Limit Load of Cellular Beams Governed by Web-Post Bending Failure in Integrated Structural Systems

The continued growth of the construction industry has led to increasing demands on structural systems to deliver longer spans, lower self-weight, and better material efficiency without compromising strength and serviceability [1-3]. Within this context, cellular steel beams have gained growing interest in building engineering, as shown in Figure 1, since their web openings not only facilitate the passage of mechanical and electrical services but also enhance structural efficiency [4-7]. However, the presence of these openings significantly modifies the stiffness distribution, internal force-transfer mechanism, and stress distribution within the member, thereby introducing both global and local failure modes that must be properly understood to ensure safe and economical design [8-10].

Previous studies, from a global perspective, revealed that the structural behavior of cellular beams depended on the interaction among bending, shear, and stability effects [11-12]. Reported failure modes comprise Vierendeel action, web-post buckling, lateral torsional buckling, and overall bending- or shear-governed failure [13-16]. Taken together, these studies suggested that the behavior of cellular beams was strongly influenced by parameters such as opening geometry, spacing arrangement, loading condition, and member proportions, and that existing design codes may be either overly conservative or unconservative depending on the governing failure mode [13-16]. These observations point to the need for a more refined assessment of failure behavior in perforated steel members.

In addition to their structural efficiency, cellular beams are increasingly relevant in complex engineering systems where mechanical behavior interacts with other physical fields. In practice, the web openings often accommodate HVAC ducts, piping, and service networks, which makes these members closely connected to fluid–structure interaction in building systems, thermo-mechanical effects under fire or elevated temperature, and vibration–acoustic performance in integrated floor systems. From this perspective, understanding the local failure behavior of cellular beams is important not only for structural safety, but also for the reliable design of multifunctional and multiphysics-coupled engineering systems. At the local scale, stress concentrations around the opening boundaries and within the web-post region play a crucial role in governing resistance and failure progression. Over the years, both numerical and experimental studies have examined several local failure mechanisms, including localized bending, web-post buckling, Vierendeel action, web-post horizontal shear failure, and web-post horizontal moment failure (WPHMF) [17-20]. Although these efforts have substantially advanced the understanding of local behavior, they also reveal that existing design methods do not always provide consistent predictions of local strength in members containing web openings. In particular, the combined influence of local bending demand, shear transfer, and geometric characteristics remains inadequately captured in current design formulations.

Among the local failure mechanisms, WPHMF has received relatively limited attention. This bending-dominated mode commonly develops in cellular beams with small opening ratios and relatively short spans, where high horizontal shear transfer generates substantial bending demand in the web-post ligament. Existing studies have generally addressed this mechanism only indirectly within broader parametric analyses or have focused primarily on web-post horizontal shear failure [20]. Consequently, specifications of current steel design, including ANSI/AISC 360-16 [21], do not explicitly provide provisions for evaluating web-post bending resistance or identifying the associated failure location under WPHMF. This represents a significant research gap, particularly because preliminary evidence suggested that the direct use of current code-based formulations might lead to considerable errors in predicting both web-post resistance and the critical failure location.

To address the identified research gap, the present study focused on the load-carrying limit associated with WPHMF in cellular beams within a comprehensive FE framework. Three-dimensional models were developed and validated in ABAQUS [22], and 100 simulations were carried out through a systematic parametric study involving variations in beam section size, slenderness ratio, and opening ratio. This study formed part of the broader research conducted by Sae-Long et al. [20]; however, it differed in that it specifically addressed the load-carrying limit. In contrast, Sae-Long et al. [20] focused solely on local responses, namely the web-post horizontal moment and the failure location. When compared with existing works [18-20], the novelty of the current study lied in its advanced understanding of WPHMF by delivering a more rigorous assessment of structural behavior and improved design-oriented formulations for safer and more efficient cellular beam design.

