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Abstract

Tall timber buildings are prone to serviceability problems (e.g. lateral displacements and wind-induced accelerations). This article investigates the feasibility of timber outrigger system to build up to 20 storeys using linear elastic finite element analysis and relevant European and international standards such as EN 1990, EN 1991-1-1, EN 1991-1-4, EN 1995-1-1 and ISO 10137. The location of up to two outriggers was optimised based on different serviceability criteria. Various outrigger layouts were investigated, and their stiffness demands were discussed. The efficiency of outrigger structures in reducing lateral displacements and wind-induced accelerations is highlighted. A feasibility study considering serviceability requirements was performed using different basic wind velocities, number of storeys and gravity loads. Although the focus of the article is on serviceability requirements, some ultimate limit state considerations (forces and stresses) were briefly discussed. The results demonstrate the feasibility of building up to 16 storeys under medium to high wind velocities.

Keywords

outriggers tall timber buildings wind-induced acceleration serviceability of timber buildings wind load

Introduction

The increase in world population results in higher urbanisation. On the other hand, the construction industry is a major contributor to greenhouse gas emissions worldwide.¹ The increased urbanisation can further increase greenhouse gas emissions which have unfavourable impacts on the environment. Therefore, the use of sustainable building materials is of great importance. Timber is a renewable material that can serve as an alternative to concrete and steel to reduce the environmental impact of construction. Eliassen et al.² performed a comparative study using life cycle analysis (LCA) and concluded that using timber can reduce greenhouse gas emissions by more than 13% compared to reinforced concrete and steel. Another LCA study by Skullestad et al.³ on buildings up to 21 storeys showed that timber buildings have 34% to 84% lower climate change impact than reinforced concrete buildings with similar load-carrying capacity.

Timber buildings, due to their lightweight and moderate stiffness, are often susceptible to excessive accelerations and lateral deformations under wind loads.^4–13 Excessive accelerations can cause occupants discomfort, and excessive lateral deformations can cause damage and may influence the functionality of the building. The acceleration due to wind can be reduced by increasing the building's mass,¹⁰ damping,¹⁴ lateral stiffness,¹³ or a combination.

Several structural systems can be used for multi-storey timber buildings. Cross-laminated timber (CLT) is commonly used for multi-storey timber buildings, for example the 9-storey residential building Stadthaus in London.¹⁵ However, such structures are usually cellular and may not be architecturally spacious. Braced structures are also prevalent in tall timber buildings. Global diagonal bracing was successfully employed in Treet (14 stories)¹⁶ and Mjøstarnet (18 stories)⁵ in Norway. The use of such structures requires large diagonal elements running along the full height of the building, affecting aesthetics and architecture flexibility. Moment resisting timber frames (MRTFs)¹⁷ provide good architectural flexibility. MRTFs achieve lateral stiffness by means of semi-rigid beam-to-column connections. Vilguts et al.⁴ performed a parametric analysis on MRTFs and suggested that such systems can be used up to 8 storeys with 2.4 m spacing between adjacent frames.

Outrigger (OR) structural system has been used in many concrete, steel, and composite tall buildings around the world.^18,19 High-rise buildings usually incorporate a central elevator core(s) together with walls and columns. Outriggers are stiff horizontal structural elements that connect the building's core/wall to the exterior columns.^20,21 The use of outriggers couples the core, walls and columns, resulting in a higher lateral stiffness and thus increases the possibility of building taller buildings.^20,21 The structural behaviour of outrigger structures is illustrated in Figure 1. When the central core/wall deflects laterally under lateral loads, a tension-compression couple is generated in the exterior columns, resulting in a restoring moment at the outrigger level. The restoring moment at the outrigger level reduces the lateral displacement and the bending moment at the central core/wall.

Figure 1.

Structural behaviour of outrigger structural system.²²

The location of outriggers is important and greatly influences the structural behaviour.²² Typically, the location is coordinated with the architect, considering that the presence of an outrigger imposes architectural constraints on the respective floor. Several studies have investigated the optimum location of outriggers.^22–28 In these studies,^22–28 the optimum location was selected mainly to achieve smallest lateral displacements. The optimum location of the outrigger depends on the structural characteristics of the building,²² the type of loading,²⁶ and the optimisation criterion.²⁹ However, as a first estimate, the location of outriggers can be reasonably assumed as suggested by Taranath,^20,21 see Figure 2.

Figure 2.

