Tubular K-joints Research Articles

Design equations for maximum stress concentration factors for concrete-filled steel tubular K-joints

Stress concentration factors (SCFs) for welded tubular joints can be decreased by filling the chord with concrete leading to a longer fatigue life. However, there are currently no design formula available in guidelines to predict the SCF of concrete-filled circular hollow section (CFCHS) K-joints, thus limiting their applicability in bridge design. To address this gap, finite element models for CFCHS K-joints were developed and compared against test results to ensure their accuracy. Then, a comprehensive parametric study was conducted to establish relationships between maximum SCFs and four variables: brace-to-chord diameter ratio (β), chord diameter-to-thickness ratio (2γ), brace-to-chord thickness ratio (τ), and the angle between braces and chord (θ). A total of 480 FE models were examined under three loading conditions including brace and chord loading: balanced axial force, chord axial force, and chord bending. Design equations to predict the maximum SCF for CFCHS K-joints were established by multiple regression analyses of the numerical results. A comparison of maximum SCFs between circular hollow section (CHS) and CFCHS K-joints was made, and it was concluded that average reductions of 42% and 33% in maximum SCFs in CFCHS K-joints at the locations of the chord and brace were found compared to CHS joints for balanced axial force, respectively. Finally, a case study illustrating how to use the proposed equations for fatigue safety verification was presented.

Collar plate effect on local joint flexibility of tubular K-joints under IPB moments: Parametric study and predictive equations

This study delves into the Local Joint Flexibility (LJF) of tubular K-joints reinforced with the collar plates under in-plane bending moments (IPBMs). 348 reinforced K-joints were simulated to analyze the impacts of the loading conditions (balanced and unbalanced moments), collar plate size (like the length and thickness) alongside the joints’ parameters (θ, γ, β, ξ) on the fLJF and its proportionality (ψ). The research outcomes demonstrate that factors such as η, λ, and β play a significant role in determining ψ, whereas the influence of ξ, and γ on ψ appears to be negligible. Also, in the reinforced joints, the fLJF is decreased by 77.4 % compared to the equivalent un-reinforced joint. While the role of the collar plate on the fLJF is remarkable, the matter had not been investigated on K-joints. Therefore, following the detailed parametric study, two novel equations are proposed to safety estimate the fLJF for such scenarios.

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.

Behaviour of concrete-filled circular steel tubular K-joints in wind turbine towers

The advantages of concrete-filled steel tubular lattice towers in stress efficiency, material consumption, and industrial construction are significant for the future development of ultra-long blades, ultra-high towers, and large-capacity units. The stress state of the joints is a key component of a wind tower structure. Therefore, experiments were conducted on four concrete-filled circular steel tubular (CFCST) K-joints in a lattice wind turbine tower, along with one hollow circular steel tubular (HCST) K-joint for comparison. The test results revealed that the CFCST K-joints failed due to local and overall buckling of the compression web, whereas no plastic deformation occurred on the chord. The stiffness of the CFCST K-joints significantly improved, and the stress concentration around the intersecting line was significantly reduced. Existing structural codes, both domestic and international, underestimate the bearing capacity of CFCST K-joints because the contribution of the core concrete cannot be accounted for. Finite element analyses indicate that the bearing capacity of the CFCST K-joints is dependent on the failure mode, primarily influenced by the thickness ratio τ and the angle θ. To prevent joint failure in the CFCST lattice wind turbine towers, specifically suggest τ ≤ 1 and θ ≤ 45°. Based on the bearing capacity calculation method proposed by CIDECT for HCST K-joints, design equations were obtained to predict the punching shear bearing capacity of CFCST K-joints using the least-squares method. The established formula exhibited high accuracy through regression verification.

