BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES

Transcription

1 Guide fo Buckling and Ulimae Sengh Assessmen fo Offshoe Sucues GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES APRIL 4 (Updaed Augus 18 see nex page) Ameican Bueau of Shipping Incopoaed by Ac of Legislaue of he Sae of New Yok Ameican Bueau of Shipping. All ighs eseved. ABS Plaza Nohchase Dive Houson, TX 776 USA

2 Updaes Augus 18 consolidaion includes: Januay 18 vesion plus Coigenda/Edioials Januay 18 consolidaion includes: Januay 17 vesion plus Noice No. 3 Januay 17 consolidaion includes: Febuay 14 vesion plus Coigenda/Edioials Febuay 14 consolidaion includes: Mach 13 vesion plus Coigenda/Edioials Mach 13 consolidaion includes: Febuay 1 vesion plus Coigenda/Edioials Febuay 1 consolidaion includes: Novembe 11 vesion plus Noice No. Novembe 11 consolidaion includes: July 11 vesion plus Noice No. 1 July 11 consolidaion includes: July 1 vesion plus Coigenda/Edioials July 1 consolidaion includes: Ocobe 8 vesion plus Coigenda/Edioials Ocobe 8 consolidaion includes: June 7 vesion plus Coigenda/Edioials June 7 consolidaion includes: June 6 Coigenda/Edioials June 7 Coigenda/Edioials and added lis of updaes

3 Foewod Foewod This Guide fo he Buckling and Ulimae Sengh Assessmen of Offshoe Sucues is efeed o heein as his Guide. This Guide povides cieia ha can be used in associaion wih specific Rules and Guides issued by ABS fo he classificaion of specific ypes of Offshoe Sucues. The specific Rules and Guides ha his Guide supplemens ae he laes ediions of he following. Rules fo Building and Classing Offshoe Insallaions [fo seel sucue only] Rules fo Building and Classing Mobile Offshoe Dilling Unis (MODUs) Rules fo Building and Classing Single Poin Mooings (SPMs) Rules fo Building and Classing Floaing Poducion Insallaions (FPIs) [fo non ship-ype hulls]. In case of conflic beween he cieia conained in his Guide and he above-menioned Rules, he lae will have pecedence. These cieia ae no o be applied o ship-ype FPIs, which ae being eviewed o eceive a SafeHullelaed Classificaion Noaion. (This includes ship-ype FPIs eceiving he SafeHull-Dynamic Load Appoach Classificaion Noaion) In hese vessel-elaed cases, he cieia based on he conens of Pa 5C of he ABS Rules fo Building and Classing Seel Vessels (SVR) apply. The cieia pesened in his Guide may also apply in ohe siuaions such as he ceificaion o veificaion of a sucual design fo compliance wih he Regulaions of a Govenmenal Auhoiy. Howeve, in such a case, he cieia specified by he Govenmenal Auhoiy should be used, bu hey may no poduce a design ha is equivalen o one obained fom he applicaion of he cieia conained in his Guide. Whee he mandaed echnical cieia of he cognizan Govenmenal Auhoiy fo ceificaion diffe fom hose conained heein, ABS will conside he accepance of such cieia as an alenaive o hose given heein so ha, a he Owne o Opeao s eques, boh ceificaion and classificaion may be ganed o he Offshoe Sucue. ABS welcomes quesions on he applicabiliy of he cieia conained heein as hey may apply o a specific siuaion and pojec. ABS also appeciaes he eceip of commens, suggesions and echnical and applicaion quesions fo he impovemen of his Guide. Fo his pupose, enquiies can be sen eleconically o sd@eagle.og. ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 iii

4 Table of Conens GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES CONTENTS SECTION 1 Inoducion Geneal Scope of his Guide Toleances and Impefecions Coosion Wasage... 9 Loadings Maximum Allowable Sengh Uilizaion Facos... SECTION Individual Sucual Membes Geneal Geomeies and Popeies of Sucual Membes Load Applicaion Failue Modes Coss Secion Classificaion Adjusmen Faco Membes Subjeced o a Single Acion Axial Tension Axial Compession Bending Momen Membes Subjeced o Combined Loads Axial Tension and Bending Momen Axial Compession and Bending Momen Tubula Membes Subjeced o Combined Loads wih Hydosaic Pessue Axial Tension, Bending Momen and Hydosaic Pessue Axial Compession, Bending Momen and Hydosaic Pessue Local Buckling Tubula Membes Subjeced o Axial Compession Tubula Membes Subjeced o Bending Momen Tubula Membes Subjeced o Hydosaic Pessue Plae Elemens Subjeced o Compession and Bending Momen... 1 iv ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

5 TABLE 1 Geomeies, Popeies and Compac Limis of Sucual Membes... 6 TABLE Effecive Lengh Faco... 1 TABLE 3 Minimum Buckling Coefficiens unde Compession and Bending Momen, k s... FIGURE 1 Load Applicaion on a Tubula Membe... 4 FIGURE Effecive Lengh Faco FIGURE 3 Definiion of Edge Sesses... 1 SECTION 3 Plaes, Siffened Panels and Cougaed Panels Geneal Geomey of Plae, Siffened Panel and Cougaed Panels Load Applicaion Buckling Conol Conceps Adjusmen Faco Plae Panels Buckling Sae Limi Ulimae Sengh unde Combined In-plane Sesses Unifom Laeal Pessue Siffened Panels Beam-Column Buckling Sae Limi Flexual-Tosional Buckling Sae Limi Local Buckling of Web, Flange and Face Plae Oveall Buckling Sae Limi Gides and Webs Web Plae Face Plae and Flange Lage Backes and Sloping Webs Tipping Backes Effecs of Cuous Siffness and Popoions Siffness of Siffenes Siffness of Web Siffenes Siffness of Suppoing Gides Popoions of Flanges and Faceplaes Popoions of Webs of Siffenes Cougaed Panels Local Plae Panels Uni Cougaion Oveall Buckling Geomeic Popeies Siffened Panels Cougaed Panels FIGURE 1 Typical Siffened Panel... 4 FIGURE Secional Dimensions of a Siffened Panel... 4 FIGURE 3 Typical Cougaed Panel... 5 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 v

6 FIGURE 4 Secional Dimensions of a Cougaed Panel... 5 FIGURE 5 Pimay Loads and Load Effecs on Plae and Siffened Panel... 6 FIGURE 6 Failue Modes ( Levels ) of Siffened Panel... 7 FIGURE 7 Unsuppoed Span of Longiudinal FIGURE 8 Effecive Beadh of Plaing s w FIGURE 9 Lage Backes and Sloping Webs FIGURE 1 Tipping Backes SECTION 4 Cylindical Shells Geneal Geomey of Cylindical Shells Load Applicaion Buckling Conol Conceps Adjusmen Faco Unsiffened o Ring-siffened Cylindes Bay Buckling Limi Sae Ciical Buckling Sess fo Axial Compession o Bending Momen Ciical Buckling Sess fo Exenal Pessue Geneal Buckling Cuved Panels Buckling Sae Limi Ciical Buckling Sess fo Axial Compession o Bending Momen Ciical Buckling Sess unde Exenal Pessue Ring and Singe-siffened Shells Bay Buckling Limi Sae Ciical Buckling Sess fo Axial Compession o Bending Momen Ciical Buckling Sess fo Exenal Pessue Geneal Buckling Local Buckling Limi Sae fo Ring and Singe Siffenes Flexual-Tosional Buckling Web Plae Buckling Faceplae and Flange Buckling Beam-Column Buckling Sess Calculaions Longiudinal Sess Hoop Sess Siffness and Popoions Siffness of Ring Siffenes Siffness of Singe Siffenes Popoions of Webs of Siffenes Popoions of Flanges and Faceplaes vi ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

7 FIGURE 1 Ring and Singe-siffened Cylindical Shell FIGURE Dimensions of Siffenes FIGURE 3 Typical Buckling Modes of Ring and Singe Cylindical Shells SECTION 5 Tubula Joins Geneal Geomey of Tubula Joins Loading Applicaion Failue Modes Classficaion of Tubula Joins Adjusmen Faco Simple Tubula Joins Join Capaciy Join Cans Sengh Sae Limi Ohe Joins Muliplana Joins Ovelapping Joins Goued Joins Ring-Siffened Joins Cas Joins... 7 TABLE 1 Sengh Faco, Q u FIGURE 1 Geomey of Tubula Joins FIGURE Examples of Tubula Join Caegoizion FIGURE 3 Examples of Effecive Can Lengh FIGURE 4 Muliplana Joins... 7 FIGURE 5 Goued Joins... 7 APPENDIX 1 Review of Buckling Analysis by Finie Elemen Mehod (FEM) Geneal Engineeing Model FEM Analysis Model Soluion Pocedues Veificaion and Validaion ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 vii

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9 Secion 1: Inoducion SECTION 1 Inoducion 1 Geneal (18) The cieia in his Guide ae pimaily based on exising mehodologies and hei aendan safey facos. These mehods and facos ae deemed o povide an equivalen level of safey, eflecing wha is consideed o be appopiae cuen pacice. I is acknowledged ha new mehods and cieia fo design ae consanly evolving. Fo his eason, ABS does no seek o inhibi he use of an alenaive echnological appoach ha is demonsaed o poduce an accepable level of safey. The cieia in his Guide is pesened in he Woking Sess Design (WSD) foma, also known as he Allowable Sess (o Sengh) Design (ASD) foma. Alenaive sucual design cieia in a Load and Resisance Faco Design (LRFD) foma ae povided in he ABS Guide fo Buckling and Ulimae Sengh Assessmen of Offshoe Sucues (LRFD Vesion). 3 Scope of his Guide This Guide povides cieia ha should be used on he following sucual seel componens o assemblages: Individual sucual membes (i.e., discee beams and columns) [see Secion ] Plaes, siffened panels and cougaed panels [see Secion 3] Siffened cylindical shells [see Secion 4] Tubula joins [see Secion 5] Addiionally, Appendix 1 conains guidance on he eview of buckling analysis using he finie elemen mehod (FEM) o esablish buckling capaciies. 5 Toleances and Impefecions The buckling and ulimae sengh of sucual componens ae highly dependen on he ampliude and shape of he impefecions inoduced duing manufacue, soage, anspoaion and insallaion. Typical impefecions causing sengh deeioaion ae: Iniial disoion due o welding and/o ohe fabicaion-elaed pocess Misalignmens of joined componens In geneal, he effecs of impefecions in he fom of iniial disoions, misalignmens and weld-induced esidual sesses ae implicily incopoaed in he buckling and ulimae sengh fomulaions. Because of hei effec on sengh, i is impoan ha impefecions be monioed and epaied, as necessay, no only duing consucion, bu also in he compleed sucue o ensue ha he sucual componens saisfy oleance limis. The oleances on impefecions o which he sengh cieia given in his Guide ae consideed valid ae lised, fo example, in IACS Recommendaion No. 47 Shipbuilding and Repai Qualiy Sandad. Impefecions exceeding such published oleances ae no accepable unless i is shown using a ecognized mehod ha he sengh capaciy and uilizaion faco of he impefec sucual componen ae wihin pope age safey levels. ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 1

10 Secion 1 Inoducion 7 Goss Scanlings (18) The buckling and ulimae sengh fomulaions povided in his Guide ae inended o be used along wih he goss scanlings of sucual componens. 9 Loadings Condiions epesening all modes of opeaion of he Offshoe Sucue ae o be consideed o esablish he mos ciical loading cases. The ABS Rules and Guides fo he classificaion of vaious ypes of Offshoe Sucues ypically define wo pimay loading condiions. In he ABS Rules fo Building and Classing Mobile Offshoe Dilling Unis (MODU Rules), hey ae Saic Loadings and Combined Loadings, and in he ABS Rules fo Building and Classing Offshoe Insallaions (Offshoe Insallaions Rules), he ABS Rules fo Building and Classing Single Poin Mooings (SPM Rules) and he ABS Rules fo Building and Classing Floaing Poducion Insallaions (FPI Rules) hey ae Nomal Opeaion and Sevee Som. The componen loads of hese loading condiions ae discussed below. The deeminaion of he magniudes of each load componen and each load effec (i.e., sess, deflecion, inenal bounday condiion, ec.) ae o be pefomed using ecognized calculaion mehods and/o es esuls and ae o be fully documened and efeenced. As appopiae, he effecs of sess concenaions, seconday sess aising fom eccenically applied loads and membe displacemens (i.e., P-Δ effecs) and addiional shea displacemens and shea sess in beam elemens ae o be suiably accouned fo in he analysis. The pimay loading condiions o be consideed in he MODU Rules ae: i) Saic Loadings. Sesses due o saic loads only, he saic loads include opeaional gaviy loads and he weigh of he uni, wih he uni afloa o esing on he seabed in calm wae. ii) Combined Loadings. Sesses due o combined loadings, he applicable saic loads, as descibed above, ae combined wih elevan envionmenal loadings, including acceleaion and heeling foces. The pimay loading condiions o be consideed in he Offshoe Insallaions Rules, SPM Rules and FPI Rules ae: i) Nomal Opeaions. Sesses due o opeaing envionmenal loading combined wih dead and maximum live loads appopiae o he funcion and opeaions of he sucue ii) Sevee Som. Sesses due o design envionmenal loading combined wih dead and live loads appopiae o he funcion and opeaions of he sucue duing design envionmenal condiion The buckling and ulimae sengh fomulaions in his Guide ae applicable o saic/quasi-saic loads, Dynamic (e.g., impulsive) loads, such as may esul fom impac and fluid sloshing, can induce dynamic buckling, which, in geneal, is o be deal wih using an appopiae nonlinea analysis. 11 Maximum Allowable Sengh Uilizaion Facos The buckling and ulimae sengh equaions in his Guide povide an esimae of he aveage sengh of he consideed componens while achieving he lowes sandad deviaion when compaed wih nonlinea analyses and mechanical ess. To ensue he safey of he sucual componens, maximum allowable sengh uilizaion facos, which ae he invese of safey facos, ae applied o he pediced sengh. The maximum allowable sengh uilizaion facos will, in geneal, depend on he given loading condiion, he ype of sucual componen and he failue consequence. The maximum allowable sengh uilizaion facos, η, ae based on he facos of safey given in he Offshoe Insallaions Rules, MODU Rules, SPM Rules and FPI Rules, as applicable. The maximum allowable sengh uilizaion facos have he following values. i) Fo a loading condiion ha is chaaceized as a saic loading of a Mobile Offshoe Dilling Uni o nomal opeaion of an Offshoe Insallaion, Floaing Poducion Insallaion and Single Poin Mooing: η.6ψ ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

11 Secion 1 Inoducion ii) Fo a loading condiion ha is chaaceized as a combined loading of a Mobile Offshoe Dilling Uni o sevee som of an Offshoe Insallaion, Floaing Poducion Insallaion and Single Poin Mooing: η.8ψ ψ adjusmen faco, as given in subsequen secions of his Guide. Unde he above-menioned Rules and Guides, i is equied ha boh of he chaaceisic ypes of loading condiions (i.e., saic and combined, o nomal opeaion and sevee som) ae o be applied in he design and assessmen of a sucue. The loading condiion poducing he mos sevee equiemen govens he design. In he Secions ha follow concening specific sucual componens, diffeen adjusmen facos may apply o diffeen ypes of loading (i.e., ension o bending vesus pue compession). To epesen he values of η applicable o he diffeen ypes of load componens, subscips ae someimes added o he symbol η (e.g., in Secion, η 1 and η, apply, especively, o axial compession o ension/bending in he individual sucual membe.). ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 3

