tubular joints. Characteristic strength is comparable to lower bound strength. Care should thereore be taken in using the results o limited tests programs or analytical investigations to provide an estimate o joint resistance. Consideration shall be given to the imposition o a reduction actor on the calculation o joint resistance to account or a small amount o data or a poor basis or the calculation. Analytical or numerical techniques should be calibrated and benchmarked to suitable test data. The ormulas in this section are based upon drat to ISO , /13/. NORSOK standard Page 110 o 488

119 Rev. 1, December 1998 Comm General Detailing practice Joint detailing is an essential element o joint design. For simple tubular joints, the recommended detailing nomenclature and dimensioning are shown in Figure 6-1. This practice indicates that i an increased wall thickness o chord or special steel, is required, it should extend past the outside edge o incoming bracing a minimum o one quarter o the chord diameter or 300 mm, whichever is greater. Short chord can lengths can lead to a downgrading o joint resistance. The designer should consider speciying an increase o such chord can length to remove the need or resistance downgrading (see ). An increased wall thickness o brace or special steel, i required, should extend a minimum o one brace diameter or 600 mm, whichever is greater. Neither the cited chord can nor brace stub dimension includes the length over which thickness taper occurs. The minimum nominal gap between adjacent braces, whether in- or out-o-plane, is normally 50 mm. Care should be taken to ensure that overlap o welds at the toes o the joint is avoided. When overlapping braces occur, the amount o overlap should preerably be at least d/4 (where d is diameter o the through brace) or 150 mm, whichever is greater. This dimension is measured along the axis o the through member. Where overlapping o braces is necessary or preerred, the brace with the larger wall thickness should be the through brace and ully welded to the chord. Further, where substantial overlap occurs, the larger diameter brace should be speciied as the through member. This brace require an end stub to ensure that the thickness is at least equal to that o the overlapping brace. Comm Joint classiication Case (h) in Figure 6- is a good example o the actions and classiication hierarchy that should be adopted in the classiication o joints. Replacement o brace actions by a combination o tension and compression orce to give the same net action is not permitted. For example, replacing the orce in the horizontal brace on the let hand side o the joint by a compression orce o 1000 and tension orce o 500 is not permitted, as this may result in an inappropriate X classiication or this horizontal brace and a K classiication or the diagonal brace. Special consideration should be given to establish the proper gap i a portion o the action is related to K-joint behaviour. The most obvious case in Figure 6- is (a), or which the appropriate gap is between adjacent braces. However, i an intermediate brace exists, as in case (d), the appropriate gap is between the outer loaded braces. In this case, since the gap is oten large, the K-joint resistance could revert to that o a Y-joint. Case (e) is instructive in that the appropriate gap or the middle brace is gap 1, whereas or the top brace it is gap. Although the bottom brace is treated as 100% K classiication, a weighted average in resistance is required, depending on how much o the acting axial orce in this brace is balanced by the middle brace (gap 1) and how much is balanced by the top brace (gap ). Comm Strength actor Q u The Q u term or tension orces is based on limiting the resistance to irst crack. NORSOK standard Page 111 o 488

120 Rev. 1, December 1998 Comm Ringstiened joints For ringstiened joints, the load eects determined by elastic theory will, in general, include local stress peaks. In the ULS check, such peaks may be reduced to mean values within limited areas. The extent o these areas shall be evaluated or the actual geometry. An assumed redistribution o stress should not lead to signiicant change in the equilibrium o the dierent parts o the joint. E. g. i an action in a brace is resisted by a shear orce over a ringstiener with an associated moment, a removal o local stress peaks should not imply signiicant reduction in this moment required or equilibrium. Ringstiened joints may be designed according to plastic theory provided that all parts o the joint belongs to cross section class 1 or o NS 347. Load eects may be determined by assuming relevant plastic collapse mechanisms. The characteristic resistance shall be determined by recognised methods o plastic theory. The design resistance is determined by dividing the characteristic resistance by γ M = The resistance may also be determined based on non-linear analysis. The computer programme used or such analysis should be validated as providing reliable results in comparison with other analysis and tests. Also the type o input to the analysis should be calibrated to provide reliable results. This includes type o element used, element mesh and material description in terms o stress strain relationship. Comm Local buckling under axial compression Platorms generally have a very small number o cones. Thus, it might be more expeditious to design the cones with a geometry such that the axial resistance is equal to that o yield, see Section Comm Junction yielding The resistance o the junction is checked according to von Mises yield criterion when the hoop stress is tensile. Comm Hoop buckling Hoop buckling is analysed similarly to that o a tubular subjected to external pressure using equivalent geometry properties. Comm Junction yielding and buckling The load eect rom external pressure is directly added to the existing stress at the junction or utilisation check with respect to yielding and buckling. Comm Junction rings without external hydrostatic pressure The resistance o stieners at a junction is checked as a ring where the eective area o the tubular and the cone is added to that o the ring section. Comm Junction rings with external hydrostatic pressure The required moment o inertia is derived as the sum o that required or the junction itsel and that due to external pressure. NORSOK standard Page 11 o 488

121 Rev. 1, December 1998 Comm Intermediate stiening rings Design o intermediate ring stieners within a cone is perormed along the same principles as used or design o ring stieners in tubulars. Comm Failure modes Stocky plate elements need only to be checked against excessive yielding. With stocky plates are understood plates with suicient low slenderness so the resistance against compressive stresses is not reduced due to buckling. I.e. the plate elements satisy the requirements or sections class 3 in NS347 or Eurocode 3. By excessive yielding is meant yielding which is associated with ailure or collapse o the structure or structural component. Methods or resistance checks o plates against yielding include: elastic analysis with check o von Mises yield criteria at all points (a conservative check against excessive yielding), yield line theory, and non-linear inite element analysis. Comm Buckling o plates Slender plates designed according to the eective width ormula utilise the plates in the post critical range. This means that higher plate stresses than the buckling stress according to linear theory or the so-called critical buckling stress are allowed. Very slender plates, i.e. span to thickness ratio greater than 150, may need to be checked or serviceability limit states or atigue limit states. Failure modes in the serviceability limit states are reduced aesthetic appearance due to out o plane distortions or snap through i the plate is suddenly changing its out o plane deormation pattern. As the main source or the distortions will be due to welding during abrication, the most eective way to prevent these phenomena is to limit the slenderness o the plate. The likelihood o atigue cracking at the weld along the edges o the plate may increase or very slender plates i the in plane loading is dynamic. This stems rom bending stresses in the plate created by out o plane delection in a delected plate with in plane loading. For plates with slenderness less than 150, ordinary atigue checks where out o plane delections o plate are disregarded will be suicient. Comm General For wide langes the stresses in the longitudinal direction will vary due to shear deormations. (Shear lag). For buckling check o langes with longitudinal stieners shear lag eects may be neglected as long as the lange width is less than 0.L to each side o the web (bulkhead). L being length between points o counterlexure. Comm Interaction ormulas or axial compression and lateral pressure The equations (6.143) and (6.144) may be seen as interaction ormulas or the stiener and plate side respectively or a section at the support. Equations (6.145) and (6.146) are likewise interaction checks at the mid-span o the stiener. See also Figure 1-6. NORSOK standard Page 113 o 488

122 Rev. 1, December 1998 l/ l/ Figure 1-6 Check points or interaction equations With the lateral load on the stiener side, the stresses change sign and the equations (6.147) to (6.150) shall be used. The sections to be checked remain the same. The eccentricity z* is introduced in the equations to ind the maximum resistance o the stiened panel. In the ultimate limit state a continuos stiened panel will carry the load in the axis giving the maximum load. For calculation o the orces and moments in the total structure, o which the stiened panel is a part, the working point or the stiened panel should correspond to the assumed value o z*. In most cases the inluence o variations in z* on global orces and moments will be negligible. See also Figure 1-7. Figure 1-7 Deinition o z *. Positive value shown Comm Buckling o girders When a stiened panel supported by girders is subjected to lateral loads the moments rom this load should be included in the check o the girder. I the girder is checked according to method 1, the stiener and plate should also be checked or the σ y stresses imposed by the bending o the girder. NORSOK standard Page 114 o 488

123 Rev. 1, December 1998 In method, the σ y stresses imposed by the bending o the girder can be neglected when checking plate and stiener. Comm. 6.7 Design o cylindrical shells A tubular section in air with diameter/thickness ratio larger than 60 is likely to ail by local buckling at an axial stress less than the material yield strength. Based on Eurocode 3 the upper limit o section class 3, where an axial stress equal yield strength can be achieved, is a D/t ratio o 1150/ y where y is material yield strength in MPa. The resistance o members ailing due to local buckling is more sensitive to geometric imperections than members that can sustain yielding over the thickness and allow some redistribution o local stresses due to yielding. The ailure o such members is normally associated with a descending post-critical behaviour that may be compared more with that o a brittle structure, i. e. the redistribution o load can not be expected. Structures with this behaviour are denoted as shells. A deinition o a shell structure should not only include geometry and material resistance, but also loading as the axial resistance is reduced by e. g. increasing pressure. Design equations have been developed to account or dierent loading conditions, see Annex B. The background or these design equations is given by Odland //. Comm. 9 Accidental Damage Limit States Examples o ailure criteria are: Critical deormation criteria deined by integrity o passive ire protection. To be considered or walls resisting explosion pressure and shall serve as ire barrier ater the explosion. Critical delection or structures to avoid damage to process equipment (Riser, gas pipe, etc). To be considered or structures or part o structures exposed to impact loads as ship collision, dropped object etc. Critical deormation to avoid leakage o compartments. To be considered in case o impact against loating structures where the acceptable collision damage is deined by the minimum number o undamaged compartments to remain stable. Comm Grouted joints This clause is based on drat ISO , /13/. Recommended Q U values are given in Table 1-1. Table 1-1 Values or Q u or grouted joints K / Y X Brace action Axial Tension K a In-plane Bending.5 β γ 1.5 β γ 1.5 β γ.5 β γ 1.5 β γ K a Out-o-plane bending 1.5 β γ Q β 1 1 K a = ( 1+ ) sinθ NORSOK standard Page 115 o 488

124 Rev. 1, December 1998 No Q U term is given or axial compression, since the compression resistance o grouted joints in most cases are limited by that o the brace. - o0o - NORSOK standard Page 116 o 488

125 Annex A Rev. 1, December 1998 DESIGN OF STEEL STRUCTURES ANNEX A DESIGN AGAINST ACCIDENTAL ACTIONS NORSOK standard Page 117 o 488

