Cellular Beams Research Articles

Numerical study of cellular beams under different types of loading

The integration of cellular metal beams in high-rise buildings allows for optimized space utilization for technical equipment, while also reducing floor height and, consequently, the overall weight of the superstructure. However, while these openings provide design flexibility, they can also decrease structural stability by causing deformations in the web posts, especially under concentrated loads. This study focuses on evaluating the strength and stability of open-section beams under various load conditions, using numerical simulations and three-point bending tests. Specific reinforcement solutions were developed to counter instability phenomena and enhance mechanical performance. The results indicate that the finite element model used in simulations provides accurate and consistent predictions with experimental data, validating its utility for in-depth analysis of displacements and failure modes. Notably, the addition of stiffeners proved effective in reducing displacements and enhancing beam stability. This work, still in its exploratory phase, aims to develop a theoretical formula to estimate the contribution of supports to elastic stiffness, paving the way for advances in the use of reinforced metal beams in high-rise construction.

Experimental study and finite element analysis on the shear performance of steel-bamboo composite cellular beam

To study the influence of opening ratio on the shear performance of steel-bamboo composite cellular beams (SBCC), taking the opening size as the basic parameter, experimental research was carried out on five test beams. The failure modes and deformation characteristics of the specimens were observed, and the influence and law of the change of hole size on the shear performance of steel-bamboo composite cellular beams were analyzed. Through nonlinear finite element simulation calculation, multi-parameter analysis was carried out on the composite cellular beams, and the contribution of flanges to the shear performance of cellular composite beams was studied. The results show that the integrity of steel-bamboo composite cellular beams is good. The failure is mainly manifested as the fracture of bamboo web at the beam hole area, the buckling of section steel and the debonding and separation of steel-bamboo interface. The opening ratio has a great influence on the shear performance of steel-bamboo composite cellular beams. The thickness of bamboo flange cannot be ignored for the shear contribution of cellular beams. The shear capacity of cellular beams is shared by flanges and webs. The larger the opening ratio, the greater the shear contribution of flanges to composite cellular beams.

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.

Five Machine Learning Models Predicting the Global Shear Capacity of Composite Cellular Beams with Hollow-Core Units

The global shear capacity of steel–concrete composite downstand cellular beams with precast hollow-core units is an important calculation as it affects the span-to-depth ratios and the amount of material used, hence affecting the embodied CO2 calculation when designers are producing floor grids. This paper presents a reliable tool that can be used by designers to alter and optimise grip options during the preliminary design stages, without the need to run onerous calculations. The global shear capacity prediction formula is developed using five machine learning models. First, a finite element model database is developed. The influence of the opening diameter, web opening spacing, tee-section height, concrete topping thickness, interaction degree, and the number of shear studs above the web opening are investigated. Reliability analysis is conducted to assess the design method and propose new partial safety factors. The Catboost regressor algorithm presented better accuracy compared to the other algorithms. An equation to predict the shear capacity of composite cellular beams with hollow-core units is proposed using gene expression programming. In general, the partial safety factor for resistance, according to the reliability analysis, varied between 1.25 and 1.26.

Experimental study and numerical simulation of cellular I-beam manufactured using refill friction stir spot welding technology

The paper presents analyses of thin-walled I-beams constructed from 6061-T6 aluminum alloy using refill friction stir spot welding (RFSSW). A parametrized finite element model of the reference cellular beam was developed, and the results from numerical simulations and experiments were compared. Subsequently, the validated numerical model was utilized to conduct an in-depth analysis of three additional beams featuring distinct cross-sections. To assess the weld behavior, experiments were conducted on samples composed of two sheets connected by two spot welds. The outcomes of these investigations underscore the suitability of RFSSW as a method for constructing thin-walled structures in civil engineering applications.

Elastic lateral-torsional buckling of cellular beams

Cellular beams are I-shaped steel sections with advantages provided by their circular web openings. This type of beam can have greater spans, be more slender and higher than the solid beams, being more prone to failure by lateral-torsional buckling. Given there is still no specific standard for cellular beams and owing to the importance of safety verification, this paper numerically investigated the lateral-torsional buckling of these beams. Considering the torsional constant as the most important parameter in the design of web-opening beams, this study proposes a new torsional constant and approaches four different calculation methods of weighted average torsional constants. The elastic critical moment of cellular beams was numerically modelled using ANSYS software and compared with analytical results according to European standards, varying the torsional constants. The weighted average torsional constant based on an equivalent area and using the proposed torsional constant was the most efficient, showing the best analytical results when compared with the numerical ones considering the load condition of constant bending moment. Furthermore, from all the geometric parameters evaluated, the height of the cellular beam was what most influenced the elastic critical moment of the cellular beams.

