Application of steel-concrete-steel sandwich deep beams into coupled shear walls

Abstract

Coupled shear walls are widely used as the primary lateral load resisting element in high-rise buildings. But the coupling beams, which are often designed as deep members, usually suffer from brittle shear failure. The steel-concrete-steel sandwich deep beams showed high bearing capacity and great ductile performance during shear failure. Therefore, it is proposed that the steel-concrete-steel members can be used into deep coupling beams instead of conventional reinforced concrete members, to improve the shear strength and deformability. The shear failure of steel-concrete-steel deep beams is characterized by plastic yielding of the outer steel plates in the triangular areas, rather than concrete diagonal crushing. Reliable shear transfer paths are maintained by the interaction between the outer steel plates and the diagonal concrete struts, so excellent strength and ductile performance can be expected after critical diagonal cracking. The triangular failure areas are able to dissipate seismic energy, thus effectively avoiding overall collapse. The shear strength of steel-concrete-steel deep coupling beams is developed with simple expressions.

Keywords

coupling beam ductile performance energy dissipation shear strength steel-concrete-steel

Introduction

High-rise buildings have experienced rapid developments since the middle of the 20th century. As height increases, lateral loads like the wind and seismic effects, instead of gravity loads, become the dominant factor in structural analysis (Coull, 1967; Paulay, 1971; Tissios, 1996; Zhou et al., 2014).

Coupled shear walls are preferred in high-rise buildings for their good performance in both functional flexibilities and mechanical properties (Cheng et al., 2015). In the coupled shear wall system, the design of coupling beams is so critical that they not only restrict the wall piers and affect the overall stiffness but also serve as the primary energy dissipation element under horizontal seismic excitations. The bearing capacity and ductile behavior of coupling beams have long been the focus of attention (Naish et al., 2013a, 2013b). The coupling beams are expected to have sufficient deformability while being able to maintain the bearing capacity, so that seismic energy is efficiently dissipated and thus avoiding overall collapse (Harries, 2001; Park and Yun, 2005).

Deep coupling beams (span/depth ratio (λ) less than 2) are commonly used in coupled shear walls. The design of deep coupling beams, which is quite sensitive to shear stress and shear deformation, has long been a difficult issue, and the measures to improve their ductility and energy dissipation capacity have been extensively studied for the past several decades (Galano and Vignoli, 2000; Paulay and Binney, 1974; Salonikios, 2002; Tegos and Penelis, 1988; Teng et al., 1999). However, in practice, the deep coupling beams usually fail in brittle diagonal shear manners, including diagonal compression failure and shear compression failure, although with careful calculations and supplementary constructional measurements.

In this article the steel-concrete-steel (SCS) sandwich deep beams, which combine the advantages of reinforced concrete (RC) and steel structures, are proposed to be used in coupled shear walls, as shown in Figure 1. The composite members have shown excellent shear capacity and deformability in tests (Leng et al., 2015a, 2015b).

Figure 1.

Typical arrangement of the SCS coupling beams.

Features of conventional RC deep coupling beams

Force diagram

The coupled shear walls resist lateral loads through the combinations of (1) the individual flexural reaction of the wall piers (M₁ and M₂) and (2) the “frame” action generated from the coupling beams: an axial force couple (N) is developed in the wall piers through the accumulation of shear in the coupling beams, as shown in Figure 2. An evaluation of the structural behavior is referred to as the “degree of coupling” (Lu and Chen, 2005), which is defined as the ratio of the overturning moment resisted by the axial couple in the walls to the total structural overturning moment

β_{c} = \frac{N \cdot Z_{L}}{N \cdot Z_{L} + M_{1} + M_{2}}

(1)

Figure 2.

Force distribution and deformation of a coupled shear wall under lateral loads.

Improving the stiffness of the coupling beams will increase the axial force couple (N), thus results in larger degree of coupling and larger lateral stiffness. However, it raises the problem that the coupling beam may fail in a rather brittle shear manner, which is called over coupling. Yet, light coupling is also unfavorable that it causes the system to behave like two isolated walls with insufficient strength and stiffness.

The span/depth ratio (λ = L_n/h, as shown in Figure 3) of coupling beams is usually quite smaller than that of conventional frame beams. Instead of gravity loads, a deep coupling beam is mainly subjected to significant shear forces and bending moments resulting from lateral loads. The force couple (N in Figure 2) is transferred through accumulation of the shear stresses in the coupling beams in each story. Neglecting the vertical load effects, the typical distribution of inner forces in a coupling beam is shown in Figure 3, and the shear force along the beam can be expressed as

V = \frac{M_{L} + M_{R}}{L_{n}}

(2)

Figure 3.

