Tubular K-joints Research Articles

Mode mixity for tubular K-joints with weld toe cracks

This paper examines the mode-mixity of stress-intensity factors for surface cracks located near weld toes of the crown point at the toe of the tension brace in circular hollow section K-joints under different chord/brace end constraints. The remote loading applies a uniform stress at the end of the brace along its axis. The 3-D finite element models employ mesh-tieing between a topologically continuous, global mesh and a separate, local crack-front mesh. The linear-elastic analyses compute the mixed-mode stress-intensity factors along the crack front using an interaction-integral approach. The analyses for three different crack locations along the brace–chord intersection demonstrate that the critical location for the surface flaw lies at the crown point of the brace toe. The numerical investigation of six different boundary conditions indicate that the unbalanced loading conditions cause significant bending stresses in the chord and generate a considerably larger mode I stress-intensity factor than found for the balanced loading case. The mixed-mode stress-intensity factors indicate that the crack front experiences predominantly mode I loading, with K III → 0 near the deepest point on the front ( ϕ = π/2). The non-dimensional, mode I crack driving force, described by F I = K I / σ ¯ br π a , reaches a maximum value at the deepest point of the crack for the crack aspect ratio a/ c = 0.25 considered here. The mode-mixity angle, ψ = tan −1( K II/ K I), at ϕ = π/2 is compared for a range of practical K-joint configurations. The present study demonstrates that the mode-mixity angle ψ becomes significantly larger in the balanced loading conditions than in the unbalanced loading condition. Values of the non-dimensional stress-intensity factors ( F I = K I / σ ¯ br π a and F II = K II / σ ¯ br π a ), however, decrease for the balanced loading condition. Variations in the brace-to-chord diameter ratio ( β) and chord radius to wall thickness ratio ( γ) generate significant changes in the mode mixity. Thin-walled joints ( γ = 20) generally experience a larger crack driving force with a higher mode-mixity angle.

Stress Intensity Factor Solutions for Semi-Elliptical Weld-Toe Cracks in Tubular K-Joints

Stress intensity factors (SIFs) are generally used to predict the remaining life of cracked tubular K-joints used in the offshore structures. The accuracy of SIFs depends very much on accurate modelling of the surface crack. In this paper, a new mesh generation method is proposed for any cracked tubular K-joint where five types of elements are adopted in modelling the surface crack so as to avoid high elements aspect ratio around the crack front. The mesh of any K-joint is obtained by merging the mesh of several distinct regions, and each region is generated separately according to different requirements. To check the accuracy of the computed SIFs, two large scale K-joint specimens were tested to failure under fatigue loading conditions. The alternating current potential drop (ACPD) technique is used to monitor the rate of crack propagation of the surface crack located at the crown position. The experimental test results are then used to validate the numerical results. Generally, they agree well and the relative errors are acceptable.

Experimental study on the fatigue behaviour of welded tubular K-joints for bridges

Fatigue tests were carried out on welded circular hollow section K-joints typical to bridges. The tests specimens were large-scale (approximately 9 m long and 2 m high) trusses loaded in the plane of the truss. Measured member stresses showed that a significant proportion of the load in a truss member may be due to bending, underlining the importance of considering correctly this load case in the design of these structures. Measured hot-spot stresses in the joints were compared with hot-spot stresses calculated using the current design guidelines. It was found that the measured values are considerably lower than the calculated values, calling into question the applicability of the design guidelines to these types of (bridge) structures. The S – N fatigue results from the current study, on the other hand, showed that the fatigue resistance of the joints that were tested is lower than the corresponding S – N design curves. This means that when the considerably higher calculated hot-spot stress range is applied to the corresponding design curve, the predicted resistance is similar to the resistance predicted using the lower measured hot-spot stresses in combination with the lower measured S – N curve too. This has highlighted the importance of relating hot-spot stresses to the appropriate, corresponding S – N curves. Evidence from the fatigue tests has clearly demonstrated the effect of size on the fatigue strength of welded tubular joints. A comparison of fatigue S – N results from smaller and larger welded circular hollow section (CHS) joints has shown the same trend indicated in design specifications: a thicker failed member results in a lower fatigue strength. The size correction factor integrated into the S – N design curves of the specifications, however, does not seem to represent this significant effect justly. In light of the size effect results presented in this paper and the major influence of this effect on the design of welded CHS joints in general, it is recommended that a soundly based solution with targeted S – N curves and a representative size effect should be sought.