Data-driven design approach for the lateral-distortional buckling in steel-concrete composite cellular beams using machine learning models

Composite steel-concrete beams are presented as an interesting solution for covering long spans. These profiles are characterized by the existence of sequentially spaced openings along the beam web. A very common particular use of this type of structure is in continuous or semi-continuous floors, in which the existence of intermediate supports in the span of the structural member leads to the occurrence of points with negative bending moment. Steel structures in this condition can present different types of instability due to the compression of the bottom flange, such as lateral-distortional buckling and web-post buckling. In this context, a comprehensive parametric study was carried out through finite element simulation aiming to obtain the resistance capacity of this type of structural system. It was observed that different analytical procedures aimed at calculating the ultimate moment of this type of structure fail to predict the bearing capacity of the elements successfully. Thus, aiming to promote more precise design approaches, the modeling of the resistant load of these structures was performed using different supervised machine learning techniques. It was found that machine learning techniques have the potential to correctly predict the bearing capacity of the studied members, having a better agreement with the numerical data obtained, when compared to the approaches presented by analytical procedures described in the literature and design codes. Different machine learning algorithms were trained based on a dataset obtained via FEM: artificial neural networks, support vector machines, XGBoost and Random Forest. All models showed considerable effectiveness, with statistical determination coefficients (R²) higher than 0.9. Among these, the best prediction capacity was obtained with the XGBoost model in terms of correlation coefficient and Mean Square Error, presenting itself as the model that came closest to the set of numerical data used as reference.

The Effect of Opening Size and Expansion Ratio on the Flexural Behavior of Hot Rolled Wide Flange Steel Beams with Expanded Web

In some design cases, such as in castellated beams, cellular beams, or steel beams with expanded web, it is advantageous to strengthen and enhance the performance of steel beams by increasing the web depth. However, expanding the web of a steel beam is a unique engineering strategy. This modification not only enhances its ability to bear heavy loads but also reduces any bending or flexing while enabling longer distances between supports. The expanded steel beams can be achieved by making a horizontal cutting in the steel beam web and then adding an increment plate (with the same web thickness), called spacer plate, between the two halves of the web sections, thus improving stiffness and strength. To evaluate the behavior of such beams, nine specimens of HEA steel beams with expanded web ratios of 150%, 200%, and 250%, and one specimen as a reference beam, were fabricated. The specimens were evaluated under two-point load over a clear span length of 280 cm. From the experimental work it was found that for steel beams with expanded web that have 18 openings with 80 mm, the beams with an expansion ratio of 150% had the best performance according to load-deflection behavior with a reduction in load capacity by only 11%. Additionally, the beams with expansion ratios of 200% and 250% had no economic viability according to the analysis of load-deflection behavior with a reduction in load capacity by 49% and 62%, compared with the solid expanded steel beam with the same expansion ratio. For the second type of steel beam with expanding web with 9 openings of 160 mm width, the beams with expansion ratios of 200% and 250% were observed to perform better than the first type with a reduction in load capacity by 28% and 50%. Using larger opening width and a smaller opening number is considered the best option for beams with expansion web ratios of 200% and 250%, while on the contrary, using smaller opening width and higher numbers seems to be a better option for beams with 150% expansion web ratio. Expanding the depth of a steel beam provides design flexibility, reduces deflections, and allows for longer spans. These benefits enhance material efficiency and open up new architectural possibilities.

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.

Parametric analysis on hybrid design method for steel cellular beams

Parametric analysis on hybrid design method for steel cellular beams

Numerical investigation of steel beams with web openings obtained from topology optimisation

The use of web openings in I-section beams has become increasingly common in recent years, and these elements can be observed in various civil engineering applications. This design approach results in an improved weight-to-stiffness ratio in steel beams, enabling their use over longer spans without a significant increase in material cost and deflections due to self-weight. It also avoids the cutting of holes in inappropriate locations for electrical, hydraulic, and air conditioning installations. Steel beams fabricated with web openings also represent an important solution when height constraints are imposed on multi-story buildings due to design regulations and economic considerations. It is recognised that the use of the traditional web opening shapes - namely, circular, rectangular, and hexagonal - in civil structures can lead to issues associated with high stress concentration. The presence of these web openings can induce local instability or yielding due to inadequate shear force transfer across the openings, allowing plastic hinge formations, also known as Vierendeel mechanism, for instance. In this sense, researchers have investigated novel shapes to mitigate the impacts of the web openings in both structural and economic terms. In this sense, this work has been developed aiming to evaluate the structural performance of I-section beams obtained using structural optimisation, for a reference distributed load and different boundary conditions, compared with the cellular beams. An evaluation of the structural potential of the obtained topologies has been performed by linear elastic, buckling and complete nonlinear analyses. Results were obtained in terms of stresses, displacements, and ultimate loads for all investigated cases. It was found that when compared to a cellular beam, the optimised beams increased the ultimate resistance with superior stiffness resulting in lower displacements and presented a more adequate stress distribution with lower stress concentration. However, in some cases a poor structural performance was observed due to large zones with holes obtained from the optimisation process. Based on these results and on the work of Tsavdaridis et al., authors proposed a configuration for the openings, and its structural performance proved it to be a promising solution to be employed on beams with web openings, especially when the expected failure mode is lateral-torsional buckling. A parametric study was conducted to assess the efficiency of the proposed configuration for different steel profiles and span lengths; results indicated equivalent or superior load capacity when compared to the reference cellular beam. The configuration suggested by the authors can be easily fabricated, and, considering the constant patterns along the length, finding an expression to determine its design load is possible, like what is usually done for other shapes (circular, hexagonal).

