Column Slenderness Ratio Research Articles

Seismic Design and Ductility Evaluation of Thin-Walled Stiffened Steel Square Box Columns

This paper investigates the seismic performance of thin-walled stiffened steel square box columns, modeling bridge piers subjected to unidirectional cyclic lateral loading with a constant axial load, focusing on local, global, and local-global interactive buckling phenomena. Initially, the finite element model was validated against existing experimental results. The study further explored the degradation in strength and ductility of both thin-walled and compact columns under cyclic loading. Thin-walled, stiffened steel square box columns exhibited buckling near the base, forming a half-sine wave shape. The research also addresses discrepancies from different material models used to analyze steel tubular bridge piers. Analysis using a modified two-surface plasticity model (2SM) yielded results closer to experimental data than a multi-linear kinematic hardening model, particularly for compact sections. The 2SM, which accounts for cycling within the yield plateau and strain hardening regime, demonstrated enhanced accuracy over the multi-linear kinematic hardening model. Additionally, a parametric study was conducted to assess the impact of key design parameters—such as width-to-thickness ratio (Rf), column slenderness ratio (λ), and magnitude of axial load (P/Py)—on the performance of thin-walled stiffened steel square box columns. Design equations were then developed to predict the strength and ductility of bridge piers. These equations closely matched experimental results, achieving an accuracy of 95% for ultimate strength and 97% for ductility.

Numerical Simulation for Strength and Stability of RC Tapered Columns

This study investigates the strength and stability of Reinforced Concrete (RC) linearly tapered square columns. Evaluating the slenderness ratio of an RC column requires the radius of gyration of its cross-section, which is well-defined for a prismatic column but not for a non-prismatic one. This study primarily investigates the application of the ACI Code formulae to evaluate the slenderness ratio of RC columns with the studied geometry. Validated numerical models, using Abaqus, were employed to perform nonlinear first- and second-order analyses on the investigated columns subjected to eccentric axial loads. The concrete damaged plasticity model was employed to simulate the nonlinear behavior of concrete. The static Riks solver, available in Abaqus, was utilized for nonlinear analyses: first, with an inactivated geometric nonlinearity for a first-order analysis, and second, with an activated geometric nonlinearity to consider the effects of secondary moments (p-δ effects). The findings indicate the reliability of defining the slenderness ratio of an RC linearly tapered column based on the ACI Code formulae, using the average cross-section of the tapered column.

Axial compression behaviour of bamboo-wood composite columns fabricated with glubam and laminated veneer lumber

Both wood and bamboo are natural green biomaterials with a long application history in human society. A novel bamboo-wood composite fabricated with glued laminated bamboo (glubam) and laminated veneer lumber (LVL) was developed to reduce wood resource demand and to promote bamboo utilization efficiency. Experimental and analytical investigations were conducted to study the mechanical performance of 36 bamboo-wood composite columns with different slenderness ratios under axial compression. The three-layer composite column was composed of glubam as outer layers and LVL as a core layer, with horizontal or vertical configurations respectively. The failure modes, ultimate capacity, load and deformation behaviour were evaluated. Strength failure was the typical failure mode of the short columns while buckling was commonly observed for the longer columns. Columns with vertical LVL core had overall better performed with higher compressive strength than the ones with horizontal LVL core configuration. The ultimate load of the composite columns with thin-strip glubam as outer layers were increased by 31.6 % to 45.3 % than those of thick-strip glubam as outer layers. The compressive capacity of the specimens predicted according to three standards were compared with the experimental results. An improved expression considers the material strength and column slenderness ratio was proposed, which provides a better prediction than the current design standards.

Enabling efficient regional seismic fragility assessment of multi‐component bridge portfolios through Gaussian process regression and active learning