12 Secion : Individual Sucual Membes SECTION Individual Sucual Membes 1 Geneal This Secion povides sengh cieia fo individual sucual membes. The ypes of membes consideed in his Secion ae ubula and non-ubula membes wih unifom geomeic popeies along hei enie lengh and made of a single maeial. The cieia povided in his Secion ae fo ubula and non-ubula elemens, bu ohe ecognized sandads ae also accepable. The behavio of sucual membes is influenced by a vaiey of facos, including secional shape, maeial chaaceisics, bounday condiions, loading ypes and paamees and fabicaion mehods. 1.1 Geomeies and Popeies of Sucual Membes A sucual membe wih a coss secion having a leas one axis of symmey is consideed. The geomeies and popeies of some ypical coss secions ae illusaed in Secion, Table 1. Fo secions which ae no lised in Secion, Table 1, he equied geomeic popeies ae o be calculaed based on accepable fomulaions. 1.3 Load Applicaion This Secion includes he sengh cieia fo any of he following loads and load effecs: Axial foce in longiudinal diecion, P Bending momen, M Hydosaic pessue, q Combined axial ension and bending momen Combined axial compession and bending momen Combined axial ension, bending momen and hydosaic pessue Combined axial compession, bending momen and hydosaic pessue The load diecions depiced in Secion, Figue 1 ae posiive. FIGURE 1 Load Applicaion on a Tubula Membe z q z P M y x L M P q y D 4 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

13 Secion Individual Sucual Membes 1.5 Failue Modes Failue modes fo a sucual membe ae caegoized as follows: Flexual buckling. Bending abou he axis of he leas esisance. Tosional buckling. Twising abou he longiudinal (x) axis. I may occu if he osional igidiy of he secion is low, as fo a membe wih a hin-walled open coss secion. Laeal-osional buckling. Synchonized bending and wising. A membe which is ben abou is majo axis may buckle laeally. Local buckling. Buckling of a plae o shell elemen ha is a local pa of a membe ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 5

14 6 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 Geomey 1. Tubula membe. Squae o ecangul a hollow secion d Secional Shape D z b z TABLE 1 Geomeies, Popeies and Compac Limis of Sucual Membes y y Geomeical Paamees D Oue diamee Thickness b Flange widh d Web deph Thickness N/A Axis Popeies* Compac Limis Majo y-y Mino z-z A π[d (D ) ]/4 I y, I z π[d 4 (D ) 4 ]/64 K π (D ) 3 /4 I o π [D 4 (D ) 4 ]/3 Γ A (b + d) I y d (3b + d)/6 I z b (b + 3d)/6 b d K b + d I o (b + d) 3 /6 Γ b d ( d b) 4 b + d D b, d E E Secion Individual Sucual Membes

15 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 7 Geomey 3. Welded box shape 4. W-shape d d Secional Shape f f a b b TABLE 1 (coninued) Geomeies, Popeies and Compac Limis of Sucual Membes z z w w y b y Geomeical Paamees d Web deph w Web hickness b Flange widh f Flange hickness b Ousand d Web deph w Web hickness b Flange widh f Flange hickness Axis Popeies* Compac Limis Majo y-y Mino z-z Majo y-y Mino z-z A (b f + d w ) I y d (3b f + d w )/6 I z b (b f + 3d w )/6 K a a I o I y + I z Γ ( b 4( b + d f w d 3 d f 3 d f a + A b f + d w I y d (6b f + d w )/1 I z b 3 f /6 3 K (b f + d 3 w )/3 I o I y + I z Γ d b 3 f /4 3 d w ) 3 a d w ) a f b f d w b f, d w E E E E Secion Individual Sucual Membes

16 8 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 Geomey 5. Channel 6. T-ba d Secional Shape d w f b TABLE 1 (coninued) Geomeies, Popeies and Compac Limis of Sucual Membes b z z f w y y Geomeical Paamees d Web deph w Web hickness b Flange widh f Flange hickness d cs Disance of shea cene o cenoid d Web deph w Web hickness b Flange widh f Flange hickness d cs Disance of shea cene o cenoid Axis Popeies* Compac Limis Majo y-y Mino z-z Majo y-y Mino z-z A b f + d w I y d (6b f + d w )/1 I z d 3 w (b f + d w )/3A 3 K (b f + d 3 w )/3 I o I y + I z + A d Γ d 3 cs b f (3b f + d 1(6b + d ) f w A b f + d w I y d 3 w (4b f + d w )/1A I z b 3 f /1 3 K (b f + d 3 w )/3 I o I y + I z + A d cs Γ (b 3 f 3 + 4d 3 w 3 )/144 w ) d w b f d w b f E E E E Secion Individual Sucual Membes

17 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 9 Geomey 7. Double angles d Secional Shape w f b TABLE 1 (coninued) Geomeies, Popeies and Compac Limis of Sucual Membes z y Geomeical Paamees d Web deph w Web hickness b Flange widh f Flange hickness d cs Disance of shea cene o cenoid Axis Popeies* Compac Limis Majo y-y Mino z-z A (b f + d w ) I y d 3 w (4b f + d w )/3A I z b 3 f /3 3 K (b f + d 3 w )/3 I o I y + I z + A d cs Γ (b 3 f 3 + 4d 3 w 3 )/18 * The fomulaions fo he popeies ae deived assuming ha he secion is hin-walled (i.e., hickness is elaively small) : A coss secional aea, cm (in ) I y momen of ineia abou y-axis, cm 4 (in 4 ) I z momen of ineia abou z-axis, cm 4 (in 4 ) K S. Venan osion consan fo he membe, cm 4 (in 4 ) I pola momen of ineia of he membe, cm 4 (in 4 ) Γ waping consan, cm 6 (in 6 ) d w b f.4.4 E E Secion Individual Sucual Membes

18 Secion Individual Sucual Membes 1.7 Coss Secion Classificaion The coss secion may be classified as: i) Compac. A coss secion is compac if all compessed componens comply wih he limis in Secion, Table 1. Fo a compac secion, he local buckling (plae buckling and shell buckling) can be disegaded because yielding pecedes buckling. ii) Non-Compac. A coss secion is non-compac if any compessed componen does no comply wih he limis in Secion, Table 1. Fo a non-compac secion, he local buckling (plae o shell buckling) is o be aken ino accoun. 1.9 Adjusmen Faco Fo he maximum allowable sengh uilizaion facos, η, defined in Subsecion 1/11, he adjusmen faco is o ake he following values: Fo axial ension and bending [o esablish η below]: ψ 1. Fo axial compession (column buckling o osional buckling) [o esablishη 1 below]: ψ.87 if EA P 1.13 P / EA if EA > P EA elasic buckling sess, as defined in /3.3, N/cm (kgf/cm, lbf/in ) P popoional linea elasic limi of he sucue, which may be aken as.6 fo seel specified minimum yield poin, N/cm (kgf/cm, lbf/in ) Fo compession (local buckling of ubula membes) [o esablish η x and η θ below]: ψ.833 if Ci Ci / if Ci >.55 Ci ciical local buckling sess, epesening Ci fo axial compession, as specified in /9.1, and Cθ fo hydosaic pessue, as specified in /9.5, N/cm (kgf/cm, lbf/in ) specified minimum yield poin, N/cm (kgf/cm, lbf/in ) 3 Membes Subjeced o a Single Acion 3.1 Axial Tension Membes subjeced o axial ensile foces ae o saisfy he following equaion: /η 1 axial ensile sess, N/cm (kgf/cm, lbf/in ) P/A specified minimum yield poin, N/cm (kgf/cm, lbf/in ) P axial foce, N (kgf, lbf) A coss secional aea, cm (in ) η allowable sengh uilizaion faco fo ension and bending, as defined in Subsecion 1/11 and /1.9 1 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

19 Secion Individual Sucual Membes 3.3 Axial Compession Membes subjeced o axial compessive foces may fail by flexual o osional buckling. The buckling limi sae is defined by he following equaion: A /η 1 CA 1 A axial compessive sess, N/cm (kgf/cm, lbf/in ) P/A P axial foce, N (kgf, lbf) CA ciical buckling sess, N/cm (kgf/cm, lbf/in ) F 1 P EA ( 1 P ) F EA if if EA EA P > P P popoional linea elasic limi of he sucue, which may be aken as.6 fo seel F specified minimum yield poin fo a compac secion Cx local buckling sess fo a non-compac secion fom Subsecion /9 EA elasic buckling sess, which is he lesse of he soluions of he following quadaic equaion, N/cm (kgf/cm, lbf/in ) I ( EA Eη )( A EA ET ) EA d cs Eη Eule buckling sess abou mino axis, N/cm (kgf/cm, lbf/in ) π E/(kL/ η ) ET ideal elasic osional buckling sess, N/cm (kgf/cm, lbf/in ) EK EΓ + π.6i kl I η adius of gyaion abou mino axis, cm (in.) I η / A E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel A coss secional aea, cm (in ) I η momen of ineia abou mino axis, cm 4 (in 4 ) K S. Venan osion consan fo he membe, cm 4 (in 4 ) I pola momen of ineia of he membe, cm 4 (in 4 ) Γ waping consan, cm 6 (in 6 ) d cs diffeence of cenoid and shea cene coodinaes along majo axis, cm (in.) L membe s lengh, cm (in.) k effecive lengh faco, as specified in Secion, Table. When i is difficul o claify he end condiions, he nomogaph shown in Secion, Figue may be used. The values of G fo each end (A and B) of he column ae deemined: G I L c c I L g g F F ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 11

20 Secion Individual Sucual Membes I I c g is he oal fo columns meeing a he join consideed and L is he oal c Lg fo esaining beams meeing a he join consideed. Fo a column end ha is suppoed, bu no fixed, he momen of ineia of he suppo is zeo, and he esuling value of G fo his end of he column would be. Howeve, in pacice, unless he fooing was designed as a ficionless pin, his value of G would be aken as 1. If he column end is fixed, he momen of ineia of he suppo would be, and he esuling value of G of his end of he column would be zeo. Howeve, in pacice, hee is some movemen and G may be aken as 1.. If he esaining beam is eihe pinned (G ) o fixed (G ) a is fa end, efinemens may be made by muliplying he siffness (I g /L g ) of he beam by he following facos: Sidesway pevened Fa end of beam pinned 1.5 Sidesway pemied Fa end of beam pinned.5 Fa end of beam fixed. η 1 allowable sengh uilizaion faco fo axial compession (column buckling), as defined in Subsecion 1/11 and /1.9 TABLE Effecive Lengh Faco Buckled shape of column shown by dashed line Theoeical value Recommended k value when ideal condiions ae appoximaed Roaion fixed. Tanslaion fixed End condiion noaion Roaion fee. Tanslaion fixed Roaion fixed. Tanslaion fee Roaion fee. Tanslaion fee 1 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

21 Secion Individual Sucual Membes FIGURE Effecive Lengh Faco G A k G B G A k G B Sidesway Pevened Sidesway Pemied Noe: These alignmen chas o nomogaphs ae based on he following assumpions: 1 Behavio is puely elasic. All membes have consan coss secion. 3 All joins ae igid. 4 Fo columns in fames wih sidesway pevened, oaions a opposie ends of he esaining beams ae equal in magniude and opposie in diecion, poducing single cuvaue bending. 5 Fo columns in fames wih sidesway pemied, oaions a opposie ends of he esaining beams ae equal in magniude and diecion, poducing evese cuvaue bending 6 The siffness paamee L(P/EI) 1/ of all columns is equal. 7 Join esain is disibued o he column above and below he join in popoion o EI/L fo he wo columns. 8 All columns buckle simulaneously. 9 No significan axial compession foce exiss in he esaining beams. Adjusmens ae equied when hese assumpions ae violaed and he alignmen chas ae sill o be used. Refeence is made o ANSI/AISC 36-5, Commenay C. 3.5 Bending Momen A membe subjeced o bending momen may fail by local buckling o laeal-osional buckling. The buckling sae limi is defined by he following equaion: b /η CB 1 b sess due o bending momen M/SM e ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 13

22 Secion Individual Sucual Membes M bending momen, N-cm (kgf-cm, lbf-in) SM e elasic secion modulus, cm 3 (in 3 ) η allowable sengh uilizaion faco fo ension and bending CB ciical bending sengh, as follows: i) Fo a ubula membe, he ciical bending sengh is o be obained fom he equaion given in /9.3. ii) Fo a olled o fabicaed-plae secion, he ciical bending sengh is deemined by he ciical laeal-osional buckling sess. The ciical laeal-osional buckling sess is o be obained fom he following equaion: C(LT) E F 1 P ( LT ) ( 1 P ) F E( LT ) if if E( LT ) E( LT ) P > P P popoional linea elasic limi of he sucue, which may be aken as.6 fo seel E(LT) elasic laeal-osional buckling sess, N/cm (kgf/cm, lbf/in ) π EI C SM (kl) c η I η momen of ineia abou mino axis, as defined in Secion, Table 1, cm 4 (in 4 ) SM e secion modulus of compessive flange, cm 3 (in 3 ) Iξ ξ c I ξ momen of ineia abou majo axis, as defined in Secion, Table 1, cm 4 (in 4 ) ξ c disance fom majo neual axis o compessed flange, cm (in.) F F C Γ + I η K I η ( kl).6π E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel F, specified minimum yield poin fo a compac secion Cx, local buckling sess fo a non-compac secion, as specified in /9.7 K S. Venan osion consan fo he membe, cm 4 (in 4 ) Γ waping consan, cm 6 (in 6 ) L membe s lengh, cm (in.) k effecive lengh faco, as defined in / ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

23 Secion Individual Sucual Membes 5 Membes Subjeced o Combined Loads 5.1 Axial Tension and Bending Momen Membes subjeced o combined axial ension and bending momen ae o saisfy he following equaions a all coss-secions along hei lengh: Fo ubula membes: 1 by + η η CBy + bz CBz Fo olled o fabicaed-plae secions: by bz η η η CBy CBz.5 1 axial ensile sess fom /3.1, N/cm (kgf/cm, lbf/in ) by bending sess fom /3.5 abou membe y-axis, N/cm (kgf/cm, lbf/in ) bz bending sess fom /3.5 abou membe z-axis, N/cm (kgf/cm, lbf/in ) CBy ciical bending sengh coesponding o membe s y-axis fom /3.5, N/cm (kgf/cm, lbf/in ) CBz ciical bending sengh coesponding o membe s z-axis fom /3.5, N/cm (kgf/cm, lbf/in ) η allowable sengh uilizaion faco fo ension and bending, as defined in 1/11 and / Axial Compession and Bending Momen Membes subjeced o combined axial compession and bending momen ae o saisfy he following equaion a all coss secions along hei lengh: Fo ubula membes: When a / CA >.15: 1 1 Cmy a by 1 Cmz bz CA η CBy 1 a /( η1 Ey ) CBz 1 a /( η1 Ez ) η When a / CA.15:.5 1 η 1 a CA 1 + η by CBy + bz CBz Fo olled o fabicaed-plae secions: When a / CA >.15: η When a / CA.15: a Cmy by 1 Cmz bz η 1 /( η ) η 1 /( η ) 1 CA CBy a 1 Ey CBz a 1 Ez η 1 a CA by bz η η CBy CBz ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 15

