Maximum Stress Concentration Factor Research Articles

Optimization of fibre orientation for composite reinforcement of circular hollow section KT-joints

PurposeComposite materials are effective alternatives for rehabilitating critical members of offshore platforms, bridges, and other structures. The structural response of composite reinforcement greatly depends on the orientation of fibres in the composite material. Joints are the most critical part of tubular structures. Various existing studies have identified optimal reinforcement orientations for a single load component, but none has addressed the combined load case, even though most practical loads are multiplanar.Design/methodology/approachThis study investigates the optimal orientation of composite reinforcement for reducing stress concentration factors (SCF) of tubular KT-joints. The joint reinforcement was modelled and simulated using ANSYS. A parametric study was carried out to determine the effect of the orientations of reinforcement in the interface region on SCF at every 15° offset along the weld toe using linear extrapolation of principal stresses. The impact of orientation for uniplanar and multiplanar loads was investigated, and a general result about optimum orientation was inferred.FindingsIt was found that the maximum decrease of SCF is achieved by orienting the fibres of composite reinforcement along the maximum SCF. Notably, the optimal direction for any load configuration was consistently orthogonal to the weld toe of the chord-brace interface. As such, unidirectional composites wrapped around the brace axis, covering both sides of the brace-chord interface, are most effective for SCF reduction.Originality/valueThe findings of this study are crucial for adequate reinforcement of tubular joints using composites, offering a broader and universally applicable optimum orientation that transcends specific joint and load configuration.

Parametric study and neural network-based prediction for stress concentration factor of concrete-filled steel tubular T-joint

In this study, an extensive parametric investigation for the stress concentration factor (SCF) of concrete-filled steel tubular (CFST) T-joints was conducted based on a validated finite element (FE) model in which the weld profile, mesh, and contact simulation were specifically and precisely dealt with. Distribution of the SCF on the intersecting line was depicted. Effect of non-dimensional geometric parameters and the elastic modulus of concrete was discussed in detail. Results show that the SCF is monotonically distributed on the intersecting line in the chord side, and the maximum SCF probably located at the crown position. There is the possibility that the maximum SCF of the brace occurs at a position neither the crown nor the saddle. Reducing the length of chord or promoting the elastic modulus of concrete lowers the SCF at most positions, but has no effect on the SCF at chord saddle. A back-propagation neural network (BPNN) model was established, and was trained based on 724 FE results of the SCF from the parametric study. The trained BPNN model predicts the SCF of CFST T-joints with a low error of 14.5%, and it improves the accuracy by 62.0% compared to the current formulae.

Fatigue tests of multiplanar concrete-filled steel tubular KK-joints with inner ring stiffeners

Wind turbine structures are subjected to prolonged cyclic loading, with fatigue issues being particularly prominent. This study aims to investigate the fatigue performance of multiplanar concrete-filled steel tubular (CFST) KK-joints with inner ring stiffeners. Fatigue tests were conducted on these joints, and comparison specimens were designed, including one with a circular hollow section (CHS) tubular joint and another with a CFST joint. The results indicated that the incorporation of inner concrete and ring stiffeners led to a significant reduction in the hot spot stress within tubular joints. The maximum hot spot stress concentration factor (hot-spot SCF) of CFST KK-joints with inner ring stiffeners decreased by 39.7% compared to CHS KK-joints and by 8.7% compared to CFST KK-joints. Furthermore, an increase in the brace thickness-to-chord thickness ratio τ from 0.94 to 1.24 for CFST KK-joints with inner ring stiffeners resulted in a corresponding 74.3% increase in hot-spot SCF. Additionally, fatigue tests were conducted to ascertain the failure modes, crack propagation patterns, and fatigue lives of specimens. These measured fatigue lives were compared with the S–N curves given by different codes. Notably, it was observed that the curve proposed by DNV/CCS exhibited the most suitable correlation with the experimental results.

