Stress concentration factors of multi-planar tubular XT-joints subjected to out-of-plane bending moments
Introduction
The main structural part of a jacket-type platform, commonly used for the production of oil and gas in offshore fields (Fig. 1a), is a space frame fabricated from circular hollow section (CHS) members (Fig. 1b) by welding the prepared end of brace members onto the undisturbed surface of the chord, resulting in what is called a tubular joint (Fig. 1c).
Tubular joints are subjected to cyclic loads induced by sea waves and hence they are susceptible to fatigue damage due to the formation and propagation of cracks. Significant stress concentrations at the vicinity of the welds are highly detrimental to the fatigue life of a tubular connection. For the design purposes, a parameter called the stress concentration factor (SCF) is used to quantify the stress concentration. This calls for greater emphasis in accurate calculation of the SCFs to estimate the fatigue life of offshore structures.
The SCF, defined as the ratio of the local surface stress at the brace-to-chord intersection to the nominal stress in the brace, exhibits considerable scatter depending on the joint geometry, loading type, weld size and type, and the considered position for the SCF calculation around the weld profile. Under any specific loading condition, the SCF value along the weld toe of a tubular joint is mainly determined by the joint geometry. To study the behavior of tubular joints and to easily relate this behavior to the geometrical characteristics of the joint, a set of dimensionless geometrical parameters has been defined. Fig. 1c depicts a multi-planar tubular XT-joint with the geometrical parameters τ, γ, β, α, and αB for chord and brace diameters D and d, and their corresponding wall thicknesses T and t. Critical positions along the weld toe of the brace-to-chord intersection for the calculation of SCFs in a tubular joint, i.e. saddle and crown, have been shown in Fig. 1c.
Over the past thirty years, significant effort has been devoted to the study of SCFs in various uniplanar tubular joints (i.e. joints where the axes of the chord and brace members lay in the same plane). As a result, many parametric design formulas in terms of the joint's geometrical parameters have been proposed providing SCF values at certain positions adjacent to the weld for several loading conditions. The reader is referred for example to Kuang et al. [1], Efthymiou [2], Hellier et al. [3], UK HSE OTH 354 [4], and Karamanos et al. [5] (for the SCF calculation at the saddle and crown positions of simple uniplanar T-, Y-, X-, K-, and KT-joints); Gho and Gao [6], Gao [7], Gao et al. [8], and Yang et al. [9] (for the SCF determination in uniplanar overlapped tubular joints); Nwosu et al. [10], Ramachandra et al. [11], Hoon et al. [12], Myers et al. [13], Ahmadi et al. [14, 15], Ahmadi and Lotfollahi-Yaghin [16], and Ahmadi and Zavvar [17] (for the SCF calculation in various stiffened tubular joints); and Morgan and Lee [18, 19], Chang and Dover [20, 21], Shao [22, 23], Shao et al. [24], Lotfollahi-Yaghin and Ahmadi [25], Ahmadi et al. [26], Xu et al. [27], and Liu et al. [28] (for the study of the SCF distribution along the weld toe of various uniplanar joints).
Multi-planar joints are an intrinsic feature of offshore tubular structures. The multi-planarity effect might play an important role in the stress distribution at the brace-to-chord intersection. Thus for such multi-planar connections, the parametric formulas of simple uniplanar tubular joints may not be applicable for the SCF prediction, since such formulas may lead to highly over- or under-predicting results. Nevertheless, for multi-planar joints which cover the majority of practical applications, much fewer investigations have been reported due to the complexity and high cost involved. The reader is referred to Karamanos et al. [29] and Chiew et al. [30] (for the SCF calculation in XX-joints); Wingerde et al. [31] (for the SCF determination in KK-joints); Karamanos et al. [32] (for the study of SCFs in DT-joints); Woghiren and Brennan [33] (for the SCF calculation in stiffened KK-joints); Chiew et al. [34] (for the study of SCFs in XT-joints); and Lotfollahi-Yaghin and Ahmadi [35], Ahmadi et al. [36, 37], Ahmadi and Lotfollahi-Yaghin [38], and Ahmadi and Zavvar [39] (for the investigation of SCFs in multi-planar KT-joints under axial loads), among others.