24 Secion Individual Sucual Membes a axial compessive sess fom /3.3, N/cm (kgf/cm, lbf/in ) by bending sess fom /3.5 abou membe y-axis, N/cm (kgf/cm, lbf/in ) bz bending sess fom /3.5 abou membe z-axis, N/cm (kgf/cm, lbf/in ) CA ciical axial compessive sengh fom /3.3, N/cm (kgf/cm, lbf/in ) CBy ciical bending sengh coesponding o membe y-axis fom /3.5, N/cm (kgf/cm, lbf/in ) CBz ciical bending sengh coesponding o membe z-axis fom /3.5, N/cm (kgf/cm, lbf/in ) Ey Eule buckling sess coesponding o membe y-axis, N/cm (kgf/cm, lbf/in ) π E/(k y L/ y ) Ez Eule buckling sess coesponding o membe z-axis, N/cm (kgf/cm, lbf/in ) π E/(k z L/ z ) E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel y, z adius of gyaion coesponding o he membe y- and z-axes, cm (in.) k y, k z effecive lengh facos coesponding o membe y- and z-axes fom /3.3 C my, C mz momen facos coesponding o he membe y- and z-axes, as follows: i) Fo compession membes in fames subjeced o join anslaion (sidesway): C m.85 ii) Fo esained compession membes in fames baced agains join anslaion (sidesway) and wih no ansvese loading beween hei suppos: C m.6.4m 1 /M iii) bu no less han.4 and limied o.85, M 1 /M is he aio of smalle o lage momens a he ends of ha poion of he membe unbaced in he plane of bending unde consideaion. M 1 /M is posiive when he membe is ben in evese cuvaue, negaive when ben in single cuvaue. Fo compession membes in fames baced agains join anslaion in he plane of loading and subjec o ansvese loading beween hei suppos, he value of C m may be deemined by aional analysis. Howeve, in lieu of such analysis, he following values may be used. Fo membes whose ends ae esained: C m.85 Fo membes whose ends ae unesained: C m 1. η 1 allowable sengh uilizaion faco fo axial compession (column buckling), as defined in Subsecion 1/11 and /1.9 η allowable sengh uilizaion faco fo ension and bending, as defined in Subsecion 1/11 and / ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

25 Secion Individual Sucual Membes 7 Tubula Membes Subjeced o Combined Loads wih Hydosaic Pessue Appopiae consideaion is o be given o he capped-end acions on a sucual membe subjeced o hydosaic pessue. I should be noed ha he equaions in his Subsecion do no apply unless he cieia of /9.5 ae saisfied fis. 7.1 Axial Tension, Bending Momen and Hydosaic Pessue The following equaion is o be saisfied fo ubula membes subjeced o combined axial ension, bending momen and hydosaic pessue: c η Tθ by + bz + 1 η CBθ c calculaed axial ensile sess due o foces fom acions ha include he capped-end acions due o hydosaic pessue, N/cm (kgf/cm, lbf/in ) Tθ axial ensile sengh in he pesence of hydosaic pessue, N/cm (kgf/cm, lbf/in ) C q CBθ bending sengh in he pesence of hydosaic pessue, N/cm (kgf/cm, lbf/in ) C q CB CB ciical bending sengh excluding hydosaic pessue fom /3.5 ξ C q [ 1 +.9B B.3B] B θ /(η θ Cθ ) ξ 5 4 Cθ / θ hoop sess due o hydosaic pessue fom /9.5, N/cm (kgf/cm, lbf/in ) Cθ ciical hoop buckling sengh fom /9.5, N/cm (kgf/cm, lbf/in ) specified minimum yield poin, N/cm (kgf/cm, lbf/in ) η allowable sengh uilizaion faco fo ension and bending, as defined in Subsecion 1/11 and /1.9 η θ allowable sengh uilizaion faco fo local buckling in he pesence of hydosaic pessue, as defined in Subsecion 1/11 and / Axial Compession, Bending Momen and Hydosaic Pessue Tubula membes subjeced o combined compession, bending momen and exenal pessue ae o saisfy he following equaions a all coss secions along hei lengh. When ac / CAθ >.15 and ac >.5 θ :.5 1 C 1 1 η ac θ my by mz bz + + η ac ac CAθ η CBθ θ Ey 1 C η 1 Ez.5 θ 1 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 17

26 Secion Individual Sucual Membes When ac / CAθ.15: a η 1 CAθ 1 + η by CBθ + bz CBθ.5 1 ac calculaed compessive axial sess due o axial compession ha includes he cappedend acions due o hydosaic pessue, N/cm (kgf/cm, lbf/in ) θ hoop sess due o hydosaic pessue fom /9.5, N/cm (kgf/cm, lbf/in ) CBθ ciical bending sengh in he pesence of hydosaic pessue fom /7.1, N/cm (kgf/cm, lbf/in ) CAθ axial compessive sengh in he pesence of hydosaic pessue EA F Λ if if EA EA P F (1 > P (1 F θ θ / F ) / ) EA elasic buckling sess in he absence of hydosaic pessue fom /3.3, N/cm (kgf/cm, lbf/in ) F Λ ( ζ + ζ + 4ω ) / ζ 1 P (1 P ) F / EA θ / F ω.5( θ / F )(1.5 θ / F ) Ey Eule buckling sess coesponding o membe y-axis fom /5.3, N/cm (kgf/cm, lbf/in ) Ez Eule buckling sess coesponding o membe z-axis fom /5.3, N/cm (kgf/cm, lbf/in ) C my, C mz momen facos coesponding o he membe y- and z-axes fom /5.3 P popoional linea elasic limi of he sucue, which may be aken as.6 fo seel E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel F, specified minimum yield poin fo he compac secion Cx, local buckling sess fo he non-compac secion fom /9.7 η 1 allowable sengh uilizaion faco fo axial compession (column buckling), as defined in Subsecion 1/11 and /1.9 η allowable sengh uilizaion faco fo ension and bending, as defined in Subsecion 1/11 and /1.9 When x >.5η θ Cθ and η x x >.5η θ Cθ, he following equaion is o also be saisfied: x.5η θ Cθ η.5η x Cx θ Cθ θ + ηθ C θ 1 x maximum compessive axial sess fom axial compession and bending momen, which includes he capped-end acions due o he hydosaic pessue, N/cm (kgf/cm, lbf/in ) ac + b ac calculaed compessive axial sess due o axial compession fom acions ha include he capped-end acions due o hydosaic pessue, N/cm (kgf/cm, lbf/in ) 18 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

27 Secion Individual Sucual Membes b sess due o bending momen fom /3.5, N/cm (kgf/cm, lbf/in ) Cx ciical axial buckling sess fom /9.1, N/cm (kgf/cm, lbf/in ) Cθ ciical hoop buckling sess fom /9.5, N/cm (kgf/cm, lbf/in ) C my, C mz momen facos coesponding o he membe y- and z-axes, as defined in /5.3 9 Local Buckling η x maximum allowable sengh uilizaion faco fo axial compession (local buckling), as defined in Subsecion 1/11 and /1.9 η θ maximum allowable sengh uilizaion faco fo hydodynamic pessue (local buckling), as defined in Subsecion 1/11 and /1.9 Fo a membe wih a non-compac secion, local buckling may occu befoe he membe as a whole becomes unsable o befoe he yield poin of he maeial is eached. Such behavio is chaaceized by local disoion of he coss secion of he membe. When a deailed analysis is no available, he equaions given below may be used o evaluae he local buckling sess of a membe wih a non-compac secion. 9.1 Tubula Membes Subjeced o Axial Compession Local buckling sess of ubula membes wih D/ E/(4.5 ) subjeced o axial compession may be obained fom he following equaion: Ex Cx ( ) 1 P 1 P Ex if if Ex Ex P > P P popoional linea elasic limi of he sucue, which may be aken as.6 fo seel specified minimum yield poin, N/cm (kgf/cm, lbf/in ) Ex elasic buckling sess, N/cm (kgf/cm, lbf/in ).6E/D D oue diamee, cm (in.) hickness, cm (in.) Fo ubula membes wih D/ > E/(4.5 ), he local buckling sess is o be deemined fom 4/ Tubula Membes Subjeced o Bending Momen Ciical bending sengh of ubula membes wih D/ E/(4.5 ) subjeced o bending momen may be obained fom he following equaion: CB ( SM p / SM e ) [ D /( E)]( SM [ D /( E)]( SM p p / SM / SM e e ) ) fo fo fo D ( E).. < D D ( E) >.1 ( E).1 SM e elasic secion modulus, cm 3 (in 3 ) (π/64)[d 4 (D ) 4 ]/(D/) SM p plasic secion modulus, cm 3 (in 3 ) (1/6)[D 3 (D ) 3 ] D oue diamee, cm (in.) ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 19

28 Secion Individual Sucual Membes hickness, cm (in.) E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel specified minimum yield poin Fo ubula membes wih D/ > E/(4.5 ), he local buckling sess is o be deemined fom 4/ Tubula Membes Subjeced o Hydosaic Pessue Tubula membes wih D/ E/(4.5 ) subjeced o exenal pessue ae o saisfy he following equaion: θ /η θ Cθ 1 θ hoop sess due o hydosaic pessue qd/() q exenal pessue Cθ ciical hoop buckling sengh, N/cm (kgf/cm, lbf/in ) Φ Bθ Φ plasiciy educion faco 1 fo fo.55 < 1.6 fo 1.6 < < 6.5 1/ fo 6.5 Eθ / Eθ elasic hoop buckling sess C θ E/D C θ buckling coefficien.44/d fo µ 1.6D/.44/D +.1(D/) 3 /µ 4 fo.85d/ µ < 1.6D/.737/(µ.579) fo 1.5 µ <.85D/.8 fo µ <1.5 µ geomeic paamee / D D / lengh of ubula membe beween siffening ings, diaphagms o end connecions D oue diamee hickness E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel specified minimum yield poin η θ maximum allowable sengh uilizaion faco fo local buckling in he pesence of hydosaic pessue, as defined in Subsecion 1/11 and /1.9 Fo ubula membes wih D/ > E/(4.5 ), he sae limi in 4/3.3 is o be applied. ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

29 Secion Individual Sucual Membes 9.7 Plae Elemens Subjeced o Compession and Bending Momen The ciical local buckling of a membe wih olled o fabicaed plae secion may be aken as he smalles local buckling sess of he plae elemens compising he secion. The local buckling sess of an elemen is o be obained fom he following equaion wih espec o uniaxial compession and in-plane bending momen: Ex Cx ( ) 1 P 1 P Ex if if Ex Ex P > P P popoional linea elasic limi of he sucue, which may be aken as.6 fo seel specified minimum yield poin, N/cm (kgf/cm, lbf/in ) Ex elasic buckling sess, N/cm (kgf/cm, lbf/in ) k s π E 1(1 ν ) s E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel ν Poisson s aio,.3 fo seel s deph of unsuppoed plae elemen hickness of plae elemen k s buckling coefficien, as follows: i) Fo a plae elemen wih all fou edges simply suppoed, he buckling coefficien is o be obained fom following equaion: 8.4 k s κ κ + 1κ fo fo κ 1 1 κ < κ aio of edge sesses, as defined in Secion, Figue 3 amin / amax ii) Fo a plae elemen wih ohe bounday condiions, he buckling coefficien is obained fom Secion, Table 3 FIGURE 3 Definiion of Edge Sesses amax amax Plae Elemen amin amin ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 1

30 Secion Individual Sucual Membes TABLE 3 Minimum Buckling Coefficiens unde Compession and Bending Momen, ks * Loading amin / amax 1 (Unifom compession) Boom Edge Simply Suppoed Top Edge Fee Boom Edge Fixed Top Edge Simply Suppoed Boom Edge Fee Top Edge Fixed amin / amax 1 (Pue Bending) amin / amax * Noe: ks fo inemediae value of amin/amax may be obained by linea inepolaion. ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

31 Secion 3: Plaes, Siffened Panels and Cougaed Panels SECTION 3 Plaes, Siffened Panels and Cougaed Panels 1 Geneal The fomulaions povided in his Secion ae o be used o assess he Buckling and Ulimae Sengh Limis of plaes, siffened panels and cougaed panels. Two Sae Limis fo Buckling and Ulimae Sengh ae nomally consideed in sucual design. The fome is based on buckling and he lae is elaed o collapse. The cieia povided in his Secion apply o Offshoe Sucues, SPMs, SEDUs, CSDUs and FPIs of he TLP and SPAR ypes, and i is no in he scope of his Guide o use he cieia wih ship-ype FPIs. In his lae case, see Secion 5A-3-4 of he FPI Rules. The design cieia apply also o siffened panels fo which he momen of ineia fo he ansvese gides is geae han he momen of ineia of he longiudinal siffenes. I is no in he scope of his Guide o use he cieia fo ohoopically siffened plae panels. Alenaively, he buckling and ulimae sengh of plaes, siffened panels o cougaed panels may be deemined based on eihe appopiae, well-documened expeimenal daa o on a calibaed analyical appoach. When a deailed analysis is no available, he equaions povided in his secion shall be used o assess he buckling sengh. 1.1 Geomey of Plae, Siffened Panel and Cougaed Panels Fla ecangula plaes and siffened panels ae depiced in Secion 3, Figue 1. Siffenes in he siffened panels ae usually insalled equally spaced, paallel o pependicula o panel edges in he diecion of dominan load and ae suppoed by heavie and moe widely-spaced deep suppoing membes (i.e., gides). The given cieia apply o a vaiey of siffene pofiles, such as fla-ba, buil up T-pofiles, buil up inveed angle pofiles and symmeic and non-symmeic bulb pofiles. The secion dimensions of a siffene ae defined in Secion 3, Figue. The siffenes may have sengh popeies diffeen fom hose of he plae. Cougaed panels, as depiced in Secion 3, Figue 3, ae self-siffened and ae usually cougaed in one diecion, suppoed by sools a he wo ends acoss he cougaion diecion. They may ac as waeigh bulkheads o, when conneced wih fasenes, hey ae employed as cougaed shea diaphagms. The dimensions of cougaed panels ae defined in Secion 3, Figue 4. The buckling sengh cieia fo cougaed panels given in Subsecion 3/11 ae applicable o cougaed panels wih cougaion angle,, beween 57 and 9 degees. ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 3

32 Secion 3 Plaes, Siffened Panels and Cougaed Panels FIGURE 1 Typical Siffened Panel Longiudinal Gide Backe Gide Siffene Tansvese Gide s s y z s s Longiudinal Siffene x s Plae FIGURE Secional Dimensions of a Siffened Panel z b f f b b 1 y Cenoid of Siffene d w z w y s e 4 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

33 Secion 3 Plaes, Siffened Panels and Cougaed Panels z FIGURE 3 Typical Cougaed Panel y x L B FIGURE 4 Secional Dimensions of a Cougaed Panel a z d φ c b Cenoid z y s 1.3 Load Applicaion The plae and siffened panel cieia accoun fo he following load and load effecs. The symbols fo each of hese loads ae shown in Secion 3, Figue 5. Unifom in-plane compession, ax, ay * In-plane bending, bx, by Edge shea, τ Laeal loads, q Combinaions of he above * Noe: If unifom sess ax o ay is ensile ahe han compessive, i may be se equal o zeo. ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 5

34 Secion 3 Plaes, Siffened Panels and Cougaed Panels FIGURE 5 Pimay Loads and Load Effecs on Plae and Siffened Panel Edge Shea xmax τ s y x xmin ymax ymin xmax ax + bx xmin ax bx ymax ay + by In-plane Compession and Bending q Laeal Pessue ymin ay by 1.5 Buckling Conol Conceps (1 Febuay 1) The failue of plaes and siffened panels can be soed ino hee levels, namely, he plae level, he siffened panel level and he enie gillage level, which ae depiced in Secion 3, Figue 6. An offshoe sucue is o be designed in such a way ha he buckling and ulimae sengh of each level is geae han is peceding level (i.e., a well designed sucue does no collapse when a plae fails as long as he siffenes can esis he exa load hey expeience fom he plae failue). Even if he siffenes collapse, he sucue may no fail immediaely as long as he gides can suppo he exa load shed fom he siffenes. The buckling sengh cieia fo plaes and siffened panels ae based on he following assumpions and limis wih espec o buckling conol in he design of siffened panels, which ae in compliance wih ABS ecommended pacices. The buckling sengh of each siffene is geneally geae han ha of he plae panel i suppos. Siffenes wih hei associaed effecive plaing ae o have momens of ineia no less han i, given in 3/9.1. If no saisfied, he oveall buckling of siffened panel is o be assessed, as specified in 3/5.7. The deep suppoing membes (i.e., gides) wih hei associaed effecive plaing ae o have momens of ineia no less han I s, given in 3/9.5. If no saisfied, he oveall buckling of siffened panel is also necessay, as given in 3/5.7. In addiion, ipping (e.g., osional/flexual insabiliy) is o be pevened if ipping backes ae povided, as specified in 3/7.7. Faceplaes and flanges of gides and siffenes ae popoioned such ha local insabiliy is pevened (see 3/9.7). Webs of gides and siffenes ae popoioned such ha local insabiliy is pevened (see 3/9.9). Fo plaes and siffened panels ha do no saisfy hese limis, a deailed analysis of buckling sengh using an accepable mehod should be submied fo eview. 6 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