Stress distribution and failure characteristics around U-shaped caverns with different height-to-width ratios under biaxial compression

Understanding the stress distribution and failure characteristics around a U-shaped cavern is vital to the stability analysis of rock structures such as tunnels and roadways. In this study, the stress distribution around a U-shaped cavern with different height-to-width (h/w) ratios under biaxial compression was first analyzed based on the complex variable theory. Then, numerical simulations were conducted using PFC2D to study the failure process and energy evolution around a U-shaped cavern with different h/w ratios. Theoretical solution shows that the maximum stress concentration factor occurs at the bottom corner of the U-shaped cavern. With the h/w ratio increasing from 0.75 to 3.0, the stress concentration factor around the sidewall shows a declining trend, while the opposite trend is observed in the vault and floor. Numerical results show that when the maximum principal stress is parallel to the vertical direction, the thin slab buckling occurs in the sidewall of the cavern with low h/w ratios (h/w = 0.75 and 1.0), accompanied by the release of relatively high kinetic energy. Instead, the wedged-shaped slab spalling occurs in the sidewall of the cavern with high h/w ratios (h/w = 1.5, 2.0 and 3.0), which can be considered as a static process. Although the U-shaped cavern with low h/w ratios has higher integrity after failure, more stain energy is accumulated in the remaining surrounding rock, which is likely to cause rockbursts under a higher stress state or dynamic disturbance. When the maximum principal stress is horizontal, the rock slab separates from the cavern floor and presents a reverse trend with the increasing h/w ratio. The above results indicate that the h/w ratio and the direction of maximum principal stress should be considered comprehensively in the design of the support system of U-shaped caverns.

Fatigue tests and design of Q460 CHS-CHS T-joints under axial loading and in-plane bending

Previous research has primarily focused on stress concentration factors (SCFs) and fatigue life of tubular joints made from low-strength steel (nominal yield strength of 235–360 MPa). The fatigue behavior of high-strength tubular joints remains insufficiently studied. In this study, a total of sixteen CHS-CHS T-joints fabricated from Q460 steel were designed, eight of which were subjected to axial load and eight of which were under in-plane bending. Static and fatigue tests were conducted to analyze the distribution of hot spot stress, fatigue crack propagation, and fatigue failure modes. The experimental results showed that the crack initiation consistently occurred at location of maximum hot spot stress for all specimens. The maximum SCFs were concentrated at the saddle (90°) for specimens under axial loads and around the position of 22.5° for those under in-plane bending. The modified SCF design formula for in-plane bending was proposed based on regression analysis. Prior to crack initiation, all specimens exhibited a relatively slow stiffness degradation due to cumulative damage from fatigue loading. Through least squares analysis of the test data, the fatigue design Srhs-N curve for Q460 CHS-CHS T-joints was developed. The proposed Srhs-N curve is capable of accurately predicting the fatigue life of Q460 CHS-CHS T-joint subject to axial loads and in-plane bending. Comparison with previous research and existing design guidelines shows that under the same stress amplitude level, the fatigue lives of CHS-CHS T-joints subjected to axial loading of Q460 steel are comparable to that of low-strength steel (WFG36Z). Under in-plane bending, the fatigue lives for Q460 steel are higher than that for low-strength steels (C350L0, t < 4 mm).

An Artificial Neural Network Model for the Stress Concentration Factors in KT-Joints Subjected to Axial Compressive Load

