Influence of core stiffness on the behavior of tall timber buildings subjected to wind loads

Abstract

This study analyzes the feasibility of the use of cross-laminated timber (CLT) as a load-bearing structural element in a 40-story building based on Chinese design requirements. The proposed design of the high-rise concrete–CLT building utilizes the core–outrigger system. Concrete is used for the central core and outriggers, and CLT is used for the rest of the structure of the building. Finite element models with different types of connections were developed using SAP2000 to analyze the lateral behavior of the building under wind action. The finite element models with rigid connections deduce the wind load distributions on individual structural elements, which determine the total number and the stiffness of fasteners of the CLT panels. Accordingly, spring links with equivalent stiffness that simulate the mechanical fasteners were employed in SAP2000. The results indicate that CLT increases the lateral flexibility of the building. A closed concrete core was substituted by two half cores to measure the requirement of the maximum lateral deflection. However, the acceleration at the building top still exceeded the limitation prescribed in Chinese Code JGJ 3–2010 owing to the lightweight of CLT and decreased stiffness of the hybrid building. To restrict this top acceleration within the limit, further approaches to increase the stiffness in the weak direction of the building are required. Methods such as the modification of the floor layout, increase in the thickness of walls, and addition of extra damping capacity should be considered and verified in the future.

Keywords

cross-laminated timber / tall timber buildings / finite element analysis / horizontal deflection / top acceleration

Introduction

In the last decades, a growing number of multi-story timber buildings have been constructed using cross-laminated timber (CLT) elements, e.g., the Murray Grove (30 m, completed in 2008) in London UK and the Forté Building (32 m, completed in 2012) in Melbourne Docklands, Australia. CLT is a lightweight material with only about one-sixth the weight of conventional concrete that shows several advantages in construction, such as reduction in dead load, shorter crane operation time, faster building assemblage, and environmental friendliness owing to the storage of CO₂.

Over the same period of the worldwide spread of mid-rise CLT constructions, many studies have proved the reliable characteristics and performances of CLT elements. In 2007, a series of seismic tests were carried out on a 7-story CLT building, and none of the CLT panels tested were significantly damaged after the tests [¹]. In 2010, Dujic et al. [²] developed a numerical model of the tested 7-story CLT building and compared the calculated and measured results. In addition to full wood buildings, wood-concrete hybrid structures have also been studied. Xiong and Jia [³] demonstrated that 3-story wood-concrete hybrid buildings kept standing even when the maximum interstory drift reached 1/49 under seismic action. These studies focused on the seismic response of buildings. Their results demonstrated that the CLT elements have strong resistance to lateral loads, and CLT buildings offer engineers the flexibility to repair the damaged part of panels and connectors after a major seismic event [¹].

There are also a few studies on high-rise timber buildings. Smith and Frangi [⁴] proposed the concept of a tall modern timber building system with 10–20 stories. Van de Kuilen et al. [⁵] presented a preliminary design of 40-story-high residential concrete–CLT buildings. Both studies applied a hybrid structural system with concrete and timber mainly for fire safety, structural safety, and horizontal shear stiffness. Connolly et al. [⁶] substituted the concrete cores of an 18-story wood-concrete hybrid building with mass timber cores. They suggested thicker timber walls in the core and additional shear walls to realize the assumption of the 18-story building built entirely of timber. Skidmore, Owings & Merrill, LLP [⁷] implemented a strategic research of timber tower with a “concrete jointed timber frame” system based on a concrete benchmark building with 42 stories built in the 1970s. They argued that the timber tower system relying on supplementary concrete/steel is technically feasible from a structural engineering point of view. To date, diverse hybrid structural systems of high-rise timber buildings have been proposed, and the performances of these structural systems must be further studied and verified.