Optimum location of outrigger(s) according to Ref.²⁰

Employing outriggers can enhance the structural robustness in the event of a sudden loss of a local structural element or a connection.^20,29 This is achieved by providing alternative load paths that can prevent progressive collapse and redistribute the forces upon any local failure.²⁰ In timber structures, and due to the brittle nature of wood under tension and shear, addressing this issue is of great importance.^30,31

Several studies have been conducted on the use of outriggers in concrete, steel and composite structures, but little research has been done on timber structures. A study by Bollards³² showed that timber structures up to 20 storeys are possible using outriggers together with a large central CLT core ( $9 m \cdot 9 m$ ). Tesfamariam et al.³³ investigated the use of outriggers in timber structures to mitigate earthquake-induced vibrations using shape memory alloy dampers. In previous studies, the lateral displacements (top floor displacement and inter-storey drift) were chosen as the optimisation criteria. However, in timber structures, wind-induced accelerations are very decisive in the design and dimensioning of the structural elements.^4–11,13 The feasibility of using outriggers in timber buildings and their advantages are not extensively investigated, especially with respect to wind-induced acceleration requirements.

The aim of this article is to investigate the feasibility, advantages and limitations of using outriggers in multi-storey timber buildings. To achieve this, parametric analysis using finite element method (FEM) was performed in conjunction with the respective Eurocodes and standards. The optimum location of one and two outriggers was investigated considering lateral displacements and wind-induced accelerations as optimisation criteria. Several outrigger layouts were investigated, and their efficiency is compared. The effects of several parameters such as outrigger stiffness, number of storeys and wind velocity were also investigated.

Timber structures, due to their lightweight and moderate stiffness, are typically governed by the serviceability limit state (SLS).^4–11 Therefore, this article focuses on the SLS. However, since the introduction of an outrigger may cause force concentration in structural members and connections at the outrigger level, ultimate limit state (ULS) should be considered as well. In this article, some ULS considerations are briefly discussed to validate the feasibility of such structural system in timber buildings.

Materials and methods

The structural system

Figure 3 shows a 3D view of an example multi-storey timber building. The lateral load resisting system (LLRS) in X direction consists of two continuous interior CLT walls, two continuous exterior glued laminated timber (glulam) columns, glulam beams with semi-rigid moment connections and an outrigger. The LLRS in Y direction consists of global diagonal bracings and CLT walls. This article focuses on the structural system in X direction (interior frame with $C / C = 5 m$ , see Figure 3). The connections details of the LLRS in X direction are explained in more details in section ‘Finite element method and analytical model’.

Figure 3.

3D view of an example multi-storey timber building.

In this article, six variations of outrigger layouts were analysed (see Figure 4), and their performance is compared. The variations shown in Figure 4(a)–(e) combine MRTFs with outriggers. The first four variations (Figure 4(a)–(d)) employ a glulam truss as outrigger. One variation (Figure 4(e)) employs a CLT panel as outrigger. In the last variation, each of the interior CLT walls was replaced with diagonal truss bracing (consisting of two glulam columns and glulam global diagonal bracing); see Figure 4(f). The span length between each pair of glulam columns replacing an interior CLT wall is equal to the CLT wall width. In this variation (Figure 4(f)), all connections were assumed pinned. The purpose is to compare the variation shown in Figure 4(f) with the variations shown in Figure 4(a)–(e), which relies on moment connections. For all variations shown in Figure 4, the number of storeys was varied from 12 to 20 storeys. Hereafter, the different variations are referred to as variations (a)–(f).

Figure 4.

Variations of outrigger layouts (a) variation a, (b) variation b, (c) variation c, (d) variation d, (e) variation e and (f) variation f.

Material properties and cross-sections

Wood is an anisotropic material with different properties in different directions.³⁴ The material can be modelled as orthotropic with three orthogonal symmetry planes.³⁴ Further practical simplification is to model wood with equal properties across the grain. In this study, the glulam was assumed of strength class GL30c as defined by EN 14080.³⁵

In this study and to simplify the modelling using FEM, equivalent material properties of CLT were calculated using the method proposed by.³⁶ A uniform cross-section with a thickness equal to the actual thickness of the CLT and equivalent material properties was used, that is the cross-lamination is considered indirectly. It was assumed that (2/3) of the layers are along the longitudinal (main) direction and the remaining (1/3) are along the orthogonal direction, confer Figure 5(c). This simplified modelling approach is shown to properly capture the in-plane behaviour of CLT.³⁷ The lamellae constituting the CLT panels were assumed of strength class C24 as defined by EN 338.³⁸

Figure 5.

Material axes and cross-sections (a) glulam, (b) C24 lamellae and (c) CLT element.

The elastic constants of the glulam, the C24 lamellae, and the equivalent CLT are summarised in Table 1. The corresponding material axes are shown in Figure 5.

Table 1.

Elastic constants of glulam, C24 lamellae and equivalent CLT.

