Development of a Probability Distribution Model for SCFs in Uniplanar Tubular KT-Joints of Offshore Structures under IPB Moment Loading

Authors

1 Faculty of Civil Engineering, University of Tabriz

2 Faculty of Engineering, University of Maragheh

Abstract

One of the crucial parameters in the fatigue reliability assessment of an offshore structure’s tubular joints is the stress concentration factor (SCF). Depending on the joint geometry and loading type, the SCF exhibits considerable scatter which emphasizes the significance of deriving its governing probability distribution function. In the present paper, results of 144 finite element (FE) stress analyses, verified against experimental measurements, were used to develop a set of probability density functions (PDFs) for the SCFs in uniplanar tubular KT-joints under four types of in-plane bending (IPB) moment load cases. Based on a parametric FE investigation, a sample database was created for the chord-side SCFs of central and outer braces; and density histograms were generated for respective samples. Nine theoretical PDFs were fitted to the developed histograms and the maximum likelihood method was applied to evaluate the parameters of fitted PDFs. The Kolmogorov−Smirnov test was applied to each case to assess the goodness of fit. Finally, the Inverse Gaussian and Gamma models were proposed as the governing probability distribution functions for the central- and outer-brace SCFs, respectively. After substituting the values of estimated parameters, 10 fully defined PDFs were presented for the chord-side SCFs of central and outer braces in uniplanar tubular KT-joints under four types of IPB loading.