This study aims to determine the lateral behavior of a 40-story concrete–CLT building subjected to wind loads. The main structure of this building is based on the one proposed by Van de Kuilen et al. [⁵], which comprises two independent concrete cores in the middle and CLT panels in all the residual parts of the building. Finite element (FE) models of the building were implemented using SAP2000 [⁸]. First, a model of a common concrete building with an identical structure was evaluated in SAP2000 as a reference for comparison with the hybrid building in terms of building deformations, wind load distributions, and modes of vibration. Then, a model of a rigid connected concrete–CLT building was analyzed to determine the distribution of wind loads on the cores and sidewalls, which determine the design of the mechanical connections between CLT panels and vice versa. Lastly, according to the previous analysis results, the FE model was further readjusted. The dispersed joints in the CLT structure were simulated using linear spring elements. The configuration of the core was altered to improve the lateral force resisting system of the hybrid structure. The preliminary analysis and results of static wind loads were determined in accordance with Chinese Code GB 50009–2012 [⁹] to predict the horizontal behavior of the concrete–CLT building.

Design of high-rise concrete–CLT building

Structural design

In this study, we consider a 40-story residential building in Shanghai with three apartments per story of approximately 100 m² [⁵]. Its layout is simplified by neglecting original interior details and applying it to the assumed tall concrete–CLT building. The hybrid building is estimated to have a 132 m height, with an identical story height of 3.3 m (included floors) and a floor plan dimension of 33.7 m × 15.7 m (Fig. 1).

From a structural engineering point of view, a centrally located core plays an essential role in bearing both horizontal and gravity loads. From a fire-safety point of view, escape routes should be made of non-combustible material and have high fire resistance, so they can be used without danger for a longer period to evacuate occupants and ensure the safety of rescue teams [¹⁰]. Therefore, two centrally located cores are composed of concrete and CLT elements constitute the rest of the structure in the form of the apartments surrounding the two small cores, taking part of the horizontal forces and supplying occupants a pleasant and environmentally friendly living space. The corresponding FE model developed in SAP2000 is shown in Fig. 2, with only two stories displaying its cross-section. The concrete material in the FE model is shown in blue, and CLT is shown in brown color.

In an ideal case, i.e., without considering transport limitations, six CLT panels can compose the exterior walls of a single story: two panels with a 10.3 m span are arranged on the short side of the Y-axis, and four panels with a 13.2 m span (Fig. 3) are arranged on the long side of the X-axis. The door or window openings in the walls have heights of 2.5 and 1.65 m, respectively. The thickness of CLT walls maintains 300 mm and the thickness of CLT floors maintains 250 mm in the entire building.

To improve its overturning strength and stiffness, concrete floors or full concrete stories acting as outriggers are also modeled in the hybrid building. Smith and Coull [¹¹] suggested that outriggers can reach their optimum performance when they are evenly arranged along the height of a building; thus, in the concrete–CLT building considered in this study, the outriggers are set in every tenth story, as shown in Fig. 4. In this case, they act not only as horizontal cantilevers to increase the lateral stiffness of the structure but also as fire isolators to separate wooden parts.

Unbonded tendons can be employed to integrate the CLT elements of this hybrid building in the vertical direction. In the project ‘Limnologen’ in Växjö, Sweden [¹²,¹³], unbonded tension rods were applied instead of load transferring connections between wall elements to resist wind loads and especially uplift forces. The tendons cannot only considerably reduce the amount of hold-downs but can also compensate for the tensile stress in CLT walls by providing prestressing forces if they are post-tensioned.

In this study, the tendons were embedded and extended in the CLT panels from the foundation to the concrete outriggers [⁵,¹⁴]. The endpoints of the tendons were anchored through endplates, and couplers, which could be placed at any point in the cavities, ensured the tendon extension through CLT stories until the next concrete outrigger (Fig. 4). The normal force was transferred between the CLT walls and down to the foundation.

CLT and the other structural materials design

CLT is fabricated as an engineered wood product from several orthogonally glued layers of timber boards (Fig. 5), commonly used for walls, floors, and roofs in construction. During the fabrication, the major defects of wood, such as notches and grooves, can be cut off. These strips compose the large CLT panels, resulting in fewer defects and more homogeneity than in comparable solid timber. Furthermore, owing to the crosswise arrangement of layers, CLT could mitigate the anisotropic properties of wood. These features lead to the homogenization of wood material and the increase in the load-carrying ability of CLT panels in both directions. Considering their low density, CLT panels have a high ratio of stiffness and strength relative to their weight.