Parametric Equation of Stress Intensity Factor for Tubular K-joints under In-plane Bending Load

Stress intensity factor (SIF) is frequently used by designers to predict the integrity and residual life of a tubular joint containing a surface crack. In this study, a new numerical modelling method for cracked tubular K-joints has been presented. The proposed model has been verified from experimental results to be accurate and reliable in evaluation of the stress intensity factor for any tubular K-joint with a surface crack. Thereafter, parametric study for more than five thousand numerical models of tubular K-joints with a surface crack subjected to balanced in-plane bending load (IPB) has been carried out. A parametric equation to estimate the SIF value of any cracked tubular K-joint under IPB is then proposed based on the computed numerical results. Error analysis has been also carried out and it shows that the proposed equation can provide reliable and accurate estimation of the SIF value for cracked tubular K-joints under IPB.

Validation of surface crack stress intensity factors of a tubular K-joint

Tubular K-joints are encountered widely in offshore structures, and the prediction of damaged joints depends very much on the accuracy of stress intensity factor solutions (SIFs). No parametric equations and very few results have been proposed and published in the literature for estimating the SIFs of any K-joints subjected to complex loading conditions. In this paper, a mesh generation method proposed previously for the Y-joint and T-joint has been extended to the K-joint. This method is realized by dividing the K-joint into several sub-zones with each zone consisting of different types of elements and mesh densities. This method has a distinct advantage of controlling the mesh quality, and most importantly the aspect ratio of the elements along the crack front. When the mesh of all the sub-zones has been generated automatically and completely, they are merged to form the complete model. The two most commonly used methods, namely the J-integral and displacement extrapolation, are used to evaluate the SIF values along the crack front of a typical K-joint. To validate the accuracy of these computed SIFs, a full-scale K-joint specimen was tested to failure under fatigue loading conditions. The standard alternating current potential drop (ACPD) technique was used to monitor the rate of crack propagation of the surface crack located at the hot spot stress region. Using the given material parameters C and m, the experimental SIFs were deduced, and they are found to be in good agreement with the computed SIFs obtained from the generated models. Hence, the proposed finite element models are both efficient and reliable.

Experimental and numerical analysis of fatigue behaviour for tubular K-joints

In this paper, a full-scale K-joint specimen was tested to failure under cyclic combined axial and in-plane bending loads. In the fatigue test, the crack developments were monitored step by step using the alternating current potential drop (ACPD) technique. Using Paris` law, stress intensity factor, which is a fracture parameter to be frequently used by many designers to predict the integrity and residual life of tubular joints, can be obtained from experimental test results of the crack growth rate. Furthermore, a scheme of automatic mesh generation for a cracked K-joint is introduced, and numerical analysis of stress intensity factor for the K-joint specimen has then been carried out. In the finite element analysis, J-integral method is used to estimate the stress intensity factors along the crack front. The numerical stress intensity factor results have been validated through comparing them with the experimental results. The comparison shows that the proposed numerical model can produce reasonably accurate stress intensity factor values. The effects of different crack shapes on the stress intensity factors have also been investigated, and it has been found that semi-ellipse is suitable and accurate to be adopted in numerical analysis for the stress intensity factor. Therefore, the proposed model in this paper is reliable to be used for estimating the stress intensity factor values of cracked tubular K-joints for design purposes.

Analysis of stress intensity factor (SIF) for cracked tubular K-joints subjected to balanced axial load

Numerical modelling of cracked tubular K-joint is presented in this study. A new mesh generator for a tubular K-joint with a surface crack was developed and finite element analysis of stress intensity factor (SIF) for cracked K-joint was conducted by using the proposed numerical modelling. Numerical results of SIF were then verified from experimental tests on a full-scale K-joint specimen. The verifications show that numerical results agree reasonably well with experimental results. Based on the accuracy of numerical analysis, 5120 numerical models of K-joints subjected to balanced axial load were analyzed. SIF results of these numerical models were used to build up a database. An interpolation method was introduced to calculate SIF of each model in a valid range by using the analyzed SIF results in the database. The accuracy of the SIF obtained from interpolation method was verified from 972 numerical models which were also analyzed from finite element analysis. The comparisons between SIFs from interpolation method and numerical results show that the introduced interpolation method can provide accurate SIF values for cracked tubular K-joints and thus it is both reliable and efficient to be used in design in practice.