Property	Glulam	CLT		Unit
Property	GL30c	Lamellae (C24)	Equivalent	Unit
$E_{1}$	13000	11000	7467	$N / m m^{2}$
$E_{2}$	300	400	3933	$N / m m^{2}$
$E_{3}$	300	400	400	$N / m m^{2}$
$G_{12}$	650	690	517	$N / m m^{2}$
$G_{13}$	650	690	98	$N / m m^{2}$
$G_{23}$	65	50	54	$N / m m^{2}$

Walls, columns, beams, outriggers and global diagonal bracing were assumed of double cross-section, see Figure 3. Dimensions of walls, columns, beams, were reasonably assumed and summarised in Table 2. Dimensions of outriggers were varied, and the global diagonal bracing were modelled in terms of their axial stiffness as will be explained in section ‘Finite element method and analytical model’.

Table 2.

Cross-sections of walls, columns, beams, outriggers and global bracing.

Structural element	Variation	Cross-section	Unit
CLT walls	a/b/c/d/e	$b \cdot h = 215 \cdot 3000$ ^a	mm²
Exterior glulam columns	all	$b \cdot h = 215 \cdot 810$ ^a	mm²
Glulam beams	all	$b \cdot h = 215 \cdot 585$ ^a	mm²
Truss outrigger	a/b/c/d/f	$EA = variable$ ^b	kN
CLT outrigger	e	$Thickness = variable$	mm
Interior glulam columns	f	$b \cdot h = 215 \cdot 810$ ^a	mm²
Global diagonal bracing	f	$EA / L = 200$ ^b	kN/mm

Double cross-sections.

Further explanation is provided in section ‘Finite element method and analytical model’.

Finite element method and analytical model

CSI SAP2000³⁹ was used to perform 2D linear elastic FEM. The open application programming interface was used to drive the software externally. Figure 6 shows the analytical model of variation (b), with example connections details based on Refs.^6,16,40,41 Glulam columns and beams were modelled using linear elements (considering both bending and shear deformations) with material properties and cross-sections in Tables 1 and 2. The CLT walls were modelled using linear elements with equivalent properties and cross-sections in Tables 1 and 2. The linear elements representing the CLT walls were verified against the layered shell elements available in CSI SAP2000³⁹ under in-plane loading. The verification was done on both stresses and deformations and the difference was less than 5%. Hence, linear elements were deemed to have sufficient accuracy for the purpose of this study.

Figure 6.

Analytical model with example connections details, (a) 2D frame with truss outrigger, (b) rigid zone in beam-to-wall/column connections, (c) diagonal/truss element and (d) CLT outrigger.

The CLT panels used as an outrigger in variation (e) were modelled using shell elements with the equivalent properties in Table 1. The shell elements are connected to the main structural system using link elements as shown in Figure 6(d). The link elements represent the connections (e.g. self-taping screws) between the CLT outrigger and the main structural system. The link elements have only axial and shear stiffness (no rotational stiffness).

The beam-to-wall/column connections were assumed semi-rigid with finite rotational stiffness. The stiffness was reasonably assumed based on the experimental work done by Vilguts et al.⁴² and the analytical method proposed by Stamatopoulos et al.⁴³ The stiffness values of the connections are summarised in Table 3.

Table 3.

Rotational stiffness of the connections.

Variation	Connection	Rotational stiffness (kN.m/rad)
a–e	CLT wall-to-foundation $(K_{θ, w})$	$300, 000$
a–e	Glulam column-to-foundation	$0.0$ (pinned)
a–e	Beam-to-column/wall $(K_{θ, b})$	$20, 000$
F	All connections	$0.0$ (pinned)

CLT walls and glulam columns have finite cross-sectional dimensions. Modelling them as linear elements connected at nodes results in larger beam spans, leading to a softer structural system. To account for the fact that the clear spans of beams are shorter than the centreline-to-centreline spans, the end length offset option available in CSI SAP2000³⁹ was used. The concept of the end length offset is illustrated in Figure 6(b). At the beam ends, a length equal to half the wall/column width is assumed rigid for bending and shear deformations.

The truss outrigger and the global diagonal bracing elements (confer Figure 4) were modelled using linear elements with pinned ends. The presence of connections at the ends implies the need to use two link elements representing the connections, see Figure 6(c). This situation resembles three springs in series, which can be replaced by one spring with an effective stiffness:

\frac{1}{K_{effective}} = \frac{1}{K_{connection, 1}} + \frac{1}{K_{diagonal}} + \frac{1}{K_{connection, 2}}

(1)where

K_{effective}

is the effective axial stiffness of the equivalent spring,

K_{connection, 1}

and

K_{connection, 2}

are the axial stiffness of the connections at both ends of the element and

K_{diagonal}

is the axial stiffness of the diagonal, see Figure 6(c).

The diagonal can then be modelled using only one linear element with axial stiffness $K_{effective}$ . The effective axial stiffness of the elements used in the truss outrigger was varied. The effective axial stiffness of the global diagonal bracing (confer Figure 4(f), red lines) was set to 200 kN/mm. In CSI SAP2000,³⁹ this was achieved by using a linear element with pinned ends and an effective area $A_{effective}$ to consider the presence of connections:

K_{effective} = \frac{E_{1} \cdot A_{effective}}{L}

(2)where L is the length of the element and

E_{1}

is young modulus from Table 1.