AbstractRegional seismic fragility assessment of bridge portfolios must address the embedded uncertainties and variations stemming from both the earthquake hazard and bridge attributes (e.g., geometry, material, design detail). To achieve bridge‐specific fragility assessment, multivariate probabilistic seismic demand models (PSDM) have recently been developed that use both the ground motion intensity measure and bridge parameters as inputs. However, explicitly utilizing bridge parameters as inputs requires numerous nonlinear response history analyses (NRHAs). In this situation, the associated computational cost increases exponentially for high‐fidelity bridge models with complex component connectivity and sophisticated material constitutive laws. Moreover, it remains unclear how many analyses are sufficient for the response data and the resulting demand model to cover the entire solution space without overfitting. To deal with these issues, this study integrates Gaussian process regression (GPR) and active learning (AL) into a multistep workflow to achieve efficient regional seismic fragility assessment of bridge portfolios. The GPR relaxes the probability distribution assumptions made in typical cloud analysis‐based PSDMs to enable heteroskedastic nonparametric seismic demand modeling. The AL leverages the varying standard deviation to select the least but most representative bridge‐model‐ground‐motion sample pairs to conduct NRHA with much‐improved efficiency. Both independent and correlated multi‐output GPRs are proposed to deal with bridge portfolios with seismic demand correlations among multiple components (column, bearing, shear key, abutment, unseating, and joint seal). Considering a single benchmark highway bridge class in California as the case study, the AL‐GPR framework and the associated component‐level fragility results are investigated in terms of their efficiency, accuracy, and robustness. The fragility results show that 70 AL‐selected samples would enable the GPR to derive bridge‐specific fragility models comparable to the ones using the multiple stripes analysis approach with 1950 ground motions considered for each individual bridge. The AL‐GPR model also successfully captures the physics of how bridge span length, deck area, column slenderness, and steel reinforcement ratio would change the damage state exceedance probabilities of different bridge components. The efficiency of AL stems from the fact that, with the multi‐output independent GPR, a stable and reliable fragility model can be achieved using 50 AL‐selected samples compared to at least 270 randomly chosen samples. The proposed methodology advances the state of the art in enabling more efficient and reliable regional seismic fragility assessment of multi‐component bridge portfolios.

Experimental and numerical investigations of circular concrete filled steel double-skin and double-tube columns exposed to fire

Circular concrete-filled steel double-tube (CFSDT) columns have shown excellent ductility and load-carrying capacity. However, research on the fire resistance of CFSDT columns is still limited. This paper presents the fire tests, finite element (FE) modeling, behavior, and design of circular CFSDT columns and concrete-filled steel double-skin (CFSDS) columns exposed to fire. The fire resistance tests of one CFSDS and six CFSDT columns are described. Analysis is given on the effects of the material strength, the thickness of the inner steel tube, and the load ratio on the fire resistance of the specimens. Finite element models are developed that simulate the fire behavior of filled composite columns with double tubes and are verified by fire test results. The verified FE models are employed to undertake parametric studies on the structural responses of CFSDS and CFSDT columns under fire exposure. A design model is proposed for calculating the fire resistances of CFSDT columns. The results show that the load ratio and the column slenderness ratio have the most significant effect on the fire resistance of CFSDT columns; the cross-sectional parameters remarkably affect the fire resistance; and the material strength has a moderate impact on the fire resistance of CFSDT columns. Compared with CFSDS specimens, the existence of the core concrete significantly increases the fire resistance of CFSDT columns. The proposed design model for fire resistance can yield a safe prediction.

Effects of structure size on post-earthquake fire resistance of CCBCC joints at non-uniform elevated temperatures

The probability of secondary fires caused by earthquakes is very high. Due to the residual stress and deformation caused by earthquakes, the mechanical behavior of cruciform combined beam-CFST column (CCBCC) joints is extremely complex. In view of this, the goal of this study is to investigate the effects of structure size on the post-earthquake fire failure mechanism of CCBCC joints under gradient temperatures. The calculation model in this article was validated using existing experimental results, subsequently 20 computational models were established to conduct parameter analysis, including the width-to-thickness ratio (γ) of the CFST column, the slenderness ratio (λ) of the CFST column, the width-to-thickness ratio (α) of beam flange, the height-to-thickness ratio (β) of beam web and the damage variable (D̃). The results have demonstrated that the post-earthquake fire resistance of CCBCC joints is mostly affected by damage variable. Parameters β, α, λ and γ also have a significant impact on the failure of these joints. An empirical bearing capacity prediction model of CCBCC joints is obtained. The research results can provide reference and data support for the design, maintenance, and reinforcement of CCBCC joints under post-earthquake fire.

