Chord Wall Thickness Research Articles

Stiffened Hollow Structural Section Joints in Fire

This research examines the ability of stiffened Hollow Structural joints to withstand elevated temperatures when subjected to axial compressive loads on the brace. Extensive numerical simulations were conducted to assess the impact of geometrical factors in the main members and reinforcing plate on the fire resistance of SHS T-joints. The accuracy of the numerical models was verified by comparing them to existing test results. The findings demonstrate that the use of stiffener significantly enhances the ability of SHS T-joints to withstand elevated temperatures. The fire resistance of the reinforced joints primarily relied on the brace-to-chord width ratio and the reinforcing plate thickness to chord wall thickness ratio. However, increasing the reinforcing plate thickness beyond 1.5 times the chord wall thickness did not yield any beneficial effects on fire resistance. Additionally, factors such as half-width to thickness ratio of the chord, reinforcing length, and reinforcing type had negligible effects as long as they adhered to the required limit values based on Eurocode 3 EN 1993-1-8.

Experimental and numerical studies on stress concentration factors of high strength steel fabricated box X-joints

High strength steel (HSS) is commonly available in the form of steel plates. The built-up box tube with sharp corners which is welded from four steel plates is usually fabricated for construction. The stress concentration factor (SCF) is crucial for the determination of the hot spot stress range which governs the high-cycle fatigue resistance of tubular joints. This paper presents experimental and finite element (FE) investigations on the SCF of HSS fabricated box X-joints. Four X-joints which are fabricated from built-up box tubes with a nominal yield stress of 890 MPa are tested under brace axial compression. The SCFs at typical hot spot locations are obtained using strip strain gauges. A FE model which has been validated against the test results is employed to conduct the parametric study on totally 112 fabricated box X-joints. The loading cases of brace and chord axial loading are covered. The effects of brace to chord width ratio, chord width to wall thickness ratio and brace to chord wall thickness ratio on the SCFs at the hot spot locations are revealed. The CIDECT SCF formulae are shown to be not suitable for the fabricated box X-joints under brace and chord axial loading. More accurate SCF equations are proposed to calculate the SCFs at the hot spot locations of the box X-joints.

Finite element study on axially loaded reinforced Square Hollow Section T-joints at elevated temperatures

Abstract This study numerically investigates the elevated temperature resistance of collar plate and doubler plate reinforced Square Hollow Section (SHS) T-joints subjected to brace axial compressive load. The extensive numerical simulations were performed to examine the effects of the geometrical parameters of main members and reinforcing plate on the fire resistance of reinforced SHS T-joints after verification of the numerical models based on the available test results. The corresponding unreinforced joints were also analysed as reference resistance at five different temperature levels (20 °C, 400 °C, 500 °C, 600 °C, and 700 °C). Results indicate that the elevated temperature capacity of SHS T-joints can be significantly increased by using a collar plate or a doubler plate. Although the initial stiffness of the doubler plate reinforced joints was higher than the collar plate reinforced joints, their capacity was similar to each other. Also, the fire resistance of the reinforced joints mainly depended on the brace-to-chord width ratio and reinforcing plate thickness to chord wall thickness ratio. However, there was no beneficial effect on the fire resistance of reinforced joints when the thickness of the reinforcing plate was greater than 1.5 times the chord wall thickness. Moreover, there was an insignificant effect of half-width to thickness ratio of the chord, reinforcing length and reinforcing type as long as the required limit values of the reinforcing length and width were used based on the Eurocode 3 EN 1993-1-8. It is worth mentioning that modifying the steel yield strength in the ambient temperature design method to calculate the capacity of the reinforced SHS T-joints at elevated temperatures may be unsafe. A new design method was developed to predict the capacity of a collar plate and doubler plate reinforced SHS T-joints subjected to brace compressive load in fire.