126 Annex A Rev. 1, December 1998 CONTENTS A.1 SYMBOLS 10 A. GENERAL 13 A.3 SHIP COLLISIONS 14 A.3.1 General 14 A.3. Design principles 14 A.3.3 Collision mechanics 15 A Strain energy dissipation 15 A.3.3. Reaction orce to deck 16 A.3.4 Dissipation o strain energy 16 A.3.5 Ship collision orces 17 A Recommended orce-deormation relationships 17 A.3.5. Force contact area or strength design o large diameter columns. 19 A.3.6 Force-deormation relationships or denting o tubular members 19 A.3.7 Force-deormation relationships or beams 131 A General 131 A.3.7. Plastic orce-deormation relationships including elastic, axial lexibility 131 A Bending capacity o dented tubular members 134 A.3.8 Strength o connections 134 A.3.9 Strength o adjacent structure 135 A.3.10 Ductility limits 135 A General 135 A Local buckling 135 A Tensile Fracture 137 A Tensile racture in yield hinges 138 A.3.11 Resistance o large diameter, stiened columns 139 A General 139 A Longitudinal stieners 139 A Ring stieners 139 A Decks and bulkheads 140 A.3.1 Energy dissipation in loating production vessels 140 A.3.13 Global integrity during impact 140 A.4 DROPPED OBJECTS 141 A.4.1 General 141 A.4. Impact velocity 141 A.4.3 Dissipation o strain energy 143 A.4.4 Resistance/energy dissipation 144 A Stiened plates subjected to drill collar impact 144 A.4.4. Stieners/girders 145 A Dropped object 145 A.4.5 Limits or energy dissipation 145 A Pipes on plated structures 145 A.4.5. Blunt objects 145 A.5 FIRE 146 A.5.1 General 146 NORSOK standard Page 118 o 488

127 Annex A Rev. 1, December 1998 A.5. General calculation methods 146 A.5.3 Material modelling 147 A.5.4 Equivalent imperections 147 A.5.5 Empirical correction actor 147 A.5.6 Local cross sectional buckling 148 A.5.7 Ductility limits 148 A General 148 A.5.7. Beams in bending 148 A Beams in tension 148 A.5.8 Capacity o connections 148 A.6 EXPLOSIONS 149 A.6.1 General 149 A.6. Classiication o response 149 A.6.3 Failure modes or stiened panels 150 A.6.4 SDOF system analogy 15 A Dynamic response charts or SDOF system 155 A.6.5 MDOF analysis 158 A.6.6 Classiication o resistance properties 158 A Cross-sectional behaviour 158 A.6.6. Component behaviour 158 A.6.7 Idealisation o resistance curves 159 A.6.8 Resistance curves and transormation actors or plates 160 A Elastic - rigid plastic relationships 160 A.6.8. Axial restraint 161 A Tensile racture o yield hinges 16 A.6.9 Resistance curves and transormation actors or beams 16 A Beams with no- or ull axial restraint 16 A.6.9. Beams with partial end restraint. 165 A Eective lange 168 A Strength o adjacent structure 169 A Strength o connections 169 A Ductility limits 169 A.7 RESIDUAL STRENGTH 170 A.7.1 General 170 A.7. Modelling o damaged members 170 A.7..1 General 170 A.7.. Members with dents, holes, out-o-straightness 170 A.8 REFERENCES 171 A.9 COMMENTARY 17 NORSOK standard Page 119 o 488

128 Annex A Rev. 1, December 1998 A.1 SYMBOLS A Cross-sectional area A e Eective area o stiener and eective plate lange A s Area o stiener A p Projected cross-sectional area B Width o contact area C D Hydrodynamic drag coeicient D Diameter o circular sections, plate stiness E Young's Modulus o elasticity, E p E kin E s F H I J K K LM L M M P N P T N N Sd N Rd R R 0 V W P W Plastic modulus Kinetic energy Strain energy Lateral load, total load Non-dimensional plastic stiness Moment o inertia, impuls Mass moment o inertia Stiness, characteristic stiness, plate stiness Load-mass transormation actor Beam length Total mass, cross-sectional moment Plastic bending moment resistance Plastic axial resistance Fundamental period o vibration Axial orce Design axial compressive orce Design axial compressive capacity Resistance Plastic collapse resistance in bending Volume, displacement Plastic section modulus Elastic section modulus a a s a i b b c Added mass Added mass or ship Added mass or installation Width o collision contact zone Flange width Factor NORSOK standard Page 10 o 488

129 Annex A Rev. 1, December 1998 c c lp c w d d c y Axial lexibility actor Plastic zone length actor Displacement actor or strain calculation Smaller diameter o threaded end o drill collar Characteristic dimension or strain calculation Generalised load Characteristic yield strength g Acceleration o gravity, 9.81 m/s h w Web height or stiener/girder i Radius o gyration k Generalised stiness k l Load transormation actor k m Mass transormation actor k lm Load-mass transormation actor l Plate length, beam length m Distributed mass m s Ship mass m i Installation mass m eq Equivalent mass m Generalised mass p Explosion pressure p c Plastic collapse pressure in bending or plate r Radius o deormed area s Distance, stiener spacing s c Characteristic distance s e Eective width o plate t Thickness, time t d Duration o explosion t Flange thickness t w Web thickness v s Velocity o ship v i Velocity o installation v t Terminal velocity w Deormation, displacement w c Characteristic deormation w d dent depth w Non-dimensional deormation x Axial coordinate y Generalised displacement, displacement amplitude y el Generalised displacement at elastic limit z Distance rom pivot point to collision point NORSOK standard Page 11 o 488

130 Annex A Rev. 1, December 1998 α β ε ε cr ε y Plate aspect parameter Cross-sectional slenderness actor Yield strength actor, strain Critical strain or rupture Yield strain Plate eigenperiod parameter Displacement shape unction η φ λ Reduced slenderness ratio µ Ductility ratio ν Poisson's ratio, 0.3 θ Angle ρ Density o steel, 7860 kg/m 3 ρ w Density o sea water, 105 kg/m 3 τ Shear stress τ cr Critical shear stress or plate plugging ξ Interpolation actor ψ Plate stiness parameter NORSOK standard Page 1 o 488

131 Annex A Rev. 1, December 1998 A. GENERAL This Annex deals with the design to maintain the load-bearing unction o the structures during accidental events. The overall goal o the design against accidental actions is to achieve a system where the main saety unctions o the installation are not impaired. Design Accidental Actions and associated perormance criteria are determined by Quantiied Risk Assessment (QRA), see NORSOK N-003 /1/. In conjunction with design against accidental actions, perormance criteria may need to be ormulated such that the structure or components or sub-assemblies thereo - during the accident or within a certain time period ater the accident - shall not impair the main saety unctions such as: usability o escapeways, integrity o shelter areas, global load bearing capacity. The perormance criteria derived will typically be related to: energy dissipation local strength resistance to deormation (e.g braces in contact with risers/caissons, use o escape ways) endurance o ire protection ductility (allowable strains) - to avoid cracks in components, ire walls, passive ire protection etc. The inherent uncertainty o the requency and magnitude o the accidental loads as well as the approximate nature o the methods or determination analysis o accidental load eects shall be recognised. It is thereore essential to apply sound engineering judgement and pragmatic evaluations in the design. The material actor to be used or checks o accidental limit states is γ M = 1.0 NORSOK standard Page 13 o 488

132 Annex A Rev. 1, December 1998 A.3 SHIP COLLISIONS A.3.1 General The ship collision action is characterised by a kinetic energy, governed by the mass o the ship, including hydrodynamic added mass and the speed o the ship at the instant o impact. Depending upon the impact conditions, a part o the kinetic energy may remain as kinetic energy ater the impact. The remainder o the kinetic energy has to be dissipated as strain energy in the installation and, possibly, in the vessel. Generally this involves large plastic strains and signiicant structural damage to either the installation or the ship or both. The strain energy dissipation is estimated rom orce-deormation relationships or the installation and the ship, where the deormations in the installation shall comply with ductiliy and stability requirements. The load bearing unction o the installation shall remain intact with the damages imposed by the ship collision action. In addition, the residual strength requirements given in Section A.7 shall be complied with. The structural eects rom ship collision may either be determined by non-linear dynamic inite element analyses or by energy considerations combined with simple elastic-plastic methods. I non-linear dynamic inite element analysis is applied all eects described in the ollowing paragraphs shall either be implicitly covered by the modelling adopted or subjected to special considerations, whenever relevant. Oten the integrity o the installation can be veriied by means o simple calculation models. I simple calculation models are used the part o the collision energy that needs to be dissipated as strain energy can be calculated by means o the principles o conservation o momentum and conservation o energy, reer Section A.3.3. It is convenient to consider the strain energy dissipation in the installation to take part on three dierent levels: local cross-section component/sub-structure total system Interaction between the three levels o energy dissipation shall be considered. Plastic modes o energy dissipation shall be considered or cross-sections and component/substructures in direct contact with the ship. Elastic strain energy can in most cases be disregarded, but elastic axial lexibility may have a substantial eect on the load-deormation relationships or components/sub-structures. Elastic energy may contribute signiicantly on a global level. A.3. Design principles With respect to the distribution o strain energy dissipation there may be distinguished between, see FigureA.3-1: strength design ductility design shared-energy design NORSOK standard Page 14 o 488

133 Annex A Rev. 1, December 1998 Energy dissipation Ductile design Shared-energy design Strength design ship installation Relative strength - installation/ship Figure A.3-1 Energy dissipation or strength, ductile and shared-energy design Strength design implies that the installation is strong enough to resist the collision orce with minor deormation, so that the ship is orced to deorm and dissipate the major part o the energy. Ductility design implies that the installation undergoes large, plastic deormations and dissipates the major part o the collision energy. Shared energy design implies that both the installation and ship contribute signiicantly to the energy dissipation. From calculation point o view strength design or ductility design is avourable. In this case the response o the «sot» structure can be calculated on the basis o simple considerations o the geometry o the «rigid» structure. In shared energy design both the magnitude and distribution o the collision orce depends upon the deormation o both structures. This interaction makes the analysis more complex. In most cases ductility or shared energy design is used. However, strength design may in some cases be achievable with little increase in steel weight. A.3.3 Collision mechanics A Strain energy dissipation The collision energy to be dissipated as strain energy may - depending on the type o installation and the purpose o the analysis - be taken as: Compliant installations E s 1 = (m s + a s )v s i v i 1 v s ms + a 1+ m + a s i (A.3.1) Fixed installations 1 E + s = (ms a s )vs (A.3.) NORSOK standard Page 15 o 488