The sizes of manufacturing equipments of different manufacturers (e.g., binderholz CLT BBS, KLH Massivholz GmbH) limit the CLT panel sizes, in general, the largest ones can be more than 20 m long, up to 3.5 m wide, and up to 500 mm thick. Given these large dimensions, CLT is suitable for constructing one-piece (multi-)story walls with prefabricated openings for windows and doors. Compared to small-size panels, fewer connectors are needed for CLT panels owing to their large dimensions. The hoisting time of CLT in a tall building is only approximately one-third of that of concrete elements [⁵] owing to its lightweight, allowing an easier and faster assembly on-site. For instance, the Murray Grove in London was constructed by four men in just 27 d [¹⁵].

CLT panels are normally symmetric around the center plane. The CLT panel behaves distinctly in different directions, while the behaviors of its layers are symmetric in one direction. Figure 6 illustrates an eight-layered CLT panel with double parallel layers on the faces and center, and two cross layers between them. The mechanical properties of CLT are not only related to the types of loads exerted out of the plane of the panel (F) or in the plane of the panel (tension F_t and compression F_c) (Fig. 6) but also to the direction of the loads parallel or perpendicular to the grain direction of the outer layers (plate behavior). Owing to the natural characteristics of wood and orthogonal glued layers, the major strength and stiffness direction of CLT generally corresponds to the grain orientation of the outer layers. Nevertheless, to avoid large discrepancies between the calculation and test results, Blass and Fellmoser [¹⁶] proposed homogenizing a solid wood panel with cross layers into a one-layer orthotropic material by considering the rolling shear of the cross layers using composition factors for strength and stiffness analysis. This simplification is necessary for the FE model, where orthotropic shell elements are used for modeling CLT panels. Blass and Fellmoser [¹⁶] also recommended applying the strength class of GL28 [¹⁷] for CLT panels with regard to the lamination effect, when the panels are made up of wood strips of strength class C24 [¹⁸], as commonly assumed.

In 2008, Dujic et al. [¹⁹] used the commercial FE program SAP2000 to perform a parametric study of 36 configurations of openings in walls of three different lengths to predict the racking behavior of CLT walls. They compared the experimentally obtained moduli of elasticity (MoE) of CLT panels and the calculated values by using the composition factors proposed by Blass and Fellmoser [¹⁵], which showed good agreement.

Table 1 lists the values of the effective MoE of CLT used in FE models based on glued laminated timber properties of strength class GL28. In the Table 1, E_0,ef and E_90,ef are the MoE parallel and perpendicular, respectively, to the grain direction of the outer layers of the CLT, which are defined for walls in two plane directions or floors in two directions out of the plane. The effective values of the tensile (f_t,0,ef) and compressive (f_c,0,ef) strength of wall panels are also computed from the characteristic values of 19.5 and 26.5 N/mm², respectively, based on glued laminated timber of class GL28. Table 1 lists the material properties of CLT, concrete, and tendons defined in the FE models.

Mechanical connections for CLT structure

Mechanical fasteners are indispensable for the connections between CLT and CLT elements, and between CLT elements and concrete cores. Horizontal connections for the on-site assembly of CLT elements are mostly self-tapping screws, nails/screws in combination with metal plates or angle brackets, and bolts/dowels. Because CLT panels are much more rigid than the connectors, most of the shear and flexural deflections of the CLT panels due to the in-plane loads become negligible. Consequently, the flexibility concentrates in the connections, making them the determinant factor of the load-carrying capacity of the CLT structure [²⁰].

The Chinese National Standard Code for Design of Timber Structures GB50005-2003 [²¹] stipulates the constitution requirements of tooth joints, bolted connections, and nail/screw connections. The design load-carrying capacity of each shear plane of the bolt or nail/screw connection is calculated as follows:

(1)N_{\mathrm{v}}=k_{\mathrm{v}}{d}^{\mathrm{2}}\sqrt{f_{\mathrm{c}}},

where N_{\mathrm{v}} is the designed load carrying capacity of each shear plane, k_{\mathrm{v}} is the coefficient of bearing capacity, dis the diameter of the fastener, and f_{\mathrm{c}} is the effective compressive strength of timber.

