Behavior and Design of Distributed Belt Walls as Virtual Outriggers for Concrete HighRise Buildings
 219 Downloads
Abstract
A new lateral forceresisting structural system for concrete highrise buildings, distributed belt wall system, is proposed. Unlike conventional belt structures, the belt walls infilling the space between perimeter columns are distributed separately along the overall building height. In this study, the force transfer mechanism and performance of the distributed belt walls, acting as virtual outriggers under lateral load, are investigated. For the reinforcement of the belt walls subjected to high shear demand, a reinforcing method using highstrength prestressing strands (i.e. PSC belt wall) is suggested, and the shear strength of the PSC belt walls is estimated based on the compression field theory. By performing nonlinear finite element analysis, the shear behavior of the PSC belt walls, including cracking and yield strengths, is investigated in detail. Based on these investigations, recommendations for the shear design of the belt walls reinforced by highstrength prestressing strands are given.
Keywords
belt wall outrigger shear design prestressed concrete compression field theory lateral forceresisting system highrise building1 Introduction
To overcome such disadvantages, alternative outrigger systems such as the offset outrigger and virtual outrigger have been studied (Stafford Smith et al. 1996; Nair 1998; Dean et al. 2001; Choi and Joseph 2012; Eom et al. 2013). As shown in Fig. 1b, in such alterative outrigger systems, the conventional outriggers connecting directly the core wall with the perimeter columns are not used. Instead, only belt structures to tie the adjacent perimeter columns are used. Although the core wall is not connected directly with the perimeter columns, a portion of the horizontal shear force acting on the core wall is transferred to the belt structures through the upper (or lower) floor slab, and the shear force is returned to the core wall through the lower (or upper) floor slab. Through this process, axial tension and compression forces are induced in the perimeter columns tied to the belt structures, while the bending moment acting on the core wall is reduced (Nair 1998).
Thus, a new lateral forceresisting system for concrete highrise buildings, distributed belt wall system, is proposed in this study. In the distributed belt wall system, first, belt walls are used without outrigger, and thus they contributes to the lateral force resistance of the building by acting as virtual outriggers (Stafford Smith et al. 1996; Nair 1998). Second, by distributing the belt walls over the building height, instead of concentrating at a specific floor, such as the midheight and roof, space loss at the floor where outrigger and/or belt structures are installed is minimized. Third, in the constructional viewpoint, by using concrete belt walls, it is possible to minimize interference with the concrete construction process of the adjacent perimeter columns and core walls.
The behavior and design method of the distributed belt wall system are studied as follows. By performing a parametric study, the force transfer mechanism and lateral driftdecreasing performance of the distributed belt walls acting as virtual outriggers are investigated. In addition, considering high shear demand in the distributed belt walls, a reinforcing method using highstrength prestressing strands is proposed and the belt wall shear strengths at cracking and strand yielding are estimated, based on the compression field theory. Finally, the shear behavior of the prestressed concrete belt walls such as concrete cracking and postcracking behavior is verified by performing nonlinear finite element analysis.
2 Distributed Belt Wall Structure System
In this section, the force transfer mechanism of the conventional belt wall system (i.e. concentrated belt wall system) and proposed distributed belt wall system are investigated through parametric study. For the parametric study, a commercial structural analysis and design software, MIDAS/GEN, was used (MIDAS IT 2006).
2.1 Concentrated Belt Wall System
2.2 Distributed Belt Wall System
The horizontal and vertical shear forces, V_{u} and V_{v}, indicate that the belt wall is subjected to pure shear. In addition, since the vertical shear force V_{v} should be cancelled out by the reaction forces at the bottom of the boundary elements, a vertical axial force, which is equal to V_{v}, is induced to the perimeter columns. Such axial force is imposed as additional axial loads on the perimeter columns. This indicates that the shear demand of belt walls can be obtained by examining the axial forces acting on the upper and lower columns of the belt wall.

Since only a portion of the building façade is covered by belt walls, restrictions on architectural planning at the floor where the belt walls are placed is alleviated.

For the belt wall systems planned as virtual outriggers, the floor slabs are subjected to high inplane shear demand. If the belt walls are concentrated at one floor, the shear force acting on the slabs increases significantly. The distributed belt wall system can be an alternative to reduce the high inplane shear demand of the slabs.
3 Shear Strength of Belt Walls
As discussed in the previous section, the belt wall is subjected to pure shear. Thus, the conventional shear strength equations for structural walls subjected to combined bending and shear, such as V_{n} = 0.17√f_{c}′bd + f_{yt}A_{v}d/s, may not be directly used for the design of the belt walls (b and d = width and effective depth, respectively, and f_{yt} and s = yield strength and spacing of shear reinforcement, respectively). Furthermore, the shear stress level of the belt wall, defined as τ_{u} = V_{u}/[l_{w}t_{w}], is mostly higher than the allowable maximum stress, 0.83√f_{c}′, specified in concrete design codes such as ACI 31814 and KCI 2012.