Static behavior of X-joints with SHS chord and CHS braces

This paper investigates the behavior of X-joints with square hollow section (SHS) chord and circular hollow section (CHS) braces (XSCCB) under brace axial loading. A total of twenty-nine specimens were designed, including twenty-three empty specimens, three specimens filled with concrete only in the square chord and three specimens filled with concrete only in the circular braces. The effect of four influential factors was studied, including brace diameter to chord width ratio (β = d/b), chord width to double wall thickness ratio (γ = b/2 T), brace wall thickness to chord wall thickness ratio (τ = t/T) and partial concrete filling on the behavior of XSCCB under brace axial loading. Initial stiffness and ultimate bearing capacity of empty XSCCB increase as the β increases and the γ decreases. The ductility coefficient of empty XSCCB increases as β increases, while γ has little effect on their ductility coefficient. Also, τ has a minor effect on the ultimate bearing capacity, initial stiffness and ductility coefficient of empty XSCCB. However, for XSCCB filled with concrete only in the chord member, the initial stiffness, ultimate bearing capacity and ductility coefficient increase as τ increases. For the XSCCB filled with concrete only in the braces, τ has little effect on the ultimate bearing capacity, initial stiffness and ductility coefficient. Chinese Code and Eurocode 3 are generally conservative for designing empty XSCCB under brace axial loading. Hence, the corresponding formulas are proposed for calculating the ultimate bearing capacity of empty XSCCB under brace axial loading.

Compressive Behavior of Damaged Tubular T-joints Retrofitted with Collar Plate

The static bearing capacity and failure modes of damaged tubular T-joints retrofitted with collar plates under axial compression were investigated. Two-step loading was applied: First, the chord deformation was loaded to the pre-designed degree, followed by unloading and collar plate installation. Subsequently, the specimens were reloaded. The maximum capacity and corresponding displacement (Δ1,m) were determined, and the ratio of the chord deformation of the other joints to Δ1,m was utilized to define the damage degree. The maximum capacity of retrofitted tubular T-joints could be up to 13–77% in second step loading, compared with that of unreinforced T-joints; however, the capacity decreased by 2–10% compared to that of directly reinforced T-joints. Sixty-nine finite element models were generated. The effects of chord wall thickness, chord diameters and collar plate lengths on the bearing capacity under different damage degrees were analyzed. A satisfactory effect could be obtained by using a suitable size of expanded collar plates under a constant damage degree. Retrofitting with collar plates could mitigate the development of equivalent plastic strain in the joint intersection, even for considerably damaged tubular T-joints. A modified formula considering the damage degree was proposed for bearing capacity prediction of retrofitted tubular T-joints.

Ultimate Load Capacity Analysis of Q690 High-Strength Steel KK-Type Tube–Gusset Plate Connections

A KK-type tube–gusset plate joint is a typical joint configuration used widely in the tubular structures of transmission towers. The mechanical characteristics of KK-joints, compared with K-joints, are more complex owing to the multiplanar effects in the actual structure. Based on material experiments and tubular K-joint ultimate load capacity experiments of Q690 high-strength steel, a parameter analysis is conducted on KK-type tube–gusset plate connections. Additionally, geometric parameters, axial load of the chord, and other factors that influence the ultimate bearing capacity of multiplanar KK-joints are studied in detail. The analysis indicates that the axial compression load of the chord, chord wall thickness, chord diameter, and loading ratio of the bracing members significantly affect the ultimate load capacity of KK-joints. According to the experimental and finite-element (FE) analysis results, a formula is developed to predict the ultimate load capacity of KK-joints using the virtual work principle.

Capacity of tubular X-joints reinforced with collar plates under tensile brace loading at elevated temperatures

This paper investigates the effect of the collar plate size and the joint geometry on the static behavior of the collar plate reinforced X-joints under tensile load at elevated temperatures. At the first step, a finite element model was developed and validated by results of the experimental tests. At the next step, extensive numerical simulations were carried out on the collar plate strengthened X-joints considering a wide range of geometrical parameter. Using these numerical simulations, the structural behavior under different high temperatures (200 °C, 400 °C, 600 °C, and 800 °C) was investigated and compared to the behavior at ambient temperature (20 °C). Results showed that the ratio of joint strength at elevated temperature to that at ambient temperature increases with the decrease in the ratio of chord diameter to twice the chord wall thickness (γ). Also, for the joints at elevated temperatures, the increase of the collar plate length and thickness remarkably leads to the increase of both the initial stiffness and the ultimate strength. Moreover, the use of the collar plate with big sizes can significantly improve the failure mechanisms of the joints. Also, it was found that for the collar plate reinforced X-joints under tensile load, the joint strength reduction at increasing temperatures follows closely the reduction in the elastic modulus of steel at elevated temperatures. Hence, in the proposed design method for determining the ultimate strength of the collar plate reinforced X-joints under tensile load at elevated temperatures, the Young's modulus reduction factor is used as a modification factor.