134 Annex A Rev. 1, December 1998 Articulated columns 1 = (m v i 1 v s + a s ) msz 1+ J Es s (A.3.3) m s = ship mass a s = ship added mass v s = impact speed m i = mass o installation a i = added mass o installation v i = velocity o installation J = mass moment o inertia o installation (including added mass) with respect to eective pivot point z = distance rom pivot point to point o contact In most cases the velocity o the installation can be disregarded, i.e. v i = 0. The installation can be assumed compliant i the duration o impact is small compared to the undamental period o vibration o the installation. I the duration o impact is comparatively long, the installation can be assumed ixed. Jacket structures can normally be considered as ixed. Floating platorms (semi-submersibles, TLP s, production vessels) can normally be considered as compliant. Jack-ups may be classiied as ixed or compliant. A.3.3. Reaction orce to deck In the acceleration phase the inertia o the topside structure generates large reaction orces. An upper bound o the maximum orce between the collision zone and the deck or bottom supported installations may be obtained by considering the platorm compliant or the assessment o total strain energy dissipation and assume the platorm ixed at deck level when the collision response is evaluated. Collision response Model Figure A.3- Model or assessment o reaction orce to deck A.3.4 Dissipation o strain energy The structural response o the ship and installation can ormally be represented as load-deormation relationships as illustrated in Figure A.3-3. The strain energy dissipated by the ship and installation equals the total area under the load-deormation curves. NORSOK standard Page 16 o 488

135 Annex A Rev. 1, December 1998 R s R i E s,s E s,i dw s Ship Installation dw i Figure A.3-3 Dissipation o strain energy in ship and platorm E s = E s,s + E s,i = w s,max R sdw s + 0 wi,max 0 R dw i i (A.3.4) As the load level is not known a priori an incremental procedure is generally needed. The load-deormation relationships or the ship and the installation are oten established independently o each other assuming the other object ininitely rigid. This method may have, however, severe limitations; both structures will dissipate some energy regardless o the relative strength. Oten the stronger o the ship and platorm will experience less damage and the soter more damage than what is predicted with the approach described above. As the soter structure deorms the impact orce is distributed over a larger contact area. Accordingly, the resistance o the strong structure increases. This may be interpreted as an "upward" shit o the resistance curve or the stronger structure (reer Figure A.3-3). Care should be exercised that the load-deormation curves calculated are representative or the true, interactive nature o the contact between the two structures. A.3.5 Ship collision orces A Recommended orce-deormation relationships Force-deormation relationships or a supply vessels with a displacement o 5000 tons are given in Figure A.3-4 or broad side -, bow-, stern end and stern corner impact or a vessel with stern roller. The curves or broad side and stern end impacts are based upon penetration o an ininitely rigid, vertical cylinder with a given diameter and may be used or impacts against jacket legs (D = 1.5 m) and large diameter columns (D = 10m). The curve or stern corner impact is based upon penetration o an ininitely rigid cylinder and may be used or large diameter column impacts. In lieu o more accurate calculations the curves in Figure A.3-4 may be used or square-rounded columns. NORSOK standard Page 17 o 488

136 Annex A Rev. 1, December Broad side D = 10 m = 1.5 m D Impact orce (MN) 30 0 Stern corner Stern end D = 10 m = 1.5 m D 10 D Bow Indentation (m) Figure A.3-4 Recommended-deormation curve or beam, bow and stern impact The curve or bow impact is based upon collision with an ininitely rigid, plane wall and may be used or large diameter column impacts, but should not be used or signiicantly dierent collision events, e.g. impact against tubular braces. For beam -, stern end and stern corner impacts against jacket braces all energy shall normally be assumed dissipated by the brace, reer Comm. A Force [MN] Bulb orce b a a b Contact dimension [m] Force [MN] a b Force s upers tructure a b Contact dimension [m] Deormation [m] Deormation [m] Figure A.3-5 Force -deormation relationship or tanker bow impact (~ dwt) Force-deormation relationships or tanker bow impact is given in Figure A.3-5 or the bulbous part and the superstructure, respectively. The curves may be used provided that the impacted structure (e.g. stern o loating production vessels) does not undergo substantial deormation i.e. strength design requirements are complied with. I this condition is not met interaction between the bow and the impacted structure shall be taken into consideration. Non-linear inite element methods or NORSOK standard Page 18 o 488

137 Annex A Rev. 1, December 1998 simpliied plastic analysis techniques o members subjected to axial crushing shall be employed /3/, /5/. A.3.5. Force contact area or strength design o large diameter columns. The basis or the curves in Figure A.3-4 is strength design, i.e. limited local deormations o the installation at the point o contact. In addition to resisting the total collision orce, large diameter columns have to resist local concentrations (subsets) o the collision orce, given or stern corner impact in Table A.3-1 and stern end impact in Table A.3-. Table A.3-1 Local concentrated collision orce -evenly distributed over a rectangular area. Stern corner impact Contact area a(m) b (m) Force (MN) b a Table A.3- Local concentrated collision orce -evenly distributed over a rectangular area. Stern end impact Contact area a (m) b(m) Force (MN) b a I strength design is not aimed or - and in lieu o more accurate assessment (e.g. nonlinear inite element analysis) - all strain energy has to be assumed dissipated by the column, corresponding to indentation by an ininitely rigid stern corner. A.3.6 Force-deormation relationships or denting o tubular members The contribution rom local denting to energy dissipation is small or brace members in typical jackets and should be neglected. The resistance to indentation o unstiened tubes may be taken rom Figure A.3-6. Alternatively, the resistance may be calculated rom Equation (A.3.5): NORSOK standard Page 19 o 488

138 Annex A Rev. 1, December 1998 R/(kRc) b/d = w d /D Figure A.3-6 Resistance curve or local denting R R c t D R c = y 4 t B c1 = + 1. D 1.95 c = B D k = 1.0 N k = 1.0 N k = 0 c w d = kc1 D Sd Rd 0. N N Sd Rd 0. N 0. < N N 0.6 N Sd Rd Sd Rd < 0.6 (A.3.5) N Sd = design axial compressive orce N Rd = design axial compressive resistance B = width o contact area w d = dent depth The curves are inaccurate or small indentation, and they should not be used to veriy a design w where the dent damage is required to be less than d < D NORSOK standard Page 130 o 488

139 Annex A Rev. 1, December 1998 A.3.7 Force-deormation relationships or beams A General The response o a beam subjected to a collision load is initially governed by bending, which is aected by and interacts with local denting under the load. The bending capacity is also reduced i local buckling takes place on the compression side. As the beam undergoes inite deormations, the load carrying capacity may increase considerably due to the development o membrane tension orces. This depends upon the ability o adjacent structure to restrain the connections at the member ends to inward displacements. Provided that the connections do not ail, the energy dissipation capacity is either limited by tension ailure o the member or rupture o the connection. Simple plastic methods o analysis are generally applicable. Special considerations shall be given to the eect o : elastic lexibility o member/adjacent structure local deormation o cross-section local buckling strength o connections strength o adjacent structure racture A.3.7. Plastic orce-deormation relationships including elastic, axial lexibility Relatively small axial displacements have a signiicant inluence on the development o tensile orces in members undergoing large lateral deormations. An equivalent elastic, axial stiness may be deined as 1 K = 1 K node! + EA (A.3.6) K node = axial stiness o the node with the considered member removed. This may be determined by introducing unit loads in member axis direction at the end nodes with the member removed. Plastic orce-deormation relationship or a central collision (midway between nodes) may be obtained rom : Figure A.3-7 or tubular members Figure A.3-8 or stiened plates in lieu o more accurate analysis. The ollowing notation applies: 4c1M P R 0 =! plastic collapse resistance in bending or the member, or the case that contact point is at mid span w w = c 1 w c non-dimensional deormation 4c 1Kw c c = y A! non-dimensional spring stiness c 1 = or clamped beams c 1 = 1 or pinned beams NORSOK standard Page 131 o 488

140 Annex A Rev. 1, December 1998 D w c = characteristic deormation or tubular beams 1.WP w c = A characteristic deormation or stiened plating W P = plastic section modulus! = member length For non-central collisions the orce-deormation relationship may be taken as the mean value o the orce-deormation curves or central collision with member hal length equal to the smaller and the larger portion o the member length, respectively. For members where the plastic moment capacity o adjacent members is smaller than the moment capacity o the impacted member the orce-deormation relationship may be interpolated rom the curves or pinned ends and clamped ends: R = ξr where clamped + ( 1 ξ) R pinned (A.3.7) actual R 0 0 ξ = 1 1 MP 4! (A.3.8) actual R 0 = Plastic resistance by bending action o beam accounting or actual bending resistance o adjacent members R actual 0 = 4M P + M! P1 + M P (A.3.9) M = M M i = adjacent member no i, j = end number {1,} (A.3.10) Pj i Pj,i P M Pj,i = Plastic bending resistance or member no. i. Elastic, rotational lexibility o the node is normally o moderate signiicance NORSOK standard Page 13 o 488

141 Annex A Rev. 1, December ,5 6 5,5 R/R 0 5 4,5 4 3,5 3,5 1,5 c = , K Bending & membrane Membrane only F (collision load) w K 1 0, ,5 1 1,5,5 3 3,5 4 Deormation w Figure A.3-7 Force-deormation relationship or tubular beam with axial lexibility 5 4,5 4 3,5 Bending & membrane Membrane only R/R 0 3,5 1,5 c= K F (collision load) w K 1 0 0, ,5 1 1,5,5 3 3,5 4 Deormation w Figure A.3-8 Force-deormation relationship or stiened plate with axial lexibility. NORSOK standard Page 133 o 488

142 Annex A Rev. 1, December 1998 A Bending capacity o dented tubular members The reduction in plastic moment capacity due to local denting shall be considered or members in compression or moderate tension, but can be neglected or members entering the ully plastic membrane state. Conservatively, the lat part o the dented section according to the model shown in Figure A.3-9 may be assumed non-eective. This gives: M M M red P P = θ cos = D y w θ = arccos 1 D t 1 sinθ d w d = dent depth as deined in Figure A.3-9. (A.3.11) 1 Mred/MP 0,8 0,6 0,4 w d D 0, 0 0 0, 0,4 0,6 0,8 1 wd/d Figure A.3-9 Reduction o moment capacity due to local dent A.3.8 Strength o connections Provided that large plastic strains can develop in the impacted member, the strength o the connections that the member rames into has to be checked. The resistance o connections should be taken rom ULS requirements in this standard or tubular joints and Eurocode 3 or NS347 or other joints. For braces reaching the ully plastic tension state, the connection shall be checked or a load equal to the axial resistance o the member. The design axial stress shall be assumed equal to the ultimate tensile strength o the material. I the axial orce in a tension member becomes equal to the axial capacity o the connection, the connection has to undergo gross deormations. The energy dissipation will be limited and rupture has to be considered at a given deormation. A sae approach is to assume disconnection o the member once the axial orce in the member reaches the axial capacity o the connection. NORSOK standard Page 134 o 488

