Stress Concentration Factor Analysis for Uniplanar Tubular DKT-Joints and Proposing Parametric

Stress concentration factor analysis for uniplanar tubular DKT-Joints and proposing parametric equation for SCF distribution

Keywords: Offshore Structures, Fatigue, Tubular DKT-joint, Parametric Equation, Stress Concentration Factor (SCF)

Abstract

Despite the frequent use of tubular DKT-joints in offshore structures, no parametric equation is available for determining the distribution of stress concentration factors (SCFs) along the brace-chord intersection of such joints. In the present paper, the effect of non-dimensional geometrical parameters and brace-to-chord inclination angle on the distribution of SCFs along the weld toe of tubular DKT-joints under the balanced axial loads is studied. Thereafter, a parametric equation is proposed for predicting the distribution of SCFs along the 360° spatial curve of weld toe. The proposed equation satisfies the acceptance criteria recommended by UK Department of Energy, and consequently can reliably be used for design purposes.

Introduction

In order to meet the demands of energy requirements, many offshore platforms have been installed all over the world for exploration and exploitation of oil and gas reserves from hydrocarbon reservoirs below the seabed. In the construction of offshore platforms, steel circular hollow sections (CHSs) have been extensively used in the industry because of their high strength-to-weight ratio, non-directional buckling and bending strength, and low wave resistance. In a tubular joint, circular hollow members (tubulars) are connected by welding the prepared end of the brace members onto the surface of the chord member. Fig. 1 shows a tubular DKT-joint with the three commonly named locations along the brace-chord intersection: saddle, crown toe and crown heel, and the geometrical parameters for chord and brace diameters D and d, and the corresponding wall thicknesses T and t. Tubular joints in offshore structures such as jacket templates and jack-up rigs are subjected to cyclic wave loading and are thus susceptible to fatigue damage. Design against fatigue and periodic in-service inspections are necessary in order to ensure their safety and integrity. In order to assess the approximate fatigue life of offshore structures, the Stress-Life (S-N) curves are frequently adopted by researchers. In this method, the number of loading cycles that the structure can sustain before failure is estimated from the corresponding hot spot stress (HSS) range. The hot spot stress range can be determined from a parameter called the stress concentration factor (SCF). The SCF is the ratio of the local surface stress to the nominal direct stress in the brace. The structural discontinuity at the brace-to-chord intersection regions incurs a large amount of stress concentration.

During the last 40 years, a significant number of papers have been published on stress concentrations in tubular steel joints with CHS members. Some researchers proposed parametric equations which are useful to determine the values of SCF in the welded region. However, almost all these research results are focused on the values of the SCF at the saddle and crown positions, and they have ignored HSS at other locations along the weld toe. Although the results of these research efforts are useful, it is worth mentioning that there are some important reasons to determine the SCF distribution along the weld toe instead of only at certain locations such as at the crown and saddle. The main reasons can be summarized as follows:

• Through determining the SCF distribution along the intersection region, it is possible to accurately estimate the location of hot spot stress (HSS). It is well known that fatigue induced surface crack initiates from the position of the hot spot stress. Therefore, such position is very important for determining the crack propagating way and the fatigue life. If the parametric equations can present only the values of SCF at the saddle and crown positions, then it is impossible to determine the location of HSS.

• Tubular members of offshore structures are subjected to multi-axis loading i.e. combined axial force, in-plane bending (IPB) and out-of-plane bending (OPB) loading moments. The HSS may be located at any point along the intersection under these loads. The conventional method adopted by API code [1] to determine the HSS, is to sum the products of the nominal stresses due to each load type and the corresponding maximum SCFs. Obviously, this approach does not take the location of the HSS into account and it normally leads to excessively conservative estimate of fatigue lives [2]. More accurate HSS can be obtained by the superposition of stress distributions from each of the uni-axis load modes.
• It is probable that the difference between the value of the peak stress concentration factor (SCFHSS) and the values of SCF at saddle and crown positions would be considerable. Therefore, the use of the parametric equations which present the values of SCF only at saddle and crown positions leads to under-predicted estimates of HSS values. This is important because it is impractical in service to inspect all underwater members due to the high cost of inspections by divers. Thus inspections can only be carried out on some selected critical joints [3]. When the joint is more susceptible to fatigue damage, the fatigue life is determined by the value of its HSS range. Therefore, it is crucial to accurately predict the HSS.
• The information on the stress distribution is also needed for predicting fatigue crack growth and remaining life for in-service cracked joints when advanced fracture mechanics models are used such as O-integral, AVS and TPM. Thus, it is very important to have an accurate stress distribution along the intersection under each uni-axis loading.