Data-driven machine learning methodology for designing slender FRP-RC columns

Current design guidelines for reinforced concrete (RC) with fiber-reinforced polymers (FRP) bars lack provisions for designing slender columns. Limited attempts were made to modify the moment magnification procedure to accommodate FRP-RC columns. This study proposes a novel approach for designing FRP-RC slender columns based on suggesting a simplified slenderness reduction factor to account for the slenderness (ϕslender). The novel reduction factor has been developed using data-driven machine learning, where the available experimental database of short and slender FRP-RC columns has been employed to train a robust generalized artificial neural network (ANN) model. The ANN model is then utilized to generate reduction-factor curves, facilitating a straightforward approach to designing slender FRP-RC columns. For design practice purposes, genetic expression programming (GEP) was used to generate a mathematical equation for calculating ϕslender. The proposed ϕslender is a function of concrete compressive strength, reinforcement ratio, eccentricity, and column slenderness ratio. Statistical correlation analysis indicated that implementing the ϕslender eliminates the axial capacity correlation to the slenderness ratio, indicating a very good representation of the slenderness effect on the FRP-RC columns. The proposed approach revealed higher accuracy and consistent conservatism compared to the moment magnification procedure in predicting the strength of the slender FRP-RC columns.

Seismic Behaviors of Novel Steel-Reinforced Concrete Composite Frames Prestressed with Bonding Tendons

To investigate the seismic behaviors of novel steel-reinforced concrete composite frames prestressed with bonding tendons (PSRCFs), 15 groups of PSRCF specimens were designed with the following main parameters: the cubic compressive strength of high-strength concrete (fcu), the axial compression ratio of frame columns (n), the slenderness ratio of frame columns (β), the steel ratio of angle steel (α), the span–height ratio of frame beams (L/hb), and the prestressing degree (λ). Based on the modified concrete constitutive model proposed by Mander and the prestressing effect applied by the cooling method, the finite element models of PSRCFs were established by using ABAQUS software, the static analysis on the frame structures under the combined actions of axial forces and horizontal loads was carried out, and the monotonic load–displacement curves were explored. By comparing with the skeleton curves obtained by the experimental hysteretic curves, the rationality of the modeling method was verified. The PSRCFs had good mechanisms of strong columns and weak beams. Based on this, the influences of different parameters on the seismic behaviors such as hysteretic curves, skeleton curves, stiffness degradations, energy dissipation capacities, and ductility of the specimens were investigated. The results show that the hysteretic curves of the PSRCFs are full and have no pinch phenomenon. The ultimate load and the stiffness degradation of specimens can be improved significantly by increasing α, and on the contrary, the ultimate load and stiffness degradation decreased by increasing β. The ductility of the specimens decreased gradually with the increasing β and n. The energy dissipation capacity of the specimens decreased with the increasing β. The trilinear model of the skeleton curves and the restoring force model of PSRCFS were established by statistical regression, which agree well with the numerically simulated results. These can provide theoretical support for the elastoplastic analysis on this kind of PSRCF structure.

STRENGTH AND DUCTILITY EVALUATION OF THIN-WALLED STEEL TUBULAR BRIDGE PIERS UNDER CYCLIC LOADING

Numerical simulations are being conducted on the behavior of thin-walled steel tubular bridge piers under cyclic lateral loading in the presence of constant axial compression loads. The effects of cyclic lateral loading on the behavior of the thin-walled steel tubular bridge piers have been evaluated through analysis of the hysteresis curve, envelope curve, stiffness, and strength degradation characteristics, and energy-dissipating capacity, including interaction effects of local buckling and flexural buckling, and post-buckling regimes. This study also compares the numerical analysis with experimental results available in the literature to validate the accuracy of the proposed finite element model. Based on this model, a range of relevant material and structural parameters will be investigated in future work. Numerous numerical specimens will be designed and analyzed, gaining further information about the influence of width-to-thickness ratio, Rt, column slenderness ratio, , material properties of the embedded shell plate, spacing of transverse stiffening ribs of the shell, height, and properties of partially infill concrete, and axial compression load.

Study on axial compression behaviors of dense-steel-column sandwich wall

As an innovative structural system, the modular steel structure building has been widely used. This paper presents a new modular structure called dense-steel-column sandwich wall. Eight walls were subjected to axial compression tests to investigate the effects of column section size and diagonal brace on the axial compression behavior of the wall. The results show that the bearing capacity can be improved by setting diagonal brace or increasing the column width, additionally, diagonal brace can improve the deformation ability of the wall. The wall tends to change from global instability failure to local instability failure as the column width increases. Based on the test results, refined finite element analysis models were established and compared with the tests, followed by multi-parameter analysis. The failure mode and peak load of the specimens obtained by numerical simulation closely matched the test results, showing the correctness of the finite element model. Moreover, the results of finite element analysis demonstrate that increasing of wall length to column spacing ratio, column thickness, and decreasing of column slenderness ratio can significantly improve the bearing capacity and axial compressive stiffness of the wall. Finally, the axial compression capacity calculation formulas were put forward, and the research findings can provide a reference for the engineering application of the dense-steel-column sandwich wall.