Moments and shear force in a coupling beam.

Failure patterns of RC deep coupling beams under seismic loads

The preferred failure pattern of RC coupled shear wall systems under horizontal seismic action is that the coupling beams yield first, followed by yielding at the bases of the wall piers. The coupling beams should fail by flexural yielding at the end rather than diagonal shear damage. The plastic hinge at the end has been proved well capable of dissipating seismic energy without much loss of the bearing capacity (Paulay and Santhakumar, 1976). Such energy dissipation capacity can reduce seismic damage in other regions. Slender coupling beams can basically ensure the appearance of the plastic hinges at the end. However, the restriction between the wall piers is also weak, leading to insufficient lateral strength and stiffness.

In deep coupling beams, which is usually unavoidable, the end moments result in significant shear stress. As lateral loads change directions constantly under reversed seismic loads, the end moments change directions correspondingly. So the deep coupling beams usually suffer from severe crossed diagonal cracks (Kwan and Zhao, 2002; Wang, 2008). Deep coupling beams generally suffer from diagonal compression failure and shear compression failure. The diagonal compression failure results from the local compression of the reaction at the support, and concrete between the support and the concentrate load is crushed by diagonal compression stress, while the reinforcement has not yielded, thus no effective energy dissipation mechanism can form. Therefore, diagonal compression failure is usually tried to be prevented by limiting the maximum sectional shear stress.

In frame beams, considerable deflection may develop before shear compression failure, but in coupling beams, it showed poor deformation capacity. In shear compression failure mode, the shear resistance of RC coupling beams consists of the shear strength of the residual concrete compression zone, the tensile strength of the stirrups, the aggregate interlock along the diagonal cracks, and the dowel action of the longitudinal bars, among which the first two components take the dominant portion. The aggregate interlock subsides rapidly as the crack opens, and the dowel action of the longitudinal reinforcements is usually negligible since the concrete tend to be torn along the steel bars by the dowel shear forces. The shear strength of the residual concrete compression zone, which is reliable in frame beams under static loads, become less dependable under cyclic seismic excitations, especially after 1 or 2 loading cycles. The brittle shear failure of coupling beams will further result in a sudden decrease of lateral strength and stiffness of the wall system, accompanied with secondary overturning moment which may increase the possibility of overall collapse.

As a consequence, it is suggested in the design process that the safety factor for shear resistance should be larger than that for flexural capacity. But in most cases, the difficulties to design the coupled shear walls in a ductile manner under current codes should not be underestimated. It is attributed to the strength and stiffness requirements.

The SCS deep coupling beams

Some current design methods

If a coupling beam, especially deep beam, is subjected to shear force that exceeds its maximum capacity, the section depth is suggested to be decreased to reduce the absorption of seismic shear forces. But the overall stiffness is also compromised.

At present, another valid solution is the diagonal reinforcements in deep coupling beams, as shown in Figure 4 (Galano and Vignoli, 2000; Paulay and Binney, 1974; Tissios, 1996). Some current design codes, like the ACI318-11 (2011)Building Code Requirements for Structural Concrete, and the GB50010-2010 (2010)Code for Design of concrete structures in China, all recognize the use of diagonal reinforced coupling beams. Such reinforcement arrangements, though effective, are not commonly used due to the complexity in construction. Other innovative types of coupling beams include the parallel double coupling beams (Li et al., 2014), steel RC coupling beams (Motter et al., 2014), and so on.

Figure 4.

Diagonally reinforced concrete coupling beams.

The above measurements attempt to ensure that flexural failure occurs prior to shear failure, since shear failure is characterized by poor ductility and unreliable force transfer paths after diagonal cracking.

From another perspective, if ductility and energy absorption capacity are achieved during the shear failure process, there is no need to compromise the lateral stiffness to ensure flexural yielding. The unique shear resisting pattern and failure mechanism of the SCS sandwich deep beams can exactly solve this problem and open a new thought for the design of deep coupling beams.

Experimental study on SCS deep beams under anti-symmetric loads

Some SCS deep beams were tested under anti-symmetric loads in a previous work (Leng et al., 2015a). The moment and shear force distribution in the continuous span (the tested region) were very similar to that in a coupling beam, as shown in Figure 5. The tested continuous span was subjected to reversed bending moments at the ends, with a contra-flexural point in mid-span. In order to obtain the failure mode and shear strength of the continuous span, the cantilever spans were strengthened with vertical steel plates to prevent premature failure.