Strength of external-ring-stiffened tubular X-joints subjected to brace axial compressive loading

This paper presents the results of numerical and analytical studies to obtain ultimate strength enhancement coefficient (Re) equations for external-ring-stiffened circular hollow section (CHS) X-joints under axial compression. The FE modeling approach is validated by the results of axial compressive experiments conducted in the authors’ previous research on six X-joints with and without stiffeners. In all, 160 unstiffened and ring-stiffened FE models of CHS X-joints subjected to brace axial compression were investigated. The effects of the brace-to-chord diameter ratio β, the ratio of chord diameter to twice the chord wall thickness γ, the stiffening ring width factor βr (i.e. 2br/d0 where br is the ring width and d0 is the chord diameter), and the stiffening ring thickness factor τr (i.e. tr/t0 where tr is the stiffening ring thickness and t0 is the chord wall thickness) on the structural behavior of external-ring-stiffened CHS X-joints were evaluated. Parametric analysis showed that the ultimate strength enhancement coefficient Re decreased with the increase in the diameter ratio between the brace and the chord β, but once β exceeded 0.4, the effect on Re was slight. Furthermore, the ratios of chord diameter to twice the chord wall thickness γ, the stiffening ring width factor βr, and the stiffening ring thickness factor τr were all positively correlated with improvement in the ultimate strength of the external-ring-stiffened CHS X-joints. An analytical formula based on the yield volume model was derived to predict the ultimate strength enhancement of external-ring-stiffened X-joints.

Static strength of collar-plate reinforced tubular T-joints under axial loading

To study the effect of collar-plate reinforcement on the static strength of tubular T-joints under axial loading, fundamental research work is carried out from both experimental test and finite element (FE) simulation. Through experimental tests on 7 collar-plate reinforced and 7 corresponding un-reinforced tubular T-joints under axial loading, the reinforcing efficiency is investigated. Thereafter, the static strengths of the above 14 models are analyzed by using FE method, and it is found that the numerical results agree reasonably well with the experimental data to prove the accuracy of the presented FE model. Additionally, a parametric study is conducted to analyze the effect of some geometrical parameters, i.e., the brace-to-chord diameter ratio β, the chord diameter-to-chord wall thickness ratio 2γ, collar-plate thickness to chord wall thickness ratio τc, and collar-plate length to brace diameter ratio lc/d1, on the static strength of a tubular T-joint. The parametric study shows that the static strength can be greatly improved by increasing the collar-plate thickness to chord wall thickness ratio τc and the collar-plate length to brace diameter ratio lc/d1. Based on the numerical results, parametric equations are obtained from curving fitting technique to estimate the static strength of a tubular T-joint with collar-plate reinforcement under axial loading, and the accuracy of these equations is also evaluated from error analysis.

Ultimate capacities formulae of collar and doubler plates reinforced SHS X-joints under in-plane bending

This paper presents two finite element model of collar and doubler plates reinforced SHS X-joints under in-plane bending, which were verified by the corresponding test results. The parametric study was carried out to reveal the failure modes and plasticity propagation of collar and doubler plates reinforced SHS X-joints under in-plane bending. The effects of SHS brace width to SHS chord width ratio (β), reinforced plates thickness to SHS chord wall thickness ratio (λ), and reinforced plates length to SHS brace width ratio (Δ) on the ultimate capacities of collar and doubler plates reinforced SHS X-joints were evaluated. The typical failure modes of collar and doubler plates reinforced SHS X-joints under in-plane bending were obtained from the finite element analysis, which included braces inclination, chord face concave in compression stress zone, convex in tension stress zone, collar or doubler plates bending. The ultimate capacities of joints with large β value significantly increased with the increase of reinforcement plates thickness. The in-plane bending ultimate capacity increased with the increase of β value. The ultimate capacities formulae are proposed by using multiple linear regressions for collar and doubler plates reinforced SHS X-joints under in-plane bending based on the current design equations of unreinforced SHS X-joints given in the Eurocode 3. It is shown from the comparison that the joint strengths of collar and doubler plates reinforced SHS X-joints under in-plane bending calculated using the proposed formulae agreed well with the finite element analysis results, which means the proposed formulas are verified to be accurate and safe.