In this section, the shear strengths of the proposed PSC belt walls at concrete cracking and reinforcement yielding are estimated based on the compression field theory as follows (Collins and Mitchell 1980; Vecchio and Collins 1986).
3.1 Material Models and Basic Assumptions

Since the belt wall is confined by the left and right perimeter columns and by the top and bottom floor slabs including spandrel beams, uniform stress and strain field is assumed for the internal concrete panel of the belt wall. Thus, the behavior of the concrete panel can be represented as the stresses and strains of an element, shown in Fig. 10.

The PS strands are placed along the x and y axes as reinforcements. The spacing and crosssectional area of the PS strands in both axes are the same. The prestressing force applied to each strand by posttensioning is also the same as f_{pe}, where f_{pe} is the effective prestress. Based on these conditions, a constant inclination angle of the principal stresses, θ = 45°, is assumed.
In fact, the stresses and strains of the belt wall are not uniform because the confinement effects are different at the corner and center. Such local behavior is investigated further by nonlinear finite element analysis in the next section.
3.2 Prestressing of Strands: Initial State
3.3 Shear Cracking: Behavior of Uncracked Concrete
Since the normal strains of the concrete remained constant as ε_{cx} = ε_{cy} = ε_{ci}, as shown in Fig. 12b2, the stress and strain of the PS strands do not change until the shear cracking occurs.
3.4 Yielding of PS Strands: Behavior of Cracked Concrete
As the lateral force of the belt wall increases further after shear cracking, the tensile principal stress f_{c1} decreases to 0 and the compressive principal stress f_{c2} increases in magnitude (see Fig. 12c1). In addition, the concrete dilates as the width of shear cracks increase. Consequently, the normal strains of the concrete, ε_{cx} and ε_{cy}, increase from ε_{ci} in compression to a positive value in tension by Δε, as shown in Fig. 12c2, and the strain of the PS strands also increase by the same amount, as shown in Fig. 11. In the end, it is considered that the yielding of the PSC belt wall occurs when the strain of the PS strands is equal to the yield strain, ε_{py} (= f_{py}/E_{ps}).
3.5 Shear Strength of PSC Belt Walls
When designing the PSC belt walls, V_{cr} and V_{y} can be used for strength check such as the serviceability and ultimate limit states. In this case, the horizontal shear force of the belt wall, V_{u}, transferred via the floor slab should not exceed ϕV_{cr} or ϕV_{y} (ϕ = 0.75).
 To prevent early concrete crushing, the compressive stress f_{c2} of diagonal concrete struts should not exceed the effective compressive strength f_{ce}, as discussed in Eq. (8). Thus, if the factor β_{s} is taken as 0.6 in Eq. (8) for conservative design, the reinforcement ratio ρ_{p} is limited to (ACI 31814 and KCI 2012)$$\rho_{p} \le 0.51\frac{{f^{\prime}_{c} }}{{f_{py} }}$$(12)
4 Nonlinear Finite Element Analysis
To investigate the behavior of PSC belt walls proposed to use as virtual outriggers in concrete highrise buildings, finite element (FE) analysis was performed. For the FE modeling and analysis, VecTor2 developed by Prof. F. J. Vecchio in University of Toronto was used (Wong et al. 2013). VecTor2, which is based on the modified compression field theory (Vecchio and Collins 1986), is suitable for analyzing 2dimensional structures under biaxial stresses, such as shear walls.
4.1 Finite Element Modeling and Material Behaviors
Figure 13 shows the mesh discretization of the belt wall. The bilinear rectangular element of mesh size 200 mm × 200 mm is used to model the plane concrete of the wall panel and boundary columns and slabs. The steel reinforcements used in the boundary columns and slabs are modeled as smeared reinforcement elements. On the other hand, the PS strands reinforcing the wall panel are modeled as uniaxial line elements placed horizontally and vertically with the same spacing 200 mm. To consider the behavior of unbonded PS strands, the line elements representing the PS strands and the plane elements representing the concrete panel share nodes only at the four boundaries of the wall panel.
As shown in Fig. 13, the loading and support conditions of the belt wall are applied as close to those in Fig. 7b as possible. First, the lateral load of the belt wall is applied to the top slab as a uniform line loading along the slab length, while horizontal displacements of the bottom slab are constrained (u_{x} = 0 and u_{y} ≠ 0). Second, the axial compression force 7680 kN, which is equivalent to 0.3f_{c}′ in stress, is applied to the top of the columns. At the bottom, on the other hand, vertical displacements are constrained (u_{x} ≠ 0 and u_{y} = 0).