Analysis The Effect Of Column Height Variation On The Perfomance Of Increased Building Structure

The consequences of these earthquake waves cause damage to buildings ranging from light damage to heavy damage. Dealing with the case, it is necessary to plan and implement earthquake-resistant building structures, especially in high-rise buildings. Another factor that needs to be considered is the function of the room which affects the column height when the column height is different and it causes uneven stiffness from the ground floor to the top.
 The aim of this study was to find out the effect of variations in column height on the performance of multi-storey building structures in terms of shear forces, floor drift and buckling load (Pc). The method used in this study was the response spectrum method. The spectrum response is the maximum response of a Single Degree of Freedom (SDOF) structural system, both acceleration, velocity and displacement due to the structure being loaded by a certain external force. Before carrying out the analysis using the response spectrum method, a structural model was undertaken by varying the column height on the 1st floor into 3 variations.
 Dealing with the results of the analysis on the building structure model with varying column height on the 1st floor, it indicated that the higher the column the maximum base shear force value increases. The higher the 1st floor column, the maximum floor deviation value increases. The higher the column the value of the column slenderness ratio increases and the Euler buckling load decreases.

Practical temperature calculation and fire-resistant design of special-shaped concrete-filled steel tubular columns

The fire performance of special-shaped concrete-filled steel tubular (SCFST) columns under axial load was investigated in this paper. The ABAQUS based finite element models were conducted for heat transfer and structural analysis. Twelve fire tests on SCFST columns under the ISO-834 standard fire curve by the authors' research were used to verify the model. In addition, heat transfer and fire-resistant mechanism of full-scale SCFST columns were studied; and extensive parametric studies were investigated to examine the influence of fire protection layer thickness, column limb thickness, slenderness ratio and other factors on temperature distribution and fire behavior of SCFST columns. Through the calculation and analysis of temperature field and fire resistance, a simplified temperature calculation method for steel tube, tension reinforcement, and inner steel plate are proposed along with the modularization temperature calculation method for special-shaped concrete sections. Moreover, the ultimate bearing capacity calculation method for SCFST columns under the standard temperature rise curve is proposed allowing for the influence of high temperatures on material properties, which can also be applied to determine fire resistance of SCFST column. Finally, the calculation method for the thickness of fire protection layer and the corresponding fire design is proposed based on the delaying temperature mechanism.

Simulation modeling and design of circular concrete-filled double-skin tubular slender beam-columns with outer stainless-steel tube

The stainless-steel tube has been used to construct Concrete-Filled Steel Tubular (CFST) columns because it has a high resistance to fire and corrosion, good durability, and aesthetic appearance compared to the carbon steel tube. However, there is very little published research on eccentrically loaded circular Concrete-Filled Double-skin Steel Tubular (CFDST) slender beam-columns composed of an outer stainless-steel tube and an inner carbon-steel tube. In line with this, this paper presents a fiber-based simulation model for predicting the structural performance of CFDST slender columns with external circular stainless-steel tube under eccentric compression. The simulation modeling of load-deflection curves and load-moment interaction diagrams for slender CFDST beam-columns is developed and verified by the experimental results. The verified simulation model is then used to study the effects of geometric and material properties on structural performance. The range analysis is applied to the orthogonal design to identify the relative significance of the factors that influence the structural response. The orthogonal design covers CFDST beam-columns with a hollow ratio ranging from 0.1 to 0.8. The results indicate that the column slenderness ratio is the most significant factor, followed by the loading eccentricity ratio, the outer tube thickness, stainless steel proof stress, concrete strength, and carbon steel yield strength. The accuracy of the design method specified in Australian standard AS/NZS 2327, and the proposed design methods are evaluated. The proposed equation provides accurate strength predictions of CFDST slender columns where the external skin is made of stainless steel.

