Column Slenderness Research Articles

A new similarity method for the ultimate strength of box girders subjected to the combined load of bending and lateral pressure

The ultimate strength is an important property for hull structures nowadays. For large-scale structures, scale models are needed to perform physical model tests. Therefore, similarity methods are especially important. Traditional similarity methods consider similarity criteria of cross-section properties, and modern similarity methods introduce some strength-related similarity criteria to consider the nonlinear collapse procedure. However, these two kinds of criteria may be conflicting and are hard to meet simultaneously. Most existing works concentrated on simple structures, like stiffened plates, due to the difficulty in meeting all the similarity criteria. In this paper, a new similarity method is proposed for box girders subjected to the combined load of bending moment and lateral pressure. The proposed method considers only the strength-related similarity criteria, ignoring the criteria of cross-section properties. The column slenderness, the plate slenderness, and the torsional slenderness are selected as the similarity parameters for every stiffened plate in the box girder. The new similarity relations of the ultimate moment and the applied lateral pressure are derived according to the proposed criteria. A structured step-by-step scale model design procedure is proposed to design corresponding scale models. 4 numerical examples are presented to show the correctness and advantages of the proposed method.

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.

Effect of Column Deformation for Steel Frames with Semi-rigid Connection

As semi-rigid behaviour will give a more economical design, it should be applied in the structural steel design. The properties of semi-rigid connection may affect the column design and is the main focus in this study. Complex calculation with semi-rigid consideration in design may cause unfavourable time consuming. Therefore, a simplified column design is needed to eliminate complicated procedures while accommodating the semi-rigid condition. In this analysis, the validated finite element procedure has been used for the analysis of a semi-rigid column in a non-sway frame. Parametric study was performed within variables of types of connection, loading patterns, locations of investigated column and column base fixity. The influences of column slenderness and beam flexibilities were also included and the implications towards the column design were then identified.

Interactive buckling behaviour of Q420–Q960 steel welded thin-walled H-section long column

Considering the broad application prospect of high-strength steel (HSS) in engineering structure, and the limitations present in existing studies on interactive buckling of HSS welded thin-walled box-section long column, both test and finite element analysis were employed to investigate the interactive buckling behavior exhibited by 12 specimens fabricated from Q420–Q960 steels. The detailed analysis considered various aspects, including the failure mode, axial deformation, interaction of local and overall buckling deformation, and the ultimate bearing capacity. Observations revealed that the utilization rate of steel strength diminished with an escalation in both the plate width–thickness ratio and steel strength. An increase in the plate width–thickness ratio correlated with an earlier onset of local buckling, and the influence of steel strength was found to be negligible. More importantly, the limit of the plate width–thickness ratio for columns undergoing interactive buckling increased with a rise in column slenderness and decreased with an increase in steel strength. Taking into account the influence of column slenderness and steel strength, a novel calculation formula for determining the limit of the plate width–thickness ratio was derived. It is noteworthy that Eurocode 3 and JGJ/T 483–2020 were found too conservative for calculating the ultimate bearing capacity, while ANSI/AISC 360–22 was found suitable. Additionally, a calculation method for the ultimate bearing capacity of Q420–Q960 steel welded thin-walled H-section long column was proposed based on the direct strength method.

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.

Adoption of hooped-battens in cold-formed steel built-up columns for superior axial performance

Previous research on cold-formed steel (CFS) battened columns has identified the critical factors influencing their performance and accordingly, their limiting values for improved performance have been recommended. However, these studies involved connecting battens to the chords (channels) via their flanges, leaving the slenderest component disconnected from the web. This study introduces a novel hooped-batten (tubular-element) that links both webs and flanges of the chords together, thereby improving the structural integrity of the built-up system and curtailing the half-wave buckling length in the webs. As a result, axial strength and stability in these built-up columns may improve adequately. Firstly, a numerical model of a conventional CFS battened column was developed in ABAQUS and verified against test results on the same reported in literature. Afterward, the validated model was used to simulate the behaviour of CFS built-up columns with hooped-battens. Two key parameters i.e., unbraced chord slenderness and overall column slenderness were varied to explore their influence on the axial behaviour of built-up columns in terms of peak strengths, failure modes and load-displacement characteristics. The performance of the hooped-battened columns was compared with the identical conventional battened columns, which reflects that the former exhibits superior strength and stability characteristics over the latter.

