Performance of steel coupling beam with trapezoidal corrugated web: experimental tests and numerical analysis

Steel coupling beam (SCB) is a substantial member of the hybrid coupled walls system. When coupled walls are linked by SCB rather than conventionally reinforced or diagonally reinforced coupling beams, the system’s strength and energy dissipation capacities are greatly enhanced. A corrugated web may be used in SCB instead of a flat web to improve these characteristics even more. This paper presents an experimental and numerical investigation of the shear-carrying capacity and energy-dissipating capability of steel coupling beams with both types of webs (flat and corrugated). Full-scale specimens of hybrid coupled walls with SCB made with flat web and SCB with corrugated web were prepared and tested under monotonic loading. Finite elements software (ABAQUS) was used to implement the numerical analysis. Good agreement was noticed between the experimental and the numerical results. The results of this study are promising that to the possibility to enhance the load carrying and ductility capacities of SCB using a corrugated plate instead of a flat plate as a web.


Introduction
Several types of lateral force-resisting systems such as moment-resisting frames, braced frames, and shear walls are commonly used to resist seismic and wind loads. Numerous research studies have been conducted on these systems which includes experimental, numerical as well as optimization studies (Kaveh & Farhadmanesh., 2019;Kaveh & Zakian., 2014a. Coupled walls system is commonly used in contemporary mid and high-rise buildings to resist wind and earthquake loading. Coupled walls structures are typically compromised of RC structural walls linked by coupling beams (CB). CB is utilized to boost lateral resistance, reduce seismic energy and dissipate it. There are several types of coupling beams that being implemented in existing buildings, including conventional reinforced coupling beams, diagonally reinforced coupling beams, encased steel composite coupling beams and steel coupling beams. The later was the focus of the researchers due to its advantages represented in the superior ability to dissipate energy compared to other types (Shan et al., 2020;Zuo et al., 2022).
The corrugated web section provides a low-cost alternative that is more suitable in construction than flat steel beams. Moreover, the cross-section of the corrugated webs increases the beam capability for load bearing in addition to strengthening it against shear (Erdal et al., 2021). The corrugated web has been used in many applications fields, such as building structures, bridges (Driver et al., 2006;Eldib, 2009), and steel shear walls (Bahrebar et al., , 2020. Many researchers have examined the shear buckling of the corrugated web through experimental and numerical studies (Leblouba et al., 2017;Luo & Edlund., 1996;Riahi et al., 2018). Using nonlinear finite element analysis Luo & Edlund., (1996) carried out a numerical investigation to examine the shear capacity of trapezoidal corrugated web. The effects of several parameters such as: web thickness, corrugation depth, and corrugation angle) on the maximum shear capacity were studied. The findings demonstrated that Mariam Hamza and Muthana Muhaisin contributed equally to this work. the ultimate shear capacity increased with increasing web thickness and beam depth (H), while the corrugation depth (d) and the corrugation angle had a slight effect. To understand the shear behavior of trapezoidal corrugated web steel beams under three-point loading, Leblouba et al., (2017) carried out an experimental and numerical investigation. The nonlinear finite element analysis software (ANSYS) was used to obtain the stress distribution along the corrugated webs, as it could not be obtained experimentally. The results of the tested beams showed that the post-buckling residual strength was assessed to be approximately 50% of the maximum load-carrying capacity, while the results of the nonlinear finite element analysis showed that the shear stress is at its maximum and evenly distributed throughout the web up until buckling, at which point it decreases and becomes unevenly distributed. Riahi et al., (2018) employed a nonlinear finite element analytical approach to determine the distribution of the shear stress in the web. They studied flat web beams and three different types of web corrugation (trapezoidal, zigzag, and sinusoidal). The beams were examined under three-point loading. According to their findings, three types of shear buckling: local, global, and interactive were seen on the web. Additionally, the failure of all models was caused by the web's shear buckling, where the web took almost all the shear force without the assistance of the flange.
The flexural and lateral torsional buckling behavior of corrugated web was inspected by several researchers (Elgaaly et al., 1997;Moon et al., 2009;Sayed-Ahmed, 2003). Corrugated web beams under uniform bending were the subject of experimental and numerical research by Elgaaly et al., (1997). The ABAQUS software was used to analyze the samples. The ratio between the flange and web thicknesses and yield stresses, the corrugation configuration, and the stress-strain relationship were all considered in this study. The study's findings showed that the web's contribution to the ultimate moment capacity has a negligible effect and that the ultimate moment capacity of a beam with a corrugated web is determined by the flange yield stress. The impact of the critical moment inducing lateral buckling on corrugated steel webs was studied by Sayed-Ahmed, (2003)by comparing the critical moment of plane webs to the critical moment of corrugated steel webs using numerical analysis. The results showed that a 15-37% increase in the resistance of corrugated girders to lateral torsion-flexure buckling. Based on previous studies on the lateral-torsional buckling of I-girders with corrugated webs of a steel beam under uniform bending. Moon et al., (2003) conducted a theoretical analysis to analyze the suggested approaches for determining the shear center's location and the warping constant, after comparing them with numerical analysis (finite element analysis) results, the study establishes the validity of the theoretically suggested methods' results.  and  experimentally evaluate the shear and behavior of steel plate girders with corrugated core web. The core web consists of two outer plate (skins and one middle corrugated plate), the effect shear span-todepth ratios (a/d) on the flexural and shear behavior was investigated. The effect of core depth was also examined, the results showed that the ultimate load capacities at a/d 2.5 and 1.833 were found to be approximately 16% to 29% lower than the corresponding values at a/d = 1.0. Moreover, the load capacity was influenced by the depth of the core; the girder with a lower core depth performs better than those with a larger depth in terms of ultimate load and maximum displacement.
Based on the available literature, the first work suggesting using corrugated web as alternative to flat web in steel coupling beams was carried out in (Hajsadeghi et al., 2013;Pirgholizadeh, et al., 2014;Shahmohammadi et al., 2013;Zirakian et al., 2016;Zuo et al., 2022). Trapezoidal, curved, and zigzag web corrugated steel plate coupling beams were numerically examined by Shahmohammadi et al.,(2013) using the finite elements method (ANSYS software). Elastic buckling and nonlinear analyses were carried out. The results demonstrated that when the corrugated web is utilized with the recommended geometric parameters (web thickness, number of corrugations, and corrugation angle) the rotation capacity could be enhanced in comparison to flat web steel coupling beams. Thorough numerical simulations, the performance of steel coupling beams with flat and corrugated webs were examined by (Hajsadeghi, Zirakian, Pirgholizadeh, et al., 2014). The study included the energy dissipation characteristics and the cyclic performance. The findings demonstrated that corrugated-web steel link beams have a high capacity for absorbing energy and that this capacity can be improved by suitable design. The influence of the corrugation's shape (trapezoidal, zigzag, and curve) and the web's thickness on the structural performance of the coupling beams under monotonic and cyclic loads was studied by Zirakian et al., (2016). Their study showed that corrugation parameters affect the increasing ability of steel coupling beams to rotate and dissipate energy. Zuo et al.,(2022) utilized the numerical and experimental methods to test the shear-carrying capacity and energydissipating capacity of steel corrugated-plate coupling beams (SCPCBs). Three samples were tested in the lab, two of which focus on shear-cyclic behavior and one on monotonic behavior. The loading processes of experimental specimens were numerically simulated using finite element analysis (FEA). The test findings reveal that one of samples has strong shear and ductility ability under monotonous loading, while the other two samples displayed excellent energy dissipation abilities.
It's clear from the available literature that using corrugated plate web in steel coupling beams is a relatively new approach for boosting the seismic strength and resiliency of hybrid coupled wall systems, However, there are paucity in the experimental and numerical studies on this approach. Through experimental and numerical analysis, this research aimed to investigate the performance of hybrid coupled walls with built-up steel coupling beam having a corrugated web. The finite element software ABAQUS is utilized to perform the analytical part.