Loads and limit states

In this study, three different types of loads were considered, namely: dead load $G_{k}$ , live load $Q_{k}$ and wind load $W_{k}$ . Two load scenarios were assumed, namely: light frames and heavy frames. Both scenarios are summarised in Table 4. Wind load was calculated according to EN 1991-1-4⁴⁴ assuming urban environment (IV). Gravity loads (dead and live loads) were applied as uniform line load to the beams, and wind loads were applied as uniform line load to the exterior columns.

Table 4.

Gravity loads.

Load scenario	Dead load $G_{k}$ (kN/m²)	Live load $Q_{k}$ (kN/m²)
Light frames	$1.0$ ^a	2.0 (residential areas^b)
Heavy frames	$2.0$ ^a	3.0 (office areas^b)

Including the weight of floors and finishings, excluding the own weight of beams, columns, walls and diagonals.

According to EN 1991-1-1.⁴⁵

For the calculation of lateral displacements due to wind, the characteristic load combination as defined in EN 1990⁴⁶ with wind as a leading variable was used:

E_{d} = G_{k} + W_{k} + ψ_{0} \cdot Q_{k}

(3)The combinational factor

ψ_{0}

was set to 0.70 according to the Norwegian National Annex of EN 1990.⁴⁶

EN 1995-1-1⁴⁷ recommends a deflection limit of $span / 300 - span / 500$ for simple beams under the characteristic load combination defined in EN 1990.⁴⁶ Based on this, the following limits for the top floor displacement ( $Δ$ ) and inter-story drift ( $δ$ ) were considered:

δ \leq \frac{h}{300} Δ \leq \frac{H}{300}

(4)Where h is the storey height and H is the total height of the building.

EN 1991-1-4⁴⁴ provides two equivalent procedures to estimate the wind-induced acceleration. Both procedures are based on gust factor approach but use different simplifications.⁴⁸ In this article, the wind-induced acceleration was calculated using procedure 1 available in Annex B of EN 1991-1-4.⁴⁴

For the calculation of acceleration according to EN 1991-1-4,⁴⁴ the mode shape and the fundamental frequency are required. To obtain the mode shape and the fundamental frequency, modal analysis was performed using CSI SAP2000.³⁹ In modal analysis, the mass corresponding to quasi-permanent load combination defined in EN 1990⁴⁶ was used:

E_{d} = G_{k} + 0.3 \cdot Q_{k}

(5)Damping ratio is an important parameter for acceleration calculation. There are few studies available with respect to damping ratios of timber buildings. In this article, 2% damping ratio (ξ) was assumed based on available results, see Refs.^16,49 In this study, 50% probability of exceedance in half a year was assumed, which corresponds to

c_{prob} = 0.73

. The basic wind velocity was varied from 22 m/sec to 30 m/sec. Relevant parameters used in the acceleration calculation are summarised in Table 5.

Table 5.

The parameters used in the calculation of wind-induced acceleration.

Parameter	Value
Directional factor $c_{dir}$	1.00
Seasonal factor $c_{season}$	1.00
Probability factor $c_{prob}$	0.73
Orography factor $c_{0 (z)}$	1.00
Turbulence factor $k_{l}$	1.00
Terrain category	$IV$
Reference height $Z_{t}$	200
Reference length $L_{t}$	300
Structural damping ξ	2%
Out-of-plane width of the building b	30 m
Basic wind velocity $v_{b, 0}$	22/26/30 m/sec

Human perception of acceleration is subjective, and therefore there exist several comfort criteria that can be used to assess the performance of a building under wind load.⁵⁰ In this article, the criterion provided by ISO10137⁵¹ was used. ISO10137⁵¹ covers the range from a fundamental frequency of 0.063 to 5 Hz for a maximum wind velocity with a return period of one year. The criterion is depicted in Figure 7.

Figure 7.

Evaluation curves for wind-induced accelerations according to ISO10137.⁵¹

For the calculation of forces and stresses used for discussing the ULS, the fundamental ULS combination defined in EN 1990⁴⁶ with either wind or live load as leading variable action:

E_{d} = γ_{G} \cdot G_{k} + γ_{Q} \cdot W_{k} + γ_{Q} \cdot ψ_{0, Q} \cdot Q_{k}

(6)Where

γ_{G} = 1.20

γ_{Q} = 1.50

ψ_{0, Q} = 0.70

according to the Norwegian National Annex of EN 1990.⁴⁶

E_{d} = γ_{G} \cdot G_{k} + γ_{Q} \cdot ψ_{0, W} \cdot W_{k} + γ_{Q} \cdot Q_{k}

(7)Where

γ_{G} = 1.20

γ_{Q} = 1.50

ψ_{0, W} = 0.60

according to the Norwegian National Annex of EN 1990.⁴⁶

The forces and stresses were calculated using the envelop of equations (6) and (7).