A finite element (FE)-based approach was adopted in this study to investigate the limit load of cellular beams failed by WPHMF. The methodology involved two sequential stages. First, detailed FE models were conducted by ABAQUS [22] and validated using previously published experimental and numerical results [23], [24], [25]. The validated models were then used to perform a systematic parametric study of the key geometric variables governing web-post bending-dominated failure, as shown in Figure 2.

Four-node reduced-integration shell elements were used to develop the FE models of the cellular beams, including the flanges, web, and circular openings. The steel material was modeled as homogeneous, isotropic, and elastic-perfectly plastic, consistent with the assumptions reported in literature [20]. The elastic properties were specified using a Poisson’s ratio of 0.30 and a Young’s modulus of 200 GPa, while yielding was governed by the von Mises criterion with a yield stress of 245 MPa. As demonstrated in Figure 3, the beams were idealized as simply supported. At each end section, the centroidal node was restrained against vertical and lateral displacements, and the left-end centroidal node was additionally restrained in the longitudinal direction to suppress rigid-body motion. The flange tip nodes were constrained against out-of-plane displacement to prevent end twisting. These modeling assumptions were adopted to accurately capture the local web-post behavior, leading to failure while preserving computational efficiency [18-20].

As reported in a previous study [20], the accuracy of the numerical model was evaluated through verification and validation against established benchmark results [23-25]. The global response was validated using three-point bending test data for a cellular beam specimen available in literature. The predicted load–displacement behavior showed close agreement with the experimental results, with the predicted failure load being approximately 8.9\% higher than the measured value, as illustrated in Figure 4. At the local level, the model was further verified by comparing the FE predictions of bending moment, vertical shear force, and web-post horizontal shear force with both analytical elastic-line solutions and an independent FE dataset, as shown in Figure 5a–\ref{fig5}c. The strong agreement observed in these comparisons confirmed that the proposed model was capable of accurately capturing both the global structural response and the local web-post demands, thereby providing a reliable basis for the subsequent parametric study.

The limit load associated with WPHMF was identified through force-controlled nonlinear analysis. A uniformly distributed surface pressure was applied to the top flange and increased incrementally in small steps of approximately 0.1\% of the target load. Failure was assumed to occur when yielding propagated across the web-post region to form a continuous yield path, as identified using the yield indicator in ABAQUS [22]. The corresponding pressure was then converted into an equivalent uniformly distributed line load and taken as the limit load of the cellular beam. At this stage, the web-post horizontal bending moment was evaluated along the critical horizontal failure section, and the failure location was defined as the distance from the neutral axis to the horizontal yielded band within the web-post. These parameters were subsequently used as the primary response variables in the following analyses.

A mesh analysis was conducted prior to the full parametric study to ensure that the numerical results were independent of mesh discretization, following the procedure reported in literature [20]. The largest beam considered in the study was adopted as the reference model, and the mesh was refined separately in the critical web-post region and the surrounding non-critical regions. Outside the anticipated failure zone, an element size of approximately H/30 was used, whereas a substantially finer mesh was adopted within the web-post region. Convergence was assessed in terms of the limit load and the web-post horizontal bending moment at the critical failure section. Based on the refinement results, the final production mesh in the critical region was defined using 256 elements in the vertical direction and 16 elements in the longitudinal direction, as further refinement produced only negligible changes in the predicted response while considerably increasing the computational cost [20].

It is important to note that the S4R four-node shell element was selected because it offered an efficient and reliable formulation for nonlinear analysis of thin-walled steel members with geometric discontinuities such as circular web openings. In the present study, this element provided a suitable balance between accuracy and computational cost, especially for the large parametric set under consideration. Although higher-order shell elements such as S8R could also be used, the adopted S4R formulation was found sufficient to reproduce both the global and local responses of interest after validation, as confirmed in Figures~\ref{fig4} and~\ref{fig5}. It is also noted that isogeometric FE formulations may provide an attractive alternative for thin-walled structures with complex geometry, due to their higher geometric continuity and potentially reduced mesh sensitivity, as discussed by Milić et al. [26].

