Cellular Steel Research Articles

Probabilistic resistance predictions of laterally restrained cellular steel beams by natural gradient boosting

Accurate and reliable cellular steel beam resistance predictions are essential for economical and safe designs of steel-framed buildings with such beams. This paper proposes a new machine-learning (ML) model based on the natural gradient boosting (NGBoost) algorithm to predict probabilistic load-bearing capacities of laterally restrained cellular beams subjected to uniformly distributed loads, considering all possible failure modes and their interactions. The NGBoost model was developed based on a database with 14,094 numerical simulation results and interpreted using the SHapley Additive exPlanations (SHAP) method commonly used for ML model explanation and interpretation. The resistance reduction factors required for the NGBoost model to meet the reliability requirements of the European and US design frameworks were determined via reliability analyses using the methods given in the respective standards and the improved Hasofer–Lind–Rackwitz–Fiessler (iHL-RF) method. Comparisons of the developed NGBoost model with other ML models and existing design provisions indicate that the former is as accurate as other ML models (while offering probabilistic predictions) and significantly outperforms the existing design provisions. A web application was developed and deployed online to predict the ultimate uniform loads of laterally restrained cellular beams with the developed NGBoost model. The proposed NGBoost model can facilitate preliminary cellular steel beam designs and investigating parameters affecting their resistance.

Evaluating the Structural Integrity of Cellular Steel Beams with Web Enhancements

Abstract This study investigates the analytical approach of web reinforcement techniques, including high-strength concrete and laced reinforcement, to enrich improvement for the structural behavior of these beams. The analysis compares an unmodified cellular beam (LB1) with a web-reinforced beam (LB2), including the improvements in load-carrying capacity. The study considers the effects of reinforcement on critical design limit states, such as flexural strength, Vierendeel bending, web post-buckling, and shear resistance. The outcomes reveal significant enhancements in LB2’s structural behavior, with over a 100% increase in flexural strength and local axial force capacity and a 165% increase in web post-buckling strength. This research validates the effectiveness of web reinforcement techniques in concentrating on the limitations of cellular beams and maximizing their potential in structural applications.

Strength Analysis of Cellular Steel Members under Combined Compression and Major-Axis Bending

Strength Analysis of Cellular Steel Members under Combined Compression and Major-Axis Bending

Behaviour of cellular steel beams subjected to impact load: A review

Behaviour of cellular steel beams subjected to impact load: A review

Numerical investigation of elastic-plastic buckling performance of circular arched cellular steel beam using nonlinear finite element analysis method

This study presents a numerical investigation of the in-plane elastic-plastic performance, post-buckling mode, and arched web-post shear resistance of a pinned end circular arched cellular steel beam using ABAQUS nonlinear finite element analysis package. The trustworthiness of the finite element analysis results was confirmed by comparing them to the existing experimental investigation results. The main study parameters, such as the effect of a rise-to-span ratio, the radius of curvature, the impact of opening, the types of loading on elastic-plastic performance, and the buckling mode of an arched cellular steel beam, were investigated. Furthermore, the arched web-post finite element model was proposed and the shear resistance of the arched web-post was investigated. Also, the appropriateness of the currently existing different web-post shear resistance analysis approaches was reviewed and evaluated in determining the shear resistance of arched web-posts. The results showed that the web post-structural stiffness of a circular arched cellular steel beam was improved as the rise-to-span ratio increased under the mid-span concentrated load regardless of the rise-to-span ratio. However, under uniformly distributed vertical load, increasing a rise-to-span ratio beyond 0.35 or 140° subtended angles reduces the stiffness of circular arched cellular steel beams. The web post shear resistance analyzing approaches proposed by Panedpojaman et al. and SCI P-100 overestimate and yield unsafe results in determining the web-post shear resistance of arched web post cellular steel of low rise-to-span ratio.

Design of cellular steel beams subjected to lateral torsional buckling

The present paper investigates the lateral torsional buckling resistance of cellular steel beams numerically. Such beams are quite sensitive to lateral instability owing to a substantial increase in depth of the cross-section with respect to the base profile. While a companion paper was dedicated to (i) characterising experimentally the behaviour of cellular and Angelina beams and to (ii) validating dedicated non-linear shell F.E. models, this paper details the results of extensive numerical studies. Several key parameters in the structural response are investigated, such as the base cross-section profile, bending moment distribution, size and position of the openings, steel grade and member slenderness.The results have further been used to assess an original design proposal for the lateral torsional buckling resistance of such girders. The improved design rules are shown to provide accurate yet safe ultimate load predictions. Also, in comparison with existing and available design rules, the proposal is seen to allow for substantially higher design loads – still safe-sided –, potentially leading to significant material savings.