Static Strength of Tubular K-Joints Reinforced with Outer Plates under Axial Loads at Ambient and Fire Conditions

In this paper, the effect of the outer reinforcing plate on the initial stiffness, ultimate strength, and failure mechanisms of tubular K-joints under axial load at ambient and different fire conditions is evaluated. In the first phase, a finite element (FE) model was generated and verified by 13 experimental tests. In the next step, 1057 numerical models were generated. In these models, the welds joining the chord and braces were modeled. Using the produced FE models, the structural behavior under ambient and different elevated temperatures (20, 150, 300, 450, 600, 750, and 900 °C) was evaluated. The results showed that the outer plate can enhance the ultimate strength by up to 319% under fire conditions. Despite the considerable effect of the outer plate on the stiffness, ultimate strength, failure modes, and the frequent usage of the K-joints in tubular structures, the static response of the reinforced K-joints at ambient and elevated temperatures has not been studied. Hence, according to the extensive parametric studies, a highly precise practical design equation has been proposed based on the yield volume model for determining the ultimate strength.

Experimental Research on the Calculating Method of Stress Concentration Factor for CFST K-Joint

The concrete-filled steel tubular (CFST) K-joint was taken as the research object, full-scale specimen tests and finite-element (FE) analysis of seven CFST K-joints and one steel tubular (ST) K-joint were carried out. The accuracy of CFST K-joint stress concentration coefficient (SCF) calculation using the existing K-joint SCF formula was discussed. Based on the effect of core concrete on the chord deformation mechanism, the releasing coefficient of CFST K-joint SCF was proposed. According to the relationship between releasing coefficient and stripping arc length, the calculation method of releasing coefficient was established by theoretical derivation. The calculation method of CFST K-joint SCF was then established based on the releasing coefficient and ST K-joint SCF. The obtained results show that the maximum SCF of the K-joint appears in the position of the intersecting weld between tension brace and chord near the crown toe of the chord. The maximum SCFs of the CFST and ST K-joints in order are obtained as 3.98 and 6.08, which indicates that the core concrete can reduce the SCF of the CFST K-joint by about 34.5%. The existing methods for calculating the SCF of CFST and ST K-joints fail to fully consider the influence of core concrete constraints and the coupling relationship between geometric parameters; therefore, the accuracy of CFST K-joint SCF calculation using the existing K-joint SCF calculation formula is low. By employing the proposed SCF calculation method, the calculation error of the CFST K-joint SCF can be reduced from 58.0% to 19.6%.

Study on fatigue performance of concrete-filled steel tubular K-joints with internal studs

To study the fatigue performance of concrete-filled steel tubular K-joint (CFST K-joint) with internal studs, fatigue tests on CFST K-joint without internal studs, CFST K-joint with array arrangement internal studs (CFST KSA-joint), and CFST K-joint with circular arrangement internal studs (CFST KSC-joint) were conducted. The finite element models of CFST K-joints with studs were established. The hot-spot stress distributions, fatigue crack growth processes, and fatigue failure modes of the joints mentioned above were comparatively studied. The study showed that the maximum hot-spot stress of the CFST K- and KSA-joints appeared at the crown toe, while that of the CFST KSC-joint occured at the position of 45°. As compared with CFST K-joints, the CFST KSA- and KSC-joint specimens had 34% and 12% reductions in hot-spot stress, respectively. At the location of the internal studs, the hot-spot stress decrease significantly. By reducing the chord deformation and peeling arc length, the internal studs reduce the hot spot stress and increase the fatigue life. The fatigue life of the CFST KSA-joint specimen with array internal studs was 101% higher than that of the CFST K-joint specimen. By applying the circular internal studs, the fatigue life of the CFST KSC-joint specimen was 97% higher than the CFST KSA-joint specimen with array internal studs. The internal studs delay the occurrence of fatigue cracks, and change the propagation path of fatigue cracks along the length of intersecting welds into the direction of steel tube wall thickness, therefore, improving the fatigue life of K-joints.