Figure 5.

General view of the continuous beam tests: (a) loading scheme and (b) shear force and moment distribution along the beam axis.

The shear failure pattern of the continuous beam is shown in Figure 6. During the test, flexural and diagonal cracks appeared successively as load increased. The critical diagonal crack (CDC) bridging the loading point and the support played a crucial role in shear failure, just like the crossed diagonal cracks in RC deep beams. However, in SCS deep beams, the formation of the diagonal crack did not result in ultimate failure. Figure 7 is the load-deflection responses of the tested beams, in which the vertical deflection was measured below the loading point P. In specimen CB1.5, the critical cracking load exceeded the carrying capacity after critical cracking, so the load capacity dropped after cracking. In the other two specimens, after critical cracking, the carrying capacity could still increase gradually until the formation of the top and bottom triangular damaged areas. In these two damaged areas, tensile strains of the steel plates increased rapidly, and outward deformation developed seriously, accompanied with concrete diagonal crushing (Leng et al., 2015a). In the post-peak stage, the carrying capacity decreased slowly, and all the specimens showed good ductile performance. Brittle shear failure can be prevented if the shear capacity after critical cracking exceeds the critical cracking force.

Figure 6.

Typical shear failure in the top and bottom triangular areas in continuous beams.

Figure 7.

Load-deflection responses of the continuous beams.

Shear failure of RC deep beams usually results from concrete diagonal crushing, while shear failure of SCS deep beams is characterized by steel plate yielding. The membrane action of the outer steel plates provides reliable force transfer path and excellent ductile capacity after shear cracking. The two triangular damaged areas act as ideal plastic hinges at beam ends with sufficient rotational deformability and energy dissipation ability.

The steel plates are firmly bonded to concrete with studs, thus composite action is well maintained. The action of the web concrete in the deep beams is simplified as diagonal struts developed directly from the loading point to the end support. It is exactly the strut compression acting on the outer steel plates that results in the triangular damaged areas, as shown in Figure 8. The top and bottom steel plates undergo not only axial forces but also dowel shear forces. The membrane action of the steel plates in large deformation stage can further enhance the shear performance. The bearing capacity declines gradually after large deformation, and energy is well dissipated during this process.

Figure 8.

The concrete struts and damaged areas.

Therefore, it is suggested that the SCS sandwich construction can be used in coupling beams as a simple but effective shear-strengthening method. In deep coupling beams, the seismic energy can be effectively dissipated with the formation of the top and bottom triangular damaged areas in the beam end (as shown in Figure 9), without compromising much carrying capacity.

Figure 9.

The expected shear failure mode of SCS deep coupling beams.

Shear capacity of SCS deep coupling beams

A plastic limit analytical model based on the experimentally observed failure modes has been developed to explain the force-transfer mechanism and predict the shear strength (Leng et al., 2015a). The previous study “Shear Strength of Steel-concrete-steel Sandwich Deep Beams: A Simplified Approach” extends the investigation on the shear performance of SCS deep beams, and a simplified shear predicting method is developed through parametric studies. Based on the experimental works (Leng et al., 2015a, 2015b) and the simplified mechanical model, this section further discusses the potential shear capacity of SCS deep coupling beams.

It is assumed in this approach that:

No external force acts directly on mid-span of the coupling beams, so they are subjected to a combination of reversed moments (M_L and M_R) and shear force (V) as shown in Figure 3. This is true in most cases.

Axial compression forces are neglected from a conservative view, since failure is resulting from steel plate yielding under combined tension and shear.

The aggregate interlock along the critical crack, which subsides rapidly as the crack opens, is negligible at ultimate state.

The concrete struts are supposed to be parallel to the CDC. Furthermore, it is assumed that the compressive stress in the struts is also parallel to the CDC and uniformly distributed.

After critical cracking, the deep coupling beams transfer shear forces through diagonal concrete struts as shown in Figure 10. To cut the coupling beam along the critical crack, the forces R_u and R_d represent the shear capacity of the top and bottom triangular areas, respectively. T_d and T_u are the steel plate forces at the critical cracked section with the equilibrium relation that T_d = T_u.

Figure 10.

The force diagram after critical cracking.