The coefficient of bearing capacity k_{\mathrm{v}} of steel-to-timber connections is 11.1. In GB50005-2003, the strength grade of European spruce is classified into the group of TC13-B, i.e., its compressive strength is 10 N/mm². It is presumed that screws with a diameter of 6 mm and steel angle brackets are used; thus, the design lateral load-carrying capacity of one screw can be calculated to be 1.2 kN.

Owing to the different strengths of CLT and concrete, the horizontal and vertical movements of the connected concrete and CLT elements do not coincide. Moreover, the joint area is restricted to the narrow side of CLT walls, which limits the number of fasteners. Therefore, every fastener must have a relatively high load-carrying capacity and stiffness to transfer shear forces and coordinate the movements of two connected parts. As a first assumption, anchor bolts with a thickness of 20 mm are used in these joint zones. Using Eq. (1), the designed load-carrying capacity of one bolt was calculated to be 14 kN.

The stiffness of the metal connections applied in the wooden elements is not related to GB50005-2003. Consequently, the calculation of the slip modulus (i.e., stiffness) of a single fastener per shear plane in the serviceability limit states has to refer to the guide of the European Code Eurocode 5 [²²]. Consequently, the stiffness of a 6 mm-diameter screw without pre-drilling is 2200 N/mm for timber–steel connection; the stiffness of a 20 mm diameter bolt is 6900 N/mm for a timber–timber connection and 13800 N/mm for a timber–steel/concrete connection ( = 2 × stiffness of timber–timber connection).

In this case, several spring links in the FE model with total equivalent stiffness substitute hundreds of connectors in one CLT panel, simulating the connections and transferring load effect. The total number and stiffness of fasteners in every connecting border can be determined according to the distributed forces acting on the concrete cores and CLT elements, which can be obtained from the analysis of a rigidly connected FE model. Because in this study we do not focus on the behavior of a single member or connector but on the overall response of the construction subjected to wind loads, the details of each individual connection can be ignored by properly assessing the overall stiffness or strength. This simplification is also necessary to avoid an excessive number of link members, numerous repeated operations, and the huge cost of gradient computation.

The following assumptions are also made for the analysis models with spring links. First, the number of links is simplified; their positions remain the same in every story and symmetric in relation to the central core. Figure 7 demonstrates the arrangement of the varied spring links in the CLT panels that are situated on the left side of the building.

Second, the tensile spring links in the model are concentrated in one location of the four corners for ease of programming and calculation (in practice, they are placed around the circumference). They are assumed to carry all uplift forces; the contributions of other fasteners to resisting uplift forces, such as angle brackets, are neglected.

Finally, the compressive and tensile stiffness of the spring links are assumed to be equal in the model. CLT panels are considered to be rigid compared to their connections, so the shear and tensile stiffness of the CLT system mostly depends on the connections. However, the entire CLT system has much higher strength and stiffness in compression to the connections, and the compressive forces are mostly carried by CLT panels. Therefore, applying the same value for both the compressive and tensile stiffness of the spring links will not influence the calculation results significantly.

Loads and requirements

Both dead and live vertical loads are considered in this study. The dead load is estimated as the weight of the structural elements, and the live load is set to 2 kN/m², according to the Load Code for the Design of Building Structures GB50009-2012.

Although the wind load is a type of dynamic load, it is treated as a static load by multiplying the dynamic effect factor at the primary stage. Based on GB50009-2012, a 50-year return-period wind pressure calculation is applied as follows:

(2)w_{\mathrm{k}}={\beta }_z{\mu }_{\mathrm{s}}{\mu }_z{w}_0,

where w_0 is the reference wind pressure, w_{\mathrm{k}} is the effective design wind pressure, {\mu }_{\mathrm{s}} is the shape factor or pressure coefficient, {\mu }_z is the exposure factor that allows for the height and location of the structure, and {\beta }_z is the dynamic effect factor of wind at height z.