Local joint flexibility of tubular K-joints reinforced with external plates under out of plane bending moments

ABSTRACT In this research work, the Local Joint Flexibility (LJF) of steel tubular K-joints reinforced with external plates is investigated. In the first step, a finite element (FE) model was generated and verified. In the next step, a set number of 300 FE analysis was carried out to investigated the effect of the stiffener plate size (η and λ), the angle between brace and chord (θ), the joint geometry (γ, τ, ξ and β) and the loading conditions (balanced and un-balanced OPB moments) on the LJF factor (f LJF) and f LJF ratios (ψ). The results showed that the f LJF of an external plate reinforced K-joint can be down to 26% of the f LJF of the corresponding un-reinforced joint. Also, the gap factor (ξ) has effect on the f LJF. Finally, FE results were used to derive two parametric equations for determining the f LJF in the strengthened K-joints.

Investigation of hot spot stress for welded tubular K-joints with stiffeners

Steel stiffeners can be utilized to reinforce the welded hollow section K-joints, possibly bringing about a different magnitude and distribution of hot spot stress from the traditional joints without stiffeners. There is a lack of knowledge on the hot spot stress and its calculation method for the welded tubular K-joints with stiffeners, especially under complex load cases, which has hindered the fatigue design. With regard to an engineering practice of a bridge under construction, this paper investigates the distribution and magnitude of hot spot stress and its calculation method. Experimental tests including two load cases are conducted to provide a benchmark for the finite element (FE) modelling. FE analysis is carried out to investigate the influence of stiffeners on the hot spot stress ranges at several critical locations, covering the parameters including number, thickness and position of internal ring stiffeners. The hot spot stress calculation method is then developed based on the superposition concept. It is found that the hot spot stress ranges near the stiffeners are relatively large, in addition to those at crowns and saddles. The locations of interest include not only crowns and saddles but also the locations at the intersection of stiffener contours and intersection lines. The maximum hot spot stress ranges can be reduced by 55.7% in chords and 37.4% in braces by setting stiffeners. The developed hot spot stress calculation method is verified for the welded tubular K-joints with stiffeners. In addition, a fatigue test on the welded tubular K-joints with stiffeners is performed. • Investigate the hot spot stress distribution and magnitude of the welded tubular K-joints with stiffeners. • Conduct experimental tests of the specimens in two combined load cases. • Analyze the effects of steel stiffeners on the hot spot stress ranges of welded tubular K-joints using FE modelling method. • Extend the hot spot stress calculation method for the welded tubular K-joints with stiffeners. • Perform a fatigue test on the welded tubular K-joints with stiffeners.

Simplified equivalent finite element modelling of concrete-filled steel tubular K-joints with and without studs

Concrete Filled Steel Tubular (CFST) K-joints employed for truss structures gained high interest in the last years due to their widespread use in engineering practice. The overall performances of these joints can be efficiently improved by using steel studs welded in the inner surface of the steel chord filled with the concrete, avoiding punching shear failure, and improving the overall strength and ductility. However, a reliable prediction of the structural behavior of the joints is outmost of importance for the assessment of the capacity of new and existing structures, and there are no standardized design methods nowadays. In this paper, the structural performances of CFST K-joints with and without steel studs are investigated by Finite Element Modelling (FEM) approach with the aim to provide a predictive tool for the design. A comprehensive discussion of the key parameters that govern the FEM procedure as well as the calibration of the FE models was provided to give the basis for a reliable modelling of CFST K-joints with and without studs for the predictions of the load–displacement/strain response and the strength, considering the main failure mechanisms. In this context, in addition to the detailed FEM of CFST K-joints with steel studs, a simplified equivalent FEM approach is proposed to reduce computational effort keeping the same accuracy.