The stress–strain relationships of the concrete in tension and compression are modeled as the parabolic–linear model embedded in VecTor2 (Wong et al. 2013). Confinement effects by biaxial compression, such as strength and ductility enhancement, are not considered. On the other hand, decrease in the compressive strength of concrete strut due to transverse tensile cracks (i.e. compression softening), occurring under the biaxial state of tensile and compressive stresses, is taken into account as the effective compressive strength f_{ce} (Vecchio and Collins 1986). For steel reinforcements used in the boundary columns and slabs, the linear strainhardening model is used. Bar buckling is not considered. For the highstrength PS strands, a bilinear model following the elastic modulus E_{ps} = 195 GPa and postyield modulus E_{pp} = 0.05E_{ps} is used (refer to Fig. 9b). The effective prestress applied to the PS strands, f_{pe}, is considered by adjusting the initial strain.
4.2 Results of FE Analysis
Design parameters of PSC belt wall specimens.
Specimen  Effective prestress f_{pe}  f _{ pe,max} ^{a}  Reinforcement ratio ρ_{p} (%)  ρ_{p,max} (%)^{b} 

PT23V  0.315f_{pu}  0.338f_{pu}  0.2  1.22 
PT26V  0.629f_{pu}  0.338f_{pu}  0.2  1.22 
PT43V  0.315f_{pu}  0.623f_{pu}  0.4  1.22 
PT46V  0.629f_{pu}  0.623f_{pu}  0.4  1.22 
4.3 Comparison of Belt Wall Shear Strengths
In Fig. 14, the belt wall shear strengths V_{cr} and V_{y}, computed by Eqs. (9) and (10), respectively, are compared with the V–Δ relationships obtained by the FE analysis. The lateral displacements Δ_{cr} and Δ_{y}, computed by multiplying γ_{cr} and γ_{y} by the centertocenter height of the belt wall (h_{w} = 4400 mm), are also compared (refer to the dashed lines). V_{cr} and Δ_{cr} at shear cracking are in good agreement with the results of FE analyses in all specimens, despite different f_{pe} and ρ_{p}. On the other hand, V_{y} and Δ_{y} at shear yielding are significantly different from the postcracking behavior by the FE analysis. This is because after shear cracking, the distribution of concrete stresses and strains in the wall panel become highly nonuniform, as shown in Figs. 15 and 16, and thus the compression field theory based on uniform stress and strain field does not work well.
As shown in the V–Δ relationships of PT23V and PT26V obtained by FE analyses, the belt wall shear strength at shear cracking increases with increasing effective prestress f_{pe}. In addition, as seen from the comparison of the V–Δ relationships between PT23V and PT43V, the shear strength of the belt wall increases with increasing reinforcement ratio ρ_{p}. These trends are explained well from the equation of V_{cr} in Eq. (9).
In all specimens, the peak strength by the FE analysis is greater than V_{y}, although the PS strands do not reach their yield strength at the peak strength. The belt wall shear strength greater than V_{y} is attributed to the contribution of the boundary columns. In PT46V, for example, the shear strength contributed by the internal wall panel, computed by integrating v_{cxy} at the bottom shown in Fig. 16b, is only 12,494 kN, which is less than V_{y} = 13,392 kN. Only after the shear strengths provided by the left and right boundary columns, 1340 and 3732 kN, respectively, are added, the belt wall shear strength in total (= 17,508 kN) is greater than V_{y}.
5 Design Recommendation
When designing the PSC belt walls used as virtual outriggers in highrise buildings, elastic design is desirable based on the shear strength V_{cr}. As shown in Eq. (9), early inclined cracking occurring in the wall panel subjected to high shear demand (i.e. pure shear) can be effectively restrained by adjusting the effective prestress and reinforcement ratio of PS strands, f_{pe} and ρ_{p}. However, to prevent brittle failure, limitations on f_{pe} and ρ_{p}, defined in Eqs. (11) and (12), should be satisfied.
6 Summary and Conclusions
 1.
For the distributed belt wall system, the belt walls, without direct connection to the core wall and acting as virtual outriggers, are as effective in reducing lateral drift of the highrise building as the conventional belt and outrigger structures are. The performance of the distributed belt wall system depends on the number and arrangement of belt walls.
 2.
Since the belt walls as virtual outriggers in highrise buildings are subjected to pure shear, the existing shear strength equations based on flexureshear cracking failure might not be applicable. Instead, the shear strengths of the belt walls, such as cracking and yield strengths, should be based on the belt wall panel behavior under pure shear.
 3.
The belt walls can be reinforced with highstrength prestressing strands to meet high shear demand. In this case, the belt wall shear strength at the onset of inclined shear cracking, estimated by the compression field theory based on uniform stress and strain field, is in good agreement with the results of FE analyses. By increasing the effective prestress and reinforcement ratio of PS strands, the shear resistance of the PSC belt wall can be enhanced.