Because the dynamic effect factor is related to structural damping, the effective design wind pressure varies depending on the difference in the damping of buildings with different structural materials. The ASCE 7–05 Commentary suggests a damping value of 0.02 for concrete buildings subjected to wind load. The Chinese code GB 50009–2012 gives a wind damping value of 0.05, while the JG 3–2010 specifies a value between 0.01 and 0.02 for estimating the wind-induced acceleration at the top of the building. Considering safety, in this study, we employ the most conservative critical damping ratio for the original concrete building, i.e., 0.01.

Nevertheless, there is no empirical damping value for primarily wooden buildings under wind load. Two studies [²³,²⁴] indicated that the seismic damping of full CLT buildings or CLT walls subjected to seismic load is approximately 10–18%, which is two to three times the value usually applied for concrete buildings under seismic action, i.e., 5%. Dujic used a damping value of 0.15 for the linear dynamic analysis of a 7-story CLT building under seismic action [²]. Similar to traditional buildings, the wind damping values of CLT buildings are expected to be smaller than the seismic damping values because buildings subjected to wind load generally respond within the elastic range. Therefore, we assume inherent structural damping of 0.02 and 0.015 for full CLT building and hybrid concrete–CLT buildings, respectively.

Using the calculation method provided by the Chinese code GB 50009–2012, the effective wind pressure of the original concrete building is found to increases from 0.42 kN/m² on the ground to 2.44 kN/m² on the top of the building. Meanwhile, the maximum wind pressure at the top of the concrete–CLT building and the full CLT building are 2.25 and 2.13 kN/m², respectively. In general, the dynamic effect factor and the effective wind pressure vary inversely with the damping ratio. For the design of tall buildings subjected to lateral wind loads, the issues of concern are wind-induced drift (serviceability) and acceleration (occupant comfort). The drift index is the ratio of the lateral deformation at the top level to the building height. The drift criteria for conventional structures are common in the preferred acceptable range between 1/650 and 1/350 of the building height when related to serviceability [¹⁰]. However, even small movements of buildings cause discomfort to humans. In this regard, the Chinese code Technical Specification for Concrete Structures of Tall Building JGJ 3–2010 [²⁵] complies with the interstory drift index, which is the ratio of the relative sway between two adjacent stories to the story height, to assess the occupant comfort. The interstory drift index limited to 1/800–1/1000 by the elastic calculation method for conventional concrete buildings with a shear-wall structures shorter than 150 m. Furthermore, JGJ 3–2010 restricts the maximum accelerations to 0.15 and 0.25 m/s² for apartment buildings and office buildings taller than 150 m. Even though the structures in this study are shorter than 150 m, this requirement will still be checked, as the buildings become lighter by substituting CLT elements for part of concrete elements, the accelerations are expected to increase, so the human comfort requirement becomes more relevant.

FE analysis of tall concrete–CLT buildings

Element definition of FE models

The FE program SAP2000 is used to model structural components and the entire construction. The concrete and CLT walls and floors were simulated using shell-thin elements. Concrete is defined as an isotropic material in the model, and CLT is defined as an orthotropic material owing to the difference in its material properties and strengths in different orthogonal directions. Cable elements simulate the unbonded tendons embedded in CLT walls, and linear spring link elements simulate the behavior of the mechanical fasteners.

In accordance with the evenly arranged outriggers, the hybrid structure is categorized into four groups: 1–10, 11–20, 21–30, and 31–40. The thicknesses of the core walls of these groups were 350, 300, 250, and 200 mm, respectively, and the thicknesses of the CLT walls and floors were maintained at 300 and 250 mm, respectively. The story height of 3300 mm includes a 3050 mm-high wall and a 250 mm-thick roof. All the following models were developed with the same materials’ properties and dimensions of structural elements.