143 Annex A Rev. 1, December 1998 I the capacity o the connection is exceeded in compression and bending, this does not necessarily mean ailure o the member. The post-collapse strength o the connection may be taken into account provided that such inormation is available. A.3.9 Strength o adjacent structure The strength o structural members adjacent to the impacted member/sub-structure must be checked to see whether they can provide the support required by the assumed collapse mechanism. I the adjacent structure ails, the collapse mechanism must be modiied accordingly. Since, the physical behaviour becomes more complex with mechanisms consisting o an increasing number o members it is recommended to consider a design which involves as ew members as possible or each collision scenario. A.3.10 Ductility limits A General The maximum energy that the impacted member can dissipate will ultimately - be limited by local buckling on the compressive side or racture on the tensile side o cross-sections undergoing inite rotation. I the member is restrained against inward axial displacement, any local buckling must take place beore the tensile strain due to membrane elongation overrides the eect o rotation induced compressive strain. I local buckling does not take place, racture is assumed to occur when the tensile strain due to the combined eect o rotation and membrane elongation exceeds a critical value. To ensure that members with small axial restraint maintain moment capacity during signiicant plastic rotation it is recommended that cross-sections be proportioned to Class 1 requirements, deined in Eurocode 3 or NS347. Initiation o local buckling does, however, not necessarily imply that the capacity with respect to energy dissipation is exhausted, particularly or Class 1 and Class cross-sections. The degradation o the cross-sectional resistance in the post-buckling range may be taken into account provided that such inormation is available, reer Comm. A For members undergoing membrane stretching a lower bound to the post-buckling load-carrying capacity may be obtained by using the load-deormation curve or pure membrane action. A Local buckling Circular cross-sections: Buckling does not need to be considered or a beam with axial restraints i the ollowing condition is ulilled: 14c β c1 y κ! d c 1 3 (A.3.1) where NORSOK standard Page 135 o 488

144 Annex A Rev. 1, December 1998 β = D t 35 y (A.3.13) axial lexibility actor c c = 1 c + (A.3.14) d c = characteristic dimension = D or circular cross-sections c 1 = or clamped ends = 1 or pinned ends c = non-dimensional spring stiness, reer Section A.3.7. κ! 0.5! = the smaller distance rom location o collision load to adjacent joint I this condition is not met, buckling may be assumed to occur when the lateral deormation exceeds w 1 14c y κ! = dc c c1β dc (A.3.15) For small axial restraint (c < 0.05) the critical deormation may be taken as w d c 3.5 = c y 3 1β κ! d c (A.3.16) Stiened plates/ I/H-proiles: In lieu o more accurate calculations the expressions given or circular proiles in Eq. (A.3.15) and (A.3.16) may be used with d c = characteristic dimension or local buckling, equal to twice the distance rom the plastic neutral axis in bending to the extreme ibre o the cross-section = h height o cross-section or symmetric I proiles = h w or stiened plating (or simplicity) For langes subjected to compression; β =.5 b t 35 y class 1 cross-sections (A.3.17) β = 3 b t 35 y class and class 3 cross-sections (A.3.18) For webs subjected to bending NORSOK standard Page 136 o 488

145 Annex A Rev. 1, December 1998 β = 0.7 h w t w 35 y class 1 cross-sections (A.3.19) β = 0.8 h w t w 35 y class and class 3 cross-sections (A.3.0) b = lange width t = lange thickness h w = web height t w = web thickness A Tensile Fracture The degree o plastic deormation or critical strain at racture will show a signiicant scatter and depends upon the ollowing actors: material toughness presence o deects strain rate presence o strain concentrations The critical strain or plastic deormations o sections containing deects need to be determined based on racture mechanics methods. (See chapter 6.5.) Welds normally contain deects and welded joints are likely to achieve lower toughness than the parent material. For these reasons structures that need to undergo large plastic deormations should be designed in such a way that the plastic straining takes place away outside the weld. In ordinary ull penetration welds, the overmatching weld material will ensure that minimal plastic straining occurs in the welded joints even in cases with yielding o the gross cross section o the member. In such situations, the critical strain will be in the parent material and will be dependent upon the ollowing parameters: stress gradients dimensions o the cross section presence o strain concentrations material yield to tensile strength ratio material ductility Simple plastic theory does not provide inormation on strains as such. Thereor, strain levels should be assessed by means o adequate analytic models o the strain distributions in the plastic zones or by non-linear inite element analysis with a suiciently detailed mesh in the plastic zones. When structures are designed so that yielding take place in the parent material, the ollowing value or the critical average strain in axially loaded plate material may be used in conjunction with nonlinear inite element analysis or simple plastic analysis εcr = t! where: t = plate thickness! = length o plastic zone. Minimum 5t (A.3.1) NORSOK standard Page 137 o 488

146 Annex A Rev. 1, December 1998 A Tensile racture in yield hinges When the orce deormation relationships or beams given in Section A.3.7. are used rupture may be assumed to occur when the deormation exceeds a value given by w d c = 1 c ( 1+ 4c c ε 1) w where the ollowing actors are deined; Displacement actor cr (A.3.) c w 1 W ε cr κ clp 1 clp 4 1! (A.3.3) = c W P ε y D plastic zone length actor c lp ε cr 1 ε y = ε cr 1 ε y W W W W P P H H + 1 (A.3.4) axial lexibility actor c c = 1 c + (A.3.5) non-dimensional plastic stiness H = Ep E = 1 E ε cr cr ε y y (A.3.6) c 1 = or clamped ends = 1 or pinned ends c = non-dimensional spring stiness, reer Section A.3.7. κl 0.5l the smaller distance rom location o collision load to adjacent joint W = elastic section modulus W P = plastic section modulus ε cr = critical strain or rupture y ε y = E yield strain y = yield strength cr = strength corresponding to ε cr The characteristic dimension shall be taken as: d c = D diameter o tubular beams = h w twice the web height or stiened plates = h height o cross-section or symmetric I-proiles For small axial restraint (c < 0.05) the critical deormation may be taken as NORSOK standard Page 138 o 488

147 Annex A Rev. 1, December 1998 w = d c c w ε cr (A.3.7) The critical strain ε cr and corresponding strength cr should be selected so that idealised bi-linear stress-strain relation gives reasonable results. See Commentary. For typical steel material grades the ollowing values are proposed: Table A.3-3 Proposed values or e cr and H or dierent steel grades Steel grade ε cr H S 35 0 % 0.00 S % S % A.3.11 Resistance o large diameter, stiened columns A General Impact on a ring stiener as well as midway between ring stieners shall be considered. Plastic methods o analysis are generally applicable. A Longitudinal stieners For ductile design the resistance o longitudinal stieners in the beam mode o deormation can be calculated using the procedure described or stiened plating, section A.3.7. For strength design against stern corner impact, the plastic bending moment capacity o the longitudinal stieners has to comply with the requirement given in Figure A.3-10, on the assumption that the entire load given in Table A.3- is taken by one stiener. Plastic bending capacity (MNm) Distance between ring stieners (m) Figure A.3-10 Required bending capacity o longitudinal stieners A Ring stieners In lieu o more accurate analysis the plastic collapse load o a ring-stiener can be estimated rom: NORSOK standard Page 139 o 488

148 Annex A Rev. 1, December 1998 F 0 = 4 M w c D P (A.3.8) where W P w c = = characteristic deormation o ring stiener A e D = column radius M P = plastic bending resistance o ring-stiener including eective shell lange W P = plastic section modulus o ring stiener including eective shell lange A e = area o ring stiener including eective shell lange Eective lange o shell plating: Use eective lange o stiened plates, see Chapter 6. For ductile design it can be assumed that the resistance o the ring stiener is constant and equal to the plastic collapse load, provided that requirements or stability o cross-sections are complied with, reer Section A A Decks and bulkheads Calculation o energy dissipation in decks and bulkheads has to be based upon recognised methods or plastic analysis o deep, axial crushing. It shall be documented that the collapse mechanisms assumed yield a realistic representation o the true deormation ield. A.3.1 Energy dissipation in loating production vessels For strength design the side or stern shall resist crushing orce o the bow o the o-take tanker. In lieu o more accurate calculations the orce-deormation curve given in Section A.3.5. may be applied. For ductile design the resistance o stiened plating in the beam mode o deormation can be calculated using the procedure described in section A Calculation o energy dissipation in stringers, decks and bulkheads subjected to gross, axial crushing shall be based upon recognised methods or plastic analysis, eg. /3/ and /5/. It shall be documented that the olding mechanisms assumed yield a realistic representation o the true deormation ield. A.3.13 Global integrity during impact Normally, it is unlikely that the installation will turn into a global collapse mechanism under direct collision load, because the collision load is typically an order o magnitude smaller than the resultant design wave orce. Linear analysis oten suices to check that global integrity is maintained. The installation should be checked or the maximum collision orce. For installations responding predominantly statically the maximum collision orce occurs at maximum deormation. For structures responding predominantly impulsively the maximum collision orce occurs at small global deormation o the platorm. An upper bound to the collision orce is to assume that the installation is ixed with respect to global displacement. (e.g. jack-up ixed with respect to deck displacement) NORSOK standard Page 140 o 488