The adopted methodology provided a consistent and reliable framework for identifying the initiation of web-post bending-dominated failure, determining the corresponding load-carrying limit, and assessing the effects of key geometric parameters on local resistance. By integrating validated FE modeling with a systematic parametric investigation, this study established a solid foundation for improving the prediction of WPHMF in cellular beams.

A thorough parametric investigation was conducted to examine the effects of the main geometric variables on the limit load and local response of cellular beams governed by WPHMF. Using the previously validated FE framework, a total of 100 numerical models were analyzed to represent a broad range of practical cellular beam configurations, as displayed in Figure 6. The variables being considered included the 11 beam section sizes, the slenderness ratio ($L/d$), and the 4 opening ratios ($d_0/d$), as these were identified as the primary geometric parameters influencing stress redistribution and failure progression in the web-post region. The slenderness ratio ranged from 11.43 to 20, the opening ratio from 0.8 to 1.1, and the beam sections were selected from standard rolled steel profiles commonly used in engineering practice. The ranges of these parameters came from a large parametric database, which confirmed the cellular beams failure by WPBMF [18-20]. For each numerical case, FE analysis was used to determine the principal response quantity at the onset of WPHMF, namely the limit load, defined as the equivalent uniformly distributed line load corresponding to the formation of a continuous yield path across the web-post region. The numerical results were subsequently compared with the corresponding predictions of ANSI/AISC 360-16 [21] to evaluate the adequacy of the current design approach.

The numerical simulations indicated that WPHMF emerged as a progressive local mechanism driven by the propagation and coalescence of yielding within the web-post ligament [20]. The stress distributions at failure offered direct evidence of the governing mechanics. The in-plane normal stress field exhibited the characteristic four-lobe pattern of alternating tensile and compressive stresses around adjacent openings, thus confirming that the web-post response was predominantly governed by bending. Concurrently, the shear stress field reached its highest value along the ligament centerline, to reveal strong in-plane shear transfer through the center of the web-post. The combined effect of these normal and shear stress components generated a continuous zone of elevated von Mises stress across the web-post, hence closely corresponding to the observed failure pattern associated with WPHMF. This interaction accounts for the butterfly-shaped yielding pattern observed in the FE simulations and confirms that the failure mode is governed by the coupled effects of bending-induced normal stress and shear transfer rather than pure flexure, as illustrated in Figure 7.

Figure 8 shows that the parametric study, based on 100 FE models, identified the beam section size, slenderness ratio, and opening ratio as the main parameters influencing the local response associated with WPHMF. All simulations exhibited failure in the WPHMF mode, as indicated by the von Mises stress distributions shown in Figure 9. Comparison with the ANSI/AISC 360-16 codes [21] further indicated that the code-based formulation was unable to accurately capture this local failure mechanism. On average, the predicted limit load was underestimated by about 68.85\%. This difference could be attributed to the simplified code assumptions regarding the effective resisting area of the web-post and the fixed critical-section idealization adopted in the conventional design expression. Consequently, the current standard may not provide accurate prediction of the actual load-carrying limit and local resistance of cellular beams governed by bending-dominated web-post failure.

Detailed evaluation of the geometric trends showed that decreasing the opening ratio increased the discrepancy in code-based predictions of limit load, particularly for larger beam sections. Conversely, increasing the spacing ratio reduced this discrepancy because the wider web-post ligament provided more effective area to resist local bending. The results further indicated that several of the smallest sections displayed the opposite trend in predicted limit load, as these sections were outside the applicable range of the design provisions. Therefore, the local resistance of cellular beams cannot be predicted with sufficient reliability unless the combined effects of opening size and spacing on stress redistribution within the web-post region are explicitly considered.