Stress concentration factor (SCF) is usually used to estimate the fatigue life of an offshore joint. Historically, parametric equations were used to estimate SCF based on a statistical analysis of experimental and finite element analysis (FEA) results, to reduce cost and time. These equations give the SCF at the saddle/crown position for simple joints and basic load cases. However, for modified or defective joints, the location of the maximum SCF can change. In such circumstances, the single-point SCF equation cannot be used to estimate the maximum value of SCF, as its location may have changed from saddle/crown. To our knowledge, there are no general expressions to estimate SCF around the brace axis accurately. As artificial neural networks (ANN) can approximate the trend of complex phenomena better than conventional data fitting, a mathematical model based on ANN is proposed to estimate SCF based on the weights and biases of trained ANN. Nine hundred thirty-seven finite element simulations were performed to generate SCF data for training the ANN. This ANN was used to model an empirical equation for SCF. The proposed empirical model can estimate SCF around the brace axis with less than 5% error. The current study provides a roadmap to using FEA and ANN for empirical modeling of SCF in tubular joints, and this approach can be applied to any joint type, with or without design modification or damage. Once a database of similar equations is available, it can be utilized for quickly estimating SCF instead of costly experimentation and FEA. Optimization of the ANN can further improve the accuracy of the developed mathematical model.

Parametric assessment of stress concentration factors for end-to-end joints with rotated SHSs

End-to-end joining of rotated square hollow sections (SHSs) with fillet welded intermediate plates is a novel welded tubular joint that could be well suited for truss chords irregularly crossed in two directions. This paper presents an experiment based finite element (FE) modelling for developing stress concentration factor (SCF) analytical parametric formulae of fully and partially connected cases to fill a gap in the literature limited to SHS-to-SHS joints or T Joints. Typical hot spot stress distributions for the fully connected and partially connected end-to-end joints were revealed from experimental measurement. ANSYS parametric design language was employed by introducing three nonlinear geometric parameters (λ, θm and 2γ) related to the SHS chord and the intermediate plate as main controlling variables, and the novel configurations of crown and saddle areas were accurately simulated. The accuracy of constructed FE models has been validated by comparing with experimental data of six test joints with the variation of θm. The influences of three key geometric parameters and two joint configurations on the SCFs were subsequently examined through a comprehensive parametric study including 400 models. Thereafter, a series of analytical parametric formulae for the prediction of maximum SCFs of the crown and saddle areas of the joints were developed through a multivariate regression analysis and demonstrated to be in good agreement with numerical results.

The Effect of geometric parameters on stress concentration factor of a multiplanar DKT tubular joint through finite element model

It is important to consider geometric parameters on Stress Concentration Factor (SCF) at the tubular joint, especially multi-planar joint, when designing a jacket platform. Thus, a jacket platform capable to withstand the extreme environmental loads. Many researchers use the Finite Element (FE) method to analyze stress at joints and estimate the SCF with the variation of geometric parameters. That studies obtained the result that geometric parameters have significant effect on decreasing or increasing the SCF. Therefore, this study will delve the effect of geometric parameters (β, τ, and γ) on maximum SCF caused by axial loading, in-plane bending moment, and out-of-plane bending moment at DKT tubular joint. The increase of β results in the decrease in maximum SCF at brace-side and chord-side weld toe, respectively. The increase of τ and γ results in the increase in maximum SCF at brace-side and chord-side weld toe, respectively.

Stress concentration factors in FRP-reinforced tubular DKT joints under axial loads

The stress concentration factors (SCFs) in uniplanar fibre-reinforced polymer (FRP) DKT joints are calculated under five axial loading conditions to determine the maximum SCFs. To this end, 108 finite element models of reinforced DKT joints with different FRPs and geometrical parameters are analysed. Available experimental data and formulas are used to validate the finite element models. The validated finite element models are utilized to investigate the effects of the FRP parameters along with different geometrical parameters on the stress concentration factors in uniplanar DKT joints. The simulations show a reduction of the maximum SCF by around 40% compared to unreinforced DKT joints. The reduction effect increases significantly with increasing the FRP thickness and the number of layers. Despite the notable efficacy of the FRP sheets on the drop of the SCFs in the X-connections, there is not any study or equation on the X-joints with FRP. Therefore, a precise equation is proposed for quantifying the SCFs in X-connections with FRP and is checked against the UK DoE acceptance standard.