Models with fully rigid connections (M1, M2, and M3)

Concrete building (M1)

An FE model (M1) of the designed building completely made of concrete was implemented first in SAP2000 to verify the definitions and for comparison with the concrete–CLT building model. The concrete building model was created with fully rigid connections. Because the planar structure of the building was not strictly symmetric, the walls on the right side experienced slightly higher forces than the walls on the left side. The control point that is displayed in Fig. 8 was set in every model at the XYZ coordinate (33550, 13900, and 131750 mm), where the maximum deflection of the building appeared.

CLT building (M2)

The other basic model (M2) was solely made of CLT and was analyzed as a reference system. The most important assumption of this model was that the CLT wall and floor elements were not connected by metal fasteners but were glued together to obtain an entire shear wall and rigid bonds between the panels. In other words, this was a fully rigid CLT building model with infinite spring stiffnesses without the effect of the reduced stiffness of the mechanical fasteners. This allows for a direct comparison to the full concrete model.

Concrete–CLT building (M3)

Figure 8 illustrates the model (M3) of the designed 40-story-high concrete–CLT building, in which concrete comprises two half cores at the center (displayed in blue) and CLT panels (displayed in brown) are used to construct the external sidewalls and floors. The main purpose of M3 was to obtain the distribution of wind loads on the concrete core and CLT sidewalls, which determine the required stiffness of the connections of the CLT elements. This model also assumed that CLT elements were rigidly connected, similar to model M2. The other definitions were the same as for M1. By using such a general model, a sensitivity analysis could be performed at both the building and component levels (wall thickness, materials, and fasteners).

Concrete–CLT building with two half cores applying metal fasteners (M4)

The model with completely rigid connections cannot provide proximate modeling of the real scenario of the building; therefore, model M4 using linear spring links to simulate the mechanical fasteners was developed in SAP2000. Because such high timber buildings have not been extensively used, some of the structural details are still uncertain, and the simulation and analysis are performed based the following assumptions:

- concrete outriggers are connected rigidly to the core and are fully bending moment resistant;

- CLT floors are treated as rigid diaphragms, neglecting displacements between adjacent panels;

- the flexural stiffness of the floor slab is ignored.

To further reduce the time required for the numerical analysis, spring links are also categorized into four groups in the vertical direction according to the thicknesses of the core walls. All springs in a group have the same stiffness value, namely the maximum one in the group. These values are computed based on the forces on the concrete cores and CLT walls that are derived from M3.

Concrete–CLT building with one full core applying metal fasteners (M5)

Referring to the core structure system, the drift of the buildings depends on the total building height, core performance, number of shear walls, and geometrical layout. The core absorbs most of the shear force and is also the main contributor to the shear stiffness of the building. Accordingly, extra walls are added to unite the two separate half cores into one closed core (Fig. 9); this model is denoted as M5 and is expected to have much higher stiffness than model M4. A change in CLT sidewall thickness would not significantly influence the ability of the whole building to resist lateral deformation.

Concrete–CLT building with unbonded tendons (M6)

To take up uplift loads, cable elements were introduced in model M6. These cannot resist shear or bending but carry tension forces to simulate the unbonded tendons. Because the end nodes of cable elements are rigidly connected with the nodes of the shell elements of the concrete outriggers, there is no relative movement between these nodes. Figure 10 displays the CLT walls (shown in brown) with integrated cable elements (shown in blue). Prestressing forces are simulated in the FE model by applying a certain temperature decrease that produces a corresponding thermal strain by steel contraction. The temperature change△T produces axial thermal strain in the cable element and can be calculated as follows:

(3)△T=F/\alpha E{A}_0,

where \alphais the coefficient of thermal expansion, which is 1.2 × 10⁻⁵ K⁻¹ for steel, F is the force exerted on a tendon under tension, and A_0 is the original cross-sectional area of the steel bar.

The values of the tensile forces due to the wind load that were derived from the analysis results of M3 are exerted on the unbonded tendons as their effective prestressing forces. Furthermore, the equivalent lowering temperature was set to - 250°C. Using Eq. (3), the required minimum diameters of the unbonded tendons that are assigned to the cable elements in the stories from to 1–10, 1–20, and 1–30 were determined to be 65, 46, and 32 mm, respectively. Although the tensile forces due to wind loads were offset by the dead load from stories 31–40, tendons with diameter of 16 mm were still arranged from the foundation to the top of the building as vertical connectors.