Fig. 1) Geometrical notation for a DKT-joint under balanced axial loads

Very few methods are available for predicting the stress distribution along the welding path. For tubular joints with complex geometry, it has not been reported in the literature on how to predict the location of the HSS. The stress distribution along the weld toe for tubular joints is mainly determined by the joint geometry. In order to study the behavior of tubular joints and to relate this behavior easily to the geometrical properties of the joint, a set of dimensionless geometrical parameters has been defined. In this paper, the results obtained from extensive finite element analyses are 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 θ (brace-to-chord inclination angle) on the stress distribution along the weld toe of tubular DKT-joints under the brace balanced axial loads (see Fig. 1). Thereafter, the produced FE database which has been verified against both the experimental results and predictions of Lloyd’s Register (LR) equations [4] is utilized to propose a parametric equation for determining the SCFs along the 360spatial curve of weld toe.

Literature Review

The LR equations [4] were developed as mean fit equations to the derived SCF database by minimizing the percentage difference between the measured and the estimated SCF values. The LR equations cover T-, Y-, X, K- and KT-joints. It must be noted that theses equations give the SCFs only at the saddle and crown position.Lee and Morgan [5] presented a set of parametric equations to determine the SCFs for tubular K-joints under the balanced axial loading. Chang and Dover [3] presented a set of parametric equations to predict the stress distributions along the intersection of tubular Y- and T-joints. The proposed equations covered axial, IPB and OPB loadings and presented the SCFs at both chord and brace members. Karamanos et al. [6] proposed a set of parametric equations to determine the SCFs for multi-planar welded CHS XX-connections. Chiew et al. [7] presented a set of parametric equations to determine the SCFs for multi-planar tubular XX-joints under axial, IPB and OPB loadings. Van Wingerde et al. [8] presented the equations and graphs to predict the SCFs for uni-planar K- and multi-planar KK-joints. Karamanos et al. [9] proposed SCF equations in multi-planar welded tubular DT-joints including bending effects. Shao [10] presented a set of parametric equations to determine the SCFs for gap tubular K-joints under bending moment loading. Gho and Gao [11] proposed a set of parametric equations to determine the SCFs in completely overlapped tubular K (N)-joints under lap brace axial loading.Gao [12] presented a set of parametric equations to determine the SCFs in completely overlapped tubular K (N)-joints under lap OPB loading. Woghiren and Brennan [13] proposed a set of parametric equations to predict the values of SCF in multi-planar stiffened tubular KK-joints. Shao et al. [14] presented a set of parametric equations to predict the hot spot stress distribution for tubular K-joints under basic loadings. The equations proposed by Lotfollahi-Yaghin and Ahmadi [15-16] are the first ones which can be used for prediction of SCF distribution along the weld toe of tubular KT-joints under the balanced axial loads.

It can be concluded from this section that despite the considerable volume of research on determination of SCFs at certain locations such as saddle and crown for different types of tubular joints, distribution of SCFs along the brace-chord intersection has not been extensively investigated. However, such study of SCF distribution is very important because of some reasons mentioned earlier. Furthermore, those studies which consider the peripheral distribution of SCFs, mainly cover the relatively simple joints such as T-, Y-, K-, and X-joints. Despite the frequent use of DKT-joints in offshore structures, no parametric equation is available to predict the SCF distribution along the brace-chord intersection of DKT-joints.

Finite Element Modeling Of Tubular Dkt-Joints

Geometrical characteristics of analyzed models

To study the distribution of SCFs along the weld toe in tubular DKT-joints, 51 models were generated and analyzed using the multi-purpose FE package, ANSYS [17]. All the joints were subjected to balanced axial loads exerted on the outer braces. The aim of this study is to investigate the effect of dimensionless geometrical parameters on the stress distribution along the weld toe. The parametric study was conducted in two parts. The first study consisting of 27 models investigates the effects of the joint parameters τ, γ, β on the SCF distribution along the intersection of DKT-joints. The second study focusing on outer brace inclination, examines the effects of θ on the SCF distribution, and the interaction of this parameter with the others. The total number of the models used in the second study was 24. Different values assigned to each dimensionless parameter are generally found in offshore structures.These 51 models spanned the following ranges of the geometric parameters:

According to Lotfollahi-Yaghin and Ahmadi [15-16], the relative gap (ζ=g/D) has no considerable effect on both the values and distribution pattern of SCFs along the weld toe. Hence, a realistic value of ζ = 0.4 was assigned for all the joints.

Selecting the element type

In the present study, ANSYS element type SOLID95 was used to model the chord, brace and weld profile. These elements have compatible displacements and are well suited to model curved boundaries. The element is defined by 20 nodes having three degrees of freedom per node. The element may have any spatial orientation.