Stress concentration factors of negative large eccentricity tubular N-joints under axial compressive loading in vertical brace

Negative large eccentricity tubular N-joints sometimes are used in welded trusses and offshore structures under fatigue loading. It is imperative that researches should be done on fatigue behavior of negative large eccentricity tubular N-joints under fatigue loading, though static behavior of negative large eccentricity tubular N-joints has been researched. The stress concentration factors (SCFs) are the main parameters in the fatigue behavior analysis of negative large eccentricity tubular N-joints. Four negative large eccentricity tubular N-joints specimens were separately tested for calibration and verification of finite element analysis models by considering axial compression in vertical brace case. All experimental joints were simply hinge supported at one end of chord and inclined brace end. Elastic gradient strain distributions along the intersection of joints were measured. Strain concentration factors (SNCFs) at hot spots including saddle and crown points were computed taking advantage of an extrapolation approach. As eccentricity decreased, the position of maximum SCF moved from the saddle point to the crown point at the inclined brace and vertical brace intersection near the vertical brace or the inclined brace. The maximum SCF at the chord and inclined brace intersection near the chord or the inclined brace occurred on the crown point. For the FE analysis, solid elements and certain mesh size were used to model the N-joints. Effects of brace diameter to chord diameter ratio (β), chord diameter to thickness of chord ratio (2γ), brace wall thickness to chord wall thickness ratio (τ) and eccentricity ratio (ε) on the SCFs distribution of the negative large eccentricity tubular N-joints were numerically investigated. SCF linearly increased with the increase of eccentricity ratio at the inclined brace and vertical brace intersection near inclined brace and at chord and inclined brace intersection near inclined brace. The effect of eccentricity ratio on SCF equations of small eccentricity tubular N-joints was not considered in current code. A series of parametric equations considering eccentricity ratio were proposed for calculating the SCFs of negative large eccentricity tubular N-joints based on 256 joints FEA models calculation result.

Experimental and numerical research on out-of-plane flexural property of plates reinforced SHS X-joints

The static tests of 13 SHS X-joints with different brace to chord side length ratios and different types of plates reinforcement under out-of-plane bending in brace were carried out. Experimental test schemes, failure modes of specimens, moment–vertical displacement curves, moment–deformation of the chord, and strain strength distribution curves were presented. The effects of brace to chord side length ratios and plates reinforcement types on out-of-plane flexural property of SHS X-joints were studied. Results show that punching shear of chord face disappeared, concave and convex deformation of chord decreased when either collar plates or doubler plates were welded on chord face. Moment–vertical displacement curves of all specimens have obvious elastic, elastic–plastic and plastic stages. As brace to chord side length ratio increased, the out-of-plane flexural ultimate capacity and initial stiffness of joints with the same plates reinforcement type increased, but ductility of joints decreased. With the same brace to chord side length ratio, the out-of-plane flexural initial stiffness and ultimate capacity of collar plates reinforced joints, doubler plates reinforced joints and unreinforced joints decreased progressively. Thickness of reinforcement plates had an obvious effect on out-of-plane ultimate capacity of SHS X-joints. Thickness of reinforcement plates had no obvious effect on out-of-plane flexural initial stiffness of SHS X-joints when the value of reinforcement plates to chord wall thickness ratio exceeds 1.0. As thickness of reinforcement plates increased, the ductility of reinforced X-joints decreased. The concave and convex deformation of every specimen had good symmetry. The design equations were proposed for collar and doubler plates reinforced SHS X-joints under out-of-plane bending, which were shown to be accurate and reliable.