Results and discussion

In this section, five subsections are outlined to address the optimum location of outriggers, compare the efficiency of the different variations shown in Figure 4, estimate the stiffness requirements of outriggers, show the feasibility of the system with respect to SLS, and highlight some ULS considerations. For this purpose, five parametric studies were performed. Table 6 provides an overview of the performed parametric studies.

Table 6.

Overview of the performed parametric studies.

Subsection	Overview
i-Optimum location of OR	Basic wind velocity = 26 m/s and light gravity load (Table 4). Truss outrigger: $E_{1} \cdot A_{effective} = 13 \times 10^{5} kN .$ CLT outrigger: thickness = 120 mm/stiffness = 50 kN/mm/m. Materials/sections/ stiffness (Tables 1–3). All possible locations of OR are evaluated (exhaustive search) to find the optimum location considering inter-storey drift/top floor displacement/wind-induced acceleration as optimisation criterion. Number of storeys: 12/16/20. Total number of analyses is 2544.
ii-Compare OR variations	The OR is placed in the optimum location obtained from i. Other relevant parameters are kept the same as i. The performance of all variations is compared (with respect to lateral displacements and wind-induced accelerations).
iii-OR stiffness requirements	The OR is placed in the optimum location obtained from i. Stiffness of OR ( $E_{1} \cdot A_{effective}$ for truss OR/thickness and connection stiffness for CLT OR) is varied. The influence of OR stiffness on the performance (with respect to displacements and acceleration) is evaluated. Other relevant parameters are kept the same as i. Total number of analyses is 1080.
iv-Feasibility study	The OR is placed in the optimum location obtained from i. Basic wind velocity: 22/26/30 m/s. Light and heavy gravity load (Table 4). Other relevant parameters are kept the same as i. The feasibility of the system is evaluated in terms of lateral displacements and wind induced acceleration. Total number of analyses is 216.
v-ULS considerations	The OR is placed in the optimum location with respect to wind-induced acceleration (proved to be governing from iv). Other relevant parameters are kept the same as i. Forces and stresses in a reference frame are discussed. Forces in OR connections are calculated and discussed.

Optimum location of outrigger(s)

To identify the optimum location(s) of OR, three optimisation criteria were considered, namely: top floor displacement, inter-story drift (IDR) and wind-induced acceleration in the top storey. A basic wind velocity of 26 m/s with light gravity loads (see Table 4) was assumed. Three number of storeys were considered, namely: 12, 16 and 20. Exhaustive search algorithm was used to find the optimum location.

The optimum location for one and two outriggers is shown in Figure 8(a) for variations (a)–(e) and in Figure 8(b) for variation (f). The optimal location was identical for variations (a)–(e). The location is expressed as a fraction of the total height H. It is worth mentioning that the optimum location for the cases of 12, 16 and 20 storeys differs slightly, approximately 5% of H. Therefore, an average value for the three cases was considered.

Figure 8.

Optimum location of OR based on three criteria for (a) variation a–e; and (b) variation f.

Comparing Figure 8(a) and (b), the location of OR(s) is lower (closer to the base) for variations (a)–(e) than variation (f). Assuming no OR is used, the mode shapes for variations (a)–(e) (identical for no OR case) and for variation (f) are plotted in Figure 9. Comparing the mode shapes for variations (a)–(e) and for variation (f), it is obvious that variation (f) exhibits more flexural dominant mode shape than variations (a)–(e). Hence the ORs are closer to the top for variation (f). It is also noticeable that the optimum location for wind-induced acceleration is the highest, followed by top floor displacements and inter-storey drift.

Figure 9.

Mode shapes with no outriggers.

It was observed that when the outriggers are placed at the optimum location for IDR, a reduction of over 94% in top floor displacement is attained. Therefore, it is reasonable to assumed that the optimum location for lateral displacements (considering both IDR and top displacement simultaneously) is the same as for IDR.

Comparison of outrigger variations

To compare the efficiency of the variations shown in Figure 4, the ratios of top floor displacement ( $Δ$ ), inter-story drift ( $δ$ ) and wind-induced acceleration ( $a$ ) with the use of OR to the case without OR were calculated. The effective area $A_{effective}$ of the truss elements (confer Figure 6) was set to 0.10 m² ( $E_{1} \cdot A_{effective} = 13 \times 10^{5} kN$ ). For variation (e), the thickness of the CLT panel used in the outrigger is set to 120 mm, and the connections’ shear and axial stiffness is set to 50 kN/mm/m (confer Figure 6(d)). A basic wind velocity of 26 m/s with light gravity loads (see Table 4) was assumed. Three number of storeys were considered, namely: 12, 16 and 20. Both the case of 1 and 2 ORs were considered, and the ORs were placed at the optimum locations shown in Figure 8 for top floor displacement, inter-storey drift and wind-induced acceleration, respectively. Figure 10 shows the ratios of ( $Δ$ ), ( $δ$ ) and ( $a$ ) with the use of OR to the case without OR.