149 Annex A Rev. 1, December 1998 A.4 DROPPED OBJECTS A.4.1 General The dropped object action is characterised by a kinetic energy, governed by the mass o the object, including any hydrodynamic added mass, and the velocity o the object at the instant o impact. In most cases the major part o the kinetic energy has to be dissipated as strain energy in the impacted component and, possibly, in the dropped object. Generally, this involves large plastic strains and signiicant structural damage to the impacted component. The strain energy dissipation is estimated rom orce-deormation relationships or the component and the object, where the deormations in the component shall comply with ductiliy and stability requirements. The load bearing unction o the installation shall remain intact with the damages imposed by the dropped object action. In addition, the residual strength requirements given in Section A.7 shall be complied with. Dropped objects are rarely critical to the global integrity o the installation and will mostly cause local damages. The major threat to global integrity is probably puncturing o buoyancy tanks, which could impair the hydrostatic stability o loating installations. Puncturing o a single tank is normally covered by the general requirements to compartmentation and watertight integrity given in ISO and NORSOK N-001. The structural eects rom dropped objects may either be determined by non-linear dynamic inite element analyses or by energy considerations combined with simple elastic-plastic methods as given in Sections A.4. - A.4.5. I non-linear dynamic inite element analysis is applied all eects described in the ollowing paragraphs shall either be implicitly covered by the modelling adopted or subjected to special considerations, whenever relevant. A.4. Impact velocity The kinetic energy o a alling object is given by E = kin 1 mv (A.4.1) or objects alling in air and, 1 E kin = + ( m a) v or objects alling in water. a = hydrodynamic added mass or considered motion For impacts in air the velocity is given by (A.4.) NORSOK standard Page 141 o 488

150 Annex A Rev. 1, December 1998 v = gs s = travelled distance rom drop point v = v o at sea surace (A.4.3) For objects alling rectilinearly in water the velocity depends upon the reduction o speed during impact with water and the alling distance relative to the characteristic distance or the object. -3 In air - Velocity [v/vt] ,5 1 1,5,5 3 3,5 4 0 s Distance [s/sc] In water Figure A.4-1 Velocity proile or objects alling in water The loss o momentum during impact with water is given by mδ v = 0 t d F () t dt (A.4.4) F(t) = orce during impact with sea surace Ater the impact with water the object proceeds with the speed v = v 0 Δv Assuming that the hydrodynamic resistance during all in water is o drag type the velocity in water can be taken rom Figure A.4-1 where ( m ρ V) g w v t = = terminal velocity or the object ρ C A w d NORSOK standard Page 14 o 488

151 Annex A Rev. 1, December 1998 s c m + a = ρ C A w d p a v + t 1 m = ρ wv g 1 m = characteristic distance ρ w = density o sea water C d = hydrodynamic drag coeicient or the object in the considered motion m = mass o object A p = projected cross-sectional area o the object V = object displacement The major uncertainty is associated with calculating the loss o momentum during impact with sea surace, given by Equation (A.4.4). However, i the travelled distance is such that the velocity is close to the terminal velocity, the impact with sea surace is o little signiicance. Typical terminal velocities or some typical objects are given in Table A.4-1 Table A.4-1 Terminal velocities or objects alling in water. Item Mass [kn] Terminal velocity [m/s] Drill collar Winch, Riser pump BOP annular preventer Mud pump Rectilinear motion is likely or blunt objects and objects which do not rotate about their longitudinal axis. Bar-like objects (e.g. pipes) which do not rotate about their longitudinal axis may execute lateral, damped oscillatory motions as illustrated in Figure A.4-1. A.4.3 Dissipation o strain energy The structural response o the dropped object and the impacted component can ormally be represented as load-deormation relationships as illustrated in Figure A.4-. The part o the impact energy dissipated as strain energy equals the total area under the load-deormation curves. E s ws, w 0 s s 0 i i max i, max = E + E = R dw + R dw s,s s,i (A.4.5) As the load level is not known a priori an incremental approach is generally required. Oten the object can be assumed to be ininitely rigid (e.g axial impact rom pipes and massive objects) so that all energy is to be dissipated by the impacted component.. NORSOK standard Page 143 o 488

152 Annex A Rev. 1, December 1998 R o R i E s,o E s,i dw o Object Installation dw i Figure A.4- Dissipation o strain energy in dropped object and installation I the object is assumed to be deormable, the interactive nature o the deormation o the two structures should be recognised. A.4.4 Resistance/energy dissipation A Stiened plates subjected to drill collar impact The energy dissipated in the plating subjected to drill collar impact is given by E sp = R mi K m (A.4.6) K π t d r 6c = y ( 1+ c) d r y = characteristic yield strength d.5 1 r : stiness o plate enclosed by hinge circle c = e R = πdtτ = contact orce or τ τcr reer Section A or τ cr mi = ρ pπr t = mass o plate enclosed by hinge circle m = mass o dropped object ρ p = mass density o steel plate d = smaller diameter at threaded end o drill collar r = smaller distance rom the point o impact to the plate boundary deined by adjacent stieners/girders, reer Figure A.4-3. NORSOK standard Page 144 o 488

153 Annex A Rev. 1, December 1998 r r r Figure A.4-3 Deinition o distance to plate boundary A.4.4. Stieners/girders In lieu o more accurate calculations stieners and girders subjected to impact with blunt objects may be analysed with resistance models given in Section A.6.9. A Dropped object Calculation o energy dissipation in deormable dropped objects shall be based upon recognised methods or plastic analysis. It shall be documented that the collapse mechanisms assumed yield a realistic representation o the true deormation ield. A.4.5 Limits or energy dissipation A Pipes on plated structures The maximum shear stress or plugging o plates due to drill collar impacts may be taken as τ cr = y t d (A.4.7) A.4.5. Blunt objects For stability o cross-sections and tensile racture, reer Section A NORSOK standard Page 145 o 488

154 Annex A Rev. 1, December 1998 A.5 FIRE A.5.1 General The characteristic ire structural action is temperature rise in exposed members. The temporal and spatial variation o temperature depends on the ire intensity, whether or not the structural members are ully or partly enguled by the lame and to what extent the members are insulated. Structural steel expands at elevated temperatures and internal stresses are developed in redundant structures. These stresses are most oten o moderate signiicance with respect to global integrity. The heating causes also progressive loss o strength and stiness and is, in redundant structures, accompanied by redistribution o orces rom members with low strength to members that retain their load bearing capacity. A substantial loss o load-bearing capacity o individual members and subassemblies may take place, but the load bearing unction o the installation shall remain intact during exposure to the ire action. In addition, the residual strength requirements given in Section A.7 shall be complied with. Structural analysis may be perormed on either individual members subassemblies entire system The assessment o ire load eect and mechanical response shall be based on either simple calculation methods applied to individual members, general calculation methods, or a combination. Simple calculation methods may give overly conservative results. General calculation methods are methods in which engineering principles are applied in a realistic manner to speciic applications. Assessment o individual members by means o simple calculation methods should be based upon the provisions given in Eurocode 3 Part 1.. //. Assessment by means o general calculation methods shall satisy the provisions given in Eurocode 3 Part1., Section 4.3. In addition, the requirements given in this section or mechanical response analysis with nonlinear inite element methods shall be complied with. Assessment o ultimate strength is not needed i the maximum steel temperature is below 400 o C, but deormation criteria may have to be checked or impairment o main saety unctions. A.5. General calculation methods Structural analysis methods or non-linear, ultimate strength assessment may be classiied as stress-strain based methods stress-resultants based (yield/plastic hinge) methods Stress-strain based methods are methods where non-linear material behaviour is accounted or on ibre level. NORSOK standard Page 146 o 488

155 Annex A Rev. 1, December 1998 Stress-resultants based methods are methods where non-linear material behaviour is accounted or on stress-resultants level based upon closed orm solutions/interaction equation or cross-sectional orces and moments. A.5.3 Material modelling In stress-strain based analysis temperature dependent stress-strain relationships given in Eurocode 3, Part 1., Section 3. may be used. For stress resultants based design the temperature reduction o the elastic modulus may be taken as k E,θ according to Eurocode 3. The yield stress may be taken equal to the eective yield stress, y,θ,. The temperature reduction o the eective yield stress may be taken as k y,θ. Provided that above the above requirements are complied with creep does need explicit consideration. A.5.4 Equivalent imperections To account or the eect o residual stresses and lateral distortions compressive members shall be modelled with an initial, sinusoidal imperection with amplitude given by Elasto-plastic material models * e! 1 = π σ E Y i z 0 α Elastic-plastic material models: * e! Wp = W 1 π σy E i z 0 α = 1 π σy E WP α AI α = 0.5 or ire exposed members according to column curve c, Eurocode 3 i = radius o gyration z 0 = distance rom neutral axis to extreme ibre o cross-section W P = plastic section modulus W = elastic section modulus A = cross-sectional area I = moment o inertia e * = amplitude o initial distortion! = member length The initial out-o-straightness should be applied on each physical member. I the member is modelled by several inite elements the initial out-o-straightness should be applied as displaced nodes. The initial out-o-straightness shall be applied in the same direction as the deormations caused by the temperature gradients. A.5.5 Empirical correction actor The empirical correction actor o 1. has to be accounted or in calculating the critical strength in compression and bending or design according to Eurocode 3, reer Comm. A.5.5. NORSOK standard Page 147 o 488

156 Annex A Rev. 1, December 1998 A.5.6 Local cross sectional buckling I shell modelling is used, it shall be veriied that the sotware and the modelling is capable o predicting local buckling with suicient accuracy. I necessary, local shell imperections have to be introduced in a similar manner to the approach adopted or lateral distortion o beams I beam modelling is used local cross-sectional buckling shall be given explicit consideration. In lieu o more accurate analysis cross-sections subjected to plastic deormations shall satisy compactness requirements given in Eurocode 3 : class 1 : Locations with plastic hinges (approximately ull plastic utilization) class : Locations with yield hinges (partial plastiication) I this criterion is not complied with explicit considerations shall be perormed. The load-bearing capacity will be reduced signiicantly ater the onset o buckling, but may still be signiicant. A conservative approach is to remove the member rom urther analysis. Compactness requirements or class 1 and class cross-sections may be disregarded provided that the member is capable o developing signiicant membrane orces. A.5.7 Ductility limits A General The ductility o beams and connections increase at elevated temperatures compared to normal conditions. Little inormation exists. A.5.7. Beams in bending In lieu o more accurate analysis requirements given in Section A.3.10 are to be complied with. A Beams in tension In lieu o more accurate analysis an average elongation o 3% o the member length (ISO) with a reasonably uniorm temperature can be assumed. Local temperature peaks may localise plastic strains. The maximum local strain shall thereor not exceed ε a = 15%. A.5.8 Capacity o connections In lieu o more accurate calculations the capacity o the connection can be taken as: R = k θ y,θ R 0 where R 0 = capacity o connection at normal temperature k y,θ = temperature reduction o eective yield stress or maximum temperature in connection NORSOK standard Page 148 o 488