Behaviour of circular concrete filled double skin tubes subjected to local bearing force

This paper presents the behaviour of circular concrete filled double skin tubes (CFDST) subjected to local bearing forces. This is an extension of a previous work on concrete filled steel tubes (CFST). A series of tests were conducted where some key parameters were varied, including loading angle, hollow ratio, chord wall thickness, as well as brace to chord diameter ratio. A finite element analysis (FEA) modelling was established and verified by the test data. Comparative analysis was conducted between the full-range behaviour of CFDST and CFST under local bearing. It was found that the performance of CFDST is considerably affected by the interaction of the outer tube, inner tube and the sandwiched concrete, whilst its bearing capacity depends on the hollow ratio. Finally, based on the load-transfer mechanism analysis, simplified formulae for predicting the strength of CFDST under local bearing forces are presented. Reasonable agreement between the predicted and measured values is achieved.

Static Strength of RHS T-Joints with Reinforced Chord under In-Plane Bending Load

Welded tubular structures are widely used in many constructions, such as offshore platforms, which are all consisted of welded tubular members. There is a stress concentration at the intersection between chord and brace. When subjected to loads, a crack exists in the weld toe at the intersection. Then the propagation of the crack leads to failure of the joint. So the static strength of rectangular hollow section (RHS) T-joints with local chord reinforcement under in-plane bending load is investigated by using finite element method. To study the effect of the chord reinforcement of a RHS T-joint, overall 18 T-joint models with different chord reinforcements have been analyzed numerically. This paper presents the results of a detailed parametric study of the static strength of in-plane bending loaded tubular T-joints with reinforced chord. The study, carried out using non-linear finite elements, demonstrated the accuracy of the finite element analysis to investigate the effects of different geometric parameters which influence the static strength of the stiffened joints. It is found that the effect of the chord thickness near the intersection is significant in improving the ultimate capacity of T-joint models. The ultimate strength enhances as the length of the chord reinforcement becomes longer and the chord wall thickness becomes larger. The effect of the chord wall thickness on the static strength of T-joints are remarkable. However, increasing the length of the reinforced chord to improve the static strength of Tubular T-joint is relatively ineffective.

Elasto-Plastic Behavior of Doubler Plate Reinforced Tubular T-Joints

The aim of this paper is to study elasto-plastic behavior of the doubler plate reinforced tubular T-joints (DP-T-joints) subjected to axial tension or compression loading at the top of brace. Finite-element method is adopted in the numerical parametric studies to evaluate the ultimate strength of DP-T-joints. To verify numerical analysis, a typical full-scale doubler plate reinforced tubular T joints experimental study has been modeled using ABAQUS package. The load-displacement curves of the numerical results agree with the experiment curve very well. Then, affect of parameter (doubler plate width parameter α, doubler plate length parameter Δ, doubler plate to chord wall thickness ratio λ) on the elasto-plastic behavior has been investigated.

Frequency optimization of a wind turbine blade in pitching motion

This article presents a mathematical model for optimizing frequencies of a wind turbine blade in pitching motion. Related design problems include the excessive blade torsional vibrations induced by continuous pitching, which is necessary to limit the power output and protect generator from damages in severe wind conditions. This, in turn, can have adverse effects on the fatigue life of the blades and might cause catastrophic failures near the resonant frequencies. The study considers a blade tapered linearly towards the tip representing the effective aerodynamical surface for producing the needed power. The blade inboard portion is modelled by an equivalent torsional spring simulating the torsional stiffness near the root. The model provides exact solutions of the resulting governing differential equation by utilizing analytical Bessel's functions of the first kind, where the functional behaviour of the torsional frequency has been thoroughly examined. The associated optimization problem is formulated by considering two forms of the objective function. The first one is represented by a direct maximization of the fundamental frequency, while the second one considers minimization of the square of the difference between the fundamental frequency and its target or desired value. In both strategies, an equality constraint is imposed on the total structural mass in order not to violate other economic and performance requirements. Design variables encompass the blade tapering ratio, chord, and shear wall thickness distributions, which are expressed in dimensionless form, making the formulation valid for a variety of blade configurations. In fact, the mathematical procedure implemented can be regarded as a beneficial design tool, in which significant increase in the overall stiffness/mass ratio level of the blade structure combined with full separation of the frequency from the undesired range that resonates with the pitching frequencies can be achieved.