A comprehensive and reliable investigation of axial capacity of Sy-CFST columns using machine learning-based models

The literature on predicting the load-carrying capacity of symmetrical concrete-filled steel tube (Sy-CFST) columns using different machine learning methods has mainly focused on a single method or cross-section type in each study. Sy-CFST column has been widely used in the engineering field because of its several benefits such asincreased strength due to confinement generation, better ductility due to high steel ratio, and less construction cost and time as compared to the encased reinforced concrete. This study attempted to evaluate the load-carrying capacity of these columns with circular and square cross-sections based on the simultaneous use of the two gene expression programming (GEP) and artificial neural network (ANN) approaches. The database required for extracting GEP and ANN models was based on the empirical results of 993 specimens. Variables considered here include the compressive strength of concrete (fc), yield stress of steel (fy), cross-sectional areas of concrete (Ac) and steel (As), diameter to thickness ratio of the steel tube (D/torB/t), and slenderness ratio of Sy-CFST columns (λ). Moreover, parametric and sensitivity analyses were conducted separately to assess the contribution of each effective parameter to the axial capacity. To validate the efficiency of the models, prediction values of GEP and ANN were compared with the predictions of existing codes (6 codes) and different studies (8 studies). The results indicated that the developed models provide accurate predictions for the load-carrying capacity of Sy-CFST columns. In addition, the variation of parameters in the proposed models is consistent with experimental trends observed in other studies, which confirms the consistency of the proposed numerical models with physical observations.

Hysteretic performance of Q690 high-strength steel box-section columns with slender webs

High-strength steel (HSS) has a higher yield-tensile strength ratio and a lower fracture elongation than conventional mild steel, resulting in poor ductility in comparison to the latter. This paper aims to investigate the hysteretic performance of Grade Q690 steel welded box-section columns with slender webs. Four full-scale specimens were subjected to low-cycle horizontal reciprocating loading tests, and the failure mode, evolution of plasticity in the cross-section, energy dissipation capacity and ductility were studied. A finite element modeling procedure verified from the test results was used for a more extensive parametric analysis, and the influence of the width-to-thickness ratio, the axial compression ratio and the column slenderness ratio on the evolution of plasticity in the cross-section as well as the ductility were studied. The results show that plastic local buckling dominates the failure mechanism of welded box-section columns with slender webs. With an increase of the width-to-thickness ratio, axial compression ratio and column slenderness ratio, the evolution of plasticity in the cross-section and the ductility performance of the column gradually deteriorate, and the ductility coefficient within the selected parameter range is small, but it still has the capacity for energy dissipation. Limiting the axial compression ratio and width-to-thickness ratio to meet the requirements of elastic–plastic inter-story drift, HSS box-sections with slender webs can be incorporated in seismic design with low ductility requirements based on the concept of seismic performance design. In addition, a prediction formula for the ductility coefficient is proposed, which can provide a reference for the application of high-strength steel box-section beam–columns with slender webs in seismic design.

Predictive models of behavior and capacity of FRP reinforced concrete columns

This paper proposes a new model for predicting the axial capacity and behavior of Fiber Reinforced Polymerreinforced concrete (FRP-RC) columns using a promising variant of Genetic Expression Programming (GEP). Current design codes, such as the ACI 440.1R-15 and the Canadian Code CSA S806, disregard the compressive contribution of FRP bars when used in compression members. The behavior of concentrically short FRP-RC columns has been widely investigated in the past few years; however, limited research has been dedicated to investigating the effect of load eccentricity and the slenderness ratio of FRP-RC columns. In addition, the methodologies adopted for including the effect of column slenderness remain a subject of debate, as no solid conclusions are withdrawn in this regard. In this paper, the experimental results of FRP-RC columns are gathered from the literature and used to formulate two GEP models to predict the axial capacity based on load eccentricity. The experimental data includes columns reinforced with different FRP types and subjected to concentric and eccentric axial compressive loads. In addition, the database comprises short and slender columns. The proposed GEP models are functions of concrete compressive strength, longitudinal reinforcing bars ratio, FRP bars elastic modulus, eccentricity level, and column dimensions. For the aim of comparison, a preliminary evaluation of previously suggested empirical equations/models for estimating the axial capacity of FRP-RC columns was carried out over the collected database. The proposed models showed superior accuracy in axial capacity prediction with coefficients of determination R2 equals to 0.978 and R2 equal to 0.992 for eccentric and concentric axial load, respectively. The proposed models were found to give reliable estimates of the axial capacity of columns reinforced with FRP longitudinal bars. Finally, a parametric study to evaluate the effect of each variable on the proposed models was conducted.