35 Secion 3 Plaes, Siffened Panels and Cougaed Panels FIGURE 6 Failue Modes ( Levels ) of Siffened Panel Plae Level Siffened Panel Level Deep Suppoing Membe Level Secion 3, Figue 6 illusaes he collapse shape fo each level of failue mode. Fom a eliabiliy poin of view, no individual collapse mode can be 1 pecen pevened. Theefoe, he buckling conol concep used in his Subsecion is ha he buckling and ulimae sengh of each level is geae han is peceding level in ode o avoid he collapse of he enie sucue. The failue ( levels ) modes of a cougaed panel can be caegoized as he face/web plae buckling level, he uni cougaion buckling level and he enie cougaion buckling level. In conas o siffened panels, cougaed panels will collapse immediaely upon eaching any one of hese hee buckling levels. 1.7 Adjusmen Faco Fo he maximum allowable sengh uilizaion facos, η, defined in Subsecion 1/11, he adjusmen faco is o ake he following value: ψ 1. 3 Plae Panels Fo ecangula plae panels beween siffenes, buckling is accepable, povided ha he ulimae sengh given in 3/3.3 and 3/3.5 of he sucue saisfies he specified cieia. Offshoe pacice demonsaes ha only an ulimae sengh check is equied fo plae panels. A buckling check of plae panels is necessay when esablishing he aached plaing widh fo siffened panels. If he plaing does no buckle, he full widh is o be used. Ohewise, he effecive widh is o be applied if he plaing buckles bu does no fail. 3.1 Buckling Sae Limi Fo he Buckling Sae Limi of plaes subjeced o in-plane and laeal pessue loads, he following sengh cieion is o be saisfied: η x max Cx + η y max Cy + τ ητ C 1 xmax maximum compessive sess in he longiudinal diecion, N/cm (kgf/cm, lbf/in ) ymax maximum compessive sess in he ansvese diecion, N/cm (kgf/cm, lbf/in ) τ edge shea sess, N/cm (kgf/cm, lbf/in ) ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 7

36 Secion 3 Plaes, Siffened Panels and Cougaed Panels Cx ciical buckling sess fo uniaxial compession in he longiudinal diecion, N/cm (kgf/cm, lbf/in ) Cy ciical buckling sess fo uniaxial compession in he ansvese diecion, N/cm (kgf/cm, lbf/in ) τ C ciical buckling sess fo edge shea, N/cm (kgf/cm, lbf/in ) η maximum allowable sengh uilizaion faco, as defined in Subsecion 1/11 and 3/1.7 The ciical buckling sesses ae specified below Ciical Buckling Sess fo Edge Shea The ciical buckling sess fo edge shea, τ C, may be aken as: τ E τ C τ τ ( ) 1 P 1 P τ E fo fo τ Pτ E τ > Pτ E P popoional linea elasic limi of he sucue, which may be aken as.6 fo seel τ shea sengh of plae, N/cm (kgf/cm, lbf/in ) 3 specified minimum yield poin of plae, N/cm (kgf/cm, lbf/in ) τ E elasic shea buckling sess, N/cm (kgf/cm, lbf/in ) k s π E 1 1 ( ν ) k s bounday dependen consan s s C1 E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel ν Poisson s aio,.3 fo seel lengh of long plae edge, cm (in.) s lengh of sho plae edge, cm (in.) hickness of plaing, cm (in.) C fo plae panels beween angles o ee siffenes; 1. fo plae panels beween fla bas o bulb plaes; 1. fo plae elemens, web plae of siffenes and local plae of cougaed panels 8 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

37 Secion 3 Plaes, Siffened Panels and Cougaed Panels 3.1. Ciical Buckling Sess fo Uniaxial Compession and In-plane Bending The ciical buckling sess, Ci (i x o y), fo plaes subjeced o combined uniaxial compession and in-plane bending may be aken as: Ci Ei 1 P ( 1 P ) Ei fo fo Ei Ei P > P P popoional linea elasic limi of he sucue, which may be aken as.6 fo seel Ei elasic buckling sess, N/cm (kgf/cm, lbf/in ) k s π E 1 1 ( ν ) Fo loading applied along he sho edge of he plaing (long plae): k s s 8.4 C κ κ + 1κ fo fo κ 1 1 κ < Fo loading applied along he long edge of he plaing (wide plae): k s α 1 C α α α aspec aio /s 1 18 α 1 9 α ( κ ) ( 1+ κ ) ( 1+ κ ) α α fo fo fo 1 κ < 3 1 κ < 3 1 κ 3 κ aio of edge sesses, as defined in Secion 3, Figue 5* imin / imax and and 1 α α > * Noe: Thee ae seveal cases in he calculaion of aio of edge sesses, κ: If unifom sess ai (i x, y) < (ensile) and in-plane sess bi (i x, y), buckling check is no necessay, povided edge shea is zeo; If unifom sess ai (i x, y) < (ensile) and in-plane bending sess bi (i x, y), hen imax bi and imin bi, so ha κ 1; If unifom sess ai (i x, y) > (compessive) and in-plane bending sess bi (i x, y), imax imin i, hen κ 1; If unifom sess ai (i x, y) > (compessive) and in-plane bending sess bi (i x, y), imax ai + bi, imin ai bi hen 1 < κ < 1. specified minimum yield poin of plae, N/cm (kgf/cm, lbf/in ) ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 9

38 Secion 3 Plaes, Siffened Panels and Cougaed Panels E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel ν Poisson s aio,.3 fo seel lengh of long plae edge, cm (in.) s lengh of sho plae edge, cm (in.) hickness of plaing, cm (in.) C fo plae panels beween angles o ee siffenes; 1. fo plae panels beween fla bas o bulb plaes; 1. fo plae elemens, web plae of siffenes and local plae of cougaed panels C 1. fo plae panels beween angles o ee siffenes; 1.1 fo plae panels beween fla bas o bulb plaes; 1. fo plae elemens and web plaes 3.3 Ulimae Sengh unde Combined In-plane Sesses The ulimae sengh fo a plae beween siffenes subjeced o combined in-plane sesses is o saisfy he following equaion: η x max Ux ϕ η x max Ux η y max Uy + η y max Uy + xmax maximum compessive sess in he longiudinal diecion, N/cm (kgf/cm, lbf/in ) τ ητ U 1 ymax maximum compessive sess in he ansvese diecion, N/cm (kgf/cm, lbf/in ) τ edge shea sess, N/cm (kgf/cm, lbf/in ) ϕ coefficien o eflec ineacion beween longiudinal and ansvese sesses (negaive values ae accepable) 1.-β / Ux ulimae sengh wih espec o uniaxial sess in he longiudinal diecion, N/cm (kgf/cm, lbf/in ) C x C x o Cx / β 1/ β 1. fo fo β > 1 β 1 Uy ulimae sengh wih espec o uniaxial sess in he ansvese diecion, N/cm (kgf/cm, lbf/in ) C y Cy s + s C y.1 1 ( 1 1/ ) 1 C x + β τ U ulimae sengh wih espec o edge shea, N/cm (kgf/cm, lbf/in ) τ C +.5( 3τ C )/( 1+ α + α ) τ C 1/ Cx ciical buckling sess fo uniaxial compession in he longiudinal diecion, specified in 3/3.1., N/cm (kgf/cm, lbf/in ) Cy ciical buckling sess fo uniaxial compession in he ansvese diecion, specified in 3/3.1., N/cm (kgf/cm, lbf/in ) 3 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

39 Secion 3 Plaes, Siffened Panels and Cougaed Panels τ C ciical buckling sess fo edge shea, as specified in 3/3.1.1 β slendeness aio s E E modulus of elasiciy, N/cm (kgf/cm, lbf/in ) lengh of long plae edge, cm (in.) s lengh of sho plae edge, cm (in.) hickness of plaing, cm (in.) yield poin of plae, N/cm (kgf/cm, lbf/in ) η maximum allowable sengh uilizaion faco, as defined in Subsecion 1/11 and 3/1.7. β, s e and e ae as defined in 3/3.3. Cx, Cy,, τ C and α ae as defined in 3/ Unifom Laeal Pessue In addiion o he buckling/ulimae sengh cieia in 3/3.1 hough 3/3.3, he ulimae sengh of a panel beween siffenes subjeced o unifom laeal pessue alone o combined wih in-plane sesses is o also saisfy he following equaion: q u η4. s α e plae hickness, cm (in.) α aspec aio /s lengh of long plae edge, cm (in.) s lengh of sho plae edge, cm (in.) specified minimum yield poin of plae, N/cm (kgf/cm, lbf/in ) e equivalen sess accoding o von Mises, N/cm (kgf/cm, lbf/in ) x max x max y max y max + + 3τ xmax maximum compessive sess in he longiudinal diecion, N/cm (kgf/cm, lbf/in ) ymax maximum compessive sess in he ansvese diecion, N/cm (kgf/cm, lbf/in ) τ edge shea η maximum allowable sengh uilizaion faco, as defined in Subsecion 1/11 and 3/1.7 5 Siffened Panels (1 Febuay 1) The failue modes of siffened panels include beam-column buckling, osion and flexual buckling of siffenes, local buckling of siffene web and faceplae, and oveall buckling of he enie siffened panel. The siffened panel sengh agains hese failue modes is o be checked wih he cieia povided in 3/5.1 hough 3/5.7. Buckling sae limis fo a siffened panel ae consideed is ulimae sae limis. ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 31

40 Secion 3 Plaes, Siffened Panels and Cougaed Panels 5.1 Beam-Column Buckling Sae Limi The beam-column buckling sae limi may be deemined as follows: η Cm b + 1 / A) η [1 /( η ) a CA ( Ae a E( C) a nominal calculaed compessive sess, N/cm (kgf/cm, lbf/in ) P/A P oal compessive load on siffene using full widh of associaed plaing, N (kgf, lbf) CA ciical buckling sess, N/cm (kgf/cm, lbf/in ) E(C) fo E(C) P 1 P (1 P ) fo E(C) > P E( C) P popoional linea elasic limi of he sucue, which may be aken as.6 fo seel E(C) Eule s buckling sess π E e A oal secional aea, cm (in ) A s + s A s secional aea of he longiudinal, excluding he associaed plaing, cm (in ) A e effecive secional aea, cm (in ) A s + s e s e effecive widh, cm (in.) s when he buckling sae limi of he associaed plaing fom 3/3.1 is saisfied C x C y C xy s when he buckling sae limi of he associaed plaing fom 3/3.1 is no saisfied C x / β 1/ β 1. fo fo β > 1 β 1 max y ϕ * Uy Uy y max C y ( 1.5ϕ ) * Noe: A limi fo Cy is ha he ansvese loading should be less han he ansvese ulimae sengh of he plae panels. The buckling check fo siffenes is no o be pefomed unil he aached plae panels saisfy he ulimae sengh cieia. ymax maximum compessive sess in he ansvese diecion, N/cm (kgf/cm, lbf/in ) Uy ulimae sengh wih espec o uniaxial sess in he ansvese diecion, as specified in 3/3.3, N/cm (kgf/cm, lbf/in ) 3 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

41 Secion 3 Plaes, Siffened Panels and Cougaed Panels C xy τ 1 τ ϕ 1. β/ β s E e adius of gyaion of aea, A e, cm (in.) I e A e I e momen of ineia of longiudinal o siffene, accouning fo he effecive widh, s e, cm 4 (in 4 ) E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel specified minimum yield poin of he longiudinal o siffene unde consideaion. If hee is a lage diffeence beween he yield poins of a longiudinal o siffene and he plaing, he yield poin esuling fom he weighing of aeas is o be used. N/cm (kgf/cm, lbf/in ) b bending sess, N/cm (kgf/cm, lbf/in ) M/SM w M maximum bending momen induced by laeal loads, N-cm (kgf-cm, lbf-in) qs /1 C m momen adjusmen coefficien, which may be aken as.75 q laeal pessue fo he egion consideed, N/cm (kgf/cm, lbf/in ) s spacing of he longiudinal, cm (in.) unsuppoed span of he longiudinal o siffene, cm (in.), as defined in Secion 3, Figue 7 SM w effecive secion modulus of he longiudinal a flange, accouning fo he effecive beadh, s w, cm 3 (in 3 ) s w effecive beadh, as specified in Secion 3, Figue 8, cm (in.) η maximum allowable sengh uilizaion faco, as defined in Subsecion 1/11 and 3/1.7 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 33

42 Secion 3 Plaes, Siffened Panels and Cougaed Panels FIGURE 7 Unsuppoed Span of Longiudinal Tansvese a) Suppoed by ansveses Tansvese Fla Ba Fla Ba Tansvese b) Suppoed by ansveses and fla ba siffenes Tansvese Fla Ba Fla Ba d w / d w Tansvese Tansvese c) Suppoed by ansveses, fla ba siffenes and backes 34 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

43 Secion 3 Plaes, Siffened Panels and Cougaed Panels FIGURE 8 Effecive Beadh of Plaing sw Longiudinal Bending Momen c c /s and geae s w /s Flexual-Tosional Buckling Sae Limi In geneal, he flexual-osional buckling sae limi of siffenes o longiudinals is o saisfy he ulimae sae limi given below: a η CT 1 a nominal axial compessive sess of siffene and is associaed plaing, N/cm (kgf/cm, lbf/in ) CT ciical osional/flexual buckling sess wih espec o axial compession of a siffene, including is associaed plaing, which may be obained fom he following equaions: 1 P ET ( 1 P ) ET if if ET ET P > P P popoional linea elasic limi of he sucue, which may be aken as.6 fo seel ET elasic flexual-osional-buckling sess wih espec o he axial compession of a siffene, including is associaed plaing, N/cm (kgf/cm, lbf/in ) K nπ C + Γ +.6 E n π E C I + nπ cl ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 35

44 Secion 3 Plaes, Siffened Panels and Cougaed Panels K S. Venan osion consan fo he siffene coss secion, excluding he associaed plaing, cm 4 (in 4 ) 3 b f f + d 3 3 ww I pola momen of ineia of he siffene, excluding he associaed plaing (consideed a he inesecion of he web and plae), cm 4 (in 4 ) I y + mi z + A s (y + z ) I y, I z m u momen of ineia of he siffene abou he y- and z-axis, especively, hough he cenoid of he longiudinal, excluding he plaing (x-axis pependicula o he y-z plane shown in Secion 3, Figue ), cm 4 (in 4 ) 1. d u.7. 1 b b 1 1 b f w f, unsymmeical faco y hoizonal disance beween cenoid of siffene, A s, and web plae ceneline (see Secion 3, Figue ), cm (in.) z veical disance beween cenoid of siffene, A s, and is oe (see Secion 3, Figue ), cm (in.) d w deph of he web, cm (in.) w hickness of he web, cm (in.) b f oal widh of he flange/face plae, cm (in.) b 1 smalle ousand dimension of flange/face plae wih espec o web s ceneline, cm (in.) f hickness of he flange/face, cm (in.) C 3 E 3s Γ waping consan, cm 6 (in 6 ) mi d + zf 3 3 d ww w 36 I xf 3 f b f u d As w w, cm 4 (in 4 ) cl ciical buckling sess fo associaed plaing coesponding o n-half waves, N/cm (kgf/cm, lbf/in ) α n α π E + α n 1 ν s ( 1 ) s n numbe of half-waves ha yield he smalles ET 36 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