Structure Optimization with Metaheuristic Algorithms and Analysis by Finite Element Method

In engineering, design is made by considering functionality, reliability, manufacturability, usability, and total cost. There are a wide variety of methods for design optimization. Metaheuristic methods inspired by nature are one of them. In this study, the Refinement firefly algorithm is proposed as a new method. Grey Wolf, Particle Swarm, and Firefly algorithms are compared with the proposed Refinement Firefly Algorithm. Mathematical benchmark problems are used to examine the performance of algorithms. Also, welded beam, cellular beam, and frame system designs are considered sample problems. These design examples are solved by algorithms and the sections are determined. The sections determined by optimization were analyzed using the ABAQUS CAE program and its reliability was examined. Numerical analysis with the finite element method is very useful as it provides realistic solutions. ABAQUS CAE is used to detect and show deformations in the structure. Finite element solution with ABAQUS solves the problems analytically and it is seen that the sections determined by the optimum design algorithm remain within the limits. The proposed Refinement Firefly algorithm demonstrates superior performance compared to the Firefly algorithm. However, it yields inferior results when compared to the Grey Wolf and Particle Swarm algorithms.

Regression models for ultimate hogging moment prediction of composite cellular beams

ABSTRACT This work shows the accuracy and feasibility of polynomial regression models for the ultimate hogging moment prediction of composite cellular beams utilising different numbers of simulations. It discusses an attempt to reduce the number of samples in a finite element parametric study, which consists of using only the combination of extreme levels of each factor to develop the regression models. The parametric study has five parameters: cross-section dimensions, hogging moment distribution, unbraced length, opening diameter, and web-post width. The regression models are generated based on 32 (extreme values), 162 (extreme and intermediate values), and 360 numerical model results (all values). An ANOVA was performed on each regression model to assess the parameters’ order of relevance. According to ANOVA, the profile cross-section dimensions and hogging moment distribution were the most significant parameters on the beams’ ultimate moment for all regression models. As good precision was achieved, because of the insignificant differences within the regression models, it was observed that the combination of arbitrated extreme levels for the factors could significantly reduce the number of numerical simulations in a parametric study. Still, this approach could be used for any other type of structure to reduce the computational cost of future numerical investigations.

Taguchi-enhanced Grey Wolf Optimizer for robust design of cellular beams

This research presents a comprehensive comparative analysis of optimization techniques for achieving the optimal design of cellular beams. The incorporation of gaps within cellular beams reduces the weight of the beam and increases section height, resulting in the production of lighter and stronger sections. The Taguchi method is employed to fine-tune the parameters of the Grey Wolf Optimizer, enabling the achievement of a robust design. The performance of each algorithm is evaluated through three design examples, facilitating comprehensive comparisons among the seven algorithms. Moreover, the study encompasses the modeling and analysis of optimally designed cellular beams using finite element software.

Cellular beams and prEN 1993‐1‐13: an opportunity to address environmental challenges

AbstractIn recent years, construction has faced new challenges, especially related to the reduction of environmental footprint. Measurement of construction performance in this domain is mainly done through Life Cycle Assessment (LCA).Steel and composite beams are affecting the height and the weight of buildings and one very effective solution is cellular beam. This attractive solution is not fully integrated in the current design standard. This paper presents how the second generation of Eurocodes; EN1993 and EN1994 will be adapted to enable structural engineers to design cellular beams. A technical description of the specific failure modes and concepts for design are presented in more details. A comprehensive case study developed in agreement with the future parts of Eurocode along with a comparison of different structural solutions for a typical building is shown. Typical composite designs are compared to solutions made of cellular beams.A Life Cycle Assessment, shows that up to 35% of CO2 eq. emissions can be saved by choosing the right solution. It is not only the structural solution but also the material that influences the environmental impact. Comparisons include high strength steel vs mild steel, hot‐rolled vs welded beams, and XCarb® ‐ steel made from high levels of recycled steel using 100% renewable electricity in an electric arc furnace versus average steel in Europe.