157 Annex A Rev. 1, December 1998 A.6 EXPLOSIONS A.6.1 General Explosion loads are characterised by temporal and spatial pressure distribution. The most important temporal parameters are rise time, maximum pressure and pulse duration. For components and sub-structures the explosion pressure shall normally be considered uniormly distributed. On global level the spatial distribution is normally nonuniorm both with respect to pressure and duration. The response to explosion loads may either be determined by non-linear dynamic inite element analysis or by simple calculation models based on Single Degree O Freedom (SDOF) analogies and elastic-plastic methods o analysis. I non-linear dynamic inite element analysis is applied all eects described in the ollowing paragraphs shall either be implicitly covered by the modelling adopted or subjected to special considerations, whenever relevant In the simple calculation models the component is transormed to a single spring-mass system exposed to an equivalent load pulse by means o suitable shape unctions or the displacements in the elastic and elastic-plastic range. The shape unctions allow calculation o the characteristic resistance curve and equivalent mass in the elastic and elastic-plastic range as well as the undamental period o vibration or the SDOF system in the elastic range. Provided that the temporal variation o the pressure can be assumed to be triangular, the maximum displacement o the component can be calculated rom design charts or the SDOF system as a unction o pressure duration versus undamental period o vibration and equivalent load amplitude versus maximum resistance in the elastic range. The maximum displacement must comply with ductiliy and stability requirements or the component. The load bearing unction o the installation shall remain intact with the damages imposed by the explosion loads. In addition, the residual strength requirements given in Section A.7 shall be complied with. A.6. Classiication o response The response o structural components can conveniently be classiied into three categories according to the duration o the explosion pressure pulse, t d, relative to the undamental period o vibration o the component, T: Impulsive domain - t d /T< 0.3 Dynamic domain < t d /T < 3 Quasi-static domain - 3 < t d /T Impulsive domain: The response is governed by the impulse deined by I t d = 0 F () t dt (A.6.1) NORSOK standard Page 149 o 488

158 Annex A Rev. 1, December 1998 Hence, the structure may resist a very high peak pressure provided that the duration is suiciently small. The maximum deormation, w max, o the component can be calculated iteratively rom the equation I = m eq 0 w max R ( w) dw (A.6.) where R(w) = orce-deormation relationship or the component m eq = equivalent mass or the component Quasi-static-domain: The response is governed by the peak pressure and the rise time o the pressure relative to the undamental period o vibration. I the rise time is small the maximum deormation o the component can be solved iteratively rom the equation: w max = 1 F max 0 w max R ( w) dw (A.6.3) I the rise time is large the maximum deormation can be solved rom the static condition F max = R(w max ) (A.6.4) Dynamic domain: The response has to be solved rom numerical integration o the dynamic equations o equilibrium. A.6.3 Failure modes or stiened panels Various ailure modes or a stiened panel are illustrated in Figure A.6-1. Suggested analysis model and reerence to applicable resistance unctions are listed in Table A.6-1. Application o a Single Degree o Freedom (SDOF) model in the analysis o stieners/girders with eective lange is implicitly based on the assumption that dynamic inter action between the plate lange and the proile can be neglected. NORSOK standard Page 150 o 488

159 Annex A Rev. 1, December 1998 Beam collapse plate Plastic deormation o plate Beam collapse plate plastic (i) (ii) Girder collapse beam elastic- plate elastic or plastic Girder and beam collapse plate elastic (i) or plastic (ii) Figure A.6-1 Failure modes or two-way stiened panel NORSOK standard Page 151 o 488

160 Annex A Rev. 1, December 1998 Table A.6-1 Analysis models Failure mode Elastic-plastic deormation o plate Stiener plastic plate elastic Stiener plastic plate plastic Girder plastic stiener and plating elastic Girder plastic stiener elastic plate plastic Girder and stiener plastic plate elastic Girder and stiener plastic plate plastic Simpliied analysis model SDOF SDOF SDOF SDOF SDOF MDOF MDOF Resistance models Section A.6.8 Stiener: Section A Plate: Section A Stiener: Section A Plate: Section A.6.8 Girder: Section.A Plate: Section A.6.8 Girder: Section A Plate: Section A.6.8 Girder and stiener: Section A Plate: Section A.6.8 Girder and stiener: Section A Plate: Section A.6.8 Comment Elastic, eective lange o plate Eective width o plate at mid span. Elastic, eective lange o plate at ends. Elastic, eective lange o plate with concentrated loads (stiener reactions). Stiener mass included. Eective width o plate at girder mid span and ends. Stiener mass included Dynamic reactions o stieners loading or girders Dynamic reactions o stieners loading or girders By girder/stiener plastic is understood that the maximum displacement w max exceeds the elastic limit w el A.6.4 SDOF system analogy Biggs method: For many practical design problems it is convenient to assume that the structure - exposed to the dynamic pressure pulse - ultimately attains a deormed coniguration comparable to the static deormation pattern. Using the static deormation pattern as displacement shape unction, i.e. w ( x, t) = φ( x) y( t) the dynamic equations o equilibrium can be transormed to an equivalent single degree o reedom system: m "" y + ky = (t) φ(x) = displacement shape unction y(t) = displacement amplitude m =! mφ() x dx + M iφi = generalized mass i ( x) dx + φ (t) = p(t) φ = generalized load! ( x) i F i i k =! EIφ, xx dx = generalized elastic bending stiness k = 0 = generalized plastic bending stiness (ully developed mechanism) k =! Nφ, x () x dx = generalized membrane stiness (ully plastic: N = N P ) m = distributed mass (A.6.5) NORSOK standard Page 15 o 488

161 Annex A Rev. 1, December 1998 M i = concentrated mass p = explosion pressure F i = concentrated load (e.g. support reactions) x i = position o concentrated mass/load φ i = φ( x = x i ) The equilibrium equation can alternatively be expressed as: k m My "" + Ky = F(t) l (A.6.6) where k m klm = kl = load-mass transormation actor m k m = M = mass transormation actor k l = F = load transormation actor M mdx + M i = total mass =! i F = pdx + F! i = total load k m i k K = = characteristic stiness The natural period o vibration or the equivalent system is given by T = π m k = π kl mm K The response, y(t), is - in addition to the load history - entirely governed by the total mass, loadmass actor and the characteristic stiness. For a linear system, the load mass actor and the characteristic stiness are constant. The response is then alternatively governed by the eigenperiod and the characteristic stiness. For a non-linear system, the load-mass actor and the characteristic stiness depend on the response (deormations). Non-linear systems may oten conveniently be approximated by equivalent bi-linear or tri-linear systems, see Section A.6.7. In such cases the response can be expressed in terms o (see Figure A.6-10 or deinitions): K 1 = characteristic stiness in the initial, linear resistance domain y el = displacement at the end o the initial, linear resistance domain T = eigenperiod in the initial, linear resistance domain and, i relevant, K 3 = normalised characteristic resistance in the third linear resistance domain. Characteristic stinesses are given explicitly or can be derived rom load-deormation relationships given in Section A.6.9. I the response is governed by dierent mechanical behaviour relevant characteristic stinesses must be calculated. For a given explosion load history the maximum displacement, y max, is ound by analytical or numerical integration o equation (A.6.6). NORSOK standard Page 153 o 488

162 Annex A Rev. 1, December 1998 For standard load histories and standard resistance curves maximum displacements can be presented in design charts. Figure A.6- shows the normalised maximum displacement o a SDOF system with a bi- (K 3 =0) or trilinear (K 3 > 0) resistance unction, exposed to a triangular pressure pulse with zero rise time. When the duration o the pressure pulse relative to the eigenperiod in the initial, linear resistance range is known, the maximum displacement can be determined directly rom the diagram as illustrated in Figure A Static asymptote, K 3 =0.K 1 K 3 =0.1K 1 10 Impulsive asymptote, K 3 =0.K 1 K 3 =0.K 1 1 y max /y el or system Elastic-perectly plastic, K 3 =0 F(t) td/t or system 0,1 t d 0, t d /T Figure A.6- Maximum response a SDOF system to a triangular pressure pulse with zero rise time. F max /R el = Design charts or systems with bi- or tri-linear resistance curves subjected to a triangular pressure pulse with dierent rise time are given in Figures A A6-7. Baker's method The governing equations (A.6.1) and (A.6.) or the maximum response in the impulsive domain and the quasi-static domain may also be used along with response charts or maximum displacement or dierent F max /R el ratios to produce pressure-impulse (F max,i) diagrams - isodamage curves - provided that the maximum pressure is known. Figure A.6-3 shows such a relationship obtained or an elastic-perectly plastic system when the maximum dynamic response is y max /y el =10. Pressure-impulse combinations to the let and below o the iso-damage curve represent admissible events, to the right and above inadmissible events. The advantage o using iso-damage diagrams is that "back-ward" calculations are possible: The diagram is established on the basis o the resistance curve. The inormation may be used to NORSOK standard Page 154 o 488

163 Annex A Rev. 1, December 1998 screen explosion pressure histories and eliminate those that obviously lie in the admissible domain. This will reduce the need or large complex simulation o explosion scenaries. 11 Pressure F/R Impulsive asymptote 3 Iso-damage curve or y max /y elastic = 10 Elastic-perectly plastic resistance Impulse I/(RT) Pressure asymptote Figure A.6-3 Iso-damage curve or ymax/yel = 10. Triangular pressure pulse. A Dynamic response charts or SDOF system Transormation actors or elastic plastic-membrane deormation o beams and one-way slabs with dierent boundary conditions are given in Table A.6- Maximum displacement or a SDOF system exposed to dierent pressure histories are displayed in Figures A A.6-7. The characteristic response o the system is based upon the resistance in the linear range, K=K 1, where the equivalent stiness is determined rom the elastic solution to the actual system. I the displacement shape unction changes as a non-linear structure undergoes deormation the transormation actors change. In lieu o accurate analysis an average value o the combined loadmass transormation actor can be used:. k average lm = k elastic lm + ( µ ) µ 1 k plastic lm (A.6.7) µ = y max /y el ductility ratio Since µ is not known a priori iterative calculations may be necessary. NORSOK standard Page 155 o 488

164 Annex A Rev. 1, December R el /F max =0.05 =0.1 = 0.3 = 0.5 = 0.6 = 0.7 R el /F max = 0.8 = = 1.0 y max/ y el = 1.1 = 1. = k 3 = 0 k 3 = 0.1k 1 k 3 = 0.k 1 k 3 = 0.5k t d /T F F max t d R R el k 3 = 0.5k 1 =0.k 1 =0.1k 1 Figure A.6-4 Dynamic response o a SDOF system to a triangular load (rise time=0) k 1 y el y 100 R el /F max =0.05 =0.1 = 0.3 = 0.5 = 0.6 = 0.7 R el /F max = = 0.9 y max/ y el = 1.0 = = 1. = 1.5 F R k 3 = 0.5k 1 =0.k 1 =0.1k 1 k 3 = 0 k 3 = 0.1k 1 F max R el k 3 = 0.k 1 k 1 k 3 = 0.5k td t d y el y Figure A.6-5 Dynamic response o a SDOF system to a triangular load (rise time=0.15t d ) t d /T NORSOK standard Page 156 o 488