45 Secion 3 Plaes, Siffened Panels and Cougaed Panels E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel ν Poisson s aio,.3 fo seel specified minimum yield poin of he maeial, N/cm (kgf/cm, lbf/in ) s spacing of longiudinal/siffenes, cm (in.) A s secional aea of he longiudinal o siffene, excluding he associaed plaing, cm (in ) hickness of he plaing, cm (in.) unsuppoed span of he longiudinal o siffene, cm (in.) η maximum allowable sengh uilizaion faco, as defined in Subsecion 1/11 and 3/ Local Buckling of Web, Flange and Face Plae The local buckling of siffenes is o be assessed if he popoions of siffenes specified in Subsecion 3/9 ae no saisfied Web Ciical buckling sess can be obained fom 3/3.1 by eplacing s wih he web deph and wih he unsuppoed span, and aking: k s 4C s C s 1. fo angle o ee ba.33 fo bulb plaes.11 fo fla ba 5.5. Flange and Face Plae Ciical buckling sess can be obained fom 3/3.1 by eplacing s wih he lage ousanding dimension of flange, b (see Secion 3, Figue ), and wih he unsuppoed span, and aking: k s Oveall Buckling Sae Limi (1 Novembe 11) The oveall buckling sengh of he enie siffened panels is o saisfy he following equaion wih espec o he biaxial compession: x η Gx y + η Gy 1 x calculaed aveage compessive sess in he longiudinal diecion, in N/cm (kgf/cm, lbf/in ) y calculaed aveage compessive sess in he ansvese diecion, in N/cm (kgf/cm, lbf/in ) Gx ciical buckling sess fo uniaxial compession in he longiudinal diecion, in N/cm (kgf/cm, lbf/in ) 1 P Ex ( 1 P ) Ex if if Ex Ex P > P ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 37

46 Secion 3 Plaes, Siffened Panels and Cougaed Panels Gy ciical buckling sess fo uniaxial compession in he ansvese diecion, in N/cm (kgf/cm, lbf/in ) 1 P Ey ( 1 P ) Ey if if Ey Ey P > P Ex elasic buckling sess in he longiudinal diecion, in N/cm (kgf/cm, lbf/in ) k x π (D x D y ) 1/ /( x b ) Ey elasic buckling sess in he ansvese diecion, in N/cm (kgf/cm, lbf/in ) k y π (D x D y ) 1/ /( y ) k x 4 fo /b 1 1 φ +ρ + φ x fo /b < 1 x k y 4 fo b/ 1 1 φ y +ρ + φ y fo b/ < 1 φ x ( /b)(d y /D x ) 1/4 φ y (b/ )(D x /D y ) 1/4 D x EI x /s x (1 ν ) D y EI y /s y (1 ν ) E 3 /1(1 ν ) if no siffene in he ansvese diecion ρ [(I px I py )/(I x I y )] 1/ hickness of he plae, in cm (in.), b lengh and widh of siffened panel, especively, in cm (in.) x, y equivalen hickness of he plae and siffene in he longiudinal and ansvese diecion, especively, in cm (in.) (s x + A sx )/s x o (s y + A sy )/s y s x,s y spacing of siffenes and gides, especively, in cm (in.) A sx,a sy secional aea of siffenes and gides, excluding he associaed plae, especively, in cm (in.) I px,i py momen of ineia of he effecive plae alone abou he neual axis of he combined coss secion, including siffene and plae, in cm 4 (in 4 ) I x,i y momen of ineia of he siffene wih effecive plae in he longiudinal o ansvese diecion, especively, in cm 4 (in 4 ). If no siffene, he momen of ineia is calculaed fo he plae only. E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel ν Poisson s aio,.3 fo seel P popoional linea elasic limi of he sucue, which may be aken as.6 fo seel specified minimum yield poin of he maeial, in N/cm (kgf/cm, lbf/in ) η maximum allowable sengh uilizaion faco, as defined in Subsecion 1/11 and 3/ ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

47 Secion 3 Plaes, Siffened Panels and Cougaed Panels 7 Gides and Webs In geneal, he siffness of web siffenes fied o he deph of web plaing is o be in compliance wih 3/9.3. Web siffenes ha ae oiened paallel o he face plae, and hus subjec o axial compession, ae o also saisfy 3/3.1, consideing he combined effecs of he compessive and bending sesses in he web. In his case, he unsuppoed span of hese paallel siffenes may be aken as he disance beween ipping backes, as applicable. The buckling sengh of he web plae beween siffenes and flange/face plae is o saisfy he limis specified in 3/3.1 hough 3/3.5. When cuous ae pesen in he web plae, he effecs of he cuous on he educion of he ciical buckling sesses should be consideed (See 3/7.9). In geneal, gides ae o be designed as socky so ha laeal buckling may be disegaded and osional buckling also may be disegaded if ipping backes ae povided (See 3/7.7). If his is no he case, he gide is o be checked accoding o Subsecion 3/ Web Plae The buckling limi sae fo a web plae is consideed as he ulimae sae limi and is given in 3/ Face Plae and Flange The beadh o hickness aio of faceplae and flange is o saisfy he limis given in 3/ Lage Backes and Sloping Webs The buckling sengh is o saisfy he limis specified in 3/3.1 fo he web plae. FIGURE 9 Lage Backes and Sloping Webs Sloping Plae Lage Backe Sloping Web 7.7 Tipping Backes To peven ipping of deep gides and webs wih wide flanges, ipping backes ae o be insalled wih spacing geneally no geae han 3 mees (9.84 f). P FIGURE 1 Tipping Backes TRIPPING BRACKET ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 39

48 Secion 3 Plaes, Siffened Panels and Cougaed Panels The design of ipping backes may be based on he foce, P, acing on he flange, as given by he following equaion: P. c (b f f dw b w ) c ciical laeal buckling sess wih espec o axial compession beween ipping backes, N/cm (kgf/cm, lbf/in ) ce fo ce P [1 P (1 P ) / ce ] fo ce > P ce.6e[(b f / f )( w /d w ) 3 ], N/cm (kgf/cm, lbf/in ) P popoional linea elasic limi of he sucue, which may be aken as.6 fo seel E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel specified minimum yield poin of he maeial, N/cm (kgf/cm, lbf/in ) b f, f, d w, w ae defined in Secion 3, Figue. 7.9 Effecs of Cuous The deph of a cuou, in geneal, is o be no geae han d w /3, and he calculaed sesses in he aea ae o accoun fo he local incease due o he cuou Reinfoced by Siffenes aound Boundaies of Cu-ous When einfocemen is made by insalling saigh siffenes along boundaies of a cuou, he ciical buckling sesses of he web plae beween siffenes wih espec o compession, in-plane bending and shea may be obained fom 3/ Reinfoced by Face Plaes aound Conou of Cu-ous When einfocemen is made by adding face plaes along he conou of a cu-ou, he ciical buckling sesses wih espec o compession, bending and shea may be obained fom 3/3.1, wihou educion, povided ha he coss secional aea of he face plae is no less han 8 w, w is he hickness of he web plae, and he deph of he cu-ou is no geae han d w /3, d w is he deph of he web No Reinfocemen Povided When einfocemen is no povided, he buckling sengh of he web plae suounding he cuou may be eaed as a sip of plae wih one edge fee and he ohe edge simply suppoed. k s.44 9 Siffness and Popoions To fully develop he inended buckling sengh of assemblies of sucual membes and panels, suppoing elemens of plae panels and siffenes ae o saisfy he following equiemens fo siffness and popoion in highly sessed egions. 9.1 Siffness of Siffenes In he plane pependicula o he plaing, he momen of ineia of a siffene, i, wih an effecive beadh of plaing, is no o be less han ha given by he following equaion: i 3 γ ( ν ) 1 1 s 4 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

49 Secion 3 Plaes, Siffened Panels and Cougaed Panels γ ( δ)α + 1.4α 13.α 1/ δ A s /(s) α /s s spacing of longiudinal, cm (in.) hickness of plaing suppoed by he longiudinal, cm (in.) ν Poisson s aio,.3 fo seel A s coss secional aea of he siffene (excluding plaing), cm (in ) unsuppoed span of he siffene, cm (in) 9.3 Siffness of Web Siffenes The momen of ineia, I e, of a web siffene, wih he effecive beadh of plaing no exceeding s o.33, whicheve is less, is no o be less han he value obained fom he following equaions: I e.17 3 ( /s) 3 fo /s. I e.34 3 ( /s) fo /s >. lengh of siffene beween effecive suppos, cm (in.) equied hickness of web plaing, cm (in.) s spacing of siffenes, cm (in.) 9.5 Siffness of Suppoing Gides The momen of ineia of a suppoing membe is no o be less han ha obained fom he following equaion: I G /i.(b/ ) 3 (B/s) I G momen of ineia of he suppoing gides, including he effecive plaing, cm 4 (in 4 ) i momen of ineia of he siffenes, including he effecive plaing, cm 4 (in 4 ) B unsuppoed span of he suppoing gides, cm (in.) unsuppoed span of he siffene, cm (in.), as defined in Secion 3, Figue Popoions of Flanges and Faceplaes The beadh o hickness aio of flanges and faceplaes of siffenes and gides is o saisfy he limis given below. b / f.4(e/ ) 1/ b lage ousand dimension of flange (See Secion 3, Figue ), cm (in.) f hickness of flange/face plae, cm (in.) specified minimum yield poin of plae, N/cm (kgf/cm, lbf/in ) E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 41

50 Secion 3 Plaes, Siffened Panels and Cougaed Panels 9.9 Popoions of Webs of Siffenes The deph o hickness aio of webs of siffenes is o saisfy he limis given below. d w / w 1.5(E/ ) 1/ fo angles and ee bas d w / w.85(e/ ) 1/ d w / w.4(e/ ) 1/ fo bulb plaes fo fla bas specified minimum yield poin of plae, N/cm (kgf/cm, lbf/in ) E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel d w and w ae as defined in Secion 3, Figue. 11 Cougaed Panels This Subsecion includes cieia fo he buckling and ulimae sengh fo cougaed panels Local Plae Panels The buckling sengh of he flange and web plae panels is o saisfy he following sae limi: η x max Cx + η y max Cy + τ ητ C 1 xmax maximum compessive sess in cougaion diecion, N/cm (kgf/cm, lbf/in ) ymax maximum compessive sess in ansvese diecion, N/cm (kgf/cm, lbf/in ) τ in-plane shea sess, N/cm (kgf/cm, lbf/in ) Cx ciical buckling sess in cougaion diecion fom 3/3.1, N/cm (kgf/cm, lbf/in ) Cy ciical buckling sess in ansvese diecion fom 3/3.1, N/cm (kgf/cm, lbf/in ) τ C ciical buckling sess fo edge shea fom 3/3.1, N/cm (kgf/cm, lbf/in ) η maximum allowable sengh uilizaion faco, as defined in Subsecion 1/11 and 3/ Uni Cougaion Any uni cougaion of he cougaed panel may be eaed as a beam column and is o saisfy he following sae limi: a η CA Cm b + 1 η 1 /( η )] CB[ a E(C) a maximum compessive sess in he cougaion diecion, N/cm (kgf/cm, lbf/in ) b maximum bending sess along he lengh due o laeal pessue, N/cm (kgf/cm, lbf/in ) M b /SM M b maximum bending momen induced by laeal pessue, N-cm (kgf-cm, lbf-in) q u + q sl / 1 4 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

51 Secion 3 Plaes, Siffened Panels and Cougaed Panels Ca ciical buckling sess, N/cm (kgf/cm, lbf/in ) E(C) fo E(C) P o 1 P (1 P ) E( C) fo E(C) > P E(C) elasic buckling sess, N/cm (kgf/cm, lbf/in ) π E L adius of gyaion of aea A, cm (in.) I y A E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel CB ciical bending buckling sess E(B) fo E(B) P E(B) 1 P (1 P ) fo E(B) > P E( B) elasic buckling sess of uni cougaion k c E 1(1 ν k c coefficien ) a [7.65.6(c/a) ] C m bending momen faco deemined by aional analysis, which may be aken as 1.5 fo a panel whose ends ae simply suppoed A, I y aea and momen of ineia of uni cougaion, as specified in 3/13.3 SM secional modulus of uni cougaion, as specified in 3/13.3, cm 3 (in 3 ) s widh of uni cougaion, as defined in Secion 3, Figue 4 and specified in 3/13.3 a, c widh of he compessed flange and web plaing, especively, as defined in Secion 3, Figue 4 hickness of he uni cougaion, cm (in.) L lengh of cougaed panel, cm (in.) q u, q laeal pessue a he wo ends of he cougaion, N/cm (kgf/cm, lbf/in ) P popoional linea elasic limi of he sucue, which may be aken as.6 fo seel E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel ν Poisson s aio,.3 fo seel specified minimum yield poin, N/cm (kgf/cm, lbf/in ) η maximum allowable sengh uilizaion faco, as defined in Subsecion 1/11 and 3/1.7 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 43

52 Secion 3 Plaes, Siffened Panels and Cougaed Panels 11.5 Oveall Buckling The oveall buckling sengh of he enie cougaed panels is o saisfy he following equaion wih espec o he biaxial compession and edge shea: x η Gx y + η Gy + τ ητ G 1 x calculaed aveage compessive sess in he cougaion diecion, N/cm (kgf/cm, lbf/in ) y calculaed aveage compessive sess in he ansvese diecion, N/cm (kgf/cm, lbf/in ) τ in-plane shea sess, N/cm (kgf/cm, lbf/in ) Gx ciical buckling sess fo uniaxial compession in he cougaion diecion, N/cm (kgf/cm, lbf/in ) 1 P Ex ( 1 P ) Ex if if Ex Ex P > P Gy ciical buckling sess fo uniaxial compession in he ansvese diecion, N/cm (kgf/cm, lbf/in ) 1 P Ey ( 1 P ) Ey if if Ey Ey P > P τ G ciical buckling sess fo shea sess, N/cm (kgf/cm, lbf/in ) τ E τ 1 P ( 1 P ) τ τ E if if τ P τ τ E E > P τ Ex elasic buckling sess in he cougaion diecion, N/cm (kgf/cm, lbf/in ) k x π (D x D y ) 1/ /( x B ) Ey elasic buckling sess in he ansvese diecion, N/cm (kgf/cm, lbf/in ) k y π (D x D y ) 1/ /(L ) τ E elasic shea buckling sess, N/cm (kgf/cm, lbf/in ) k S π D x 3/4 D y 1/4 /(L ) k x 4 fo L/B.5176(D x /D y ) 1/4 φ 1 x + φ x fo L/B <.5176(D x /D y ) 1/4 k y 4 fo B/L.5176(D y /D x ) 1/4 φ 1 y + φ y fo B/L <.5176(D y /D x ) 1/4 44 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