For other SCF-related investigations such as probabilistic and reliability studies, the reader is referred for example to Ahmadi et al. [40], Gaspar et al. [41], Ahmadi and Lotfollahi-Yaghin [42, 43], Ahmadi et al. [44, 45], Ahmadi [46], and Ahmadi and Mousavi Nejad Benam [47].
In the present paper, results of numerical investigations of the stress concentration in multi-planar tubular XT-joints are presented and discussed. In this research program, a set of parametric finite element (FE) stress analyses was carried out on 81 tubular XT-joint models subjected to three types of out-of-plane bending (OPB) moment loading (Fig. 2). The analysis results were used to present general remarks on the effect of geometrical parameters including τ (brace-to-chord thickness ratio), γ (chord wall slenderness ratio), β (brace-to-chord diameter ratio), and α (chord length-to-radius ratio) on the SCFs at the saddle positions. The crown positions were not studied. The reason is that under the OPB moment loading, the nominal stress at the crown positions is zero and hence the determination of SCFs is not needed. Based on the results of XT-joint FE models, verified using experimental measurements, a SCF database was prepared. Then, a new set of SCF parametric equations was established, based on nonlinear regression analyses, for the fatigue analysis and design of multi-planar XT-joints subjected to OPB moment loading. The reliability of proposed equations was evaluated according to the acceptance criteria recommended by the UK DoE [48].
Section snippets
Simulation of the weld profile
Accurate modeling of the weld profile is one of the most critical factors affecting the accuracy of SCF results. Therefore, the weld sizes must be carefully included in the FE modeling. A number of research works has been carried out on the study of the weld effect. For example, the reader is referred to Lee and Wilmshurst [49], Cao et al. [50] and Lee [51], among others. It was found that the fatigue strength of the joint can be underestimated by 20% compared to the experimental data without
Settings of parametric study
In order to study the SCFs in multi-planar tubular XT-joints subjected to three types of OPB moment loading (Fig. 2), 81 models were generated and analyzed using the FE software, ANSYS. The objective was to investigate the effects of non-dimensional geometrical parameters on the chord-side SCFs at the saddle positions. As mentioned earlier, the crown positions were not studied. The reason is that under the OPB moment loading, the nominal stress at the crown position is zero and hence the
Effect of the multi-planarity on the SCF values and the comparison of SCFs at different positions
The uniplanar and multi-planar SCF values are compared in Fig. 11 indicating that there can be a quite big difference between the SCF values at the saddle positions of uniplanar and multi-planar T-joints. For example, under the 1st OPB moment loading condition, the SCF value at the WS1 saddle position of the XT81 model is twice the SCF at the saddle position of the corresponding uniplanar T-joint (Fig. 11a); while under the 2nd OPB moment loading condition, the SCF value
Comparison of SCFs under different types of OPB moment loading
A sample set of eight multi-planar XT-joints was selected (Table 6) to depict the differences among the SCFs under the three types of OPB moment loading shown in Fig. 2. Results given in Table 7 show that the WS1 SCFs under the 1st OPB moment loading condition are the biggest values observed. It can also be seen that the WS1 SCFs under the 1st OPB load case are almost equal to the WS2 SCFs under the 2nd and 3rd OPB load cases; where, on an average basis, the WS1 SCFs under the 1st OPB load case
Deriving parametric equations for the SCF calculation
Three individual parametric equations are proposed in the present paper, to calculate the chord-side SCFs at the saddle positions on the weld toe of multi-planar tubular XT-joints subjected to OPB moment loading.
Results of multiple nonlinear regression analyses performed by SPSS were used to develop parametric SCF design formulas. Values of dependent variable (i.e. SCF) and independent variables (i.e. β, γ, τ, and α) constitute the input data imported in the form of a matrix. Each row of this
Conclusions
Results of stress analysis performed on 81 FE models verified using experimental data were used to investigate the effect of geometrical parameters on the chord-side SCFs at the saddle positions in multi-planar tubular XT-joints, also called three-planar T-joints, under three types of OPB moment loading. A set of SCF parametric equations was also developed for the fatigue design. Main conclusions are summarized as follows.
The increase of the parameters τ, γ, and β leads to the increase of SCFs
Declaration of Competing Interest
None.
Acknowledgments
The authors would like to thank the University of Tabriz for supporting this work under the Research Grant Contract No. S/2863. Useful comments of anonymous reviewers on draft version of this paper are also highly appreciated.
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