3D printed wood-fiber reinforced architected cellular composite beams with engineered flexural properties

This study explores the integration of cellulose-based compounds into a biobased polymer to create high-performance sustainable materials with improved properties. The elastic flexural characteristics of 3D printed composites, comprised of polylactic-acid (PLA) biopolymer reinforced by a variety of waste wood fiber weight percentage (2.5%−15%), are investigated. Initial steps involve producing wood-fiber reinforced PLA (WF-PLA) filaments and the 3D printing of test specimens. Experimental outcomes reveal enhanced flexural modulus (60% increase), rigidity (72% increase), strength (39% increase), and failure strain (21% increase) alongside reduced composite coupon density (5.2% decrease), attributed to wood fiber incorporation. To achieve lightweight and sustainable structural components with tunable attributes, architected composite cellular beams are introduced. These beams comprised of wood-fiber reinforced composites feature cross-sectional unit cells with one or two reflection symmetries, showcasing the synergy between architecture and material composition in enhancing quasi-isotropic flexural rigidity. Investigation on the flexural rigidity ratio ([EI]yy/[EI]xx) involves theoretical modeling, computational analysis, and experimental validation using 3D printed samples. WF-PLA filaments enable the 3D printing of engineered quasi-isotropic cellular beams, termed “Isoflex”, that demonstrate up to 130% enhanced specific flexural rigidity (bending rigidity-to-mass ratio) and up to 70% improvement in flexural rigidity ratio to have isotropic flexural properties, compared to pure PLA beams. This study introduces WF-PLA engineered cellular composites as a sustainable avenue for tuning structural properties, contributing to the realm of additive manufacturing.

The numerical assessment of stress distribution of I-beam with web opening

PurposeCastellated and cellular beams achieved the same strength as solid I-beams with the same depth, resulting in significantly lighter and more economical structures. The purpose of this study is to analyse the bending behaviour of I-beam steel sections with certain web openings by finite element analysis.Design/methodology/approachThe accuracy of finite element results allows extensive numerical analysis of sections with web openings, concentrating on the web opening sizes and web opening positions. These assumptions can increase the induced section load with various shapes of web opening depth and web opening shapes of c-hexagon, hexagon, octagon, circular and square. This also includes spacing distances, with a 50-mm edge and 150-mm centre-to-centre distance and a section with a 100-mm edge and 200-mm centre-to-centre distance. Generally, the adjustment of the opening geometry (by reducing the angle of web pitch or reducing the opening depth depending on analysed parameters) may influence the bending behaviour.FindingsAdditionally, Model 2 was found to be the optimum model compared to Model 1, mainly in terms of bending. Moreover, the I-beam with a c-hexagon shape opening exhibited the lowest displacement compared to other sections with other web opening shapes. Section with a different arrangement of web opening, Type E shows the lower displacement while higher displacement is observed for Type A and also higher displacement considered for Type G. The optimum model is associated with Type E, followed by Type D, compared to other types of certain web opening and I-beam.Originality/valueThe use of sections with different arrangements of web opening improved the performance of the perforated section in terms of structural behaviour, compared to typical I-beam, thus leading to economic design.

Analyzing the influence of perforations on the structural behavior of mild steel cellular beams

Analyzing the influence of perforations on the structural behavior of mild steel cellular beams

Flexural behavior of partially encased cellular beams: Tests and design implications

This paper focuses on a new type of composite beam designated as the partially encased cellular beam (PECB). The PECB consists of a steel wide-flange member in which its perforated web is encased by reinforced concrete. The PECB is envisioned to be superior to the conventional partially encased beam in that it can eliminate the need of shear connectors required in the conventional partially encased beam to develop the desired composite action. This feature helps alleviate reinforcement congestion that may exists in a conventional partially encased beam and minimize construction cost and effort. To investigate the flexural behavior of the proposed PECB, five specimens with representative geometries and typical materials were designed and constructed. The specimens were monotonically loaded with the four-point bending test setup. Test results show that the proposed PECB can behave satisfactorily under flexure and that the shear connectors may not be needed in a properly designed PECB for development of the composite action. Based on the classic beam theory and idealized stress/strain diagrams, this paper develops three practical models for estimating the yield flexural strength, plastic flexural strength, and initial flexural stiffness of the proposed PECB. Comparisons of the predictions from these models with the test results show that the practical models can provide reasonable predictions and can be used for future practice.