The ultimate shear strength can be expressed as the summation of the resistance from the top and bottom parts, if no vertical reinforcement is used

V_{u} = R_{d} + R_{u}

(3)

The resistance R_d depends on the strength of the bottom steel plate. The free-body diagram of the bottom triangular area (the shaded area in Figure 10), is shown in Figure 11(a). The equilibrium of horizontal forces, vertical forces, and equilibrium of moments at the application point of forces C₃ and V_c3 in the bottom triangular area gives

\begin{matrix} λ V_{c 3} = T_{s 3} - T_{d} \\ V_{c 3} = R_{d} + V_{s 3} \\ 2 λ R_{d} = T_{s 3} - T_{d} \end{matrix}} \Rightarrow {\begin{matrix} V_{s 3} = R_{d} \\ T_{s 3} = T_{d} + 2 λ R_{d} \end{matrix}

(4)

Figure 11.

Mechanical analogy of the bottom and top triangular areas: (a) bottom triangular area and (b) top triangular area.

The compressive stress in the strut is assumed to be uniformly distributed and parallel to the critical crack, so C₃ and V_c3 are acting at the mid-point of the vertical section, with a proportional relationship that C₃ = λV_c3.

In the bottom triangular area, the tensile stress of the bottom steel plate accumulates and increases owing to the concrete diagonal compression, and meets the von Mises yield criteria for plastic materials, under the interaction of T_s3 and V_s3. So the ultimate state of the bottom area can be expressed as

(T_{s 3})^{2} + 3 (V_{s 3})^{2} = (T_{d} + 2 λ R_{d})^{2} + 3 {R_{d}}^{2} = (f_{y} b t_{s})^{2}

(5)

where t_s and f_y are the thickness and yield strength of the outer steel plate,respectively, and b is the section width. Since the coupling beams are submitted to reversed cyclic loads, the top and bottom steel plates are usually required to be of equal strength and thickness, to ensure equal resistance in both directions.

From equation (5), the strength R_d can be solved as

R_{d} = \frac{- 4 λ T_{d} + \sqrt{{(4 λ T_{d})}^{2} - 4 (4 λ^{2} + 3) [{T_{d}}^{2} - {(f_{y} b t_{s})}^{2}]}}{2 (4 λ^{2} + 3)}

(6)

Similarly, in the top triangular as shown in Figure 11(b), the equilibrium of horizontal forces, vertical forces, and equilibrium of moments at the application point of forces C₄ and V_c4 gives

\begin{matrix} λ V_{c 3} = T_{s 4} + T_{d} \\ V_{c 4} = R_{u} + V_{s 4} \\ 2 λ R_{u} = T_{s 4} + T_{u} \end{matrix}} \Rightarrow {\begin{matrix} V_{s 4} = R_{u} \\ T_{s 4} = 2 λ R_{u} - T_{u} \end{matrix}

(7)

Substituting equation (7) into the von Mises yield criteria for the top steel plate, the ultimate state of the top area can be expressed as

(T_{s 4})^{2} + 3 (V_{s 4})^{2} = (2 λ R_{u} - T_{u})^{2} + 3 {R_{u}}^{2} = (f_{y} b t_{s})^{2}

(8)

From equation (8), the strength R_u can be solved as

R_{u} = \frac{4 λ T_{d} + \sqrt{{(4 λ T_{d})}^{2} - 4 (4 λ^{2} + 3) [{T_{d}}^{2} - {(f_{y} b t_{s})}^{2}]}}{2 (4 λ^{2} + 3)}

(9)

Substituting the solution of R_u and R_d into equation (3), the shear strength can be solved

V_{u} = R_{d} + R_{u} = \frac{2 \sqrt{(4 λ^{2} + 3) {(f_{y} b t_{s})}^{2} - 3 {T_{d}}^{2}}}{4 λ^{2} + 3}

(10)

From equation (10), the shear strength of a deep SCS coupling beam is dependent on the span/depth ratio, the strength of the outer steel plates, as well as the steel plate force T_d (or T_u) at the critical cracked section, while the value of T_d (or T_u) is decided by external loading conditions. When subjected to anti-symmetric loads with M_L = M_R, just like the anti-symmetric loading condition in Figure 5, the steel plate forces meet the condition that T_d = T_u = 0 and the shear resistance reaches the maximum value

V_{u, max} = \frac{2}{\sqrt{4 λ^{2} + 3}} f_{y} b t_{s} = h_{1} (λ) f_{y} b t_{s}

(11)