Influence of Stone Columns on Seismic Response of Buildings Considering the Effects of Liquefaction

In this paper, the behaviour of a soil-foundation system supported on a stone column-reinforced liquefiable soil strata is investigated through finite element analysis. The numerical analyses are performed on a five story reinforced concrete moment resisting building supported on a raft foundation. The influence of stone column slenderness ratio on liquefaction mitigation is studied by varying the length of stone columns at a constant area replacement ratio. The results are obtained based on the excess pore pressure, free-field soil settlement, foundation settlement, acceleration response, superstructure's inter-story drift, and lateral story displacement for each ground motion. The results showed that the liquefaction of free-field soil had a major impact on the foundation settlement and building lateral deformation. With the inclusion of stone columns, excess pore pressure ratio in the free-field region reduced considerably, which had immediate effects on the building's lateral deformation.

Experimental Investigation of the Axial Behaviour for Battened Tubular Columns

This paper describes a series of experiments on batten tubular specimens with various slenderness ratios. The experimental study was employed to satisfy the expectations of behaviour and axial load capability of battened tubular columns. Twelve specimens composed of four tubes having different global column slenderness and various ratios of the unbraced chord slenderness-to-the global column slenderness were chosen to cover stub, short and medium columns. The tubes were assembled with welded batten plates. A numerical model with a thin shell element considered both geometric and material nonlinearities was used to verify the experimental results. Tests result showed different failure modes, such as local, local-flexural and flexural buckling. By comparing, the finite element and tested results have a good agreement. The results revealed the strength of the battened columns, which was related to the effect of global slenderness and spacers on the buckling behaviour. Additionally, the stub, short and medium column strengths were enhanced by 8%, 25%, and 78%; respectively, when the number of spacers increased to four batten plates. Eventually, predicted strengths of the battened column by AISC and EC3 specifications were slightly un-conservative.

Experimental and numerical investigations into the behavior of circular concrete-filled double steel tubular slender columns

This paper describes experimental and numerical investigations into the structural behavior of circular concrete-filled double steel tubular (CCFDST) slender columns loaded concentrically to failure. Test results on 8 specimens including 6 CCFDST slender columns and 2 CCFDST short columns are reported in this study that demonstrate the influences of column slenderness ratio and the thickness of the internal steel tube on the responses of CCFDST columns. A numerical model based on fiber analysis is developed to predict the axial load–deflection responses of CCFDST slender columns. The numerical model of CCFDST columns accounts for the effects of initial imperfection, concrete confinement, material nonlinearities and the interaction between axial load and deformations. A parametric study is performed by means of employing the verified computational technique to ascertain the sensitivity of the performance of CCFDST slender columns to various important parameters. Comparative analyses are undertaken to evaluate the applicability of Eurocode 4 and AISC 360–16 for conventional concrete-filled steel tubular columns (CFST) to CCFDST slender columns. It is shown that the developed numerical modeling technique simulates well the structural behavior of CCFDST slender columns and is an efficient computer simulation tool for the analysis and design of such composite columns. Moreover, the current design codes need to be modified to be utilized for designing CCFDST columns.

Use of physical testing data for the accurate prediction of the ultimate compressive strength of steel stiffened panels

ABSTRACT Physical testing data can be used to predict the ultimate compressive strength of steel stiffened panels. Moreover, useful empirical formulae have been developed by fitting curves to data from relevant testing databases. A representative example is the Paik–Thayamballi formula, which is based on physical testing data available until 1997 and is a closed-form function of plate and column slenderness ratios. Since 1997, high-precision data-acquisition equipment and large-scale physical models have been used to generate databases contained advanced testing data of modern materials such as AH32 high-tensile steel made by the thermo-mechanical control process (TMCP) technology together with modern fabrication technologies, e.g., flux-cored arc welding technique, under a strict control of welding parameters, e.g., current, voltage, speed and heat input, to achieve a required weld leg length. It is therefore important to determine if these advanced testing data are compatible with the established empirical formulae. This paper describes benchmark studies which were conducted to determine such compatibility, with a focus on the Paik–Thayamballi formula, and summarises key findings and insights obtained from the present study.