Structural Behavior of a Fixed-End Arched Cellular Steel Beam without Lateral Support

The arched cellular beam has the advantages of both the solid-web arch and the straight beam with web opening, and has become increasingly admired by architects in recent years. In this paper, four arched cellular beam specimens are designed using an orthogonal test method (OTM) with a three-factor and two-level approach. Firstly, the static loading test is carried out to analyze the mechanical response of the arched cellular beam under concentrated load. Then, a numerical analysis based on ABAQUS finite element (FE) software is carried out. The results show that the simulation results agree well with the test results, which indicates the accuracy of the simulation analysis method. Finally, the buckling load of the arched cellular beam under three different loads is calculated using the variable parameter FE analysis. Combined with the range analysis in the OTM, the influence of the target factor on the buckling load of the arched cellular beam is determined. The results show that the order of the factors affecting the out-of-plane elastic buckling is rise–span ratio > web height–thickness ratio > diameter–depth ratio.

Inelastic Behavior of Hybrid Cellular Steel Beams Made from Hot-Rolled Parent Sections

Inelastic Behavior of Hybrid Cellular Steel Beams Made from Hot-Rolled Parent Sections

Elastic and inelastic major-axis flexural buckling of cellular steel columns

This study investigates the elastic and inelastic major-axis flexural buckling of cellular steel columns. Based on the stationary principle of potential energy, the existing elastic buckling load equation is refined to incorporate the local bending deformations at web posts. The column strength curve for determining the critical loads is then derived. For the elastic buckling, the refinement provides a significant improvement. For the inelastic buckling, the effects of residual stresses and initial geometric imperfections on the column strength are examined by the validated nonlinear finite element (FE) models. The initial geometric imperfection amplitudes of L/300 and L/500, where L is the column length, are recommended for global buckling of cellular steel columns fabricated from the parent steel shapes with h/b ≤ 1.2 and h/b > 1.2, respectively, where h/b is the depth-to-width ratio of the parent steel shapes. The developed column strength curve conservatively predicts the major-axis flexural buckling strength of practical cellular steel shapes, with an average prediction-to-FE buckling stress ratio of 0.97. A comparison also shows that the current EC3 and AISC360 equations are applicable for predicting the strength of practical cellular columns, provided that the refined elastic buckling load is adopted.

Experimental and numerical investigations towards the lateral torsional buckling of cellular steel beams

This paper deals with the response of so-called “cellular members” against lateral torsional buckling. These beams comprising regularly-spaced circular web openings are especially used for their high resistance-to-weight ratio, the possibility to integrate service pipes within their height, and for aesthetics. Such profiles usually exhibit a complex behaviour and many potential failure modes, including interactional local/global instability modes. Regarding global instability, the members are usually designed by means of approximate design rules, which often lead to an unduly conservative solution, with beams sometimes showing up to 150 % resistance reserves.The present research works aim at improving this situation, through the development of adequate design formulae. In this respect, the present paper reports on investigations led towards improved solutions for cellular members at the experimental and numerical levels. This first paper focuses on experimental activities and on the development and validation of dedicated shell F.E. models. The results of three bending tests on members spanning from 7.5 m to 11 m are reported. Cross-sectional dimensions, material properties and accurate initial geometrical imperfections were measured for each specimen and further introduced in the corresponding F.E. models, which are shown to provide predictions in close agreement with the experimental results. The companion paper [1] further makes use of the F.E. models within extensive parametric studies and proposes a new set of design rules that could be proposed for integration in Eurocode 3.

Numerical analysis of the global stability of simply supported cellular steel columns under axial compression