On the contrary, when the bending moment at one end equals zero, for instance, M_L = 0,|T_d| reaches the peak value and thus leading to the minimum V_u. M_L = 0 occurs in simply supported beams with a free end. According to the simplified mechanical model for the shear resistance for SCS deep beams in the previous study, in simply supported beams with M_L = 0, the steel plate force T_d can be obtained as

T_{d} = f (λ) \cdot f_{y} b t_{s} = (- 0.1231 λ^{2} + 0.6242 λ - 0.003) \cdot f_{y} b t_{s}

(12)

Substituting equation (12) into equation (10), the minimum shear resistance is obtained

V_{u, \min} = \frac{2 \sqrt{4 λ^{2} + 3 - 3 {(- 0.1231 λ^{2} + 0.6242 λ - 0.003)}^{2}}}{4 λ^{2} + 3} f_{y} b t_{s} = h_{2} (λ) f_{y} b t_{s}

(13)

Let

K (λ) = \frac{h_{1} (λ)}{h_{2} (λ)} = \sqrt{\frac{4 λ^{2} + 3}{4 λ^{2} + 3 - 3 {(- 0.1231 λ^{2} + 0.6242 λ - 0.003)}^{2}}}

(14)

when λ varies between 0 and 2 (the range of deep beams), the range of K(λ) is limited between 1 and 1.06. Consider the worst possible case that h₂(λ) = h₁(λ)/1.06, and the minimum shear resistance of deep coupling beam is given as

V_{u, min} = \frac{2}{1.06 \sqrt{4 λ^{2} + 3}} f_{y} b t_{s}

(15)

which is the summation of the shear resistances of the top and bottom triangular areas.

Furthermore, according to the parametric study in the previous study, the contribution of shear, the reinforcements across the CDC is about 85%–90% of their tensile yield strength, and an average value of 0.87∑A_svF_yv is adopted, where ∑A_sv is the total section area of the shear reinforcements in shear span, and F_yv is the yield strength of the shear reinforcements. The ultimate shear capacity of a deep SCS coupling beam is obtained as

V_{u} = \frac{2}{1.06 \sqrt{4 λ^{2} + 3}} f_{y} b t_{s} + 0.87 \sum A_{sv} F_{yv}

(16)

The stud spacing should also be designed according to the simplified approach, otherwise the first part of equation (16) should be revised with the reduction factor β_stu.

Conclusion

The coupled shear wall system is widely used in high-rise buildings, but designing the RC-coupled shear wall in a full ductile manner under horizontal seismic loads is not easily realized. It relies on the engineers’ experience to take some measures like using high-strength concrete or reducing the section depth thus the effective stiffness of the coupling beams, so that they fall within the allowable limits of the current codes. Neither approach is perfect, since they may compromise some other capacities like the overall lateral stiffness. This article discusses the possibility of using the SCS sandwich system into deep coupling beams to achieve better structural performance.

The outstanding shear capacity, deformability, and ductile performance of the SCS deep beams have been confirmed in previous studies. A series of SCS deep beams were tested under symmetric one-point or anti-symmetric two-point loads (Leng et al., 2015a, 2015b). In the anti-symmetric continuous beam tests, the loading condition of the continuous span was similar to that of the coupling beams under horizontal loads. Tests have shown that the shear failure of SCS deep beams was quite different from conventional RC beams.

The shear failure of SCS deep beams is characterized by the top and bottom triangular areas damaged. The dowel action of the outer steel plates, which originates from the interaction between the diagonal concrete struts and the steel plates, provides excellent shear strength and ductile ability after critical shear cracking. In addition, the membrane effect of the steel plate can further enhance the carrying capacity under larger deflection. Therefore, it is suggested that the shear strength and deformability of the deep coupling beam can be improved with the SCS sandwich construction.

Based on the mechanical model (Leng et al., 2015a) and the simplified approach in Part I, the potential shear strength of SCS deep coupling beams is developed in this study with simple expressions.

This study opens a new thought for the application of SCS members. The SCS construction shows great potential for application into deep structural members, which are sensitive to shear stress but are strictly required on their seismic performance. To apply the SCS coupling beams into high-rise shear walls, at the implementation level, it still needs more pertinent experimental research and theoretical analysis.

Footnotes

Acknowledgements

The authors would like to express their gratitude to the structural laboratory of Shanghai Jiao Tong University, where the experimental work was conducted.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors would like to acknowledge the financial support of the China Postdoctoral Science Foundation (2017M621512). This research is part of the postdoctoral project financially supported by Shanghai Jiao Tong University and the Shanghai Research Institute of Building Sciences.

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