Lateral strength evaluation of innovative and traditional composite shear wall systems

This paper proposes formulations for predicting lateral load-bearing capacity of two types of composite shear wall (CSW) systems, which consist of a steel frame and a reinforced concrete (RC) plate attached to one side using bolts. Due to the high out-of-plane stiffness of the RC plate, it can effectively provide out-of-plane constraint to prevent out-of-plane deformation of the steel plate in CSW systems. However, in traditional CSW systems, direct contact between the RC plate and the frame often results in crushing at the former under seismic loading, thereby providing insufficient restraint against out-of-plane deformation of the steel plate. In contrast, the innovative CSW system with a gap maintained at the steel frame and RC plate exhibited superior seismic behavior than its traditional counterpart. While previous studies have investigated cyclic behavior and parameter effects of CSW systems, there remains a gap in evaluating their lateral strength. The proposed formulations show a mean distinction among theoretically determined and actual lateral load-bearing capacity less than three percent.


Introduction
In recent years, steel wall (SW) systems which are composed of a steel frame and a steel plate, are commonly used in high-rise buildings to bear seismic loads.For the SW systems used in lower stories, the steel frame provides high overturning moment-bearing capacity; while the steel plate carries most of shear, and exhibits excellent energy dissipation capacity.However, the lateral strength and stiffness of steel plate could have a sudden drop, because of the inelastic out-of-plane deformation in steel plate.Moreover, due to the limitations of noise control [1][2][3], the SW systems are restricted in use since the steel plate buckling.Some researchers [4,5] indicated that some innovative configurations, such as cutting slots on steel plates, and welding stiffeners on steel plates, contributed to delay steel plate buckling, these configurations also increased the project cost and the construction difficulty.
In order to recover the disadvantages of the SW system, a new type of lateral load-bearing system, named composite shear wall (CSW) system, attaching a reinforced concrete (RC) plate to the steel plate by bolts, was developed.The CSW system exhibited superior seismic-bearing capacity compared to the SW system [7][8][9].Furthermore, due to the high out-of-plane stiffness of the RC plate, it can effectively provide out-of-plane constraint to prevent out-of-plane deformation of the steel plate, thus augmenting the seismic behavior of the CSW system [7].
As previously mentioned, due to the effective constraint of RC plate on buckling of steel plate, meticulous design of structural details for the RC panel is imperative.In a conventional CSW system, direct contact between the RC plate and the frame often results in crushing of the former under seismic loading, thereby providing insufficient restraint against out-of-plane deformation of the steel plate.To enhance this constraint, an innovative CSW system was firstly proposed by Zhao [7], wherein a gap is intentionally maintained between frame and RC plate.Figure 1 illustrates the sketch up of CSW systems, including the innovative type and the traditional type.Comparing with the traditional type, the innovative type exhibits a significant delay in RC panel crushing due to the presence of the gap mentioned above [10].According to the test results conducted by Zhao et al. [7], Li et al. [11] performed numerical analyses to investigate the lateral behavior of these two types of CSW systems.The study revealed important insights into key parameters, such as the thickness of RC plate and steel plate, the gap size maintained at the RC plate and the frame, as well as the ratio of connector distance to thickness of steel plate, would influence the lateral behavior of these systems.Despite several commendable research efforts on CSW system behavior, there is still a knowledge gap when it comes to evaluating lateral load-bearing capacity for both these two types of the CSW systems.This paper aims at deriving formulations for predicting lateral strength in both types of CSW systems using superposition method with an average difference less than 3% compared to test/simulated results.