165 Annex A Rev. 1, December R el /F max =0.05 =0.1 = 0.3 = 0.5 = 0.6 = 0.7 R el /F max = y max/ y el = F R k 3 = 0.5k 1 =0.k 1 =0.1k 1 k 3 = 0 k 3 = 0.1k 1 F max R el k 3 = 0.k 1 k 1 k 3 = 0.5k td t d y el y Figure A.6-6 Dynamic response o a SDOF system to a triangular load (rise time=0.30t d ) t d /T = 1.0 = 1.1 = 1. = R el /F max =0.05 =0.1 = 0.3 = 0.5 = 0.6 = 0.7 R el /F max = y max/ y el = = 1.0 = 1.1 = 1. F R k 3 = 0.5k 1 =0.k 1 =0.1k 1 = 1.5 k 3 = 0 k 3 = 0.1k 1 F max R el k 3 = 0.k 1 k 1 k 3 = 0.5k td t d y el y Figure A.6-7 Dynamic response o a SDOF system to a triangular load (rise time=0.50t d ) t d /T NORSOK standard Page 157 o 488

166 Annex A Rev. 1, December 1998 A.6.5 MDOF analysis SDOF analysis o built-up structures (e.g. stieners supported by girders) is admissible i - the undamental periods o elastic vibration are suiciently separated - the response o the component with the smallest eigenperiod does not enter the elastic-plastic domain so that the period is drastically increased I these conditions are not met, then signiicant interaction between the dierent vibration modes is anticipated and a multi degree o reedom analysis is required with simultaneous time integration o the coupled system. A.6.6 A Classiication o resistance properties Cross-sectional behaviour Moment elasto-plastic Curvature Figure A.6-8 Bending moment-curvature relationships Elasto-plastic : The eect o partial yielding on bending moment accounted or Elastic-perectly plastic: Linear elastic up to ully plastic bending moment The simple models described herein assume elastic-perectly plastic material behaviour. Any strain hardening may be accounted or by equivalent (increased) yield stress. A.6.6. R Component behaviour K K R R R K K 3 K 1 K 1 K1 K 1 Elastic w w w w Elastic-plastic (determinate) Elastic-plastic (indeterminate) Elastic-plastic with membrane Figure A.6-9 Resistance curves NORSOK standard Page 158 o 488

167 Annex A Rev. 1, December 1998 Elastic: Elastic material, small deormations Elastic-plastic (determinate): Elastic-perectly plastic material. Statically determinate system. Bending mechanism ully developed with occurrence o irst plastic hinge(s)/yield lines. No axial restraint Elastic-plastic (indeterminate): Elastic perectly plastic material. Statically indeterminate system. Bending mechanism develops with sequential ormation o plastic hinges/yield lines. No axial restraint. For simpliied analysis this system may be modelled as an elastic-plastic (determinate) system with equivalent initial stiness. Elastic-plastic with membrane: Elastic-perectly plastic material. Statically determinate (or indeterminate). Ends restrained against axial displacement. Increase in load-carrying capacity caused by development o membrane orces. A.6.7 Idealisation o resistance curves The resistance curves in clause A.6.6 are idealised. For simpliied SDOF analysis the resistance characteristics o a real non-linear system may be approximately modelled. An example with a trilinear approximation is illustrated in Figure A R K 3 R el K =0 K 1 w el w Figure A.6-10 Representation o a non-linear resistance by an equivalent tri-linear system. In lieu o more accurate analysis the resistance curve o elastic-plastic systems may be composed by an elastic resistance and a rigid-plastic resistance as illustrated in Figure A = Elastic Rigid-plastic Elastic-plastic with membrane Figure A.6-11 Construction o elastic-plastic resistance curve NORSOK standard Page 159 o 488

168 Annex A Rev. 1, December 1998 A.6.8 Resistance curves and transormation actors or plates A Elastic - rigid plastic relationships In lieu o more accurate calculations rigid plastic theory combined with elastic theory may be used. In the elastic range the stiness and undamental period o vibration o a clamped plate under uniorm lateral pressure can be expressed as: p = Kw = pressure-displacement relationship or plate center D K = ψ = plate stiness 4 s 4 π ρts T = = natural period o vibration η D 3 t D = E = plate stiness 1( 1 ν ) The actors ψ and η are given in Figure A ψ η ψ η λ/s 0 Figure A.6-1 Coeicients ψ and η. The plastic load-carrying capacity o plates subjected to uniorm pressure can be taken as: p p c p p c ( 3 α) α 1 w + = + 9 3α α( α) 1 = w 1 + ( 3 α 3w 1) w 1 w 1 (A.6.8) Pinned ends : w w = t p c yt 6 =! α NORSOK standard Page 160 o 488

169 Annex A Rev. 1, December 1998 Clamped ends : w = w t p c yt 1 =! α α = s s 3 + ( )! = plate aspect parameter!!! ( > s) = plate length s = plate width t = plate thickness p c = plastic collapse pressure in bending or plates with no axial restraint Load-carrying capacity [p/pc] l/s = Relative displacement w Figure A.6-13 Plastic load-carrying capacities o plates as a unction o lateral displacement A.6.8. Axial restraint Unlike stieners no simple method with a clear physical interpretation exists to quantiy the eect o lexible boundaries or a continuous plate ield under uniorm pressure. Full axial restraint may probably be assumed. At the panel boundaries assumption o ull axial restraint is non-conservative. In lieu o more accurate calculation the axial restraint may be estimated by removing the plate and apply a uniormly distributed unit in-plane load normal to the plate edges. The axial stiness should be taken as the inverse o the maximum in-plane displacement o the long edge. The relative reduction o the plastic load-carrying capacity can calculated according to the procedure described in Section A.6.9. or a beam with rectangular cross-section (plate thickness x unit width) and length equal to stiener spacing, using the diagram or α =. NORSOK standard Page 161 o 488

170 Annex A Rev. 1, December 1998 For a plate in the middle o a continuous, uniormly loaded panel a high degree o axial restraint is likely. A non-dimensional spring actor c= 1.0 is suggested. I membrane orces are likely to develop it has to be veriied that the adjacent structure is strong enough to anchor ully plastic membrane orces. A Tensile racture o yield hinges In lieu o more accurate calculations the procedure described in Section A may be used or a beam with rectangular cross-section (plate thickness x unit width) and length equal to stiener spacing. A.6.9 Resistance curves and transormation actors or beams Provided that the stieners/girders remain stable against local buckling, tripping or lateral torsional buckling stiened plates/girders may be treated as beams. Simple elastic-plastic methods o analysis are generally applicable. Special considerations shall be given to the eect o: Elastic lexibility o member/adjacent structure Local deormation o cross-section Local buckling Strength o connections Strength o adjacent structure Fracture A Beams with no- or ull axial restraint Equivalent springs and transormation actors or load and mass or various idealised elasto-plastic systems are shown in Table A.6-. NORSOK standard Page 16 o 488

171 Annex A Rev. 1, December 1998 Table A.6- Transormation actors or beams with various boundary and load conditions. Load case Resistance domain Load Factor k l Mass actor k m Concentrated mass Uniorm mass Load-mass actor Concentrated mass k lm Uniorm mass Maximum resistance R el Characteristic stiness K Dynamic reaction V F=pL Elastic M L p 384EI 5L R F L Plastic bending Plastic membrane M L p 0 4N P L 038. R 01. F el + N P y max L L/ F L/ Elastic Plastic bending Plastic membrane M L 4 M L p p 48EI 3 L 0 4N P L 078. R 08. F 075. R 05. F el N P y max L F/ F/ Elastic M L p 56. 4EI 3 L 055. R 0. 05F L/3 L/3 L/3 Plastic bending Plastic membrane M L p 0 6N P L 05. R 00. F el 3N P y max L F=pL L Elastic Elastoplastic bending Plastic bending Plastic membrane M L ps ( ps + Pm) 8 M M L ( ps + Pm) 8 M M L 384EI 3 L 384EI 5L 3 307EI 3 L 0 4N P L 036. R F 039. R 011. F el R 01. F el + N p y max L L/ F L/ Elastic Plastic bending Plastic membrane ( ps + Pm ) 4 M M L ( ps + Pm ) 4 M M L 19EI 3 L 0 4N P L 071. R 01. F 075. R 05. F el N P y max L NORSOK standard Page 163 o 488

172 Annex A Rev. 1, December 1998 Load case Resistance domain Load Factor k l Mass actor k m Concentrated mass Uniorm mass Load-mass actor k lm Concentrated mass Uniorm mass Maximum resistance R el Characteristic stiness K Dynamic reaction V V 1 F=pL L V Elastic Elastoplastic Bending Plastic bending ( 8M L ps 4 Mps + M L 4 Mps + M L Pm ( Pm ) 185EI 3 L 384EI 5L 3 160EI 3 L 0 V1 = 06. R F V = 043. R F 039. R F ± M L Ps 038. R F ± M L Ps Plastic membrane N P L N P y max L V 1 F L/ L/ V Elastic Elastoplastic Bending Plastic bending Plastic membrane M 3L Ps ( Mps + MPm ) L ( Mps + MPm ) L 107EI 3 L 48EI 3 L 106EI 3 L 0 4N P L V1 = 05. R F V = 054. R F 078. R 08. F ± M Ps L 075. R 05. F ± M Ps L N P y max L V 1 F/ F/ L/3 L/3 L/3 V Elastic Elastoplastic Bending Plastic bending Plastic membrane M Ps L Mps + 3M L ( Pm) ( Mps + MPm ) 3 L 13EI 3 L 56EI 3 L 1EI 3 L 0 6N P L V1 = 017. R F V = 033. R F 055. R 0. 05F ± M Ps L 05. R 00. F ± M el Ps L 3N P y max L NORSOK standard Page 164 o 488