Experimental test of specimens
To investigate the effect of using the corrugated web as a replacement for conventional flat web, two specimens of hybrid coupled walls were prepared and tested. Because of the symmetry in the geometry and loading, only onehalf full-scale specimens were cast and tested. As shown in Fig 1, it was assumed that the steel coupling beam in this test specimen would behave as a cantilever beam with a mount of fixity at its end supported by the shear wall under a concentrated load on the free end. The first specimen consists of an RC wall linked to two steel coupling beams with flat web (one from each side) the left SCB has stiffeners each 150 mm while at the other end the stiffeners spaced at 300 mm. The dimensions and reinforcement details are shown in Fig 2a and Table 1.
The second specimen has the same dimensions and details as the first specimen except that corrugated plates were used as a web in the SCB instead of flat webs (see Fig 2b). Details and dimensions of the corrugated web are shown in Fig 2c and Table 1. to provide stability and prevent the beam from slipping out of the concrete, four Steel studs with 20 mm in diameter and 80 mm long were welded to the top and bottom of the flanges at the embedment part of each specimen. A total of 4 steel coupling beams were tested. But in this study will be deal with two samples as follows.
1. SCBFW150 is a steel coupling beam having a flat web with stiffeners at 150 mm. 2. SCBCW150 is a steel coupling beam having a corrugated web with stiffeners at 150 mm.
Preparing, pouring the concrete, transportation, and testing stages are shown in Fig 3. Material properties for the concrete, reinforcing steel, and steel plates are listed in Table 3. A hydraulic device with a 1000 KN capacity was used to test the specimens. All specimens were fabricated and tested at the structural laboratory of the Department of Civil Engineering at AL-Qadisiyah University. Fig 3 shows the hybrid coupled wall specimens at a different stages of testing.