The slenderness ratio was also discovered to have a pronounced effect on the failure response. In general, decreasing the span-to-depth ratio increased the discrepancy between the FE predictions and those of ANSI/AISC 360-16 [21], especially for larger sections. This suggested that the current code provisions became increasingly conservative for deeper cellular beams under the WPHMF conditions to be considered. Mechanistically, lower slenderness ratios enhance shear transfer across the web-post ligament and, in turn, increase the local bending demand between adjacent openings, whereas higher slenderness ratios promote a more bending-dominated global response and reduce the local shear-driven demand. Taken together, the results indicated that slenderness, spacing ratio, opening ratio, and section size act in combination to govern the initiation and severity of this failure mode.

From a design standpoint, these observations suggest that WPHMF should be recognized as a distinct governing local limit state in cellular beams with small spacing ratios, rather than being assessed indirectly through simplified code-based expressions. The persistent discrepancy between the FE results and the ANSI/AISC 360-16 predictions [21] indicated that the current design provisions did not fully represent the actual stress path and yielding progression within the web-post region. The proposed equations therefore provided a more rational basis for estimating both the magnitude and location of failure and might enable safer as well as more economical design of cellular beams within the investigated geometric ranges. However, these conclusions should be considered in light of the assumptions adopted in the numerical model, including monotonic loading, perfectly plastic material behavior, and the omission of detailed geometric imperfections and residual stresses.

Although the present analysis was conducted under monotonic loading, the identified WPHMF mechanism might be modified under coupled service conditions. Under cyclic or dynamic loading, repeated stress reversals and local demand amplification may accelerate yielding accumulation and alter the progression of the critical plastic zone within the web-post ligament. Likewise, under elevated temperature or thermo-mechanical coupling, the local stiffness and strength degradation of the steel may reduce the limit load and shift the critical failure path. These considerations suggest that WPHMF should also be examined within broader multiphysics loading frameworks in future studies.

This study examined the limit load and behavior of cellular beams under WPHMF using a validated three-dimensional FE model developed in ABAQUS [22]. A total of 100 numerical simulations were performed by varying the beam section size, slenderness ratio, and opening ratio, with the limit load defined by the formation of a continuous yield path across the web-post region. The results demonstrated that WPHMF is a distinct and governing local failure mode in cellular beams with closely spaced openings, occurring before web-post horizontal shear failure and Vierendeel action.

Besides, stress analysis revealed that this mechanism was controlled by the combined action of in-plane normal stress and shear stress, leading to the characteristic butterfly-shaped yielding pattern within the web-post region. The parametric study showed that the limit load was strongly dependent on the opening ratio, slenderness ratio, and section size. Relative to the FE results, the ANSI/AISC 360-16 codes [21] underestimated the limit load by an average of 68.85\%, with larger discrepancies observed for beams with smaller opening ratios, lower slenderness ratios, and larger section sizes. These findings suggested that current design provisions did not adequately represent the true load-carrying limit associated with bending-dominated web-post failure, and that WPHMF should be recognized as a distinct local limit state in the design of cellular beams with closely spaced openings.

For the benefits of complex engineering systems, these findings are relevant to the safer design of integrated structural members that must simultaneously satisfy load-carrying, service-integration, and performance requirements. Improved prediction of web-post limit states could support the optimization of multifunctional cellular beams used in buildings and infrastructure where structural efficiency is combined with routing of mechanical and utility systems. The present results may provide a useful structural basis for future multiphysics modeling frameworks that should take into account coupled effects such as thermal actions, fluid–structure interaction, and dynamic loading in perforated steel members.

Future research should extend the present work beyond the assumptions adopted in the numerical model, including monotonic loading, elastic–perfectly plastic material behavior, and the exclusion of residual stresses and detailed geometric imperfections. Experimental investigations are recommended to further verify the observed failure mechanism and the predicted limit load, particularly for beams with closely spaced openings and large section sizes. In addition, broader numerical and experimental studies covering wider geometric ranges, different loading conditions, and more realistic material and fabrication effects would be valuable for improving the reliability and general applicability of the findings in practical design.