Parametric equation of stress intensity factor for tubular K-joint under balanced axial loads

In this paper, an automatic mesh generation method, which is for a uni-planar tubular K-joint containing an arbitrary surface crack located along the chord weld toe, is developed for producing the complete finite element mesh model. Using the proposed model, the stress intensity factors along the crack front have been evaluated by an interaction J-integral method in this study. To evaluate the reliability and accuracy of the numerical stress intensity factor results, a full-scale K-joint specimen was tested to failure. Using alternating current potential drop (ACPD) technique, the crack growth rate is captured and the stress intensity factors of the specimen are obtained using Paris' equation. It has been found that numerical stress intensity factor results agree with experimental results quite well. Thereafter, altogether 5120 numerical models of tubular K-joints containing a surface crack at the crown subjected to balanced axial loads have been analyzed. A parametric stress intensity factor equation has then been proposed. The accuracy of the proposed stress intensity factor equation has been assessed by comparing the computing results from the equation with the numerical results. Error analysis has been conducted and it shows that the proposed equation can provide reliable and accurate estimation of stress intensity factor for cracked tubular K-joints under balanced axial loads.

Mesh modelling and analysis of cracked uni-planar tubular K-joints

In this paper, a new modeling method is proposed for a uni-planar tubular K-joint containing an arbitrary surface crack located along the chord weld toe. The crack is defined first in a 2-D plane and then mapped onto a 3-D curved crack surface. Subsequently, an automatic mesh generation is developed for producing the complete finite element mesh model. This technique can be realized by sub-dividing the entire structure into distinct zones. In each zone, the mesh is generated separately. After the mesh of all the zones have been completed, the complete model is obtained by merging the mesh of every zone. It has been proved to be efficient and effective in producing different quality mesh at different zones. In order to locate the likely crack initiation position, the hot spot stresses and hence the stress concentration factors (SCFs) need to be determined precisely. The hot spot stress correlated to the number of cycles, i.e. the S–N curve, has been used to predict the life of uncracked tubular K-joints. For a cracked tubular K-joint, its remaining service life depends on the fracture parameter called the stress intensity factors (SIFs). Two different methods, namely the displacement extrapolation and J -integral methods, are used to evaluate the SIFs along the crack front for different crack shapes in this study. Convergence tests for numerical analysis have been carried thoroughly to check the accuracy of the computed SIFs. The two sets of numerical results are in complete agreement. To evaluate the accuracy of numerical modeling, a full-scale fatigue test on tubular K-joint subjected to combined axial load and in-plane bending load was conducted. Comparison between the numerical and experimental results again shows a good agreement. Therefore, the proposed modelling and mesh generation methods demonstrate that the estimated stress intensity factors for any tubular K-joints are both accurate and reliable.

Proposed Equations of Stress Concentration Factor (SCF) for Gap Tubular K-Joints Subjected to Bending Load

In this paper, geometrical and numerical modelling for tubular K-joints has been presented. Stress concentration factors (SCFs) along the weld of the joint have been obtained from an experiment on a K-joint specimen subjected to in-plane bending (IPB) load. Experimental results showed that numerical analysis by using the above models is accurate enough. Therefore, this numerical modelling technique can be safely and accurately used to analyze SCF of K-joints. Based on this, about 1,000 numerical models have been analyzed for K-joints under IPB in a special range. Equations to predict SCF of K-joints under IPB thus have been proposed by using curve fitting from numerical analysis results. The equations were validated by comparing with other equations. The comparisons show the proposed SCF equations are accurate enough and thus it is possible to apply these equations in practice conveniently and safely.