Fatigue Performance Test and Finite-Element Analysis of Concrete-Filled Steel-Tube K-Joints

To avoid fatigue cracking of K-joints in concrete-filled steel-tube (CFST) truss arch bridges, fatigue performance tests and finite-element analysis were conducted to investigate the hot spot stress distribution, fatigue performance evolution, and final fatigue failure pattern of the CFST K-joints. The results of a CFST K-joint were compared with those of a steel tube (ST) K-joint, to reveal the influence of concrete filled in a chord on the fatigue performance of the CFST K-joint. The results show that the hot spot stress of a CFST K-joint can be obtained by quadratic extrapolation. The stress concentration factor (SCF) on the chord side of the intersecting weld of CFST K-joints is larger than those on the brace side, and the maximum SCF is located at the crown point on the chord side of the intersecting weld connecting the tensioned brace to the chord. Because the constraint action of the core concrete improves the radial stiffness of the chord, making the section radial deformation of the CFST K-joint much smaller than that of the ST K-joint, the in-chord concrete could relieve the SCF of CFST K-joints by 19.5%–49.7%. Since the existing SCF calculation methods of ST K-joints and CFST K-joints do not consider the effect of in-chord concrete or the coupling effect of geometric parameters, they are not applicable to the SCF calculation of CFST K-joints. The fatigue crack growth process of a CFST K-joint can be divided into four stages: crack initiation, slow propagation, rapid propagation, and sharp fracture. The fatigue crack propagation speed of the CFST K-joint is obviously slower than that of the ST K-joint due to the effect of the in-chord concrete. The number of cycles corresponding to the 15% change of the peak dynamic strain is recommended as the fatigue life of the CFST K-joint. An S-N curve for fatigue life evaluation of CFST K-joints is proposed. Comparing with the fatigue test in this paper and existing fatigue test of other CFST joints, the proposed S-N curve for CFST K-joints has high precision and safety.

Field concentration and distribution in three-dimensional magneto-electro-elastic plates with open holes

In this work, the field concentration and distribution along the wall of elliptic holes in three-dimensional thick plates of anisotropic magneto-electro-elastic (MEE) materials are systematically analyzed using a three-dimensional weak finite-element formulation implemented in the COMSOL software. The proposed model is validated against existing solutions, and then applied to the analysis and design of multiferroic composites with an open hole, including multicoated circular fibrous MEE composites and MEE sandwich made of piezoelectric (BaTiO3) and magnetostrictive (CoFe2O4) materials. The distribution of field concentration factor, hoop stress, radial stress, and out-of-plane stress along the wall of elliptic holes for MEE plates under typical far-field uniform loads are analyzed, as well as the influence of hole shape, plate thickness and stacking sequence. Under far-field electric or magnetic fields, various unique features are observed which should be very helpful for strength and fatigue designs of MEE materials with notches and holes. An empirical formula is derived to predict accurately the maximum stress concentration factor along the thickness direction of the elliptical hole.

Mechanical Stress in Rotors of Permanent Magnet Machines—Comparison of Different Determination Methods

In this work, different analytical methods for calculating the mechanical stresses in the rotors of permanent magnet machines are presented. The focus is on interior permanent magnet machines. First, an overview of eight different methods from the literature is given. Specific differences are pointed out, and a brief summary of the analytical approach for each method is provided. For reference purposes, a finite element model is created and simulated for each rotor geometry studied. A total of seven rotors rom representative automotive powertrains are considered in their specific speed range. The analytical methods are used to determine the maximum mechanical stress concentration factors for the seven rotor geometries, in which we are determined to find maximum mechanical stress as a final step of the analytical process. For each geometry and each respective operating speed range, the deviations from the finite element reference are determined. In addition, the error in the selected geometry variations is evaluated. A recommendation for the method with the lowest error considering all cases studied is given specifically for the stress in the airgap bridge and the central bridge.

