Full length articleStability behavior of Steel–concrete Composite Beams subjected to hogging moment
Introduction
Steel–concrete composite beams (SCCB) under hogging moment may fail due to the occurrence of Local Buckling (LB) modes, Lateral Distortional Buckling (LDB) or through the combination of these buckling modes [2], [3]. LDB (Fig. 1) is characterized by a web distortion due to lateral displacement () and rotation () of the unrestricted bottom flange [1], [4], [5], [6], [7], [8]. This displacement and rotation occur due to the fact that the top flange is totally restrained, through the concrete slab, to the lateral displacement [9]. As a result, LDB in SCCB behaves very differently from the stability modes of steel I-beams, in a way that the well-known Vlasov assumption [10], that the plane-webbed sections still forms a plane, not valid.
In order to solve this problem, investigations were carried out about LDB in SCCB. These investigations focused on analyzing the elastic behavior [4], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26] in an attempt to obtain a method for determining the elastic critical moment, or sought to analyze the LDB strength of SCCB [1], [2], [6], [7], [8], [27], [28], [29], [30], [31], [32], [33], [34]. The correct determination of the LDB elastic critical moment is fundamental to resolve the LDB strength. The current standard procedures require the elastic distortional critical moment determination to estimate the LDB strength of SCCB. In the EC4 [35] previous version (EN 1994-1-1:1992), the methodology proposed by Roik et al. [16] to determine the elastic distortional critical moment was adopted. This methodology is still used in the Brazilian code [36] (ABNT NBR 8800:2008). However, studies [11], [20], [21] have shown divergences between elastic distortional critical moment, obtained through numerical analysis, when compared with the methodologies proposed by Roik et al. [16], Svensson [13], Williams and Jemah [14] and Hanswille et al. [18]. Therefore, the use of these methodologies for the elastic distortional critical moment estimation can result in the mistaken obtaining of the strength of SCCB under the action of hogging moment by the standard procedures. In addition, standard codes such as Eurocode 4 [37], AISC [38], AASHTO [39], NBR 8800:2008 [36] and Australian codes [40], [41] make use of the same design curves proposed for steel elements to determine the LDB strength of SCCB. Rossi et al. [2], Zhou and Yan [1] and Liu et al. [8] showed very conservative situations in the standard codes when compared with FEA (Finite Element Analysis) results obtained for SCCB subjected to uniform hogging moment. In this context, there is a need for further investigation into the instability modes of SCCB, as the estimation of the strength of these elements is not yet fully understood.
Therefore, this paper aims to investigate the behavior of SCCB under the action of hogging moment. For this, buckling and post-buckling numerical analyzes with the ABAQUS [42] software were developed. With the buckling analysis it is possible to determine the elastic critical moment, which is compared with the analytical procedures present in the literature. In the post-buckling numerical analysis, the initial geometric imperfection, residual stress, real shear connector, geometric nonlinearity, and material nonlinearity were considered. These results are compared with standard and analytical procedures. The beams are considered simply supported, with restrictions on lateral slab displacement and are subjected to a uniform hogging moment distribution. The influences of the following parameters are analyzed: longitudinal reinforcement ratio, different I-sections, unrestrained span length, the slab height and the differences in the use of solid slabs and precast hollow core slabs. The analyses showed in this work can provide a reference for future research and specification reviews.
Section snippets
Literature review
SCCB can be used as simply supported elements and therefore subjected to sagging moments. Consequently, the concrete slab is in compression and the steel I-section is in tension [43]. However, in the construction of buildings the use of rigid and semi-rigid connections has been frequent, causing hogging moments in the beams which leads to tensile stresses in the concrete slab and compression in the steel I-section [4], [44], [45]. Compression stresses in the bottom flange of the steel
LDB standard and analytical procedures
The standard procedures that address the LDB phenomenon use the conventional lateral–torsional buckling theories for the buckling of partially restrained beams or the inverted U-frame model. Eurocode 4 (EN 1994-1-1) [37] considers the inverted U-frame model in determining the LDB elastic critical moment and uses the same design curves developed for the LTB analysis in I-beams. The Brazilian standard code, ABNT NBR 8800:2008 [36], is also based on the inverted U-frame model to determine of the
Numerical model
For the development of numerical analyses, the ABAQUS software [42] was used. With this software it is possible to develop elastic buckling analyses and post-buckling analyses (physical and geometric nonlinear analyses). For the elastic buckling analysis, the buckle linear perturbation method was used to estimate the critical elastic stability load by obtaining eigenvalues and their eigenvectors. In this method, the critical elastic stability load is obtained by the product of the first
Numerical model verification
The numerical model developed to analyze the behavior of SCCB with solid slab under hogging moment was validated in the previous papers, Rossi et al. [2], [58], through the experimental tests of Tong et al. [66]. However, as no experimental study in SCCB with PCHCS under hogging moment has been found in the literature, Lam’s [75] experimental tests (sagging moment), also presented by Lam, Elliott and Nethercott [76], were analyzed to verify the validity of the numerical model developed with
Parametric study
In the parametric study, the LDB elastic critical moment and the LDB strength of SCCB was investigated. For this, buckling and post-buckling numerical analysis were performed in the ABAQUS software. The influence of the following factors on the stability phenomenon of SCCB was investigated: I-section, unrestrained length, longitudinal reinforcement ratio, the slab height and the possible influence of solid slabs and PCHCS on the behavior of SCCB under hogging moment. The composite beams were
Results and discussion
The analysis developed in this paper aimed to investigate the stability behavior of SCCB under the action of uniform hogging moment distribution by analyzing the occurrence of LDB and local stability modes. The following parameters were investigated: I-section, unrestrained length, longitudinal reinforcement ratio, the slab height and the possible influence of solid slabs and PCHCS. The results of the numerical buckling analysis were compared with the elastic critical moment values obtained by
Conclusion
This study investigated the stability behavior of SCCBs under uniform hogging moment. Buckling and post-buckling numerical analyses were performed using ABAQUS software. The following parameters were investigated: I-section, unrestrained length, longitudinal reinforcement ratio, the slab height and the possible influence of solid slabs and PCHCS. The buckling analysis results were compared with the LDB elastic critical moment values obtained by analytical procedures. Posteriorly, the
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
This study was financed by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.
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2022, Thin-Walled StructuresCitation Excerpt :Through this software it is possible to perform buckling and post-buckling numerical analyses [26]. The buckling analyses were performed using the linear buckle perturbation method, in which it was possible to estimate the critical buckling load (bifurcation point) by obtaining eigenvalues and eigenvectors [27,28]. To carry out the post-buckling analyses, the initial imperfections of the model, both physical and geometric, were considered.
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2022, Engineering StructuresCitation Excerpt :With this, it is sought to faithfully represent the real behavior of the structure. The numeric model developed to analyze the LDB behavior of SCCB under hogging moment was validated in the previous papers, Rossi et al. [39,52,69]. The numerical validation was developed considering the experimental specimens tested by Tong et al. [43].