Mesh generation process

The most tedious task in the FE analysis of the tubular joints (including the weld profile modeling) is the mesh generation process. The reason is the geometrical complexity of the joint, especially along the brace-chord intersection.

In order to guarantee the mesh quality, a sub-zone mesh generation method was used during the FE modeling. In this method, the entire structure is divided into several different zones according to the computational requirements. In sub-zone mesh generation process, the mesh of each zone is generated separately. The mesh of the entire structure is obtained by merging the meshes of all the sub-zones. This method can easily control the mesh quantity and quality and avoid badly distorted elements. The mesh generated by this method for a tubular DKT-joint is shown in Fig. 2. To verify the convergence of FE analysis, converging test was done and the meshes with different densities were used in this test, before generating the 51 models.

Modeling of weld profile

One of the most critical factors affecting the accuracy of stress distribution results is accurate modeling of the weld profile. In this study, the welding size along the brace-chord intersection satisfies the AWS specifications [18]. As defined by AWS [18], the dihedral angle ψ is an important parameter used to determine the weld thickness, and is the angle between the chord and brace surface along the intersection curve.

Boundary conditions and load application

Due to the symmetry in geometry and loading conditions, only one fourth of the entire DKT-joint was modeled. Displacements of the nodes on the symmetry plane were restrained perpendicular to the plane.

According to Morgan and Lee [19], changing the end restraint from fixed to pinned results in a maximum increase in SCF of 15% at crown heel for α=6 joints, and this increase reduces to only 8% for α=8. In view of the fact that the effect of chord end restraints is only significant for joints with α < 8 for high β and γ values, which do not commonly occur in practice, both chord and central brace ends were assumed to be fixed, with the corresponding nodes restrained. Efthymiou [20] showed that sufficiently long chord greater than six chord diameters (i.e. α ≥ 12) must be used to ensure that the stresses at the brace-chord intersection are not affected by the end condition. Hence, in this study, a value of α=12 was assigned for all the models and it can be concluded from Efthymiou [20] that the results of the present study are valid for α ≥ 12. The effect of brace length on SCF has been studied by Chang and Dover [21]. It was concluded that there is no effect when the ratio αB is greater than the critical value. In the present study, αB for all the joints was assigned to a realistic value of 8 in order to avoid the effect of short brace length.

In order to ease the calculation of SCF, the load in this study was applied such that the corresponding nominal stress was equal to 1 MPa. Using this approach, the value of the stress along the weld toe derived from FE analysis is then equal to the SCF value.

Fig. 2) The mesh generated for a tubular DKT-joint using the sub-zone mesh generation method

Analysis and extrapolation method

According to N’Diaye et al. [22], static numerical calculations of the linear elastic type are appropriate to determine the SCFs in tubular joints. This type of analysis was used in the present study. The Young’s modulus and poison’s ratio were taken to be 207 GPa and 0.3, respectively.

The widely accepted conventional approach for fatigue strength assessment of tubular joints is to use the geometric stresses at the weld toe. According to IIW-XV-E [23], the peak stress is calculated from extrapolating the geometrical stresses at the two points in a linear way to the weld toe position. The minimum and maximum distances from the extrapolation region to the weld toe for chord member are 0.4T and 1.4T respectively; where T is the thickness of chord member. Therefore, the value of peak stress can be calculated as follows:

σ weldtoe = 1.4σ1 - 0.4σ2 (2)

where σ1 and σ2 are the von Mises stresses measured at the distance of 0.4T and 1.4T from the weld toe, respectively.

Verification of the FE model

In comparison with experimental study, finite element analysis is more efficient and convenient for determining the stress distribution along the brace-chord intersection of tubular joints. However, the accuracy of the FEA predictions should be verified by experimental test results. As far as the authors are aware, there is no experimental database of SCFs for steel tubular DKT-joints currently available in the literature. In order to validate the finite element model, several related geometries including T-, Y- and K-joints were modeled and the FE results validated against the LR equations [4] and test results published in HSE OTH 354 report [4].

Verification results which are separately presented at saddle and crown positions are summarized in Table 1. In this table, e1 denotes the percentage of relative difference between the predictions of LR equations and test results, and e2 denotes the percentage of relative difference between the results of FE model and experimental results. Hence, |e1|-|e2| indicates the difference between the accuracy of LR equations and FE model. Positive sign for value of |e1|-|e2| means that the FE model presented in this study is more accurate for predicting the values of SCF in comparison with LR equations. It can be concluded from the comparison of the FE results with experimental data and the values predicted by LR equations that the finite element model is considered to be adequate to produce valid results.

Table 1) Comparison of FE analytical results with experimental data and predictions of LR Eqs. [4]

* e1= (Test-LR Eqs.)/Test ** e2= (Test-FE)/Test *** ζ = 0.15