Experiments on concrete filled and reinforced tubular K-joints of truss girder

This paper describes an experimental study on the ultimate strength and fatigue strength of concrete filled and additionally reinforced tubular K-joint of truss girder. The loading condition, which was balanced depending on axial reaction load on diagonal members, represented the main live load pattern on the joints of a chord member and diagonal members on a railway truss. Six different types of specimens of the static test, composed of concrete non-filled, concrete filled and reinforcement, were used. The static test results indicated that the ultimate load resistance of the concrete filled specimen was about twice that of the concrete non-filled specimen. However, to reduce localized stress at the weld toe of the joint, reinforcement was needed. Therefore, one fatigue specimen was selected from static test specimens and two fatigue specimens were designed from the viewpoint of fabrication facility. The lapped joint specimen whose centerlines of members meet at one point and the specimen with the gusset are appropriate for the joint of the chord and the diagonals.

FATIGUE PERFORMANCE OF COMPOSITE TUBULAR K-JOINTS FOR TRUSS TYPE BRIDGE

The structural performances of composite tubular K-joint leading to real truss bridge construction of high speed Shinkansen train are presented. The experimental studies on improving the fatigue performance of welded steel tubular joints by upgrading the structural joint details and improving the weld toe profiles were carried out on ten tubular K-joints under repeated constant amplitude load. The behaviour of all joints were examined through the analyses and the tests. The results suggest that concrete filled tubular joints are able to improve the fatigue strength substantially compared to unfilled joint.

FATIGUE PERFORMANCE OF COMPOSITE TUBULAR K-JOINTS FOR TRUSS TYPE BRIDGE

The structural performances of composite tubular K-joint leading to real truss bridge construction of high speed Shinkansen train are presented. The experimental studies on improving the fatigue performance of welded steel tubular joints by upgrading the structural joint details and improving the weld toe profiles were carried out on ten tubular K-joints under repeated constant amplitude load. The behaviour of all joints were examined through the analyses and the tests. The results suggest that concrete filled tubular joints are able to improve the fatigue strength substantially compared to unfilled joint.

Design Equation for Overlap Tubular K-Joints under Axial Loading

Using a previously presented finite-element study of axially loaded overlap tubular K-joints as a platform, this paper presents further work that aimed at extending and enhancing the strength estimation equation already presented. The current work includes extending the θ (brace angle) validity range to 30° ≤ θ ≤ 60°; investigating the effects of the yield stress/ultimate tensile strength ratio and the brace/chord yield stress ratio; exploring the influence of loading reversal; and quantifying the reduction in strength caused by the absence of the hidden weld. The end result of these studies is a new, extended capacity equation. The accuracy of the proposed equation to predict the axial capacity of test joints was established by assessing it using an experimental database. The applicability of the proposed equation for design practice was further ascertained by investigating strength sensitivities to material curve variations, different chord end support conditions, and joints with unequal brace inclinations. The proposed design equation is found to be both accurate and conservative and is therefore recommended to be used in practice.

Static Strength of Axially Loaded Tubular K-Joints. I: Behavior

This paper reports the results of an extensive finite-element study into the static behavior of axially loaded tubular K-joints. The emphasis of the study was on the effects of the geometric parameters and the overlap amount on the behavior of overlap joints. The results of some K-joints with small gaps were also included for comparative purposes. The study reveals new insight into how the behavior of axially loaded overlap K-joints varies across the practical range of geometric parameters. Certain overlap geometries were seen to be 100% efficient, with the joints reaching the brace member squash load capacity. Other failure modes of chord bending, brace local buckling, and in particular, combined chord bending and brace local buckling were evident. Examination of the load-deformation characteristics for the sharp falls in the postpeak load—reflecting sudden joint failures, which have been a suggested cause for concern in the past—has revealed that relatively few overlap geometries exhibit such behavior. ...

Static Strength of Axially Loaded Tubular K-Joints. II: Ultimate Capacity

The ultimate capacity results from an extensive finite-element study of balanced axially loaded K-joints (reported in a companion paper) are reviewed and compared with predictions from available design guidance. Both overlap and small-gap K-joints are included. Overlapping the braces was shown to have a beneficial effect on joint strength for the joints with relatively thick brace walls, where the strength was found to be up to four and a half times that of the corresponding gap joint. The performance of the available onshore and offshore design guidance for predicting joint capacities was poor, particularly for the overlap joints. The interactive effects of varying geometric parameters are not fully accounted for, generally resulting in high levels of conservatism. A new strength equation developed for the overlap joints has been shown to predict the capacities of the numerical joints studied, as well as those from a test database, with a high degree of accuracy.