Fracture analyses of bonded tubular FRP composite K-joints with braces subjected to balanced axial load

Fracture analyses of bonded tubular FRP composite K-joints with braces subjected to balanced axial load

Stress concentration factors of CFRP-reinforced tubular K-joints via Zero Point Structural Stress Approach

The SCFs of the tubular K-joints reinforced with carbon fiber reinforced polymer (CFRP) were computed using the zero-point structural stress (ZPSS) method. After employing several sets of data to verify the proposed finite element (FE) model, a comparison between the ZPSS and hot spot stress (HSS) approaches was established. The results indicate that ZPSS approach is superior to HSS approach in calculating the SCFs. Then 319 models were established to parametrically assess the efficiency of the CFRP strengthening on the fatigue performance of the tubular K-joints. The findings show that the CFRP strengthening dramatically minimizes SCFs at the weld toe's heel, saddle, and crown. In addition, the orientation of the first layer of the CFRP laminate and the layups had significant effects on the SCFs along the weld toe. Moreover, three precise equations were proposed to determine the SCFs of CFRP-reinforced K-joints at the heel, saddle, and crown, respectively.

Local joint flexibility of tubular K-joints reinforced with external plates under IPB loads

In the present paper, the Local Joint Flexibility (LJF) of tubular K-joints reinforced with external plates is investigated. For this purpose, in the first step, a finite element (FE) model was generated and verified with the results of several available experimental tests and equations. In the next step, a set number of 450 FE analysis on the 150 FE models were conducted to investigate the effect of the plate size (η and λ), the joint geometry (γ, τ, ξ, and β), the angle between brace and chord (θ), and the loading conditions on the fLJF and the fLJF ratios (ψ). In the FE models, the welds were generated to join the braces to the chord. The results showed that the fLJF of the reinforced K-joints is remarkably smaller than the corresponding un-reinforced joints. Despite the considerable effect of the plates on the fLJF in K-joints under IPB moments, there is no study or formula on any reinforced K-joints. Consequently, the results were utilized to propose two design formulas for determining the fLJF in K-joints reinforced with plates under different IPB moments.

Finite Element Analysis and Optimization of the Planar Steel Tubular K-Joints

Planar steel tubular K-joints feature various geometric forms and intricate load states, whose bearing capacity is influenced by a number of factors. To address the problems above, a research on the bearing capacity of common planar K-joints in practical engineering projects was conducted. Based on numerical simulation, nonlinear finite element analysis on four kinds of planar K-joints was carried out in ANSYS. The bearing capacity and failure modes of those K-joints were figured out. The bearing capacity of each combination was compared. The results provided by finite element analysis was compared with those derived from codes. The design of K-joints was optimized, thereby improving the bearing capacity and satisfy requirements of engineering projects.

Bearing Capacity and Failure Mode of a Light-Steel Tubular K-joint Connected by a Novel U-shape Connector

This study aims to investigate the ultimate bearing capacity of a novel tubular K-joint used for light-steel structures consisting of thin-walled square hollow section members, a U-shape connector and self-drilling screws, and the effect of three patterns of stamping indentation fabricated on the U-shape connector on the ultimate bearing capacity of the proposed K-joint. Firstly, a total of 12 K-joint specimens were tested to failure under monotonic brace axial compressive loading. Secondly, failure mode and the ultimate bearing capacity of each specimen were investigated and analyzed. Finally, finite element analyses were carried out to study the effect of three key parameters, including chord axial stress ratio, half width-to-thickness ratio of the chord and brace-to-chord wall thickness ratio, on the ultimate bearing capacity of the proposed K-joints using the recommended U-shape connector. It was found that failure mode of the proposed K-joint is governed by both the deformation of the U-shape connector and the chord local plastification. Besides, the K-joint specimen using a U-shape connector with the strip stamping grooves in the horizontal direction generally has a higher bearing capacity and a much smaller connector deformation. Similar to the welded tubular joints, chord axial stresses may also significantly reduce the ultimate bearing capacity of the proposed K-joint.