Nonlinear finite element analysis of partially encased composite columns under non-uniform moments

This paper presents a numerical investigation to evaluate the behavior of partially encased composite (PEC) columns with compact sections of three different heights submitted to non-uniform moment distribution. A 3D finite element model developed using the software ABAQUS was calibrated based on results from previous experimental research. The influence of concrete constitutive model parameters, column slenderness, load eccentricities, and moment distribution along height was investigated. The parametric study showed that constant moment distribution (case 1) is the most critical compared to linear moment variation (cases 2 and 3). This pattern is a direct consequence of the larger displacements at the mid-height section that causes higher second-order moments in the case 1 column. Long columns activated more confinement when a single curvature bending moment was applied at a minor axis. An increase in slenderness decreased the load capacity for non-uniform bending moments through the major axis.

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.

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.

Misalignment effect on the ultimate strength of welded stiffened panels under uniaxial compression

Longitudinal stiffener misalignment (LSM) is inevitable in the manufacturing process of stiffened hull panels, affecting the geometric appearance and bearing capacity. However, the knowledge of the effect of LSM on the ultimate strength of stiffened panels is limited. In this paper, continuous numerical simulations are first conducted regarding forced alignment, welding process and ultimate strength analysis by using the nonlinear finite element method. A simplified model is then derived considering LSM and initial deflection based on a comparative study of the ultimate strength and collapse patterns. Influences of various combinations of LSM and initial deflection on the strength characteristics and failure behaviors are documented and discussed. According to the parametric analysis, it is found that the LSM imperfection decreases the ultimate strength, but the degree of reduction depends on the shape and amplitude of the panel initial deflection. The maximum reduction rate is 8.71% occurring in the case where the deflection shape with slight amplitude is symmetric. On the basis of 120 numerical results, an empirical formula is proposed for predicting the residual strength as a function of the dimensionless misalignment degree together with panel and column slenderness.

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.

A general scaled model design method of stiffened plate subjected to combined longitudinal compression and lateral pressure considering the ultimate strength and collapse modes

A general and efficient scaled method for stiffened plates subjected to combined longitudinal compression and lateral pressure is proposed based on slenderness, simply by adjusting the number of stiffeners. The design method makes it easier to determine the dimensions of the scaled model for a given scale ratio compared with the previously proposed method. The emphasis is on the influence of the plate slenderness, the column slenderness, and the non-dimensional parameter of the lateral pressure on the ultimate strength. By maintaining the consistency of the plate slenderness and column slenderness, the proposed method is applicable for designing scaled models with materials of different yield stresses and Young's moduli. A similar effect of the lateral pressure on the ultimate strength of the prototype and scaled models is achieved by maintaining the non-dimensional parameter. In addition, the applicability of the scaled method to the initial deflection is considered, which provides a reference for similar models. The similitude of the scaled method is verified for several typical buckling modes, including the beam–column, tripping, web and overall collapse modes. Given the numerical results, the proposed general and fast scaled method can provide reasonable dimensions of scaled stiffened plates subjected to combined loads.

Novel approach to the stability assessment of reinforced concrete columns

Geometric and material nonlinearities inherent in slender reinforced concrete (RC) columns have often limited the accuracy of stability models in determining the deformational response under axial and lateral loading. Design codes for slender RC columns in code provisions employ a factor of safety to compensate for the complex interactions associated with the nonlinearities which results in large discrepancies and magnified for increasing column slenderness. The present study introduces a novel approach in quantifying the moment- rotation relationship of RC column sections parallel to a partial-interaction tension-stiffening model. The moment-rotation model is used to determine axial and lateral load–deflection relationships in addition to stability curves to assess buckling capacities of RC columns for various loading conditions. Extensive experimental studies on the structural behaviour of slender RC columns are used to validate models developed in the study. Results show the effectiveness of the moment-rotation model in predicting column behaviour, and the accuracy of the stability model in determining failure behaviour.

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.

Experimental study on the effects of whole heating cycle on post-fire behavior of restrained high strength structural steel columns

This paper presents the results of an experimental study of post-fire behavior and residual strength of restrained high strength structural steel (HSSS) columns, including loading tests of columns at ambient temperature to failure, restrained columns under sustained loading going through heating and cooling cycle in fire and then followed by post-fire loading tests to failure. All the columns were axially restrained in fire. The investigated parameters include with and without rotational restraint, load eccentricity, load ratio and maximum experienced temperature. It was found that if the column failure mode was predominantly overall buckling (columns without rotational restraint in this study), the heating and cooling process would result in a large residual lateral deflection in the column, and the post-fire load carrying capacity of the column would be much lower than without fire exposure. On the other hand, if the column slenderness was low and its failure mode was mainly cross-section yielding (columns with rotational restraint in this study), the post-fire residual lateral deflection was low and the post-fire column would be able to retain a very high proportion of its load carrying capacity without fire exposure, and sometimes even exceeded this value due to strain hardening, which indicated complete reusability of such columns.

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.