Results and discussion

Horizontal displacements and drifts of the six models

The maximum lateral deflections, including both bending and racking shear deformations, calculated by treating the two half cores as coupled shear walls [²⁶] are first compared with the results obtained from the FE analysis of the three rigid connected models (M1, M2, and M3). The top deformations of M1, M2, and M3 were calculated to be 139, 532, and 309 mm, respectively, which are quite close to the values obtained from the numerical analysis (Table 2). From an engineering point of view, the approximate values indicate that the FE models are appropriately developed and can successfully simulate the building using a linear elastic approach.

Table 2 also presents the maximum interstory deflections and interstory drift index of the six models, which were used to assess occupant comfort. The maximum interstory drift index of 1/870 of M1 appears at the 29th story, which is within the 1/1000–1/800 range set by JGJ 3–2010. However, the maximum interstory drift indexes of M2 and M3 are significantly larger than the acceptance, indicating that these two models do not meet the human comfort standards.

Figure 11 shows the distribution of the lateral load on different structural components of M3. The central core has to take up a larger percentage of the lateral load when the CLT panels substitute the concrete sidewalls. Figure 12 shows the shear forces in the four joint zones of M3. Because the outrigger floors are made of concrete, the shear loads change significantly every ten stories. Table 3 displays the maximum values of uplift forces in every group of ten stories of M3 as well as the shear forces on the sidewall panels in the Y and X directions, and the shear forces in joint zone I. The stiffness calculated from these values are shown in Table 4 and are assigned to the corresponding spring links applied in M4. Consequently, the top deformation of M4 is 395 mm, which is 85 mm greater than that of M3. Its interstory drift is 1/265, which cannot fulfill the human comfort requirements of the Chinese code JGJ 3–2010. This result reveals that the current structural design, which works for concrete buildings, is not sufficient for a hybrid tall building. Therefore, the stiffness of building structures need to be increased.

M5 has a continuous-structure closed core with a higher stiffness than two separated half cores and is more effective in resisting lateral loads. As a result, its top deflection decreased to 153 mm (Table 2), but its interstory drift index of 1/780, which almost meets the threshold of the human comfort criterion defined in JGJ 3–2010, is only outside the required range by 2% (although it is related to conventional concrete buildings). The FE analysis indicates that the single closed concrete core of M5 carries more than 90% of the shear forces, and the CLT sidewalls carry a relatively small part of these forces.

M6 has the same closed core layout of M5, but utilizes cable elements instead of tensile spring links. Although the arrangement of cable elements is different from that of the tensile links in the model, M6 has almost the same lateral behavior as M5. Cables can stiffen the structural system in the vertical direction, and while the fundamental period of M6 is slightly smaller than that of M5, it cannot reduce the lateral deformation due to the wind load.

Additionally, the second-order (P-∆) effect and the maximum compressive and tensile stresses at the basement of the building (Table 5) were checked under the combined loads of the dead, live, and wind loads. An exception is M6, from which the computed values include the effect of the prestressing load. The geometrically nonlinear analysis demonstrates that the P-∆ effect increases the maximum deflections by 2%–5% of the six models. The P-∆ effect is greater in lighter (M2) and more flexible (M4) structures. The uplift forces due to the wind load on the sidewalls are completely offset by the self-weight of the building in the lower stories, except in M2. However, only a full concrete building can offset the uplift force at the bottom of the core owing to its heavyweight. The unbonded tendons with prestressing load in M6 help to decrease the tensile stress in the concrete core walls, so that the tensile stress at the bottom part of the concrete core of M6 is within an acceptable range.