Test results and discussion
All the specimens were subjected to monotonic concentrated load at the free end. The model test are shown in Fig. 4. The load-displacement curve of SCBFW150 specimen is shown in Fig. 5. Local buckling was observed a vertical displacement of about 18 mm. The ultimate loading capacity and displacement were about 218.8 kN, and 20.2 mm, respectively. As for the corrugated web, local buckling is the failure type as shown in Fig. 6. The SCBCW150 model is shown in the load-displacement curve in Fig. 7. Model SCBCW150 has the highest ultimate loading capacity value, moreover, it showed greater ductility. The increase in ultimate load and ductility may be attributed to effect of corrugation in strengthening the beam against buckling. The ultimate loading capacity and displacement at maximum load were about 258 kN, and 44.29 mm, respectively.

Finite element modeling
Numerical modeling and simulation for engineering systems has grown rapidly as a result of the advent and the development of computer technologies (Kaveh., 2014). There are many software commercial packages based on FE method available on the market that meet the simulation requirements, SolidWorks, Ansys and Abaqus. The Abaqus software was used in this study to simulate the behavior of the tested specimens. The software delivers accurate and robust solutions for challenging nonlinear problems. Shell element S4F, solid element C3D8R, and Truss element T3D2 was utilized to model the steel beams, concrete shear walls, and reinforcing bars (including longitudinal and transverse) respectively. Material properties indicated in Table 2 were  used in the simulation. Poisson's ratio for concrete and steel materials were assumed to be 0.2 and 0.3, respectively. Mesh sensitivity study was conducted to choose the optimum mesh size. Both sources of nonlinearity (materials and geometric) were considered in this study.

Results and discussion
The experimental test results and finite element findings (Abaqus software results) are presented, compared, and discussed in this section. The finite element simulations and stress results of the tested specimens are displayed in Figs. 8 and 9. Figures 10 and 11 show the load deflection curves for the specimens SCBFW150 and SCBCW150 respectively. Good agreement in term of ultimate load, maximum displacement as well as the stiffness of the specimens was noticed between the numerical and the experimental results of both specimens. The percentage differences of ultimate load and maximum displacement between the numerical and experimental results are summarized in Table 3. The load deflection curves of the experimental results for both specimens (steel coupling beam with flat web (SCBFW150) and steel coupling beam with corrugated web (SCBCW150) are depicted in Fig. 12. Summary of the experimental results is listed in Table 4, According to Fig. 12, and Table 4 can be noted that the strength and ductility of the specimen with corrugated web (SCBCW150) higher by 10% and 64% respectively compared to the specimen with flat web

Conclusion
In this study, the feasibility of increasing the strength and ductility of steel coupling beam using a corrugated web instead of the conventional flat web was investigated. The work includes an experimental test as well as numerical analyses using finite element software. Two full-scale hybrid coupled walls, one with a steel coupling  beam having a flat web while the second specimen with a steel coupling beam having a corrugate plate web, was constructed and tested. The findings are summarized as follows: (1) Using the corrugated web instead of the flat web in the built-up steel coupling beam increases the ultimate load capacity as well as the ductility. The percentage of increase in terms of ultimate load and ductility was about 22% and 28%, respectively. (2) Increasing the strength and ductility is a sign that the hybrid coupled walls system with SCB having corrugated web have higher strength and are more resilient than the coupled walls having SCB with flat web. (3) The results of this study (See Table 4) are promising to the feasibility of enhancing the load-carrying, energy absorption capacities, and resiliency of the hybrid coupled walls system using SCB with a corrugated plate web instead of a flat plate web.
Acknowledgements Special word of thanks to Mr. Ghanim Deham for his effort in this paper throughout the experimental work.    Funding The authors declare that no funds, grants, or other support were received during the preparation of this manuscript. In addition, they have no relevant financial or non-financial interests to disclose.

Data availability
No data was used for the research described in the article.