Parametric equations for distributions of stress concentration factors in tubular K-joints under out-of-plane moment loading

An extensive parametric study, using finite elements, of the stress concentration factors in tubular K-joints commonly found in offshore platforms is presented. This study covers a comprehensive range of geometric joint parameters for unbalanced out-of-plane moment loading. The results of the study were first used to assess the widely used parametric equations of Efthymiou (Proceedings of the Conference on Recent Developments in Tubular Joints Technology, Surrey, 1988, p. 2–1) and Lloyds Register (Proceedings of the 1st International Society of Offshore Polar Engineers Conference, 1991, Edinburgh), which provide predictions of stress concentration factors at the saddle on the outer surfaces of the chord and the brace as a function of the joint geometric ratios. The database of thin shell finite element results generated was then used to develop parametric equations for predicting stress concentration factors at key locations around the joint intersection on the outer, as well as the inner, surfaces of the chord. The reliability of the proposed and existing parametric equations was then assessed using the acrylic joint database published by the UK Department of Energy (Draft Background to New Fatigue Design Guidance for Steel Joints and Connections in Offshore Structures, 1995). The paper concludes with fracture mechanics fatigue calculations to demonstrate that the information provided from the proposed equations could be utilised to obtain accurate, and safe, fatigue life estimates.

Stress Concentration Factors in Tubular K-Joints under In-Plane Moment Loading

An extensive parametric study is presented of the distributions of stress concentration factors in tubular K-joints commonly found in offshore platforms. The study covers a comprehensive range of geometric joint parameters for balanced in-plane moment loading. The results of the study were first used to assess two sets of widely used parametric equations, which predict the maximum stress concentration factors on the outer surfaces of the chord and the brace. The new database of finite-element results was then used to develop parametric equations for predicting stress concentration factors at key locations around the intersection on the outer as well as the inner surfaces of the chord. The reliability of the proposed and existing parametric equations was then assessed using an acrylic test joint database and some published test data measured from a steel model. Fracture mechanics fatigue calculations were also performed to demonstrate that the information provided from the proposed equations could be utilized to obtain accurate, and safe, fatigue life estimates.

Prediction of stress concentrations and degrees of bending in axially loaded tubular K-joints

An extensive database of stress concentrations and degree of bending in tubular K-joints under balanced axial loading, generated recently in a finite element parametric study, has been used to develop parametric equations. The study covers a comprehensive range of geometric joint parameters which are commonly found in offshore structures. This database of thin shell finite element results was used to develop parametric equations for estimating stress concentration factors and the degree of bending at key locations on both the chord and brace. Formulae for the stress distributions around the intersection of K-joints were also derived using the parametric equations at key locations as input parameters, thus allowing the stress distributions to be predicted from the geometric joint parameters. Fracture mechanics fatigue calculations were performed to demonstrate that the information provided from the proposed equations could be used to obtain safe estimates of fatigue lives of tubular K-joints.

New parametric equations for stress concentration factors in tubular K-joints under balanced axial loading

An extensive parametric study is presented on stress concentrations in tubular K-joints calculated using thin shell finite elements. This study covers a comprehensive range of geometric joint parameters under balanced axial loading. The results of this investigation were used to assess the existing parametric equations of Efthymiou ( Proc. Conf. Recent Dev. Tubular Joints Technol., Surrey, 1988, p. 2-1) and Lloyds Register ( Proc. 1st Int. Soc. Offshore Polar Eng. Conf., 1991, Edinburgh). These equations predict stress concentration factors on the chord and the brace at selected locations as a function of the joint geometry, and are based upon databases which cover relatively narrow ranges of geometric parameters. The new database of thin shell finite element results was used to develop new parametric equations for estimating stress concentration factors on the chord and on the brace. The reliability of the proposed parametric equations was then assessed using the database of steel and acrylic joints published recently by the Department of Energy (Draft Background to New Fatigue Design Guidance for Steel Joints and Connections in Offshore Structures, 1995).