Keywords


[1] American Petroleum Institute (API) (2007) Recommended practice for planning, designing and constructing fixed offshore platforms: Working stress design: RP2A-WSD. 21st Edition, Errata and Supplement 3, Washington DC, US. [2] Yiyi C and Wei W (2003) Flexural behavior and resistance of uni-planar KK and X tubular joints. Steel and Composite Structures 3(2): 123−140. [3] Choo YS (2005) Recent development and innovation in tubular structures. Advances in Structural Engineering 8(3): 217−230. [4] Lie ST, Shao YB, Lee CK and Chiew SP (2006) Stress intensity factor solutions for semi-elliptical weld-toe cracks in tubular K-joints. Advances in Structural Engineering 9(1): 129−139. [5] Gao F, Zhu HP and Liu XN (2013) Failure behavior of axially loaded tubular Y-joints under fire. Advances in Structural Engineering 16(9): 1523−1533. [6] Liu H, Shao YB, Lu N and Wang Q (2015) Hysteresis of concrete-filled circular tubular (CFCT) T-joints under axial load. Steel and Composite Structures 18(3): 739−756. [7] Cui MJ and Shao YB (2015) Residual static strength of cracked concrete-filled circular steel tubular (CFCST) T-joint. Steel and Composite Structures 18(4): 1045−1062. [8] Shao YB (2016) Static strength of collar-plate reinforced tubular T-joints under axial loading. Steel and Composite Structures 21(2): 323–342. [9] Nassiraei H, Lotfollahi-Yaghin MA and Ahmadi H (2016) Structural behavior of tubular T/Y-joints with collar plate under static in-plane bending. Journal of Constructional Steel Research 123(8): 121−134. [10] Efthymiou M and Durkin S (1985) Stress concentrations in T/Y and gap/overlap K-joints. Proceedings of the Conference on Behavior of Offshore Structures, Delft, Netherlands. [11] Efthymiou M (1988) Development of SCF formulae and generalized influence functions for use in fatigue analysis. OTJ 88, Surrey, UK. [12] Hellier AK, Connolly M and Dover WD (1990) Stress concentration factors for tubular Y and T-joints. International Journal of Fatigue 12: 13–23. [13] Smedley P and Fisher P (1991) Stress concentration factors for simple tubular joints. Proceedings of the International Offshore and Polar Engineering Conference (ISOPE), Edinburgh, UK. [14] UK Health and Safety Executive (1997) OTH 354: stress concentration factors for simple tubular joints-assessment of existing and development of new parametric formulae. Prepared by Lloyd’s Register of Shipping, London (UK): Health and Safety Executive. [15] Karamanos SA, Romeijn A and Wardenier J (2000) Stress concentrations in tubular gap K-joints: mechanics and fatigue design. Engineering Structures 22: 4–14. [16] Gho WM and Gao F (2004) Parametric equations for stress concentration factors in completely overlapped tubular K(N)-joints. Journal of Constructional Steel Research 60: 1761–1782. [17] Gao F (2006) Stress and strain concentrations of completely overlapped tubular joints under lap brace OPB load. Thin-Walled Structures 44: 861–871. [18] Gao F, Shao YB and Gho WM (2007) Stress and strain concentration factors of completely overlapped tubular joints under lap brace IPB load. Journal of Constructional Steel Research 63: 305–316. [19] Morgan MR and Lee MMK (1998a) Parametric equations for distributions of stress concentration factors in tubular K-joints under out-of-plane moment loading. International Journal of Fatigue 20: 449–461. [20] Morgan MR and Lee MMK (1998b) Prediction of stress concentrations and degrees of bending in axially loaded tubular K-joints. Journal of Constructional Steel Research 45(1): 67–97. [21] Chang E and Dover WD (1999a) Parametric equations to predict stress distributions along the intersection of tubular X and DT-joints. International Journal of Fatigue 21: 619–635. [22] Chang E and Dover WD (1999b) Prediction of stress distributions along the intersection of tubular Y and T-joints. International Journal of Fatigue 21: 361–381. [23] Shao YB (2004) Proposed equations of stress concentration factor (SCF) for gap tubular K-joints subjected to bending load. International Journal of Space Structures 19: 137–147. [24] Shao YB (2007) Geometrical effect on the stress distribution along weld toe for tubular T- and K-joints under axial loading. Journal of Constructional Steel Research 63: 1351–1360. [25] Shao YB, Du ZF and Lie ST (2009) Prediction of hot spot stress distribution for tubular K-joints under basic loadings. Journal of Constructional Steel Research 65: 2011–2026. [26] Lotfollahi-Yaghin MA and Ahmadi H (2010) Effect of geometrical parameters on SCF distribution along the weld toe of tubular KT-joints under balanced axial loads. International Journal of Fatigue 32: 703–719. [27] Pang NL and Zhao XL (2009) Finite element analysis to determine stress concentration factors of dragline tubular joints. Advances in Structural Engineering 12(4): 463−478. [28] Karamanos SA, Romeijn A, and Wardenier J (1990) Stress concentrations in multi-planar welded CHS XX-connections. Journal of Constructional Steel Research 50: 259–282. [29] Chiew SP, Soh CK and Wu NW (2000) General SCF design equations for steel multiplanar tubular XX-joints. International