Experiments on stainless steel hybrid K-joints with square braces and circular chord

This paper presents an experimental investigation on the load-bearing capacities of stainless steel hybrid tubular K-joints with square braces and circular chord. All test specimens were made from austenitic stainless steel of grade AISI 304. For gapped K-joints, as the gap (g) increased, initial stiffness and load-bearing capacities of joints decreased continuously. For overlapped K-joints, the overlap ratio (Ov) did not have a significant effect on the initial stiffness and load-bearing capacities of joints. For the same series of joints with the identical cross-sectional dimensions, the load-bearing capacities of overlapped K-joints were higher than those of gapped K-joints. Test results were also compared against the design predictions in accordance with the current design guidelines of CIDECT (2008), Eurocode 3 (EC3) (2005), Australian/New Zealand Standard (AS/NZS) (2001) and Chinese Code (GB 50017) (2017). Upon comparison, it was found that the GB 50017 (2017) can predict the load-bearing capacities of stainless steel hybrid tubular gapped K-joints accurately, being around 5% conservative to the test results. However, CIDECT (2008) predictions were found to be conservative by 23% on average. In comparison, the nominal strengths calculated from the EC3 (2005) and AS/NZS (2001) are conservative by 28% and 15%, respectively, when compared to the test results for stainless steel hybrid tubular overlapped K-joints.

Nonlinear behaviour and design of stainless steel hybrid tubular K-joints with SHS-to-CHS

This paper presents a finite-element (FE) investigation on the bearing capacity of stainless steel hybrid tubular K-joints with square braces and circular chord. The nonlinear finite-element (FE) models were developed and validated against the test results available in the literature, which were then used to conduct a parametric study including 162 models. The parametric study results showed that the joint strengths of the stainless steel hybrid tubular gapped K-joints increased when the β and τ values increased and when the 2γ and e values decreased. On the other hand, the joint strengths of overlapped K-joints increased when the β, τ, and Ov values increased and when the 2γ values decreased. Furthermore, the bearing capacities obtained from the parametric study were compared with the design strengths calculated from the current design guidelines. The comparison showed that the current design rules of Chinese Code (GB 50017–2017) were generally un-conservative for stainless steel hybrid tubular K-joints. The coefficient of variations (COVs) obtained from the comparison of EC3 (2005), AS/NZS (2001) and GB 50017 (2017) were very large. However, the design strengths calculated from the International Committee for the Development and Study of Tubular Structures (CIDECT) were relatively close to the FE strengths. Therefore, modified design rules are proposed in this paper. New design formulas were developed by applying correction factors (ψg and ψo) to the current design rules of CIDECT (2008) for carbon steel CHS tubular K-joints, considering the effects of key geometric parameters of β, τ, 2γ and Ov, respectively. The proposed design rules can accurately predict the bearing capacity of stainless steel hybrid tubular K-joints with square braces and circular chord, being only 1% conservative to the FE strengths.

Experimental and numerical study of the ultimate load for collar-plate-reinforced tubular K-joints at fire-induced elevated temperatures

ABSTRACT The fire resistance of collar-plate-stiffened uniplanar tubular K-joints was studied and formulated in the present research. After establishing a finite element (FE) model and its verification against the results of experimental tests, a total of 1440 numerical simulations were performed on 360 FE models of collar-plate-stiffened uniplanar tubular K-joints at four different temperatures (20, 400, 550, and 700°C). The studied joints were analysed under the axial loading and the reinforcing effect of the collar plate was investigated. Results showed that the resistance enhancement coefficient (Rs ) increases by increasing the γ, θ, and τ; while it decreases by rising the β. Results of the parametric investigation were utilised to establish new design equations to determine the bearing capacity of collar-plate-stiffened tubular K-joints under the brace axial loads at fire condition.

A numerical study and proposed design rules for stress concentration factors of stainless steel hybrid tubular K-joints