173 Annex A Rev. 1, December 1998 A.6.9. Beams with partial end restraint. Relatively small axial displacements have a signiicant inluence on the development o tensile orces in members undergoing large lateral deormations. An equivalent elastic, axial stiness may be deined as 1 K = 1 K node! + EA (A.6.9) k node = axial stiness o the node with the considered member removed. This may be determined by introducing unit loads in member axis direction at the end nodes with the member removed. Plastic orce-deormation relationship or a beam under uniorm pressure may obtained rom Figure A.6-14, Figure A.6-15 or Figure A.6-16 i the plastic interaction between axial orce and bending moment can be approximated by the ollowing equation: M M P N + α = 1 1< α < N P (A.6.10) In lieu o more accurate analysis α = 1. can be assumed or stiened plates. 8c1M P R 0 = p! =! = plastic collapse load in bending or the member.! = member length w w = c 1 w c = non-dimensional deormation WP w c = α A = characteristic beam height or beams described by plastic interaction equation (A.6.10). W P = zgae = plastic section modulus or stiened plate A = As + st = total area o stiener and plate lange A e = A s + s et = eective cross-sectional area o stiener and plate lange, z g = distance orm plate lange to stiener centre o gravity. A s = stiener area s = stiener spacing s e = eective width o plate lange see A z g = distance rom stiener toe to centre o gravity o eective crosssection. 4c1kw c c = ya! = non-dimensional spring stiness c 1 = or clamped beams c 1 = 1 or pinned beams NORSOK standard Page 165 o 488

174 Annex A Rev. 1, December R/R0 4 3 α = 1. Bending & membrane Membrane only F (explosion load) c = K w K ,5 1 1,5,5 3 3,5 4 Deormation w Figure A.6-14 Plastic load-deormation relationship or beam with axial lexibility (α=1.) α = 1.5 Bending & membrane Membrane only R/R0 4 F (explosion load) 3 c = K w K ,5 1 1,5,5 3 3,5 4 Deormation w Figure A.6-15 Plastic load-deormation relationship or beam with axial lexibility (α=1.5) NORSOK standard Page 166 o 488

175 Annex A Rev. 1, December α = R/R c = K Bending & membrane Membrane only F w (explosion load) K 0 0 0,5 1 1,5,5 3 3,5 4 Deormation w Figure A.6-16 Plastic load-deormation relationship or beam with axial lexibility (α=) For members where the plastic moment capacity o adjacent members is smaller than the moment capacity o the exposed member the orce-deormation relationship may be interpolated rom the curves or pinned ends and clamped ends: R = ξr where clamped + ( 1 ξ) R pinned (A.6.11) actual R 0 0 ξ = 1 1 M P 8! (A.6.1) actual R 0 = Collapse load in bending or beam accounting or actual bending resistance o adjacent members R actual 8M = P + 4M! P1 + 4M P (A.6.13) M = M M ; i = adjacent member no i, j = end number {1,} (A.6.14) Pj i Pj,i P M Pj,i = Plastic bending moment or member no. i. Elastic, rotational lexibility o the node is normally o moderate signiicance NORSOK standard Page 167 o 488

176 Annex A Rev. 1, December 1998 A Eective lange For deormations in the elastic range the eective width (shear lag eect) o the plate lange, s e, o simply supported or clamped stieners/girders may be taken rom Figure A s e/s Uniorm dis tribution or n > 6 n = 5 n = 4 n = nf i λ = L nf i λ = 0.6L λ/s Figure A.6-17 Eective lange or stieners and girders in the elastic range In the elasto-plastic and plastic range the eective width is to be reduced i the plate lange is on the compression side due to plate buckling: - For stieners it is only necessary to reduce the plate lange or buckling at stiener midsection. - For girders with transversely stiened plate lange reduction due to plate buckling is also to be considered at ends. The eective plate lange is aected by explosion induced permanent deormations. Eective width o unstiened plates with conventional imperections is given in Section In lieu o accurate calculations the eective width may be taken as s e s se = s 0.4 w 1 λp t max s e = eective width according to Section λ p = plate slenderness ratio, see Section w max = maximum lateral displacement o plate The eective width or elastic deormations may be used when the plate lange is on the tension side. NORSOK standard Page 168 o 488

177 Annex A Rev. 1, December 1998 A Strength o adjacent structure The adjacent structure must be checked to see whether it can provide the support required by the assumed collapse mechanism or the member/sub-structure A Strength o connections The capacity o connections can be taken rom recognised codes The connection shall be checked or the dynamic reaction orce given in Table A.6-. For beams with axial restraint the connection should also be checked or lateral - and axial reaction in the membrane phase: I the axial orce in a tension member exceeds the axial capacity o the connection the member must be assumed disconnected. I the capacity o the connection is exceeded in compression and bending, this does not necessarily mean ailure o the member. The post-collapse strength o the connection may be taken into account provided that such inormation is available. A Ductility limits Reerence is made to Section A.3.10 The local buckling criterion in Section A and tensile racture criterion given in Section A may be used with: d c = characteristic dimension equal to twice the distance rom the plastic neutral axis in bending to the extreme ibre o the cross-section c = non-dimensional axial spring stiness calculated in Section A.6.9. y max Alternatively, the ductility ratios µ = in Table A.6-3 may be used. y el Table A.6-3 Ductility ratios µ beams with no axial restraint Boundary Load Cross-section category conditions Class 1 Class Class 3 Cantilevered Concentrated Distributed Pinned Fixed Concentrated Distributed Concentrated Distributed NORSOK standard Page 169 o 488

178 Annex A Rev. 1, December 1998 A.7 RESIDUAL STRENGTH A.7.1 General The second step in the accidental limit state check is to veriy the residual strength o the installation with damage caused by the accidental load. The check shall be carried out or unctional loads and design environmental loads. The partial saety actor or loads and material can be taken equal to unity. Ater the action o the accidental load an internal, residual stress/orce ield remains in the structure. The resultant o this ield is zero. In most cases the residual stresses/orces have a minor inluence on the residual capacity and may be neglected. Any detrimental eect o the residual stress on the ultimate capacity should, however, be subject to explicit consideration. I necessary, the residual stresses should be included in the analysis. I non-linear FE analysis is used, the residual stress ield can be conveniently included by perorming integrated analysis: 1) Application o design accidental loading ) Removal o accidental load by unloading 3) Application o design environmental load A.7. Modelling o damaged members A.7..1 General Compressive members with large lateral deormations will oten contribute little to load-carrying and can be omitted rom analysis. A.7.. Members with dents, holes, out-o-straightness Tubular members with dents, holes and out-o-straightness, reerence is made to Chapter 10. Stiened plates/beams/girders with deormed plate lange and out-o-straightness, reerence is made to Chapter 10. NORSOK standard Page 170 o 488

179 Annex A Rev. 1, December 1998 A.8 REFERENCES /1/ NORSOK Standard N-003 Action and Action Eect // NS-ENV Eurocode 3: Design o Steel structures Part 1-. General rules - Structural ire design /3/ Amdahl, J.: Energy Absorption in Ship-Platorm Impacts, UR-83-34, Dept. Marine Structures, Norwegian Institute o Technology, Trondheim, /4/ SCI 1993: Interim Guidance Notes or the Design and Protection o Topside Structures against Explosion and Fire /5/ Amdahl, J.: Mechanics o Ship-Ship Collisions- Basic Crushing Mechanics.West Europene Graduate Shcool o Marine Technology, WEGEMT, Copenhagen, 1995 NORSOK standard Page 171 o 488

180 Annex A Rev. 1, December 1998 A.9 COMMENTARY Comm. A.3.1 General For typical installations, the contribution to energy dissipation rom elastic deormation o component/substructures in direct contact with the ship is very small and can normally be neglected. Consequently, plastic methods o analysis apply. However, elastic elongation o the hit member as well as axial lexibility o the nodes to which the member is connected, have a signiicant impact on the development o membrane orces in the member. This eect has to be taken into account in the analysis, which is otherwise based on plastic methods. The diagrams in Section A.3.7. are based on such an approach. Depending on the structure size/coniguration as well as the location o impact elastic strain energy over the entire structure may contribute signiicantly. Comm. A.3. Design principles The transition rom essentially strength behaviour to ductile response can be very abrupt and sensitive to minor changes in scantlings. E.g. integrated analyses o impact between the stern o a supply vessel and a large diameter column have shown that with moderate change o (ring - and longitudinal) stiener size and/or spacing, the energy dissipation may shit rom predominantly platorm based to predominantly vessel based. Due attention should be paid to this sensitivity when the calculation procedure described in Section A.3.5 is applied. Comm. A Recommended The curve or bow impact in Figure A.3-4 has been derived on the assumption o impacts against an ininitely rigid wall. Sometimes the curve has been used erroneously to assess the energy dissipation in bow-brace impacts. Experience rom small-scale tests /3/ indicate that the bow undergoes very little deormation until the brace becomes strong enough to crush the bow. Hence, the brace absorbs most o the energy. When the brace is strong enough to crush the bow the situation is reversed; the brace remains virtually undamaged. On the basis o the tests results and simple plastic methods o analysis, orce-deormation curves or bows subjected to (strong) brace impact were established in /3/ as a unction o impact location and brace diameter. These curves are reproduced in Figure A.9-1. In order to ulil a strength design requirement the brace should at least resist the load level indicated by the broken line (recommended design curve). For braces with a diameter to thickness ratio < 40 it should be suicient to veriy that the plastic collapse load in bending or the brace is larger than the required level. For larger diameter to thickness ratios local denting must probably be taken into account. Normally sized jacket braces are not strong enough to resist the likely bow orces given in Figure A.9-1, and thereore it has to be assumed to absorb the entire strain energy. For the same reasons it has also to be assumed that the brace has to absorb all energy or stern and beam impact with supply vessels. NORSOK standard Page 17 o 488

181 Annex A Rev. 1, December 1998 Impact orce [MN] Recommended design curve or brace impact Between a stringer (D= 1.0 m) On a stringer (D= 0.75 m) Between stringers (D= 0.75) m Indentation [m] Figure A.9-1 Load-deormation curves or bow-bracing impact /3/ Comm. A.3.5. Force contact area or strength design o large diameter columns. Total collision orce distributed over this Area with high orce intensity Deormed stern corner Figure A.9- Distribution o contact orce or stern corner/large diameter column impact Figure A.9- shows an example o the evolution o contact orce intensity during a collision between the stern corner o a supply vessel and a stiened column. In the beginning the contact is concentrated at the extreme end o the corner, but as the corner deorms it undergoes inversion and the contact ceases in the central part. The contact area is then, roughly speaking, bounded by two concentric circles, but the distribution is uneven. NORSOK standard Page 173 o 488