Journal of Fatigue 22: 283–293. [30] Wingerde AM, Packer JA and Wardenier J (2001) Simplified SCF formulae and graphs for CHS and RHS K- and KK-connections. Journal of Constructional Steel Research 57: 221–252. [31] Karamanos SA, Romeijn A and Wardenier J (2002) SCF equations in multi-planar welded tubular DT-joints including bending effects. Marine Structures 15: 157–173. [32] Ahmadi H, Lotfollahi-Yaghin MA and Aminfar MH (2012a) The development of fatigue design formulas for the outer brace SCFs in offshore three-planar tubular KT-joints. Thin-Walled Structures 58: 67–78. [33] Ramachandra Murthy DS, Madhava Rao AG, Ghandi P and Pant PK (1992) Structural efficiency of internally ring stiffened steel tubular joints. Journal of Structural Engineering: ASCE 118(11): 3016–3035. [34] Nwosu DI, Swamidas ASJ and Munaswamy K (1995) Numerical stress analysis of internal ring-stiffened tubular T-joints. Journal of Offshore Mechanics and Arctic Engineering 117: 113–125. [35] Ramachandra DS, Gandhi P, Raghava G and Madhava Rao AG (2000) Fatigue crack growth in stiffened steel tubular joints in seawater environment. Engineering Structures 22: 1390–1401. [36] Hoon KH, Wong LK and Soh AK (2001) Experimental investigation of a doubler-plate reinforced tubular T-joint subjected to combined loadings. Journal of Constructional Steel Research 57: 1015–1039. [37] Myers PT, Brennan FP and Dover WD (2001) The effect of rack/rib plate on the stress concentration factors in jack-up chords. Marine Structures 14: 485–505. [38] Woghiren CO and Brennan FP (2009) Weld toe stress concentrations in multi planar stiffened tubular KK Joints. International Journal of Fatigue 31: 164–172. [39] Ahmadi H, Lotfollahi-Yaghin MA, Shao YB and Aminfar MH (2012b) Parametric study and formulation of outer-brace geometric stress concentration factors in internally ring-stiffened tubular KT-joints of offshore structures. Applied Ocean Research 38: 74−91. [40] Ahmadi H and Zavvar E (2015) Stress concentration factors induced by out-of-plane bending loads in ring-stiffened tubular KT-joints of jacket structures. Thin-Walled Structures 91: 82–95. [41] Kirkemo F (1998) Applications of probabilistic fracture mechanics to offshore structures. Applied Mechanics Review 41: 61–84. [42] Pillai TMM and Prasad AM (2000) Fatigue reliability analysis in time domain for inspection strategy of fixed offshore structures. Ocean Engineering 27: 167–186. [43] Mosayyebi AR and Aghakuchak AA (2000) Fatigue reliability analysis of tubular joints of offshore structures using response surface method. Asian Journal of Civil Engineering 1: 75–87. [44] Rajasankar J, Iyer NR and Appa Rao TVSR (2003) Structural integrity assessment of offshore tubular joints based on reliability analysis. International Journal of Fatigue 25: 609–619. [45] Ahmadi H and Lotfollahi-Yaghin MA (2013) Effect of SCFs on S–N based fatigue reliability of multi-planar tubular DKT-joints of offshore jacket-type structures. Ships and Offshore Structures 8: 55−72. [46] Ahmadi H, Lotfollahi-Yaghin MA and Aminfar MH (2011) Effect of stress concentration factors on the structural integrity assessment of multi-planar offshore tubular DKT-joints based on the fracture mechanics fatigue reliability approach. Ocean Engineering 38: 1883−1893. [47] Ahmadi H, and Lotfollahi-Yaghin MA (2012) A probability distribution model for stress concentration factors in multi-planar tubular DKT-joints of steel offshore structures. Applied Ocean Research 34: 21−32. [48] Ahmadi H, Mohammadi AH, and Yeganeh A (2015) Probability density functions of SCFs in internally ring-stiffened tubular KT-joints of offshore structures subjected to axial load. Thin-Walled Structures 94: 485–499. [49] Ahmadi H, Mohammadi AH, Yeganeh A and Zavvar E (2016) Probabilistic analysis of stress concentration factors in tubular KT-joints reinforced with internal ring stiffeners under in-plane bending loads. Thin-Walled Structures 99: 58–75. [50] Ahmadi H. (2016). A probability distribution model for SCFs in internally ring-stiffened tubular KT-joints of offshore structures subjected to out-of-plane bending loads. Ocean Engineering 116: 184–199. [51] American Welding Society (AWS) (2002) Structural welding code: AWS D 1.1. Miami (FL), US. [52] N’Diaye A, Hariri S, Pluvinage G and Azari Z (2007) Stress concentration factor analysis for notched welded tubular T-joints. International Journal of Fatigue 29: 1554–1570. [53] IIW-XV-E (1999) Recommended fatigue design procedure for welded hollow section joints, IIW Docs, XV-1035-99/XIII-1804-99. Paris (France): International Institute of Welding. [54] Ahmadi H and Lotfollahi-Yaghin MA (2013) Effect of SCFs on S–N based fatigue reliability of multi-planar tubular DKT-joints of offshore jacket-type structures. Ships and Offshore Structures 8: 55−72. [55] Chang E, Dover WD (1996). Stress concentration factor parametric equations for tubular X and DT joints. International Journal of Fatigue 18(6): 363–387. [56] Kottegoda NT and Rosso R (2008) Applied statistics for civil and environmental engineers. 2nd Edition, Blackwell Publishing Ltd, UK.