The ultimate strength of doubler plate reinforced Y-joints under compression loading

It is common practice in the offshore industry to solve the punching shear problem due to compression by using doubler plate. The finite-element method is a useful tool for studying this problem. The aim of this paper is to study the static strength of doubler plate reinforced Y-joints subjected to compression loading. The finite-element method is adopted in numerical parametric studies. The individual influences of the geometric parameters βand τd (doubler plate to chord wall thickness ratio) and ld/d1 (dubler plate length to brace diameter ratio) on the ultimate strength are made clear. The results show the size of plate may have important effects on the strength of reinforced joints. It is found that the ultimate strength of Y-joints reinforced with appropriately proportioned doubler plates can be greatly improved nearly up tothree times to un-reinforced Y-joints.

Parametric equations for stress concentration factors in completely overlapped tubular K(N)-joints

This paper presents parametric equations to predict the stress concentration factors (SCF) of completely overlapped tubular K(N)-joints under lap brace axial compression. 192 finite element (FE) models of the joint have been created for the parametric study using a commercial FE package, MARC. In the analysis, both 8-node thick shell and 20-node solid elements are found suitable for modelling the joint. The comparison of strain concentration factors (SNCF) between the FE models and the tested specimen shows that the difference is less than 0.42. However, in view of the computational effort, the FE model with 8-node thick shell element is used for the parametric analysis. The study reveals that the effect of through brace to chord wall thickness ratio on SCF of the joint is most crucial. The maximum SCF occurs on the through brace saddle near the lap brace. The gap size on the through brace surface between the outer surfaces of the chord and the lap brace significantly affects the SCF. Based on the FE data, a set of parametric equations is derived to predict the SCF of the joint. The reliability of the equations has been verified against the requirement of the Fatigue Guidance Review Panel.

The prediction of crack shape development for in-service cracks in offshore welded tubular joints

Abstract Due to the severe cyclic environmental loading experienced by offshore structures in the North Sea, fatigue has been identified as one of the most important causes affecting the long-term structural integrity of the welded tubular joints on these structures. Fatigue damage appears in the form of fatigue crack growth. Maintenance of structural integrity therefore concentrates on carrying out periodic in-service inspection and integrity assessment of the intact and cracked structures. The aims of the maintenance programme are to ensure that either no crack is present in the structures, or if cracks are discovered, that the remaining joints are still ‘fit’ for their purpose in terms of fatigue life and static capacity. The key information linking the in-service inspection and integrity assessment is the size of the cracks. Although the crack depth is the controlling variable for fatigue analysis, both depth and length of the surface breaking cracks are needed for the assessment of remaining ultimate capacity. In the past it was.found to be difficult to correlate the analytical prediction of crack aspect ratio (depth to half-length ratio) development with measured values from full-scale test results. Many integrity assessments therefore used a predefined aspect ratio pattern for the analysis. This paper reports an extension of a methodology in order to produce a better correlation between predicted and measured aspect ratio patterns. The methodology is based on fracture mechanics analysis with structural modelling.for cracked tubular joints. The paper reviews briefly the recent progress in the analysis of fatigue crack growth in tubular joints and outlines how the new methodology i.s formulated. The results showed that the methodology was adequate.for predicting aspect ratio growth for cracks deeper than 25% of the chord wall thickness.

Internal stresses at the saddles of YT tubular joints with three different weld fillet shapes

The frozen-stress, photoelastic method was used to determine the elastic stresses along 16 lines through the chord at the saddles of YT tubular joints. Four 45–90 degree joints were simply supported at the ends of the chord and tension was applied to one brace only. The blend fillet at the intersection of the brace wall and chord wall outer surfaces was modelled as an idealised chamfer, a sharp corner, and a blended circular arc. In the chord wall near the fillet, stress distributions show predominant chord wall bending with significant tension in the direction of the chord axis. The greatest stresses occur at the weld toe where the notch effect extends to one third of the chord wall thickness. There is no stress concentration at the internal brace/chord fillet. Surface stresses are presented as mean and bending values.