Summation of Previous Test and Simulation Results
Two CSW test samples, named innovative CSW and traditional CSW, respectively, have been tested by Zhao et al. [7].Based on the test specimens detailing, Li et al. [11] developed finite element (FE) models for simulating these two types of CSWs, and validated the simulation results with the test results.Details of test specimens and FE models, as well as test results and simulation results, could be found in Reference [7] and [11], respectively.Furthermore, parametric effects of steel panel thickness (tp, considering as 2, 4, 6, 8, and 10 mm, respectively), RC thickness (tc, considering as 40, 60, 80, 100, and 120 mm, respectively), ratio of connector distance to thickness of steel plate (κ, considering as 30, 40, 50, 60, and 70, respectively), and gap size maintained at the RC plate and the frame (dg, considering as 0, 16, 32, and 48 mm, respectively), were numerically studied by Li et al. [11].
For the FE models used for conducting the parametric study, structural details, including column size with Hb×Bb×tw×tf of 333×313×18×28 mm, yield strength of column with fyc of 345 MPa, beam size with Hb×Bb×tw×tf of 310×165×6×10 mm, yield strength of beam with fyb of 345 MPa, yield strength of steel panel with fyp of 248 MPa, concrete compressive strength with f'c of 28 MPa, distance between column axes with l of 2130 mm, and distance between beam axes with h of 2142 mm, were held constant.Lateral strength of one innovative CSW test specimen, denoted as IM0, as well as a total of 17 FE models, denoted as IM1 to IM17, are given in table 1.The lateral strength of one traditional CSW test specimen, denoted as TM0, and a total of 14 FE models, denoted as TM1 to TM14, are given in table 2. Data presented in table 1 and table 2 would be used to validate the accuracy of formulations for predicting lateral strength proposed in this paper.

Innovative CSW system
For the innovative type of CSW system, there exists a gap between the frame and the RC plate, with limited involvement of the RC plate in resisting side loads until reaching peak load state.Hypotheses: 1) The strength of the boundary column is sufficient to cause steel plate damage prior to failure of the boundary column itself; 2) The RC plate gives effective out-of-plane constraint for fully exerting the strength of the steel plate; 3) The shear contribution of RC plate is disregarded.Innovative CSW relies on steel plates and boundary columns for lateral strength, where lateral strength evaluation formula can be expressed as equation ( 1), in which, Vp represents lateral strength given by steel plates; Vf represents lateral strength of columns.
According to test [7] and simulation [11], when reaching peak load state, most area of the steel plate yields.Therefore, lateral strength provided by steel plates can be expressed as equation ( 2), p = vp p = 0.6 yp p (2) in which, fvp denotes shear strength of steel plates, and equals to 0.6 fyp; b represents width of steel plates; tp signifies thickness of steel plates.Lateral displacement strength Vf provided by steel columns can be calculated based on forcedeformation relationship under peak load condition in CSW system.Deformation characteristics along both boundary column and diagonal direction are illustrated in figure 2. Elongation along diagonal direction in tensile zone can be described using equation (3), in which, a refers to height of steel plates; α indicates angle formed by deformation characteristics at boundary column interface.Yield strain εyp for steel plates is defined through equation ( 4), in which, εyp stands for yield strain value, defined as εyp = fyp / Ep; Ep represents Young's modulus for the given material properties.
The form factor β is assigned to describe the horizontal direction deformation of the steel plate within a layer.It is influenced by both the geometry and material properties of the steel plate, and can be mathematically shown as equation ( 5).Based on this, one column could offer a shear strength of f ' , which could be shown as equation ( 6), in which, Ef represents the Young's moduli of the boundary column, while I denotes the bending stiffness along lateral load direction.
According to shear flow theory, a decrease of shear stress would appear on an I-shaped section where its flange connects to the web.A peak shear stress would occur at the neutral axis of the web section, with shear stress approaching 0 at free ends of flange sections.Figure 3 illustrates this stress distribution within a section.Consequently, for an I-section, mean shear stress on its flange is lower than that on its web.To account for this reduction in shear stress on flange sections when calculating total shear stress, we consider a coefficient value of 0.7 for decreasing shear stress at column bases.When yielding occurs in such systems, equation ( 7) can express how lateral loads are distributed among adjacent boundary columns.

Conclusion
A type of lateral load-bearing system, named composite shear wall (CSW) system, attaching a reinforced concrete (RC) plate to the steel plate by bolts, was theoretically studied.This paper surveys tested and FE simulated consequences of inventive and customary CSW frameworks.In view of tested and FE simulated results, conditions were given and used to assess the parallel strength of imaginative and customary CSW frameworks tentatively tried or mathematically re-enacted by FE examinations.The typical distinction among theoretically determined and actual lateral load-bearing capacity was under three percent.For both the two types of CSW systems, equations derived in this paper might be able to make an expected prediction of their lateral load-bearing capacity.

Figure 1 .
Figure 1.Sketch up of CSW systems.

Figure 2 .
Figure 2. Schematic of column and steel panel deformation.

Figure 3 .
Figure 3. Shear flow on I-shaped section.

Figure 4 .
Figure 4.A comparison of calculated strength and simulated/tested strength of CSWs.