Distribution Of Stress Concentration Factors Research Articles

Stress Concentration Factors of Concrete-Filled Double-Skin Tubular K-Joints

Tubular joints are important connecting parts of a welded steel tube structure. The S-N curves based on the hot spot stress (HSS) method are often used to evaluate the fatigue life of tubular joints in practical engineering. The stress concentration factor (SCF) is a key parameter to calculate HSS. In this paper, stress concentration tests of hollow-section and concrete-filled double-skin tubular (CFDST) K-joints were carried out, respectively, and then finite element models of K-joints considering the weld were established. The developed models were validated with the experimental results. The influence of key geometrical parameters, such as the diameter ratio of brace to chord β, the diameter to thickness ratio of chord γ, the wall thickness ratio of brace to chord τ, brace angle θ, and hollow section ratio ζ on the distribution and key position of SCFs along the weld toe, was discussed. Parametric studies were conducted to obtain the calculating equations for the SCF values of CFDST K-joints. The results demonstrate that infill concrete can effectively reduce SCFs along the weld on the chord. When the hollow section ratio was reduced to 0.317, the SCF was reduced by 77.2%. Notably, the SCF reduction rate was sensitive to γ and θ, with a decrease observed as γ increased. The hollow section ratio ζ had a less pronounced effect on SCF distribution patterns, but as ζ decreased, the chord’s stiffness improved, suggesting a potential approach to enhance joint performance. The distribution of SCFs is similar for joints of the same type but different geometric configurations. The innovatively integrated hollow section ratio in the CFDST design equation significantly simplifies and enhances the precision of SCF calculations for CFDST K-joints.

Quantitative surface characterisation and stress concentration of additively manufactured NiTi lattice struts

With the advancement of metal additive manufacturing (AM), lattice structures become a promising solution to situations that require lightweight design and yet maintain adequate mechanical strength. Limited by the quality of feedstock materials, the layer-wise process characteristic and the dynamic nature of thermal environment, lattice structures made by AM often suffer from process-induced imperfections such as poor surface finish and notable geometric deviation. In this study, systematic quantitative characterisation methods are developed to address surface quality and geometric discrepancy of NiTi lattice struts made by laser powder bed fusion (LPBF), with a special focus on fatigue-related features such as stress concentration factors. The results show that for the examined strut diameters and inclination angles, the strut diameter plays a significant role in geometry inaccuracy and the inclination angle has a greater effect on surface texture and stress concentration factor distribution on the surface. Lattice struts with diameters greater than 0.7 mm and inclination angles over 40° with respect to the platform exhibit superior manufacturing quality among all configurations of the struts. The proposed approach not only opens a new avenue to evaluate μ-CT data in a more quantitative way but also offers opportunities to develop guidelines for lattice structure design.

Bending load effects on stress concentration factor distribution of multi-planar DTKY tubular joints

The stress concentration factor (SCF) in tubular joints is an important parameter in calculating the fatigue life of offshore structures. In design practices, estimating the SCF is usually based on standard empirical formulas, providing the majority for uni-planar tubular joints, and could not be applied directly for multi-planar joint cases. Therefore, accurate SCF estimation became critical for specific multi-planar tubular joints commonly found as members of offshore platforms. More detailed analyses of complex designs are possible with the recent development of finite element analysis and supported by advanced digital computers. Thus, this research is intended to analyze the SCF of multi-planar DTKY tubular joints with finite element analysis. The local model of the tubular joint will be simulated for bending moment load cases. The results show stress distribution characteristic of the joint at both brace and chord sides. The results indicated that the SCF of the joint under the in-plane bending (IPB) loading is higher at the brace than the chord side, with values of 2.83 and 1.47, respectively. Meanwhile, under the out-of-plane bending (OPB) loading, the SCF is 2.43 at the chord saddle location and 3.54 at the brace saddle location.