This paper presents a finite-element analysis (FEA) of the stress concentration factors (SCFs) of stainless steel hybrid tubular K-joints with square braces and circular chord and K-joints with circular braces and square chord. The developed finite-element (FE) models include material non-linearities and are validated against corresponding experimental results available in the literature. The validated FE models were used to conduct an extensive parametric study comprising 324 FE models. The critical geometric parameters of the parametric study include: brace width-to-chord diameter ratio (β1 = b1/d0), brace-to-chord thickness ratio (τ = t1/t0), chord diameter-to-thickness ratio (2γ1 = d0/t0), brace diameter-to-chord width ratio (β2 = d1/b0), chord width-to-thickness ratio (2γ2 = b0/t0), eccentricity (e), gap distance (g) of K-joints with gap, and overlap ratio (Ov) of overlapped K-joints. The results of the parametric study show that the effect of β on the SCF varies for different types of K-joints. For all hybrid tubular K-joints, the values of SCFs increases with an increase in 2γ value. For gapped K-joints, the values of SCFs increases with an increase in e value. An attempt was made to compare the numerical results against the SCFs calculated in accordance with International Committee for the Development and Study of Tubular Structures (CIDECT) (2001) for both the stainless steel hybrid tubular K-joints with square braces and circular chord and K-joints with circular braces and square chord. This comparison reveals how the design equations available in CIDECT (2001) for pure circular and square tubular joints are not suitable for predicting the SCFs of both the stainless steel hybrid tubular K-joints with square braces and circular chord and K-joints with circular braces and square chord. Therefore, improved design equations are proposed in this paper for predicting accurately the SCFs of stainless steel hybrid tubular K-joints with square braces and circular chord, as well as circular braces and square chord.

An experimental study on stress concentration factors of stainless steel hybrid tubular K-joints

This paper describes a test program on the stress concentration factors (SCFs) of stainless steel hybrid tubular (SSHT) joints with square hollow section (SHS) braces and circular hollow section (CHS) chord and SSHT joints with CHS braces and SHS chord. The load was applied to the brace for all test specimens. Twenty specimens in total, including ten overlapped and ten gapped tubular K-joints, were tested. Different geometric parameters were used which include brace width-to-chord diameter ratio (β1 = b1/d0), brace-to-chord thickness ratio (τ1 = t1/t0) and chord diameter-to-thickness ratio (2γ1 = d0/t0) for SHS-to-CHS hybrid tubular joints, brace diameter-to-chord width ratio (β2 = d1/b0), brace-to-chord thickness ratio (τ2 = t1/t0) and chord width-to-thickness ratio (2γ2 = b0/t0) for CHS-to-SHS hybrid tubular joints. A number of strain gauges were used at the hot spot locations for various tubular joints. The hot spot stress (HSS) method was used to determine the SCFs of SSHT joints using the quadratic extrapolation method. This was a consequence of the stress distributions around the intersection area of SHS-to-CHS and CHS-to-SHS hybrid tubular joints being nonlinear. Results found the maximum SCFs for hybrid overlapped tubular K-joints with square braces and circular chord to be located at the hot spot location at an angle of 135° between the SHS brace and the CHS chord. This is characterized as line A. The maximum SCFs of hybrid gapped tubular K-joints with square braces and circular chord were located at the hot spot location at an angle of 45° between the SHS tension brace and the CHS chord (characterized as line C) and at an angle of 45° between the SHS compression brace and the CHS chord (characterized as line E). The maximum SCFs of hybrid overlapped tubular K-joints with circular braces and square chord were located at the hot spot location at an angle of 180° to the CHS brace. The maximum SCFs of hybrid gapped tubular K-joints with circular braces and square chord were located generally at the hot spot location at an angle of 0° to the CHS brace. Test results were compared against the design predictions in accordance with the current design guidelines of the International Committee for the Development and Study of Tubular Structures (CIDECT, 2001). Upon comparison, it was found that the design formulas of CIDECT (2001) overestimate the maximum SCFs of SHS-to-CHS hybrid gapped tubular K-joints. For the CHS chord and SHS braces of hybrid overlapped tubular K-joints, the design formulas overestimate the maximum SCFs for most of the specimens. Furthermore, for the SHS chord and CHS braces of hybrid gapped tubular K-joints, the design formulas of CIDECT (2001) overestimate the maximum SCFs. For the SHS chord and CHS braces of hybrid overlapped tubular K-joints, the CIDECT (2001) design formulas were unconservative when determining the maximum SCFs of such joints.