Analysis of Stress Concentration Factors due to in-Plane Bending and out-of-Plane Bending Loads on Tubular TY-Joints of Offshore Structures

The aim of this work is to study the stress distributions and the location of hot spots stress in the vicinity of the intersection lines of the tubular elements of the tubular TY-joints. Using the finite element models, we analyze the effects of geometrical parameters on the stress concentration factor in the case of in-plane bending and out-of-plane bending loads, around the weld toe of the tubular joints. Our results reveal the location of the maximum stress concentration factor at the heel or toe in the case of in-plane bending loads and at the saddle point in the case of out-of-plane bending loads. Six parametric equations are established and used to calculate the stress concentration factor at critical locations using the non-linear regression method. The results obtained from the finite element analysis are close to the results of the parametric equations and the experimental data from the previous work.

Investigation of polyurethane toughened epoxy resins for composite cryotank applications. Part II: Theoretical analysis of toughening mechanisms

Based on the phase separation phenomenon, cryogenic mechanical behaviors and toughening effects for polyurethane toughened epoxy (PU/EP) systems demonstrated in our previous work (Part I), as a followed investigation, this study aims to conduct theoretical analysis of temperature-dependent toughening mechanisms. First, 3D finite element unit cells of PU/EP systems with random particle distributions are established to evaluate the maximum stress concentration factor for the theoretical fracture energy calculation. Then, the temperature-dependent fracture energies of PU/EP systems are investigated quantitatively for the first time, and the theoretical results are shown to be in good agreement with the experimental results. From 10 phr to 40 phr, the particle bridging contribution rises from 47.3% to 65.5%, which elucidates that the particle bridging plays a major role in determining the fracture energy at room temperature. As the temperature decreases from RT to −183°C, taking PU10/EP as an example, the untoughened matrix proportion goes up from 30.9% to 65.2%; the particle bridging contribution decreases from 51.8% to 27.8%; the shear banding contribution drops from 17.3% to 7%. This work explores temperature-dependent toughening mechanisms in depth and offers an accurate quantitative evaluation of fracture energies for toughened epoxy matrix for composites cryotank design.

Stress Concentration Factors of Concrete-Filled T-Joints under In-Plane Bending: Experiments, FE Analysis and Formulae.

Experimental and numerical investigations on seven cold-formed steel square hollow section (SHS) T-joints with concrete-filled chords were conducted for the determination of stress concentration factors (SCFs). The SCFs were experimentally determined using strain gauges and then numerically determined using Abaqus finite element analysis (FEA) software under static in-plane brace bending. Good agreement was observed between the two investigations. After validating the FEA results, a parametric study was conducted on the SCFs of concrete-filled SHS-SHS T-joints using Abaqus FEA to evaluate the effects of the non-dimensional parameters on the SCFs. Subsequently, design formulae for predicting the SCF of concrete-filled SHS-SHS T-joints subjected to in-plane bending were proposed. Comparable results were obtained between the numerical SCFs with SCFs calculated from the proposed design equations. The maximum SCF of concrete-filled SHS T-joints under in-plane brace bending occurred at different locations. The overall mean of the experimental reduction percentage in peak SCF due to concrete infill is 22% and the overall mean of the numerical reduction percentage in peak SCF due to concrete infill is 19%. The determination of SCFs in concrete-filled SHS-SHS T-joints under in-plane bending has been the subject of little research, and more information regarding the behavior of concrete-filled T-joints with SHS under in-plane bending needs to be provided to practicing engineers.

Stress Concentration Factor in vessels with circular crosshole: Continuous parameters analysis

In this paper, a parametric study of the Stress Concentration Factor (SCF) has been carried out in cylindrical pressure vessels with circular holes. A three-dimensional finite element analysis has been carried out performing a variation of dimensionless parameters (thickness ratio, size ratio and aspect ratio) exploring a wider range than other investigations. It is observed that the maximum value of the SCF increases as the hole size ratio and the aspect ratio increase, although the location of the maximum SCF is located from the internal area of the vessel to the external part depending on the geometric configuration, defining thus three differentiated zones. Additionally, in the final part of the document, a fit model is defined to determine the value of the maximum SCF for different continuous values of the defined dimensionless parameters. This model allows to quickly calculate or locate from a contour map the maximum value of SCF for a specific geometry of pressure vessel.