Experimental and numerical analyses on stress concentration factors of concrete-filled welded integral K-joints in steel truss bridges

A novel fully welded concrete-filled integral K-joint incorporating longitudinal perfobond ribs welded to the inner faces of the chord is proposed to improve the fatigue behavior. To evaluate the stress concentration factor (SCF) of such joints, a 1:5 scale truss specimen was fabricated and tested to measure the SCF distribution in the fatigue prone joint. A finite element model was also developed to evaluate the SCFmax of concrete-filled welded integral K-joints and was validated against the test results. A parametric study was carried out and a comprehensive database was obtained considering the effects of brace width-to-chord thickness ratio (2γ), brace-to-chord thickness ratio (τ), the angle between braces and chord (θ) on the SCFmax. Also, the following three basic loading conditions were examined: brace axial force, chord axial force and chord in-plane bending. Based on the results of 192 numerical models, new equations to predict the SCFmax of concrete-filled welded integral K-joint were derived for design purposes. Finally, the fatigue behavior of three different designs is compared in terms of SCFmax and hot spot stress range Sh-N curves. These systems are rectangular hollow section (RHS) K-joints, concrete-filled rectangular hollow section (CFRHS) K-joints and concrete-filled welded integral K-joint. It was shown that the concrete-filled integral welded K-joint has the best fatigue behavior, followed by the CFRHS K-joint, while the RHS K-joint has the poorest fatigue behavior.

Stress concentration factor distribution formulas for three-planar tubular Y-joints under axial force

As the key joint of a tripod substructure supporting offshore wind turbines (OWTs), the three-planar tubular Y-joint is normally multiplanar loaded with severe multiplanar interaction effect, which may cause the hot spot stress (HSS) to occur at places other than the crown or saddle points of the weld seam. Thus, the distributions of stress concentration factor (SCF) and multiplanar interaction factor (MIF) along weld seam are required to calculate HSS, rather than formulas only representing the values at the crown or saddle points. To fulfill this demand, a series of works are carried out in this study focusing on the stress distribution along the weld seam of three-planar tubular Y-joint under axial force. A numerical database covering a common range of parameters in practice is established using the validated finite element (FE) analysis method. Sensitivity analyses for five geometric parameters affecting the distribution along weld toe curves of SCF and MIF are conducted. Formulas for predicting SCF and MIF distributions are proposed after the multiple nonlinear fitting based on the information provided in sensitivity analyses. The accuracy and reliability of proposed formulas are verified against acceptance criteria, a numerical database and new models.

Artificial Neural network-based prediction of SCF at the Intersection of CFST Y-joints

Stress concentration factors (SCFs) are used to quantify the hot-spots stress in tubular joints with circular hollow section for fatigue assessment, which are always obtained by finite element analysis or specimens testing. According to design specifications, complex formulas are recommended to calculate the SCFs at special locations of the intersection lines weld toe of tubular joints for individual load cases. To improve the fatigue performance of the joint, the concrete is filled in the chord to form a concrete-filled steel tube (CFST) joint. The capability of back-propagation neural network-based (BPNN) model in calculation of the SCFs in CFST Y-joints was investigated in this study. Three hundred FE numerical models were investigated to evaluate the effects of changes in different geometrical parameters on the SCFs of CFST Y-joint and the FEA results were used to train and test the neural networks. The nonlinear mapping relationships between the affecting variables and the SCFs distributions were established. Research results showed that SCFs prediction results of CFST Y-joints from BPNN models are close to the FE results, and properly trained and well calibrated BPNN can be reliable alternatives to complicated SCFs equations for predicting SCFs distribution at intersection line of CFST Y-joints.

Experimental study of hot spot stress for three-planar tubular Y-joint: I. Basic loads

Various tubular joints of offshore wind turbines (OWTs) have seen rapid development in the past decades. However, experimental studies on multiplanar tubular joints have mainly been underexplored. This study designed and constructed a multiplanar loading experimental system for multiplanar tubular joints. A model test was performed using this system to investigate the hot spot stress (HSS) of a three-planar tubular Y-joint, which is critical for the fatigue design of a tripod substructure. The HSS distribution along the weld seams under the 12 basic load cases was obtained from the test analysis. The geometric stresses at the key positions of the chord and brace sides were obtained and analysed. The peak values of stress concentration factor (SCF) were obtained and compared with those calculated using the method recommended by the codes. An indirect method that explicitly considers the interaction between multiple braces was proposed and verified to calculate the SCF distribution of multiplanar tubular joints.