Figure 10.

Ratios of top floor displacement (Δ), inter-storey drift (δ) and wind-induced acceleration (a) with the use of OR to the case without OR.

As shown in Figure 10, variation (f) shows the highest efficiency for the case of 16 and 20 storeys. This is expected as the outrigger system is generally less effective when the mode shape is more shear dominant.²⁹ The most effective variation among (a)–(e) variations is variation (d) followed by variation (a). Figure 10 also shows that ORs are less effective in reducing wind-induced acceleration compared to lateral displacements.

The presence of ORs stiffens the structure and leads to an increased fundamental frequency. The ratio of the frequency with ORs ( $f_{OR}$ ) to the frequency without OR $(f_{o})$ is shown in Figure 11. Since frequency is essential in wind-induced acceleration calculations, the ORs are placed at the optimum location for accelerations. As shown in Figure 11, for all variations except variation (f), the ratio $f_{OR} / f_{o}$ decreases with the increase in number of storeys. For variation (f), the ratio $f_{OR} / f_{o}$ increases with the increase in number of storeys. For variations (a)–(e), the frequency increase is approximately 20% to 45% using one OR and 35% to 95% using 2 ORs. For variation (f), the frequency increase is approximately 40% to 60% using one OR and 75% to 100% using 2 ORs.

Figure 11.

Ratio of the frequency with the use of OR $(f_{OR})$ to the case without OR $(f_{o})$ .

The constructability of each variation is also an important aspect to be compared. For some variations, namely: (a), (c) and (f), the OR connections and the moment connections (beam-wall/column) intersect. This intersection can impose constructability difficulties. In this regard, variations (b), (d) and (e) can provide more practical alternatives. However, variation (d) has more connections than variations (b) and (e), which might be undesired.

Stiffness of outriggers

Since the lengths of the truss elements are not the same for all variations shown in Figure 4, it is best to replace the effective axial stiffness ( $K_{effective}$ ) of the element with $E_{1} \cdot A_{effective}$ . Both are related and can be calculated using equation (2). The effective area of the truss ( $A_{effective}$ ) was varied from 0 to 0.40 m², where 0 m² represents the case of no outriggers. The ORs were placed at the optimum location(s) shown in Figure 8 for top floor displacement, inter-storey drift and wind-induced acceleration, respectively. A basic wind velocity of 26 m/sec was assumed.

Figure 12 shows the lateral displacements ( $Δ$ , $δ$ ) and wind induced acceleration ( $a$ ) as function of $E_{1} \cdot A_{effective}$ . With an effective area of approximately 0.10 m² ( $E_{1} \cdot A_{effective} of 13 \times 10^{5} kN$ ), 80% to 90% of the maximum improvement can be achieved. Increasing $A_{effective}$ beyond 0.20 m² nearly shows no improvement as all response quantities ( $Δ$ , $δ$ , $a$ ) converge.

Figure 12.

Lateral displacements and acceleration ratios as function of $(E_{1} \cdot A_{effective})$ (legend: variation-number of storeys).

For variation (e), the outrigger stiffness was measured in terms of the thickness of the CLT panels used as OR, and the stiffness of the connections connecting the CLT OR to the main structure. It was assumed that these connections have shear and axial stiffness of the same magnitude. Figures 13 and 14 show the lateral displacements and wind induced acceleration as function of CLT thickness and the connections stiffness, respectively. When the CLT thickness was varied, the connections stiffness was set to 100 kN/mm/m. When the connections stiffness was varied, the CLT thickness was set to 300 mm. As shown in Figures 13 and 14, good reductions can be achieved with CLT thickness of around 100 mm and connections stiffness in the range of 25 to 50 kN/mm/m.

Figure 13.

Lateral displacements and acceleration ratios as function of CLT OR thickness for variation (e).

Figure 14.

Lateral displacements and acceleration ratios as function of axial and shear stiffness of the connections used in the CLT OR for variation (e).

Feasibility study

In this section, a parametric study is presented. The parameters used in this study are summarised in Table 7. The feasibility is evaluated in terms of top floor displacement, inter-storey drift and wind induced acceleration.

Table 7.

Parameters used in the feasibility study.

Parameter	Value
Variation	a/b/c/d/e/f (with and without ORs)
Basic wind velocity $v_{b, 0}$	22/26/30 m/s
Number of storeys	12/16/20
Number of outriggers	1/2
Location of ORs	Optimum location (Figure 8)
Gravity loads	Heavy/Light
Truss outrigger	$A_{effective} = 0.10 m^{2}$
CLT outrigger	CLT thickness = 300 mm, connections stiffness = 50 kN/mm/m

Figure 15 shows the peak acceleration for the frames in Table 7. For simplicity, variations (a)–(e) were considered one group, and variation (f) was considered the second group. For the frames shown in Table 7, Figures 16 and 17 show lateral displacements and inter-storey drift, respectively. Since linear elastic FEM was performed, gravity loads do not contribute to lateral displacements. Hence, Figures 16 and 17 are shown for the case of light frames.