53 Secion 3 Plaes, Siffened Panels and Cougaed Panels k S 3.65 L, B lengh and widh of cougaed panel x equivalen hickness of he cougaion in he cougaion diecion, as specified in 3/13.3, cm (in.) hickness of he cougaion, cm (in.) φ x (L/B)(D y /D x ) 1/4 φ y (B/L)(D x /D y ) 1/4 D x EI y /s D y E 3 1(1 ν s ) a + b + c I y momen of ineia of a cougaion wih spacing s a, b, c widh of he flanges and web plaing, especively, as defined in Secion 3, Figue 4, cm (in.) s widh of he uni cougaion, as defined in Secion 3, Figue 4, cm (in.) E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel ν Poisson s aio,.3 fo seel specified minimum yield poin of he maeial, N/cm (kgf/cm, lbf/in ) η maximum allowable sengh uilizaion faco, as defined in Subsecion 1/11 and 3/ Geomeic Popeies This Subsecion includes he fomulaions fo he geomeic popeies of siffened panels and cougaed panels. The effecive widh, s e, and effecive beadh, s w, can be obained fom 3/5.1 and Secion 3, Figue 8, especively Siffened Panels Beam-Column Buckling b f fo fla-ba f fo fla-ba b 1.5 w fo angle ba A s d w w + b f f A e s e + A s z ep [.5( + d w )d w w + (.5 + d w +.5 f )b f f ]/A e I e 3 pse d w w f b f ( + d 1 1 w ) d w w + b f f (.5 + d w +.5 f ) A e z ep e I e / Ae A w s w + A s z wp [.5( + d w )d w w + (.5 + d w +.5 f )b f f ]/A w ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 45

54 Secion 3 Plaes, Siffened Panels and Cougaed Panels I w SM w 3 pse d w w f b f ( + d 1 1 w ) d w w + b f f (.5 + d w + f ) A w z wp w w (.5 + d + ) z I f wp, b f, b 1, f, d w, w ae defined in Secion 3, Figue Tosional/Flexual Buckling A s d w w + b f f y (b 1.5b f )b f f /A s z [.5d w w + (d w +.5 f )b f f ]/A s 3 d 1 3 f b + 1 f w w 3 I y ( ) 3 d 1 3 f f b d w w + b f f d w +.5 w w I z ( ) + b f f b.5b b f, b 1, f, d w, w, y and z ae defined in Secion 3, Figue. 1 f A z s f A z 13.3 Cougaed Panels The following fomulaions of geomeical popeies ae deived, povided ha he secion is hin-walled and he hickness is small. s a + b + c cos φ x (s + A sx )/s A (a + b) + c A sx c sin φ z o d(a + c)/a I y ( a + b) ad + cd 3 Az SM I y /z o I y /(d z ), which is he less a, b, c, d,, φ and z ae defined in Secion 3, Figue 4. s 46 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

55 Secion 4: Cylindical Shells SECTION 4 Cylindical Shells 1 Geneal This Secion pesens cieia fo calculaing he buckling limi sae of ing- and/o singe-siffened cylindical shells subjeced o axial loading, bending momen, adial pessue o a combinaion of hese loads. The buckling limi sae of a siffened cylindical shell is o be deemined based on he fomulaions povided below. Alenaively, eihe well-documened expeimenal daa o a veified analyical appoach may be employed. 1.1 Geomey of Cylindical Shells The cieia given below apply o ing- and/o singe-siffened cylindical shells, as depiced in Secion 4, Figue 1, coodinaes (x,, ) denoe he longiudinal, adial and cicumfeenial diecions, especively. Siffenes in a given diecion ae o be equally spaced, paallel and pependiculas o panel edges, and have idenical maeial and geomeic popeies. Geneal ypes of siffene pofiles, such as fla ba, T-ba, angle and bulb plae, may be used. The dimensions and popeies of a ing o singe siffene ae descibed in Secion 4, Figue. The maeial popeies of he siffenes may be diffeen fom hose of he shell plaing. FIGURE 1 Ring and Singe-siffened Cylindical Shell Singe Siffene x L s Ring Siffene The fomulaions given fo ing- and/o singe-siffened shells ae applicable fo offshoe sucues wih he diamee o hickness aio in he ange of E/(4.5 ) o 1. ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 47

56 Secion 4 Cylindical Shells FIGURE Dimensions of Siffenes R F f b b f b 1 f b b f b 1 y z y Cenoid w d w z Cenoid w d w S em eo Secion of Singes Secion of Rings 1.3 Load Applicaion This Secion includes he buckling sae limi cieia fo he following loads and load effecs. Unifom compession in he longiudinal diecion, a * Bending of he oveall cylinde, b Exenal pessue, p Combinaions of he above * Noe: If unifom sess, a, is ensile ahe han compessive, i may be se equal o zeo. 1.5 Buckling Conol Conceps The pobable buckling modes of ing- and/o singe-siffened cylindical shells can be soed as follows: Local shell o cuved panel buckling (i.e., buckling of he shell beween adjacen siffenes). The singes emain saigh and he ing siffenes emain ound. Bay buckling (i.e., buckling of he shell plaing ogehe wih he singes, if pesen, beween adjacen ing siffenes). The ing siffenes and he ends of he cylindical shells emain ound. Geneal buckling, (i.e., buckling of one o moe ing siffenes ogehe wih he aached shell plus singes, if pesen). Local siffene buckling (i.e., osional/flexual buckling of siffenes, ing o singe, o local buckling of he web and flange). The shell emains undefomed. Column buckling (i.e., buckling of cylindical shell as a column). The fis hee failue modes fo ing and singe-siffened cylindical shells ae illusaed in Secion 4, Figue ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

57 Secion 4 Cylindical Shells FIGURE 3 Typical Buckling Modes of Ring and Singe Cylindical Shells Local Shell Buckling Bay Buckling Geneal Buckling A siffened cylindical shell is o be designed such ha a geneal buckling failue is peceded by bay insabiliy, and local shell buckling pecedes bay insabiliy. The buckling sengh cieia pesened below ae based on he following assumpions and limiaions: Ring siffenes wih hei associaed effecive shell plaing ae o have momens of ineia no less han i, as given in 4/15.1. Singe siffenes wih hei associaed effecive shell plaing ae o have momens of ineia no less han i s, as given in 4/15.3. Faceplaes and flanges of siffene ae popoioned such ha local insabiliy is pevened, as given in 4/15.7. Webs of siffenes ae popoioned such ha local insabiliy is pevened, as given in 4/15.5. Fo siffened cylindical shells ha do no saisfy hese assumpions, a deailed analysis of buckling sengh using an accepable mehod should be pusued. 1.7 Adjusmen Faco Fo he maximum allowable sengh uilizaion faco, η, defined in Subsecion 1/11, he adjusmen faco is o ake he following value: Fo shell buckling: * ψ.833 if Cij Cij / if Cij >.55 Cij ciical buckling sess of cylindical shell, epesening CxR, CθR, CxP, CθP, CxB o CθB, which ae specified in Subsecions 4/3, 4/5 and 4/7, especively, N/cm (kgf/cm, lbf/in ) specified minimum yield poin, N/cm (kgf/cm, lbf/in ) * Noe: The maximum allowable sengh faco fo shell buckling should be based on he ciical buckling sess, which implies ha i may be diffeen fo axial compession and exenal pessue in local shell o bay buckling. The smalles maximum allowable sengh faco should be used in he coesponding buckling sae limi. ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 49

58 Secion 4 Cylindical Shells Fo column buckling: ψ.87 if E(C) P 1.13 P / E( C) if E(C) > P E(C) Eule s buckling sess, as specified in Subsecion 4/11, N/cm (kgf/cm, lbf/in ) P popoional linea elasic limi of he sucue, which may be aken as.6 fo seel specified minimum yield poin, N/cm (kgf/cm, lbf/in ) Fo ipping of singe siffenes: ψ 1. 3 Unsiffened o Ring-siffened Cylindes 3.1 Bay Buckling Limi Sae Fo he buckling limi sae of unsiffened o ing-siffened cylindical shells beween adjacen ing siffenes subjeced o axial compession, bending momen and exenal pessue, he following sengh cieion is o be saisfied: x η CxR x ϕ R η CxR η C θ θr + η C θ θr x compessive sess in longiudinal diecion fom 4/13.1, N/cm (kgf/cm, lbf/in ) 1 θ compessive hoop sess fom 4/13.3, N/cm (kgf/cm, lbf/in ) CxR ciical buckling sess fo axial compession o bending momen fom 4/3.3, N/cm (kgf/cm, lbf/in ) CθR ciical buckling sess fo exenal pessue fom 4/3.5, N/cm (kgf/cm, lbf/in ) ϕ R coefficien o eflec ineacion beween longiudinal and hoop sesses (negaive values ae accepable) CxR + CθR 1. specified minimum yield poin, N/cm (kgf/cm, lbf/in ) η maximum allowable sengh uilizaion faco of shell buckling, as specified in Subsecion 1/11 and 4/1.7, fo ing-siffened cylindical shells subjeced o axial compession o exenal pessue, whicheve is less. 3.3 Ciical Buckling Sess fo Axial Compession o Bending Momen The ciical buckling sess of unsiffened o ing-siffened cylindical shell subjeced o axial compession o bending momen may be aken as: CxR ExR 1 P ( 1 P ) ExR fo fo ExR ExR P > P 5 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

59 Secion 4 Cylindical Shells P popoional linea elasic limi of he sucue, which may be aken as.6 fo seel ExR elasic compessive buckling sess fo an impefec cylindical shell, N/cm (kgf/cm, lbf/in ) ρ xr C CExR CExR classical compessive buckling sess fo a pefec cylindical shell, N/cm (kgf/cm, lbf/in ) E.65 C lengh dependan coefficien / z +.175z fo fo z.85 z <.85 ρ xr nominal o lowe bound knock-down faco o allow fo shape impefecions z z ( z 1) z Badof paamee fo fo fo z < 1 1 z < z 1 ν lengh beween adjacen ing siffenes (unsuppoed) mean adius of cylindical shell, cm (in.) hickness of cylindical shell, cm (in.) E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel ν Poisson s aio,.3 fo seel specified minimum yield poin, N/cm (kgf/cm, lbf/in ) 3.5 Ciical Buckling Sess fo Exenal Pessue The ciical buckling sess fo an unsiffened o ing-siffened cylindical shell subjeced o exenal pessue may be aken as: CθR Φ EθR Φ plasiciy educion faco 1 fo fo.55 < fo 1.6 < < 6.5 1/ fo 6.5 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 51

60 Secion 4 Cylindical Shells EθR / EθR elasic hoop buckling sess fo an impefec cylindical shell, N/cm (kgf/cm, lbf/in ) q ( +.5) CEθR ρθr Kθ ρ θr nominal o lowe bound knock-down faco o allow fo shape impefecions.8 K θ coefficien o accoun fo he effec of ing siffene, as deemined fom 4/13.3 q CEθR elasic buckling pessue, N/cm (kgf/cm, lbf/in ) 1.7E 1.18 AL +.5.9E AL C p E 3.75E 3 fo fo fo fo A L.5.5 < A L.8 < A.85 < A.8 L L.85 z A L k 1 4 (1 ν ) C p A L /(/) k fo laeal pessue.5 fo hydosaic pessue z Badof paamee 1 ν lengh beween adjacen ing siffenes (unsuppoed) mean adius of cylindical shell, cm (in.) hickness of cylindical shell, cm (in.) E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel ν Poisson s aio,.3 fo seel specified minimum yield poin, N/cm (kgf/cm, lbf/in ) 3.7 Geneal Buckling The geneal buckling of a ing-siffened cylindical shell involves he collapse of one o moe ing siffenes ogehe wih he shell plaing and is o be avoided due o is caasophic consequences. The ing siffenes ae o be popoioned in accodance wih Subsecion 4/15 o exclude he geneal buckling failue mode. 5 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

61 Secion 4 Cylindical Shells 5 Cuved Panels Local cuved panel buckling of ing and singe-siffened cylindical shells will no necessaily lead o complee failue of he shell, as sesses can be edisibued o he emaining effecive secion associaed wih he singe. Howeve, knowledge of local buckling behavio is necessay in ode o conol local deflecions, in accodance wih seviceabiliy equiemens, and o deemine he effecive widh o be associaed wih he singe when deemining buckling sengh of he singe-siffened shells. 5.1 Buckling Sae Limi The buckling sae limi of cuved panels beween adjacen siffenes can be defined by he following equaion: x η CxP x ϕ P η CxP η C θ θp + η C θ θp 1 x compessive sess in he longiudinal diecion fom 4/13.1, N/cm (kgf/cm, lbf/in ) θ compessive hoop sess fom 4/13.3, N/cm (kgf/cm, lbf/in ) CxP ciical buckling sess fo axial compession o bending momen fom 4/5.3, N/cm (kgf/cm, lbf/in ) CθP ciical buckling sess fo exenal pessue fom 4/5.5, N/cm (kgf/cm, lbf/in ) ϕ P coefficien o eflec ineacion beween longiudinal and hoop sesses (negaive values ae accepable),.4( CxP + CθP ). 8 specified minimum yield poin, N/cm (kgf/cm, lbf/in ) η maximum allowable sengh uilizaion faco of shell buckling, as specified in Subsecion 1/11 and 4/1.7 fo cuved panels in axial compession o exenal pessue, whicheve is he lesse 5.3 Ciical Buckling Sess fo Axial Compession o Bending Momen The ciical buckling sess fo cuved panels bounded by adjacen pais of ing and singe siffenes subjeced o axial compession o bending momen may be aken as: ExP CxP ( ) 1 P 1 P ExP fo fo ExP ExP P > P P popoional linea elasic limi of he sucue, which may be aken as.6 fo seel ExP elasic buckling sess fo an impefec cuved panel, N/cm (kgf/cm, lbf/in ) B xp ρ xp CExP CExP classical buckling sess fo a pefec cuved panel beween adjacen singe siffenes, N/cm (kgf/cm, lbf/in ) K xp π E 1(1 ν ) s ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 53

62 Secion 4 Cylindical Shells K xp z s fo z s 11.4 π.7z s fo z s > 11.4 ρ xp nominal o lowe bound knock-down faco o allow fo shape impefecions z s +.4z s z s 1 z s z 3 s fo z s 11.4 fo z s > 11.4 B xp faco compensaing fo he lowe bound naue of ρ xp λn fo fo λ > 1 n λ 1 n λ n ρ xp CExP z s 1 ν s s spacing of singe siffenes, cm (in.) mean adius of cylindical shell, cm (in.) hickness of cylindical shell, cm (in.) E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel ν Poisson s aio,.3 fo seel specified minimum yield poin, N/cm (kgf/cm, lbf/in ) 5.5 Ciical Buckling Sess unde Exenal Pessue The ciical buckling sess fo cuved panels bounded by adjacen pais of ing and singe siffenes subjeced o exenal pessue may be aken as: CθP Φ EθP Φ plasiciy educion faco 1 fo fo.55 < fo 1.6 < < 6.5 1/ fo 6.5 EθP / EθP elasic hoop buckling sess of impefec cuved panel, N/cm (kgf/cm, lbf/in ) qce θp ( +.5) Kθ 54 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

63 Secion 4 Cylindical Shells K θ coefficien o accoun fo he senghening effec of ing siffene fom 4/13.3 q CEθP elasic buckling pessue, N/cm (kgf/cm, lbf/in ) E 4 ( n + α 1) α ( ) ( ) + n + kα ν n + α n cicumfeenial wave numbe saing a.5n s and inceasing unil a minimum value of q CEθP is aained α π k fo laeal pessue.5 fo hydosaic pessue lengh beween adjacen ing siffenes (unsuppoed) mean adius of cylindical shell, cm (in.) hickness of cylindical shell, cm (in.) E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel N s numbe of singes 7 Ring and Singe-siffened Shells 7.1 Bay Buckling Limi Sae Fo he buckling limi sae of ing and singe-siffened cylindical shells beween adjacen ing siffenes subjeced o axial compession, bending momen and exenal pessue, he following sengh cieia is o be saisfied: x η CxB A e A x ϕ B η CxB A e A η C θ θb + η C x compessive sess in longiudinal diecion fom 4/13.1, N/cm (kgf/cm, lbf/in ) θ θb 1 θ compessive hoop sess fom 4/13.3, N/cm (kgf/cm, lbf/in ) CxB ciical buckling sess fo axial compession o bending momen fom 4/7.3, N/cm (kgf/cm, lbf/in ) CθB ciical buckling sess fo exenal pessue fom 4/7.5, N/cm (kgf/cm, lbf/in ) ϕ B coefficien o eflec ineacion beween longiudinal and hoop sesses (negaive values ae accepable) 1.5( CxB + CθB ). A e effecive coss secional aea, cm (in ) A s + s em A oal coss secional aea, cm (in ) A s + s ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 55