Parametric study on SCF distribution along the weld toe of internally ring-stiffened two-planar tubular KK joints under axial loading

The internal ring stiffeners have been commonly introduced in tubular joints to improve the ultimate strength and fatigue life of offshore structures. However, for internally ring-stiffened multi-planar tubular joints which are frequently used in practical application, few investigations about stress concentration factor (SCF) in the joints have been reported so far and no parametric equation of the SCF is currently available for fatigue design. In this paper, the effects of geometrical parameters on the SCF distribution along the weld toe of the internally ring-stiffened two-planar tubular KK joints under axial loading are investigated by performing a set of three-dimensional (3D) FE stress analyses. Firstly, based on the requirements of AWS D1.1-2010, an approximate model of the actual weld profile is proposed. Then, several 3D FE models of various tubular joints are established to verify the proposed model. Subsequently, the effects of multi-planarity and stiffeners on the SCF in two-planar tubular KK joints are investigated. Additionally, the influence of geometrical parameters on both the SCF and the SCF distribution of the joints under axial loading is studied. Finally, SCF parametric equations for fatigue design of the internally ring-stiffened two-planar tubular KK joints under axial loading are developed from nonlinear regression analysis.

Probabilistic analysis of the SCFs in tubular T/Y-joints reinforced with FRP under axial, in-plane bending, and out-of-plane bending loads

The stress concentration factor (SCF) is one of the most important parameters in the fatigue reliability analysis of tubular offshore structures. This parameter exhibits remarkable scatter which calls for more emphasis in accurately computing the SCFs for determining the fatigue life. As per the authors’ knowledge, no study has been conducted on the probability distribution of SCFs in tubular joints with FRP. Therefore, in this study, results of performing 288 FE analyses on 96 T/Y-joints with FRP have been used to propose a probability distribution model for SCFs in the FRP-reinforced joints subjected to axial, IPB, and OPB loads. According to the T/Y-connection FE models which were validated with several experimental tests, a set of SCF sample databases was generated. 11 various probability density functions (PDFs) were fitted to the relative frequency histograms of the SCF samples. For determining the parameters of every distribution, the maximum likelihood method was applied. Evaluating the goodness-of-fit according to the Chi-squared and Kolmogorov-Smirnov tests indicated that the Weibull distribution is the best one for the maximum SCF values in tubular T/Y-connections retrofitted with FRP under axial load. Also, the Gamma distribution was set as the governing probability function for T/Y-joints with FRP under IPB and OPB loads. In the final step, five fully defined PDFs were proposed for the maximum weld SCFs of in T/Y-joints with FRP under three different types of loadings.

Stress concentration factors around a circular hole in two fiber reinforced materials under large deformations

In this paper, we study the deformation and the stress concentration factor due to a small circular hole in a thin nonlinearly elastic large sheet reinforced by two families of fibers under a state of plane stress undergoing large deformations. We restrict our attention to the class of materials wherein the fibers are mechanically equivalent, rendering the body orthotropically symmetric with respect to the planes whose normals are along the angular bisectors of the angles between the fibers. Furthermore, we limit ourselves to the problems of equibiaxial, uniaxial and pure shear deformations of the body whose fibers are symmetrically oriented with respect to the Cartesian coordinate axes. These deformations indicate strong influence of the fiber angle on the stress concentration factors and a significant difference in the stress concentration factor distribution around the hole when using a constitutive relation based on a partial set of invariants (I4,I6) versus an extended constitutive relation that incorporates the full set of invariants appropriate for a body reinforced with fibers and reduces appropriately to the orthotropic linearized elastic case. We show how two constitutive relations that exhibit a similar biaxial behavior in the absence of discontinuities show noticeable differences under uniaxial and pure shear deformation with the dissimilarities magnified in the presence of discontinuities like a circular hole.

Prediction of elastic stresses in porous materials using fully convolutional networks

Machine learning (ML) models enable exploration of vast structural space faster than the traditional methods, such as finite element method (FEM). This makes ML models suitable for stochastic fracture problems in brittle porous materials. In this work, fully convolutional networks (FCNs) were trained to predict stress and stress concentration factor distributions in two-dimensional isotropic elastic materials with uniform porosity. We show that even with downsampled data, FCN models predict the stress distributions for a given porous structure. FCN predicted stress concentration factors 10,000 times faster than the FEM simulations. The FCN-predicted stresses combined with fracture mechanics captured the effect of porosity on the strength of porous glass. Increasing variations in pore size increased the variations in fracture strength. Furthermore, the FCN model predicts the pore configurations with the lowest and highest stresses from a set of structures, enabling ML optimization of porous microstructures for increased reliability.