The influence of geometry and materials on the instability of cellular columns has still not been clearly defined in the literature, research, and existing standards in the field. Studies on cellular profiles acting as beams can be found more frequently; however, studies are scarcer for these profiles acting as columns. Some authors have investigated the influence of physical and geometric imperfections on the strength of cellular profiles, while others have focused on the shear and bending effects that act simultaneously with compression in these profiles. The analytical procedures adopted in the main standards do not include calculation of geometric properties of the cellular profiles, which have their area reduced significantly, mainly in relation to the major axis, due to openings. In this context, a parametric study of 576 cellular columns was carried out using the ABAQUS software to investigate the behavior and resistance of these profiles in greater depth. The ultimate load results were compared and contrasted with the results of the standard procedures contained in EN 1993–1–1:2005 [1] and ABNT NBR 8800:2008 [2], using four different methods for calculating the geometric properties. It was concluded that the degree of influence of the diameter of the openings and the spacing between them decrease, along with the consideration of more slender columns.As for standard procedures based on EN 1993–1–1:2005 [1], the analytical method of surface weighting obtained the best results for S355 and S690 steel. Regarding ABNT NBR 8800:2008 [2], the “2T” section method obtained the best results for S355 steel and the line weighting method for S690 steel. However, the discrepancies among some results indicated the unpredictability involved in applying ABNT NBR 8800:2008 [2] for high-strength steel profiles. Therefore, the present study has attempted to provide a better understanding of the behavior of cellular columns, thereby contributing to the technical knowledge in the field.

Behavioural comparison between hybrid cellular steel beams and homogeneous cellular steel beams for different spans

Behavioural comparison between hybrid cellular steel beams and homogeneous cellular steel beams for different spans

A new proposal for the design of laterally unrestrained cellular steel beams under moment gradient at elevated temperatures

The laterally unrestrained cellular steel beams (CB) are more susceptible to buckling failure and collapse early due to the material degradation that occurs in a fire situation. The lateral-torsional buckling (LTB) resistance design proposed by Eurocode 3 pt. 1–2 is relatively conservative for both uniform and non-uniform bending cases and hence needs to be improved. This paper aims to investigate the influence of single and double curvature bending on the LTB resistance of cellular steel beams subjected to elevated temperatures. To carry out the present numerical study, the finite element (FE) models are first validated with a set of numerical and experimental data available from the existing literature. Extensive parametric FE analyses are performed by considering different sizes and spacing of the opening, and various beam slenderness for hinge and roller boundary conditions. Based on parametric research, a new design proposal for LTB buckling resistance of CB at elevated temperatures for various moment gradients is presented. Compared with the analytical results provided by Eurocode 3 pt. 1–2, the proposed design method is safer and conservative. The proposed approach provides better agreements than existing procedures. Moreover, a statistical analysis of the results is performed, and the accuracy of a new proposal is presented in this paper.

Behaviour of cellular steel beams at ambient and high-temperature conditions

New developments in building construction have been observed to attain sustainable design criteria and the efficient use of raw materials, as steel is an example. This led to an increase in recent research on the optimization of geometric configurations of web-opening steel sections to meet cost-effectiveness in structural design. Improvement of the design method for perforated unrestrained steel beams to assess their behaviour under lateral torsional buckling (LTB) is still an ongoing issue for scientists and designers alike. In this article, cellular beams bound to instability were studied analytically by Eurocode and numerically by the finite element method to investigate their behaviour at ambient and elevated temperatures due to fire. The analysis encompasses the effect of the coupling and the endplates' thickness on the cellular beams' collapse strength considering the initial geometric imperfections and material nonlinearities. A parametric study including changing temperature, cross-section geometry, and web aperture configurations was done for beams subjected to uniform bending and distributed load. The analyses depicted the following failure modes: LTB and LTB+ plastification of the two T-section (P-2 T) for end moment load and yielding of top tee section's flange (B-1 T), P-2 T, web post-buckling (WPB), Vierendeel mechanism (VM) and LTB for a distributed load. Combined failure modes such as LTB + WPB, LTB + VM and LTB + VM + WPB have also been observed. Buckling curves for cellular beams were assessed by comparing FE reduction factors with those of the buckling curve recommended by Eurocode 3 for equivalent solid steel beams. A new proposed formula for the plateau length of the LTB curves was obtained, based on the mean squared error method (MSE) between the numerical results and Eurocode formulae. The comparison between the numerical and the simplified design method predicted results shows that the proposed formulae have reduced the discrepancy and improved the LTB curve to better assess the cellular beams behaviour.

Performance of laterally unrestrained hybrid cellular steel beams

Performance of laterally unrestrained hybrid cellular steel beams

Numerical study of steel–concrete composite cellular beam using demountable shear connectors

Steel concrete composite beams have been increasingly used in practice due to their advantages with respect to their structural features and constructability. However, in conventional composite beam systems composite action is applied via shear connectors welded at the top flange of the down-stand steel beam and embedded in the concrete slabs, making it less favourable for the beam system to be disassembled and reused. This paper presents a numerical study of a new composite beam system consisting of a cellular steel beam, metal deck flooring and demountable shear connectors. According to the experimental study, this composite beam system made the demounting, reassembly, and member reuse possible, and did not compromise the loading capacity. In the numerical study presented in the paper, a finite element model was developed and validated against the results obtained from the previous experimental study. The parametric study further examined the effects of concrete strength, shear connector arrangements and asymmetry ratios of steel beam section to the load capacity of the composite beam system. The analysis and comparison provided a deeper insight into the behaviour of this type of shear connector. Through this numerical study, the structural merits of the composite beam system using demountable shear connectors were highlighted. Finally, the mid-span plastic moment of the composite beam was predicted using the direction method provided in SCI publications and compared with the moment–deflection relationship obtained from FE modelling.