64 Secion 4 Cylindical Shells A s coss secional aea of singe siffene, cm (in ) hickness of cylindical shell, cm (in.) s spacing of singes s em modified effecive shell plae widh s fo λ m >.53 λ m λ m s fo λ m.53 λ m modified educed slendeness aio ExP CxB ExP elasic buckling sess fo impefec cuved panel beween adjacen singe siffenes subjeced o axial compession fom 4/5.3, N/cm (kgf/cm, lbf/in ) specified minimum yield poin, N/cm (kgf/cm, lbf/in ) η maximum allowable sengh uilizaion faco of shell buckling, as specified in Subsecion 1/11 and 4/1.7, fo ing and singe-siffened cylindical shells in axial compession o exenal pessue, whicheve is he lesse 7.3 Ciical Buckling Sess fo Axial Compession o Bending Momen The ciical buckling sess of ing and singe-siffened cylindical shells subjeced o axial compession o bending may be aken as: ExB CxB ( ) 1 P 1 P ExB fo fo ExB ExB P > P P popoional linea elasic limi of he sucue, which may be aken as.6 fo seel ExB elasic compessive buckling sess of impefec singe-siffened shell, N/cm (kgf/cm, lbf/in ) c + s s elasic compessive buckling sess of singe-siffened shell, N/cm (kgf/cm, lbf/in ) ρ xb ρ xb.75.65ε As 1 + s c elasic buckling sess of column, N/cm (kgf/cm, lbf/in ) π EI ( A + s ) s se e 56 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

65 Secion 4 Cylindical Shells I se momen of ineia of singe siffene plus associaed effecive shell plae widh, cm 4 (in 4 ) se se I s + A s z s + A + s 1 s e 3 I s momen of ineia of singe siffene abou is own cenoid axis, cm 4 (in 4 ) z s disance fom ceneline of shell o he cenoid of singe siffene, cm (in.) A s coss secional aea of singe siffene, cm (in ) s e educed effecive widh of shell, cm (in.).53 s λ xp fo λ xp >.53 s fo λ xp.53 s shell plae widh beween adjacen singes, cm (in.) λ xp educed shell slendeness aio ExP ExP elasic compessive buckling sess fo impefec cuved panel beween adjacen singe siffenes fom 4/5.3, N/cm (kgf/cm, lbf/in ) lengh beween adjacen ing siffenes (unsuppoed), cm (in.) mean adius of cylindical shell, cm (in.) hickness of cylindical shell, cm (in.) E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel specified minimum yield poin, N/cm (kgf/cm, lbf/in ) 7.5 Ciical Buckling Sess fo Exenal Pessue The ciical buckling sess fo ing and singe-siffened cylindical shells subjeced o exenal pessue may be aken as CθB ( CθR + sp )K p CθR ciical hoop buckling sess fo he unsiffened shell fom 4/3.5, N/cm (kgf/cm, lbf/in ) sp collapse hoop sess fo a singe siffene plus is associaed shell plaing, N/cm (kgf/cm, lbf/in ) q s ( +.5) Kθ K θ coefficien o accoun fo he senghening effec of ing siffene fom 4/13.3 q s collapse pessue of a singe siffene plus is associaed shell plaing, N/cm (kgf/cm, lbf/in ) 16 s A s z s z s disance fom ceneline of shell o he cenoid of singe siffene, cm (in.) ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 57

66 Secion 4 Cylindical Shells A s coss secional aea of singe siffene, cm (in ) K p effecive pessue coecion faco g fo g fo g > 5 g geomeical paamee A π N I s s s I s secional momen aea of ineia of singe siffene, cm 4 (in 4 ) N s numbe of singe siffenes lengh beween adjacen ing siffenes (unsuppoed), cm (in.) mean adius of cylindical shell, cm (in.) hickness of cylindical shell, cm (in.) specified minimum yield poin, N/cm (kgf/cm, lbf/in ) 7.7 Geneal Buckling The geneal buckling of a ing and singe-siffened cylindical shell involves he collapse of one o moe ing siffenes ogehe wih shell plaing plus singe siffenes and should be avoided due o is caasophic consequences. The ing and singe siffenes ae o be popoioned, in accodance wih 4/15.1 and 4/15.3, o exclude he geneal buckling failue mode. 9 Local Buckling Limi Sae fo Ring and Singe Siffenes 9.1 Flexual-Tosional Buckling When he osional siffness of he siffenes is low and he slendeness aio of he cuved panels is elaively high, he siffenes can suffe osional-flexual buckling (ipping) a a sess level lowe han ha esuling in local o bay buckling. When he siffene buckles, i loses a lage pa of is effeciveness o mainain he iniial shape of he shell. The buckled siffene sheds load o he shell, and heefoe, should be suppessed. The flexual-osional buckling limi sae of singe siffenes is o saisfy he ulimae sae limi given below: x η CT 1 x compessive sess in he longiudinal diecion fom 4/13.1, N/cm (kgf/cm, lbf/in ) CT flexual-osional buckling sess wih espec o axial compession of a siffene, including is associaed shell plaing, may be obained fom he following equaions: 1 P ET ( 1 P ) ET if if ET ET P > P specified minimum yield poin of he singe unde consideaion, N/cm (kgf/cm, lbf/in ) 58 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

67 Secion 4 Cylindical Shells P popoional linea elasic limi of he sucue, which may be aken as.6 fo seel ET ideal elasic flexual-osional buckling sess, N/cm (kgf/cm, lbf/in ) K nπ C + Γ +.6 E n π E C I + nπ CL K S. Venan osion consan fo he siffene coss-secion, excluding he associaed shell plaing, cm 4 (in 4 ) 3 b f f + d 3 3 w w I pola momen of ineia of he siffene, excluding he associaed shell plaing, cm 4 (in 4 ) I y + mi z + A s (y + z ) I y, I z momen of ineia of he siffene abou he y- and z-axis, especively, hough he cenoid of he longiudinal, excluding he shell plaing (y-axis pependicula o he web, see Secion 4, Figue ), cm 4 (in 4 ) m 1. d u.7. 1 b u non-symmey faco w f b 1 1 b f y hoizonal disance beween cenoid of siffene and web plae ceneline (see Secion 4, Figue ), cm (in.) z veical disance beween cenoid of siffene and is oe (see Secion 4, Figue ), cm (in.) d w deph of he web, cm (in.) w hickness of he web, cm (in.) b f oal widh of he flange/face plae, cm (in.) b 1 smalle ousanding dimension of flange o face plae wih espec o web's ceneline, cm (in.) f hickness of he flange o face plae, cm (in.) C 3 E 3s Γ waping consan, cm 6 (in 6 ) I xf mi d + zf 3 3 d ww w 36 3 f b f u d As w w, cm 4 (in 4 ) ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 59

68 Secion 4 Cylindical Shells CL ciical buckling sess fo associaed shell plaing coesponding o n-half waves, N/cm (kgf/cm, lbf/in ) α /s n α π E + α n 1 υ ( 1 ) s n numbe of half-waves which yields he smalles E specified minimum yield poin of he maeial, N/cm (kgf/cm, lbf/in ) E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel s spacing of singe siffenes, cm (in.) A s secional aea of singe siffene, excluding he associaed shell plaing, cm (in ) hickness of shell plaing, cm (in.) lengh beween adjacen ing siffenes (unsuppoed), cm (in.) η maximum allowable sengh uilizaion faco, as specified in Subsecion 1/11 and 4/1.7, fo ipping of singe siffenes 9.3 Web Plae Buckling The deph o hickness aio of he web plae is o saisfy he limi given in 4/ Faceplae and Flange Buckling The beadh o hickness aio of he faceplae o flange is o saisfy he limi given in 4/ Beam-Column Buckling A cylindical shell subjeced o axial compession, o bending momen o boh; wih o wihou exenal pessue, is o be designed o esis beam-column buckling. Beam-column buckling is o be assessed if: λ xe.5 λ xe slendeness aio of cylindical shell / E ( C) E(C) Eule buckling sess, N/cm (kgf/cm, lbf/in ) π E i /(kl) i adius of gyaion of he coss secion of he cylindical shell I A T T I T momen of ineia of he coss secion of he cylindical shell; if he coss secion is vaiable along he lengh, he minimum value is o be used, cm 4 (in 4 ) A T coss secional aea of he cylindical shell; if he coss secion is vaiable along he lengh, he minimum value is o be used, cm (in ) kl effecive lengh of he cylinde, as defined in /3.3 E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel 6 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

69 Secion 4 Cylindical Shells The beam-column buckling limi sae of a cylindical shell subjeced o axial compesion, o bending o boh; wih o wihou exenal pessue, is o saisfy he following cieia a all coss-secions along is lengh: a η Ca b + 1 η 1 /( η )] Cx[ a E(C) a calculaed axial nomal compessive sess fom 4/13.1, N/cm (kgf/cm, lbf/in ) b calculaed bending sess fom 4/13.1, N/cm (kgf/cm, lbf/in ) Ca ciical compessive buckling sess, N/cm (kgf/cm, lbf/in ) Cx 1 P E( C) ( 1 P ) Cx E( C) if if E( C) E( C) P > P Cx ciical axial o bending buckling sess of bay fo ing-siffened cylindical shell Cx Cx CxR.5ϕ R C θ θr + 1 (1.5ϕ R ) C θ θr fo ing and singe-siffened cylindical shell Ae A CxB.5ϕ B C θ θb + 1 (1.5ϕ R ) C θ calculaed hoop sess fom 4/13.3, N/cm (kgf/cm, lbf/in ) A coss secional aea as defined in 4/7.1 A e effecive coss secional aea as defined in 4/7.1 η maximum allowable sengh uilizaion faco, as specified in Subsecion 1/11 and 4/1.7, fo column buckling CxR, CθR, ϕ R, CxB, CθB and ϕ B ae as defined in Subsecions 4/3 and 4/7. 13 Sess Calculaions 13.1 Longiudinal Sess The longiudinal sess in accodance wih beam heoy may be aken as: x a + b θ θb a sess due o axial foce, N/cm (kgf/cm, lbf/in ) P π (1 + δ ) b sess due o bending momen, N/cm (kgf/cm, lbf/in ) M π (1 + δ ) ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 61

70 Secion 4 Cylindical Shells P axial foce, N (kgf, lbf) M bending momen, N-cm (kgf-cm, lbf-in) δ A s s A s coss secional aea of singe siffene, cm (in ) s shell plae widh beween adjacen singe siffenes, cm (in.) mean adius of cylindical shell, cm (in.) hickness of cylindical shell, cm (in.) 13.3 Hoop Sess The hoop sess may be aken as A midway of shell beween adjacen ing siffenes: θ q ( +.5) Kθ A inne face of ing flange, (i.e., adius F in Secion 4, Figue ): θr q( +.5) F K θr 1 kν K θ 1 Gα 1 + ( + ϖ A w ) R K θr 1 + A 1 kν [ ( R w + ϖ )] A R A R, cm (in ) R cosh α cos α ϖ α(sinh α + sin α ) α 1.56 sinhα cosα + coshα sinα G α sinh α + sin α k N x /N θ fo laeal pessue N x /N θ +.5 fo hydosaic pessue A R coss secional aea of ing siffene, cm (in ) q exenal pessue, N/cm (kgf/cm, lbf/in ) N x axial load pe uni lengh, excluding he capped-end acions due o hydosaic pessue, N/cm (kg/cm, lbf/in) N θ cicumfeenial load pe uni lengh, N/cm (kg/cm, lbf/in) mean adius of cylindical shell, cm (in.) 6 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

71 Secion 4 Cylindical Shells R adius o cenoid of ing siffene, as defined in Secion 4, Figue, cm (in.) F adius o inne face of ing flange, as defined in Secion 4, Figue, cm (in.) hickness of cylindical shell, cm (in.) w siffene web hickness, cm (in.) lengh beween adjacen ing siffenes (unsuppoed), cm (in.) ν Poisson s aio, R and F ae descibed in Secion 4, Figue. 15 Siffness and Popoions To fully develop he inended buckling sengh of he assemblies of a siffened cylindical shell, ing and singe siffenes ae o saisfy he following equiemens fo siffness and popoions Siffness of Ring Siffenes The momen of ineia of he ing siffenes, i, ogehe wih he effecive lengh of shell plaing, eo, should no be less han ha given by he following equaion: 4 x ( 1+ δ ) e θ e ze E i E EKθ 1 η θr x compessive sess in longiudinal diecion fom 4/13.1, N/cm (kgf/cm, lbf/in ) θ compessive hoop sess midway beween adjacen ing siffenes fom 4/13.3, N/cm (kgf/cm, lbf/in ) θr compessive hoop sess a oue edge of ing flange fom 4/13.3, N/cm (kgf/cm, lbf/in ) δ A s /s i momen of ineia of he ing siffenes wih associaed effecive shell lengh, eo eo 1.56 e adius o he cenoid of ing siffene, accouning fo he effecive lengh of shell plaing, cm (in.) z e disance fom inne face of ing flange o cenoid of ing siffene, accouning fo he effecive lengh of shell plaing, cm (in.) K θ coefficien fom 4/13.3 specified minimum yield poin, N/cm (kgf/cm, lbf/in ) E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel s spacing of singe siffenes, cm (in.) A s coss secional aea of singe, cm (in ) hickness of shell plaing, cm (in.) lengh beween adjacen ing siffenes (unsuppoed), cm (in.) η maximum allowable sengh uilizaion faco fo siffened cylindical shells subjeced o exenal pessue ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 63

72 Secion 4 Cylindical Shells 15.3 Siffness of Singe Siffenes The momen of ineia of he singe siffenes, i s, wih effecive beadh of shell plaing, s em, is no o be less han: 3 s i o 1 1 ν γ ( ) γ ( δ)α + 1.4α 13.α 1/ δ A s /(s) α /s s spacing of singe siffenes, cm (in.) hickness of shell plae, cm (in.) ν Poisson s aio A s coss secional aea of singe siffene, cm (in ) lengh beween adjacen ing siffenes (unsuppoed), cm (in.) 15.5 Popoions of Webs of Siffenes The deph o hickness aio of webs of siffenes is o saisfy he applicable limi given below. d w / w 1.5(E/ ) 1/ fo angles and ee bas d w / w.85(e/ ) 1/ d w / w.4(e/ ) 1/ fo bulb plaes fo fla bas specified minimum yield poin, N/cm (kgf/cm, lbf/in ) E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel d w and w ae as defined in Secion 4, Figue Popoions of Flanges and Faceplaes The beadh o hickness aio of flanges and faceplaes of siffenes is o saisfy he limi given below. b / f.4(e/ ) 1/ b lage ousanding dimension of he flange/faceplae, cm (in.) f hickness of flange/face plae, cm (in.) specified minimum yield poin, N/cm (kgf/cm, lbf/in ) E modulus of elasiciy, N/cm ( kgf/cm, lbf/in ) fo seel 64 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

73 Secion 5: Tubula Joins SECTION 5 Tubula Joins 1 Geneal This Secion povides ulimae sengh cieia fo ubula joins. Each join should be consideed as being compised of a numbe of independen chod/bace inesecions, and he ulimae sengh limi sae of each inesecion is o be checked agains he design equiemen. Fo a muli-plana join, each plane should be subjeced o sepaae consideaion and caegoizaion. The fomulaions povided in his Secion may be used o assess he ulimae sengh limi of ubula joins. Alenaively, he ulimae sengh of a ubula join may be deemined based on eihe well-documened expeimenal daa o a veified analyical appoach. 1.1 Geomey of Tubula Joins The geomey of a simple join is depiced in Secion 5, Figue 1. FIGURE 1 Geomey of Tubula Joins P B M OPB M IPB g d M IPC P C M OPC D CAN CHORD T The fomulaions in his Secion ae applicable fo he sengh assessmen of ubula joins in he following geomeic anges: g/d aio of bace wall hickness o chod wall hickness /T ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 65