Influence of weld geometry on stress concentration factor distributions in tubular joints

Fatigue design of welded tubular joints relies on an extensive number of parametric equations that allow calculation of the stress concentration factors at characteristic locations around the weld circumference. These equations were developed with finite element models that either do not include a weld geometry or include a simplified representation thereof. This paper presents a new approach for modeling American Welding Society D1.1 standard compliant welds with different geometries. The generated finite element models are used to study the effect of different weld geometries on the stress concentration factor distributions in tubular joints. The results show that the geometry of the weld has a strong influence on the magnitude of the critical stress concentration factor, the shape of the stress concentration factor distribution and the expected failure location. Finally the authors highlight the need for more comprehensive guidelines regarding the determination of complete stress concentration factor distributions from finite element simulations.

A numerical framework for determination of stress concentration factor distributions in tubular joints

Fatigue design of welded tubular joints implies the calculation of stress concentration factors at distinct weld toe locations using parametric formulas for basic loading cases. A Python based framework for automated calculation of hot spot stress and stress concentration factor distributions along the entire weld is presented. Hot spot stresses are calculated based on extrapolation of surface stresses extracted from a finite element analysis output database. For each node of the weld toes, the extrapolation direction and location dependent distances are first determined. Next the complete stress tensor in each read-out point is extrapolated towards the weld toe. The hot spot stress is determined as the maximum value of three critical stress values following the guidelines of DNV.A validation study is carried out in which the framework results are compared to both experimental data and parametric equations from literature for three different load cases: axial loading, in-plane bending and out-of-plane bending. The results obtained from the developed framework show good agreement with the experimental results and capture the shape of the stress concentration factor distribution much better than reference parametric equations. Finally, the framework is used to demonstrate the importance of including the weld geometry in the finite element model of the tubular joint. The results show that using a model without a weld can result in overly conservative estimations of stress concentration factors.

Prediction of Elastic Stresses in Porous Materials Using Fully Convolutional Networks

Machine learning (ML) models enable exploration of vast structural space faster than the traditional methods, such as finite element method (FEM). This makes ML models suitable for stochastic fracture problems in brittle porous materials, where large number of tests are needed to understand the origins of the variations in fracture strength. In this work, fully convolutional networks (FCNs) were trained to predict stress and stress concentration factor distributions in two-dimensional isotropic elastic materials with uniform porosity. We show that even with downsampled data, the FCN models predict the stress distributions for a given porous structure. Stress concentration factors were predicted with a mean prediction performance greater than 0.94. FCN predicted stress concentration factors >104 times faster than the FEM simulations. Furthermore, the FCN model predicts the pore configurations with the lowest and highest stresses from a set of structures, enabling ML optimization of porous microstructures for increased reliability.

EXPERIMENTAL STRESS CONCENTRATION FACTOR IN CONCRETE-FILLED STEEL TUBULAR T-JOINTS

An experimental investigation of stress concentration factor (SCF) in Steel circular hollow section brace welded to concrete-filled circular hollow section chord (CHS-to-CFCHS) T-joints has been performed under axial tension, axial compression, in-plane bending and out-of-plane bending. The distribution of SCF around the welded brace-to-chord intersection on both the brace and chord has been investigated using three CHS-to-CFCHS T-joint specimens. The experimental SCF results have been compared with the predicted SCF in empty T-joints. The relationship between the maximum SCF in relation to parameter β, with fixed other geometrical parameters, has been investigated for the basic load conditions. The experimental maximum SCF under axial tension has been compared with the predicted maximum SCF from parametric equations for CHS-to-CFCHS T-joints previously developed by the authors. The results show that the concrete has a significant effect in reducing the SCF, mostly under axial tension and the parametric equations for predicting SCFs in empty T-joints are not suitable for CHS-to-CFCHS T-joints. The effect of parameter β on the maximum SCF in CHS-to-CFCHS T-joints is significant under axial tension and out-of-plane bending moment.

Prediction of stress concentration factor distribution for multi-planar tubular DT-joints under axial loads

The stress concentration factor (SCF) plays an important role in the fatigue life assessment of tubular joints. Although various SCF parametric equations have been proposed for uni-planar tubular joints, only few are focused on multi-planar tubular joints. In the present study, the finite element (FE) method was employed to investigate the SCF distributions along the chord–brace intersection of multi-planar DT-joints. A method of sub-zone mesh generation was developed to ensure good quality and an appropriate number of FE meshes. The effects of the geometrical parameters on the SCF distributions were investigated. A set of equations was proposed based on the results of the FE analysis. Two types of error analysis were used to verify the reliability of developed equations.