Figure 15.

Wind-induced acceleration.

Figure 16.

Lateral displacement for all variations (legend: variation-basic wind velocity).

Figure 17.

Inter-storey drift for all variations (legend: variation-basic wind velocity).

As shown in Figures 16 and 17, using only one OR, variations (a), (d) and (f) meet the requirements for top floor displacement and inter-storey drift for all basic wind velocities and all number of storeys. Based on Figures 15–17, it can be observed that wind-induced acceleration is the governing response parameter compared to lateral displacements. Based on Figures 15–17, several conclusions can be drawn, these are summarised in Table 8.

Table 8.

Conclusions based the feasibility study.

$v_{b, 0}$	No. of storeys	Conclusions
22	12	Variations (a)–(f) (light and heavy) meet the requirements of acceleration (residential) without ORs
	16	Variations (a)–(f) (light and heavy) meet the requirements of acceleration (residential) without ORs
	20	Variations (a)–(e) (light and heavy) meet the requirements of acceleration (residential) without ORs Variation (f) (light) meets the requirements for acceleration (residential) using one OR
26	12	Variations (a)–(f) (light) without ORs exceed the acceleration limit for residential buildings but meet the requirement for office buildings. Variations (a)–(f) (heavy) without ORs and variations (a)–(f) (light) with one OR meet the acceleration requirements (residential)
	16	Variations (a)–(f) (light and heavy) without ORs exceed the limit for residential buildings but meet the requirement for office buildings. For variations (a)–(f) (light), two ORs are needed to meet the requirements of residential buildings, but only one OR is needed for heavy frames.
	20	Variations (a)–(f) (light) can only meet the requirements for office buildings using either one or two ORs. Variations (a)–(f) (heavy) meet the requirements for residential buildings using one OR.
30	12	For variation (f) (light), two ORs are needed to meet the requirements of residential buildings, but only one OR is needed for heavy frames. For variations (a)–(f) (light), only office buildings requirements can be met using either one or two OR. But for heavy frames with two OR, residential buildings requirements can be met.
	16	Variations (a)–(e) (heavy) can only meet the requirements for office buildings using two ORs. Variation (f) (light) can only meet the requirements for office buildings using two ORs. But the heavy frames can meet the requirements for residential buildings using two ORs.
	20	Variations (a)–(f) (heavy) can only meet the requirements for office buildings using two ORs.

Ultimate limit state considerations

Some considerations with respect to the feasibility of the OR-system in terms of the ULS are provided in this section. In subsection ‘Stresses in an example frame’, the stress levels of the beams, columns and walls of a benchmark frame are used as a basis for discussion. In subsection ‘Forces in the OR truss members’, the force levels in the truss elements are summarised and discussed. In both subsections, the results come from the ULS design load combination given by equations (6) and (7).

Stresses in an example frame

An OR frame with the properties shown in Table 9 is used as benchmark to investigate the stress levels in the beams, columns and walls. Other parameters such as number of bays, bay length, floor height, material properties, connections stiffness and cross-sections were kept the same as in section ‘Materials and methods’ of this article. The OR is placed at the optimal location based on wind-induced acceleration criterion. Stresses in beams, columns and walls are summarised in Table 10. Stresses in the truss elements of the OR are not reported here; the ULS of the truss elements are examined in greater detail in subsection ‘Forces in the OR truss members’. As shown in Table 10, the stress-levels are not very high, and these structural elements can be designed such that they satisfy the safety requirements.

Table 9.

Parameters of the benchmark OR frame used for stresses evaluation.

Property	Value	Unit
Number of storeys	16	-
Number of outriggers	1	-
Location of outrigger	8^th floor	-
Basic wind velocity	26	m/sec
Gravity loads	Light	-
Outrigger variation	b	-
$E_{1} A_{effective}$	$13 \cdot 10^{5}$	kN

Table 10.

Maximum stresses (normal and shear) for the benchmark frame.

Element	Stress type	Stress (N/mm²)
Beams	Normal stress	5.43
Beams	Shear stress	0.59
Columns	Normal stress	6.61
Columns	Shear stress	0.36
CLT walls	Normal stress	5.80
CLT walls	Shear stress	0.47

Forces in the OR truss members

The maximum forces (tension and compression) in the truss elements of the ORs were calculated for all variations except variation (e). The ORs were placed at the optimal location with respect to wind-induced acceleration. A basic wind velocity of 26 m/s and $E_{1} A_{effective}$ of 13 × 10⁵ kN were considered. Other relevant parameters were kept the same as in section ‘Materials and methods’ of this article. Figure 18 summarises the maximum axial force-levels in the truss elements. The force levels in Figure 18 correspond to a double cross-section (see Figure 3), so the force levels per member is half the values shown in Figure 18.