Stress concentration factor (SCF) of CHS gap TT-joints reinforced with CFRP

The current study focuses on estimating the fatigue life of circular hollow section (CHS) gap TT-joints reinforced with carbon fibre reinforced polymer (CFRP) sheets based on S–N curve method. In the S–N curve, the fatigue life of a tubular joint can be predicted from the hot spot stress (HSS) which can be easily calculated from the stress concentration factor (SCF) of the tubular joint. The SCF and the fatigue life of the CFRP-reinforced and unreinforced TT-joints under axial loads were experimentally measured. The experimental results show that the maximum SCF of CHS TT-joints reinforced with CFRP sheets decreases by 14%, and the fatigue life increases by 47%. Thereafter, finite element (FE) models for both CFRP-reinforced and unreinforced TT-joints were established and verified by the experimental results. A parametric study is also carried out to investigate the effects of the number of CFRP layers and the geometrical parameters on the SCF. Finally, through regression analysis on the numerical SCF results of 704 FE models, parametric equations are proposed to estimate the SCFs at the saddle and at the crown of CFRP reinforced CHS gap TT-joints.

Concentration of stresses near the hole in contact with rigid cylinder in composite plate, taking into account lateral clearances

Problems. When designing bolted joints (BJ), it is necessary, in particular, to carry out their verification calculations for strength. At the same time, it is desirable to use express analysis: calculations by simple formulas of sufficient accuracy. For BJ of plates made of layered polymer composite materials (PCM), the problem has not yet been solved.&#x0D; The aim of the study. The task is to test the accuracy of three known formulas for quick calculation of the value of the stress concentration factor (SCF) in zone of contact of bolt-hole with a rigid cylinder (bolt). The study was carried out on contrasting examples of materials and schemes of reinforcement of plates made of PСM, taking into account possible clearance between bolt and hole in the real range: from zero to 1% of diameter.&#x0D; Methodology of implementation. Numerical calculations were made using the finite element method (contact problem) for the BJ of plates made of layered PCM. 3D orthotropy of each monolayer was provided. Three simple formulas of express analysis were tested. The results are summarized in the tables and many illustrations are given.&#x0D; Research results. Numerical estimates of depending of the SCF in zone of the surface of the bolt-hole from considered factors are obtained. The factors are the material characteristics, the schemes of reinforcement of plates made of layered PСM and the values of the clearance between bolt and hole in the plates, as well as the accuracy of the considered formulas.&#x0D; Conclusions. Changing the material and the scheme of reinforcement of plate made of layered PСM leads to a significant change in the values ​​of maximum stresses and SCF in zone of the bolt-loaded hole in the weakened by hole cross section of a plate. Considered formulas of the express analysis have insufficient accuracy for consideration of contrast properties of materials and schemes of reinforcement of a plate. Changing size of clearance between bolt and hole in the range from zero to 1% of the diameter leads to relatively small changes in SCF: up to 10% maximum. Additional research is needed.

Experimental, numerical and parametric studies on stress concentration factors of T-joints under tension

This paper investigates the behaviour of square hollow section (SHS) T-joints under static axial tension for the determination of stress concentration factors (SCFs) at the hot spot locations. Five empty and corresponding concrete-filled SHS-SHS T-joint connections were tested experimentally and numerically. The experimental investigation was carried out by attaching strain gauges onto the SHS-SHS T-joint specimens. The numerical study was then conducted by developing three-dimensional finite element (FE) T-joint models using ABAQUS finite element analysis software for capturing the distribution of the SCFs at the hot spot locations. The results showed that there is a good agreement between the experimental and numerical SCFs. A series of formulae for the prediction of SCF in concrete-filled SHS T-joints under tension were proposed, and good agreement was achieved between the maximum SCFs in SHS T-joints calculated from FE T-joint models and those from the predicted formulae.

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.