Stress concentration factor distribution of inclined brace in multiplanar offshore tubular double kt joints

The majority of tubular joints commonly found in offshore structures are in the form of multi-planar tubular joints, but very few investigations have been reported due to the complexity and high cost involved. The majority of research have been focused on the study of stress distribution at certain position such as saddle and crown points, and the hot spot stress (HSS) at other position along the weld toe of brace/chord intersection have been ignored. In this paper a 60° two-planar double KT (DKT) tubular joint is modelled as a finite element model from an offshore jacket platform. The effect of dimensionless geometrical parameters on the geometrically stress distribution and SCF distribution along the weld toe of inclined brace in axially loaded on the joint are investigated. Non-dimensional parameters that are varied include β, τ, γ and θ. Validation of the finite element model shown a good agreement to the global structural analysis results. The results of parametric studies show that the increase of the β leads to decrease of SCF. While the increase of the τ, γ and θ leads to increase of SCF. The peak SCF mostly occurs at the outer saddle point. The effect of parameters β, γ and θ on the SCF are greater than the effect of parameters τ.

Formulation of stress concentration factors for concrete-filled steel tubular (CFST) T-joints under axial force in the brace

CFST T-joints consisting of a concrete-filled circular chord and a circular hollow section brace have been used in CFST trussed arch bridges. The stress concentration factors (SCFs) of CFST T-joints have been found to be much lower than those of circular hollow section (CHS) T-joints in the existing researches. At present, no parametric formulae have been proposed for SCFs determination for fatigue design of CFST T-joints. In this study, three-dimensional finite element (FE) models of the existing experiments for CFST T-joints were developed to determine the SCFs distribution at the chord-brace intersection under axial force in the brace. After confirming the validity of the FE models by the comparison of calculated SCFs with existing experimental results, they were provided for the parametric analysis to reveal the influence of four non-dimensional parameters, i.e. diameter ratio (β), diameter to thickness ratio of chord (2γ), thickness ratio (τ) and relative chord length (α), on SCFs of CFST T-joints. In total, 212 FE models with different parameters were analyzed under tensile and compressive axial forces. Based on the results of parametric analysis, a series of parametric formulae to calculate the SCFs was proposed for CFST T-joints referring to those for CHS T-joints. The SCFs determined by the formulae showed good agreements with FE analysis results.

SCF distribution in FRP-strengthened tubular T-joints under brace axial loading

The present article is dedicated to study of the effects of different parameters of fiber reinforced polymers (FRP), as strengthening material, on a tubular T-joint subjected to brace axial loading using finite element analyses. The effectiveness of FRP materials on enhancing the fatigue life of tubular T-joints was investigated through computing the ratio of the stress concentration factors (SCFs). FRP parameters which is considered include fiber orientation, FRP thickness, effective wrapping length and FRP material properties. The FRP materials were modeled and applied onto a basic numerical FE model which was validated in the past against well-known experimental results on weld-toe SCFs. Promising results were derived from the analyses showing that the FRP strengthening method can effectively decrease the SCF values for tubular T-joints.

Stress Concentration Factor of A Two-Planar Double KT Tubular Joint due to In-Plane Bending Loading in Steel Offshore Structures

The purpose of this study is to investigate the proper Stress Concentration Factor (SCF) of a 60° two-planar DKT tubular joint of a tripod wellhead offshore structure. So far, calculation of SCF for a multi-plane tubular joint was based on the formulation for the simple/uniplanar tubular joints that yield in over/under prediction of the SCF of the joint. This situation in turn decreasing the accuracy of fatigue life prediction of the structures. The SCF is one of the most important parameters in the tubular joint fatigue analysis. The tubular joint is modelled as finite element models with bending loads acting on the braces that cover a wide range of dimensionless geometrical parameters (β, τ, γ). The effect of such parameters on the SCF distribution along the weld toe of braces and chord on the joint are investigated. Validation of the finite element model has shown good agreement to the global structural analysis results. The results of parametric studies show that the peak SCF mostly occurs at around crown 2 point of the outer central brace. The increase of the β leads to decrease the SCF. While the increase of the τ and γ leads to increase the SCF. The effect of parameter β and γ on the SCF are greater than the effect of parameter τ.