Figure 18.

Force levels at the truss elements ( $v_{b, 0} = 26 m / s$ , $E_{1} A_{effective} = 13 \times 10^{5} kN$ ).

As shown in Figure 18, the force levels are quite high for the case of 20 storeys (grey bar), which imposes some challenges on the ULS with respect to cross-sections of the truss elements but mostly with respect to the connections to the main frame. To accommodate such force-level, the connections need to have a sufficient capacity which can be challenging. Among the five variations (a, b, c, d, f), the force-levels in variation (c) tends to be higher. Variation (c) has also the most slender truss elements and buckling may be critical.

For all variations except variation (e), and for the cases of 12 and 16 storeys, the values of the axial forces are in the order of 400 kN (200 kN per cross-section) and therefore these cases are deemed more feasible. Variation (e), on the other hand, can provide uniform distribution of forces between the OR and the main structure along the CLT panels perimeter. Therefore, even though variation (e) is less effective with respect to SLS compared to some other variations (see subsection ‘Comparison of outrigger variations’ in this article), it might be advantageous with respect to ULS to avoid force concentration at the connections.

Variation of connections stiffness and outrigger stiffness

Inherent variability in timber connections can lead to variations in the internal forces and moments of MRTFs.⁵² In this subsection, the same benchmark frame in subsection ‘Stresses in an example frame’ is used to examine the effect of stiffness variability on the internal forces of the outrigger truss elements, lateral displacements and accelerations. A normal distribution with 20% coefficient of variation was assumed for $K_{θ, w}$ , $K_{θ, b}$ and $A_{effective}$ (confer Figure 6 and Table 3). A total of 3000 analyses were performed, and the following could be observed:

The mean value of top floor displacement (obtained from the 3000 analyses) is 1.02% higher than the reference case (which assumes mean $K_{θ, w}$ , $K_{θ, b}$ and $A_{effective}$ ).

The mean value of IDR is 1.20% higher than the reference case.

The mean value of peak acceleration is 0.53% higher than the reference case.

The 95% percentile of the normal force of the outrigger truss elements is 8% higher than the reference case. The use of 98% results in 10% increase in the force.

While mean lateral displacements and accelerations exhibit negligible increase, there is a more noticeable increase in outrigger forces, which should be considered in the design for the ULS. The variation in connection stiffness of MRTFs has also been shown to have an insignificant influence on lateral displacements and accelerations.⁵²

Conclusions

In this article, the feasibility of using timber outrigger structures to build up to 20 storeys was investigated using linear elastic finite element analysis together with the relevant European and international standards. The feasibility is evaluated assuming wind velocities up to 30 m/s. The optimum location of one and two outriggers was estimated considering three criteria, namely: top floor displacement, inter-storey drift and wind-induced acceleration. Different layouts of outrigger were investigated, and their efficiency was compared. The stiffness of the outriggers was varied to evaluate the stiffness requirements. The influence of connections’ stiffness variability was also investigated. Although the focus of this article was devoted to serviceability requirements, some ULS considerations were briefly discussed. The following main conclusions are drawn:

Using one outrigger, a reduction of 30% to 65% in lateral displacements (top floor displacement and inter-storey drift) and 15% to 40% in wind-induced acceleration can be achieved.

Using two outriggers, a reduction of 45% to 75% in lateral displacements and 25% to 55% in wind-induced acceleration can be achieved.

Considering serviceability requirements, building up to 16 storeys is feasible with basic wind velocity of 26 to 30 m/s. Building 20 storeys is, however, challenging and can be limited to low basic wind velocities.

Considering ultimate limit state, building up to 16 storeys is feasible. However, for 20 storeys, the forces in the connections can be challenging to design.

Variability of connections’ stiffness has negligible influence on lateral displacements and wind-induced acceleration. On the other hand, an increase on the order of 10% in the force in the outrigger truss elements was observed compared to the reference value obtained using mean stiffness values.

Footnotes

Declaration of conflicting interests

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

Funding

The authors received no financial support for the research, authorship and/or publication of this article.

ORCID iD

Osama Abdelfattah Hegeir

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Feasibility of outrigger structural system for tall timber buildings: A numerical study

Abstract

Keywords

Introduction

Materials and methods

The structural system

Material properties and cross-sections

Finite element method and analytical model

Loads and limit states

Results and discussion

Optimum location of outrigger(s)

Comparison of outrigger variations

Stiffness of outriggers

Feasibility study

Ultimate limit state considerations

Stresses in an example frame

Forces in the OR truss members

Variation of connections stiffness and outrigger stiffness

Conclusions

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

References