Figure 13 describes the deformation behaviors of the different models. It is clear that the closed core structure (M5 and M6) performs considerably more effectively than the structures with two independent half cores (M3 and M4) regardless of the connection type of CLT elements. Strengthening the concrete core, e.g., by combining two independent half cores into one closed core, could efficiently reduce the horizontal deflection of tall concrete–CLT buildings. If additional compression stiffness of springs (as in a real situation) is considered in the model, the building’s maximum deflection and drift index will be further reduced.

Wind-induced acceleration at the top of the buildings

The lightweight of CLT results in a more flexible structure. Consequently, the wind-induced accelerations of the CLT and hybrid buildings are greater than those of the concrete building, as shown in Table 6. Adding additional tension bars can carry up the uplift forces, but, because their influence on the horizontal stiffness is negligible, they do not reduce the wind-induced accelerations.

When the damping ratio is set to 0.02, the acceleration of the full concrete building is lower than the human comfort requirement of 0.15 m²/s. Based on experience from seismic research, CLT buildings usually have a larger damping ratio than concrete buildings. However, even when the damping ratio is set to 0.05, the acceleration of the hybrid buildings with the full concrete core is still above the requirement for apartment buildings. Thus, M5 and M6 achieve the requirement for office/hotel buildings (accelerations below 0.25 m²/s), but not for apartment buildings.

Vibrations and eigenperiods

The Chinese Code GB50009-2011 specifies Eq. (4) to estimate the eigenperiod(s) of a high-rise concrete building with n stories. On the other hand, the European Code Eurocode 1 [²⁷] utilizes Eq. (5) to estimate the fundamental flexural frequency (Hz) of multi-story buildings with heights larger than 50 m. Thus, according to GB50009-2012 and Eurocode 1, the eigenperiod of the hybrid building should be 2–4 s and 2.9 s, respectively. These equations are affected only by the number of stories and building height; therefore, there are no differences between the six building models.

(4)T_1=(0.05\mathrm{~}0.1)n,

(5)N_1=46/H\mathrm{.}

Table 7 presents the eigenperiod, i.e., the period of the first vibration mode, of the six models calculated from the FE analysis. It can be seen that the eigenperiods are in a reasonable range. However, the FE models predict differences between the building types. The concrete–CLT building becomes relatively more flexible, which leads to a longer eigenperiod. Furthermore, the first vibration modes of M4, M5, and M6 are along the X-axis, i.e., the short side of the building. One important reason for this is that the span of the concrete core, whether two half cores or one full core, in the X-axis direction is shorter than that in the Y-axis direction. Additionally, the use of spring links loosens the tight connection between the concrete core and sidewalls. This explains why the first modes of M4, M5, and M6 are along the X-axis, which is different from the results observed in M1, M2, and M3. It can be concluded that if a rigid model (e.g., M3) would have been applied to simulate and analyze the concrete–CLT building without considering the impact of the mechanical fasteners, the stiffness of the building would have been assumed to be too high.

Conclusions

In this study, we developed six alternative numerical models of high-rise apartment buildings to analyze the behavior of concrete–CLT combination under wind load. The structural behaviors were analyzed in terms of horizontal displacement, interstory drift, acceleration, vibration, and eigenperiod.

The results show that essential building properties can be predicted using standard software. A modification of the original layout, e.g., connecting the two half cores together, is necessary to obtain the required building stiffness of the designed hybrid building. With an efficient and well-designed core system, the concrete–CLT building with 40 stories performs well and can satisfy the lateral deflection requirements. The top deflections of M5 and M6 at the maximum wind load are within 1/650–1/350 of the building height. Considering the interstory drift index limit of 1/1000–1/800 as a human comfort criterion, even the building with closed core structure do not perform well.

Furthermore, the horizontal accelerations of concrete–CLT buildings were proved to be too high and not meet human comfort requirements specified in the Chinese code for traditional buildings above 150 m. The analysis showed that such requirements should also be applied to buildings lower than 150 m not made completely of concrete. Therefore, we propose to extend the code requirements to lighter buildings, such as those made of both concrete and CLT analyzed in this study. The analysis results also indicate that the building should not be made slenderer. If the designed building has to be thinner, extra damping capacity can be added, so timber buildings may achieve a higher level and be comfortable for occupants.

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