 4.
The results of the FE analysis show that the shear behavior of the PSC belt walls is with limited ductility and fails before reinforcement yielding. This is because, as the width of inclined shear cracks increase in the wall panel, the concrete stress are concentrated locally at the corner areas and along the diagonal struts. Thus, it is recommended that the shear design of the PSC belt walls be based on the cracking strength.
In addition to the analytical investigations, the performance of the proposed PSC belt wall system should be experimentally verified in the future. Particularly for a possible application to seismic design, the behavior of the belt wall under cyclic loading should be investigated further.
Notes
Authors’ contributions
TSE contributed to writing the manuscript as the principle author. He derived design formula based on the compression filed theory, and investigated the detailed behavior of prestressed concrete belt walls through performing nonlinear finite element analysis. HM contributed to the numerical investigations of the prototype highrise building. WY contributed to writing and reviewing the manuscript. His suggestions and comments improved the completeness and readability of the manuscript. All authors read and approved the final manuscript.
Acknowledgements
This research was supported by research grants funded by the Ministry of Land, Infrastructure, and Transport of Korea (Code 18AUDPB10632704, Architecture & Urban Development Research Program), and by National Natural Science Foundation of China (No. 51338004).
Competing interests
The authors declare that they have no competing interests.
Availability of data and materials
Not applicable.
Funding
Research grant funded by the Ministry of Land, Infrastructure, and Transport of Korea (Code 18AUDPB10632704, Architecture & Urban Development Research Program). Research grant funded by National Natural Science Foundation of China (No. 51338004).
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
References
 ACI Committee 318. (2014). Building code requirements for structural concrete (ACI 31814) and commentary. Farmington Hills, MI: American Concrete Institute.Google Scholar
 Choi, H. S., & Joseph, L. (2012). Outrigger system design considerations. International Journal of HighRise Buildings, 1(3), 237–246.Google Scholar
 Collins, M. P., & Mitchell, D. (1980). Design proposals for shear and torsion. Journal of the Prestressed Concrete Institute, 25(5), 70.Google Scholar
 Dean, B., Martin, O., Emery, D., & Chancellor, P. (2001). Tall building design innovations in Australia. In Tall buildings and urban habitat, cities in the third millennium, 6th world congress of the council on tall buildings and urban habitat (pp. 393–394). Melbourne: Planning and Architecture.Google Scholar
 Eom, T.S., Hwang, I.H., Lee, S.J., & Park, T.W. (2018). Failure mode and shear strength of nonprestressed hollowcore slabs in oneway shear. ACI Structural Journal, 115(4), 1131–1141.CrossRefGoogle Scholar
 Eom, T.S., Kim, J.Y., Kim, J.Y., Kim, J.Y., & Kim, T.Y. (2013). Shear design of concrete belt walls reinforced with posttensioning strands. Journal of Korean Society of Hazard Mitigation, 13(1), 31–39.CrossRefGoogle Scholar
 European Committee for Standardization. (2004). Eurocode2: Design of concrete structures—Part 11: General rules and rules for buildings. BS EN 199211: 2004. London: British Standards Institute.Google Scholar
 Han, S.J., Lee, D. H., Oh, J.Y., Choi, S.H., & Kim, K. S. (2018). Flexural Responses of Prestressed Hybrid Wide Flange Composite Girders. International Journal of Concrete Structures and Materials, 12(5), 581–596.Google Scholar
 Korean Concrete Institute. (2012). Design code for concrete structures (KCI2012), 2012. Seoul: Korean Concrete Institute.Google Scholar
 Lee, D. H., Han, S.J., Joo, H.E., & Kim, K. S. (2018). Control of Tensile Stress in Prestressed Concrete Members Under Service Loads. International Journal of Concrete Structures and Materials, 12(4), 453–469.Google Scholar
 Midas, I. T. (2006) Midas/Gen: General structural design system for windows, online manual, V.7.1.1 (R2), Korea.Google Scholar
 Nair, R. S. (1998). Belt trusses and basement as “virtual” outrigger for tall buildings. Engineering Journal American Institute of Steel Construction, 35(4), 140–146.Google Scholar
 Stafford Smith, B., Cruvellier, M., Nollet, M.J., & Mahyari, A. T. (1996). Offset outrigger concept for tall buildings, tall building structures—A world view. In Council on tall buildings and urban habitat (pp. 73–80).Google Scholar
 Vecchio, F. J., & Collins, M. P. (1986). The modified compressionfield theory for reinforced concrete elements subjected to shear. ACI Structural Journal, 83(2), 219.Google Scholar
 Wong, P. S., Vecchio, F. J., & Trommels, H. (2013). VecTor2 & formworks user’s manual (2nd ed.). Toronto: University of Toronto.Google Scholar
Copyright information
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.