Lateral Torsional Buckling Capacity Assessment of Cellular Steel Beams

A cellular beam is a widened I-profile section with circular web openings. This type of perforated-web beam has been used immensely throughout the world during the last two decades. Lateral torsional buckling is one of the steel beam’s limit state designs. This study aims to investigate the behavior of cellular beams against lateral torsional buckling. A validated numerical model was employed in a sort of parametric study. The examined parameters are applied load configurations and the geometrical ratios of flange width-to-thickness, web height-to-thickness, openings’ spacing-to-diameter, beam’s span-to-depth, and opening’s diameter to beam-depth. Based on the results of the parametric study, a lower-bound design formula for predicting the lateral torsional buckling moment resistance of simply supported cellular beams was proposed. The suggested design formula can predict, with an acceptable degree of accuracy, the lateral torsional bending strength of simply supported cellular beams being subjected to various types of destabilizing loads.

Numerical analysis and prediction of lateral-torsional buckling resistance of cellular steel beams using FEM and least square support vector machine optimized by metaheuristic algorithms

This study presents an advanced framework for modeling the lateral-torsional buckling behavior of cellular steel beams, which combines hybrid intelligent models with numerical simulation. The proposed hybrid intelligent models employ a large dataset-based finite element method (FEM) for training and validation the framework, as well as metaheuristic algorithms for optimal auto-hyper-parameters selection. A total of 1535 numerical models are examined in order to evaluate the lateral-torsional buckling behavior. Following that, the least square support vector machine (LSSVM) optimized using four metaheuristic algorithms (ME): particle swarm optimization (PSO), ant lion optimization (ALO), grey wolf optimizer (GWO), and Harris hawks optimization (HHO) algorithms, is utilized to estimate accurately the lateral-torsional buckling resistance. According to the findings of a comprehensive performance evaluation utilizing statistical and graphical comparing criteria, the suggested LSSVM-ME predicts the lateral-torsional buckling behavior with excellent accuracy. LSSVM-HHO, in particular, outperforms the other hybrid intelligence models, with an RMSE of 41.72 kN.m and an NSE of 0.99. Overall, the results indicate that the proposed framework has a great potential for use as a practical tool for estimating the lateral-torsional buckling behavior of cellular steel beams.

Investigation on the Fire Resistance of Cellular Steel Beam with Sinusoidal Openings

Investigation on the Fire Resistance of Cellular Steel Beam with Sinusoidal Openings

Study on anti-progressive collapse performance of cellular steel frames with different web opening shapes

In this paper, cellular beam-column joints with different opening shapes were taken as the object of study to investigate the resistance to progressive collapse of weakened beam-column joints through a combination of experiments and numerical simulations. Opening shapes include circular, rectangular and hexagonal. The development laws of failure mode, vertical force–deformation response, internal force development and resistance mechanism of the specimens were analyzed, and based on the validated finite element model, the effects of weakening parameters of openings with different opening shapes on the performance of the beam-column joints against progressive collapse were studied. The results demonstrate that the load carrying capacity and deformation capacity of cellular joints with different opening shapes have different degrees of improvement compared with the foundation joints, and exhibit the largest deformation in the first opening area near the column flange, where the ductile failure at the weakened section occurs in the hexagonal cellular opening, and the catenary effect can be fully developed, showing the best performance under the designed opening size, rectangular is the second and circular the worst. In addition, the failure mode and load carrying capacity of the specimens can be effectively improved by changing the opening weakening parameters. Increasing the opening diameter (parameter a) and opening edge distance (parameter c) within a reasonable range can effectively improve the vertical resistance and deformability of the specimens, and the effect of opening spacing (parameter b) on the structural load response is negligible. In the design of collapse resistance of cellular beam-column joints, it is recommended to increase the values of parameters a and c appropriately and to reduce the value of parameter b appropriately under the premise of ensuring the structural load carrying capacity, which is more conducive to the catenary action.