74 Secion 5 Tubula Joins β aio of bace oue diamee o chod oue diamee d/d γ aio of chod oue diamee o wo imes of chod wall hickness D/(T) g gap, cm (in.) 1.3 Loading Applicaion The ulimae sengh cieia ae povided fo he following loads and load effecs: Axial load in a bace membe, P B In-plane bending momen in a bace membe, M IPB Ou-of-plane bending momen in a bace membe, M OPB Axial load in a chod membe, P C In-plane bending momen in a chod membe, M IPC Ou-of-plane bending momen in a chod membe, M OPC Combinaions of he above menioned loads and load effecs. 1.5 Failue Modes The mode of failue of a ubula join depends on he join configuaion, join geomey and loading condiion. These modes include: Local failue of he chod: Plasic failue of he chod wall in he viciniy of he bace. Cacking leading o upue of he bace fom he chod. Local buckling in compession aeas of he chod. Global failue of he chod: Ovalizaion of he chod coss-secion. Beam bending failue. Beam shea failue beween adjacen baces. In addiion, a membe can fail away fom he bace-chod join due o chod o bace oveloading. These failue modes can be esablished following he appoach descibed in Secion fo ubula membes. 1.7 Classficaion of Tubula Joins Each chod/bace inesecion is o be classified as T/Y, K o X, accoding o hei configuaion and load paen fo each load case. The following guidelines ae o be used o classify ubula joins: Fo wo o hee bace membes on one side of a chod, he classificaion is dependen on he equilibium of he axial load componens in he bace membes. If he esulan shea on he chod membe is balanced o algebaically aound zeo, he join is o be caegoized as a K. If he shea balance check is no me, he join is o be caegoized (downgaded) as a T&Y, as shown in Secion 5, Figue. Howeve, fo baces ha cay pa of hei load as K joins and pa as Y o X joins, inepolaion is o be used based on he popoion of each join. The pocedue fo inepolaion in such cases is o be specially ageed upon wih ABS. Fo muli-bace joins wih baces on eihe side of he chod, as shown in Secion 5, Figue, cae is o be aken in assigning he appopiae caegoy. Fo example, a K classificaion would be valid if he ne shea acoss he chod is balanced o algebaically zeo. In conas, if he loads in all of he baces ae ensile, even an X classificaion may be oo opimisic due o he inceased ovalizaion effec. Classificaion in hese cases is o be specially ageed wih ABS. 66 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

75 Secion 5 Tubula Joins FIGURE Examples of Tubula Join Caegoizion P 1 K P 1 T&Y P 1 5% K, 5% T&Y P θ T θ P K θ K.9 P 1 sinθ/p 1.1 P P.9 P 1 sinθ/p P 1 sinθ/p 1.1 P 1 P 1 K K θ 1 K θ 1 θ 3 P θ 3 P 3 P 1 K.9 P 1 sinθ 1 /P 3 sinθ P 3 P 1 K.9 (P 1 sinθ 1 + P 3 sinθ 3 )/P 1.1 X K θ K θ K P θ X P θ K P P 1.9 P 1 /P P 1 sinθ/p Adjusmen Faco Fo he maximum allowable sengh uilizaion faco, η, defined in Subsecion 1/11, he adjusmen faco is o ake he following value: ψ 1. 3 Simple Tubula Joins 3.1 Join Capaciy The sengh of a simple join wihou ovelap of baces and having no gusses, gou o siffenes is o be calculaed based on he following: P u c T sin θ Q u Q f ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 67

76 Secion 5 Tubula Joins M u c T d Q sin θ u Q f P u ciical join axial sengh, N (kgf, lbf) M u ciical join bending momen sengh fo in-plane and ou-of plane bending, N-cm (kgf-cm, lbf-in) θ bace angle measued fom chod, as defined in Secion 5, Figue 1 Q u sengh faco depending on he join loading and classificaion, as deemined in Secion 5, Table 1 Q f chod load faco 1 λγa λ chod slendeness paamee.3 fo bace axial load.45 fo bace in-plane bending momen.1 fo bace ou-of-plane bending momen γ aio of chod oue adius o chod wall hickness D/(T) A chod uilizaion aio AC + η IPC oc + OPC AC nominal axial sess in he chod membe, N/cm (kgf/cm, lbf/in ) IPC nominal in-plane bending sess in he chod membe, N/cm (kgf/cm, lbf/in ) OPC nominal ou-of-plane bending sess in he chod membe, N/cm (kgf/cm, lbf/in ) c specified minimum yield poin of he chod membe, N/cm (kgf/cm, lbf/in ) D chod oue diamee, cm (in.) T chod hickness, cm (in.) d bace oue diamee, cm (in.) η maximum allowable sengh uilizaion faco, as defined in Subsecion 1/11 and 5/1.9 Axially loaded baces based on a combinaion of K, X and Y joins should ake a weighed aveage of P u depending on he popoion of each load. Join Classificaion TABLE 1 Sengh Faco, Qu Bace Load Effecs Axial Axial In-plane Compession Tension Bending K (.5+1β)γ..5 Q β Q g ( β)γ..5 Q β Q g 4.5βγ.5 3.γ (.5β²) Ou-of-plane Bending T/Y (.5+1β)γ. Q β.5 ( β)γ. Q β.5 4.5βγ.5 3.γ (.5β²) X ( β) Q β (3.3+16β) Q β 5.βγ.5 3.γ (.5β²) 68 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

77 Secion 5 Tubula Joins Q.3/[ (1.833 )] fo >.6 1. fo.6 Q g exp (-4g/D) fo g/d. g gap, cm (in.) aio of bace oue diamee o chod oue diamee d/d aio of chod oue diamee o wo imes of chod wall hickness D/(T) 3.3 Join Cans The advanage of a hicke chod may be aken fo axially-loaded T/Y and X joins. This only applies if he effecive can lengh of each bace is a leas wice he disance fom he bace oe o he neaes ansiion fom he can o he main membe, plus he bace diamee (see Secion 5, Figue 3). FIGURE 3 Examples of Effecive Can Lengh d 1 d Bace 1 Bace c 1 c D c 3 Chod Chod-can T c T Bace Effecive Can Lengh Bace 3 1 c 1 + d 1 c + d 3 c 3 + d 3 d 3 Fo K joins, he join sengh, P u, consideing he addiional effec of he can is o be calculaed based on he following equaion: P u [C + (1 C)(T/T c ) ]P u P u basic sengh of he join based on he can dimensions, N (kgf, lbf) T c can hickness, cm (in.) C coefficien, which may no be aken geae han 1 L c /(.5D) fo.9 (4 3)L c /(1.5D) fo >.9 aio of bace oue diamee o chod oue diamee d/d D chod oue diamee, cm (in.) ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 69

78 Secion 5 Tubula Joins T chod wall hickness, cm (in.) L c effecive lengh of can, cm (in.) 3.5 Sengh Sae Limi The sengh of a ubula join subjeced o combined axial and bending loads is o saisfy he following sae limi: PD ηp u M + ηm IPB uipb M + ηm OPB uopb 1 5 Ohe Joins P D axial load in he bace membe, N (kgf, lbf) M IPB in-plane bending momen in he bace membe, N-cm (kgf-cm, lbf-in) M OPB ou-of-plane bending momen in he bace membe, N-cm (kgf-cm, lbf-in) P u ubula join sengh fo bace axial load fom 5/3.1 o 5/3.3, N (kgf, lbf) M uipb ubula join sengh fo bace in-plane bending momen fom 5/3.1, N-cm (kgf-cm, lbf-in) M uopb ubula join sengh fo bace ou-of-plane bending momen fom 5/3.1, N-cm (kgf-cm, lbf-in) η maximum allowable sengh uilizaion faco, as specified in Subsecion 1/11 and 5/ Muliplana Joins The ineacion beween ou-of-plane baces can be ignoed, excep fo ovelapping baces. I is ecognized ha fo some load cases, paiculaly baces lying in wo pependicula planes ae loaded in he opposie sense (e.g., ension and compession), as shown in Secion 5, Figue 4, join sengh can be significanly educed. This sengh educion is pimaily due o he addiional ovalizaion occuing in he chod membe. The design should accoun fo his effec and is o conside applying a educed allowable uilizaion faco, especially fo ciical, highly sessed, non-edundan joins. As equied, he design of muliplana joins loaded in opposie diecions is o be based on suiable expeimenal daa o nonlinea finie elemen analysis. Nonlinea finie elemen analysis is well-suied o invesigae he effecs of individual paamees such as load aio, load sequence and ineacion of ou-of-plane baces. FIGURE 4 Muliplana Joins P 1 Bace 1 Chod Bace P 7 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

79 Secion 5 Tubula Joins 5.3 Ovelapping Joins Joins wih baces ha ovelap in plane ae o be checked using he same fomula as fo non-ovelapping baces given in Subsecion 5/3. Howeve, an addiional check is o be pefomed fo he egion of he ovelap by consideing he hough bace as he chod membe and he ovelapping bace as he bace membe. The Q g em fo ovelapped joins is o be based on he following equaion: Q g b τγ c.5.5 g/d.5 b specified minimum yield poin of he bace membe, N/cm (kgf/cm, lbf/in ) c specified minimum yield poin of he chod membe, N/cm (kgf/cm, lbf/in ) τ aio of bace hickness o chod hickness /T γ aio of chod oue adius o chod wall hickness D/(T) g gap, cm (in.) D chod oue diamee, cm (in.) Fo -.5 < g/d <., he value of Q g should be esimaed by linea inepolaion beween he value of Q g calculaed fom he above expession and 1.85, he Q g faco a g/d.. Joins ha ovelap ou-of-plane should be eaed as simple joins and checked in accodance wih Subsecion 5/3. Howeve, an addiional check should be pefomed fo he egion of ovelap by consideing he hough bace as he chod membe and he ovelapping bace as he bace membe. The join will be consideed as a T/Y join in his insance. The combined ou-of-plane bending momen beween hese offse membes is equivalen o an in-plane bending momen as defined fo a simple T/Y join. Similaly, he combined inplane bending momen is equivalen o an ou-of-plane bending momen, as defined fo a simple T/Y join. 5.5 Goued Joins Goued joins can be classified ino wo ypes: i) Those wih a fully goued chod membe and ii) Those wih an inne seel sleeve wih a gou filling he annulus beween he wo concenic ubula membes. Unde axial compession, significan inceases in join sengh have been ecoded hough es pogams. Unde axial ension, only modes sengh enhancemen is noed, which esuls pimaily fom he educion in chod ovalizaion ha occus fo he goued specimen. I is ecommended ha no benefi is aken fom gouing o inseion of an inne sleeve unde axial ension and bending in he sengh assessmen of a goued join. Howeve, unde axial compession, an enhancemen in chod hickness may be available and an effecive chod hickness may be obained fom he following equaion. T e T + T p + T g /18 T chod hickness, cm (in.) T p hickness of he inne ube, cm (in.) T g hickness of he gou-filled secion, cm (in.) D/ (T + T p ), if fully gou-filled ube D oue diamee, cm (in.) T p and T g ae depiced in Secion 5, Figue 5. ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 71

80 Secion 5 Tubula Joins FIGURE 5 Goued Joins P Bace Chod T g Gou T p Inne Sleeve 5.7 Ring-Siffened Joins As in he case of goued joins, ings enhance he join siffness subsanially. A ing-siffened join should be designed based on appopiae expeimenal o in-sevice evidence. In he absence of such evidence, an appopiae analyical check is o be pusued. As ecommended by API RP WSD A, his check is o be pefomed by cuing secions ha isolae goups of membes, individual membes and sepaae elemens of he join (e.g., gusses, diaphagms, siffenes, welds in shea and sufaces subjeced o punching shea), and veifying ha ealisic, assumed sess disibuions saisfy equilibium wihou exceeding he allowable sess of he maeial (e.g., he sengh of all elemens is sufficien o esis he applied loading). As needed, he design of a ing-siffened ubula join is also o be based on suiable expeimenal daa o nonlinea finie elemen analysis. Nonlinea finie elemen analysis is ideally suied fo sensiiviy sudies, which invesigae he effecs of individual paamees such as he geomey, locaion and numbe of siffenes. 5.9 Cas Joins Whee he use of cas joins is consideed, assisance fom qualified specialiss is o be sough. This is paiculaly elevan fo opimized cas joins unusually demanding design cieia ae poposed. Nonlinea finie elemen analysis is also o be pefomed, giving paicula consideaion o he geomeic and maeial chaaceisics of cas joins, including he effecs of casing geomey, sess-sain elaionships and casing defecs. In addiion, i should be ecognized ha he pefomance of cas joins beyond fis yield may no be simila o ha achieved in welded joins. The pos-yield behavio of cas joins should be invesigaed o ensue ha he eseve sengh and duciliy agains oal collapse ae compaable o hose of welded joins. 7 ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4

81 Appendix 1: Review of Buckling Analysis by Finie Elemen Mehod (FEM) APPENDIX 1 Review of Buckling Analysis by Finie Elemen Mehod (FEM) 1 Geneal This Appendix, in conjuncion wih API Bullein V, povides guidance on he eview of buckling analysis using FEM. If appopiae documenaion is pesened, poven numeical mehods o esablish he buckling sengh of sucual componens subjeced o vaious loads and hei combinaions ae acceped as an alenaive o he fomulaions pesened in he pevious Secions of his Guide. In some cases, especially hose involving novel sucual designs and loading siuaions, eliance on such analyical mehods ae o be pusued o povide added assuance of a poposed design s adequacy. One widely-acceped mehod elies on he use of FEM analysis, which allows he designe o model he geomey; maeial popeies; impefecions (such as ou-of-oundness), fabicaion-induced esidual sesses, misalignmen and coosion defecs; as well as bounday condiions. Key issues in an FEM analysis include he selecion of he compue pogam, he deeminaion of he loads and bounday condiions, developmen of he mahemaical model, choice of elemen ypes, design of he mesh, soluion pocedues and veificaion and validaion. Numeous decisions ae o be made duing his analysis pocess. This Appendix emphasizes some impoan aspecs ha should be saisfied in deemining he buckling sengh by FEM analysis. 3 Engineeing Model The engineeing model fo buckling analysis is a simplificaion and idealizaion of an acual physical sucual componen. Hence, i is cucial ha he modeling pocess is undeaken coecly, since he FEM analysis canno impove on a poo engineeing model. The aionale fo he following aspecs is o be appopiaely descibed and jusified: Exen of he model. The model should include he main feaues of he physical sucue elaed o buckling behavio and capue all elevan failue modes. Geomey. The use of a full model is pefeed in he FEM buckling analysis. Symmeic condiions may be uilized o educe he size of finie elemen model, if appopiae. Maeial popeies. Maeial nonlineaiy may need o be consideed in some cicumsances, paiculaly in ode o accoun fo he effecs of esidual sesses. Impefecions. Impefecions may emakably educe he buckling sengh of sucual componens. Fo his eason, he impefecions should be included. Loads. All possible loads and hei combinaions ae o be consideed. Bounday condiions. Bounday condiions ae he consains applied o he model. The bounday condiions should suiably eflec he consain elaionship beween he sucual componen and is suoundings. ABS GUIDE FOR BUCKLING AND ULTIMATE STRENGTH ASSESSMENT FOR OFFSHORE STRUCTURES. 4 73