A proposal for the capacity-design at wall- and building-level in light-frame and cross-laminated timber buildings

Abstract

Due to the brittle nature of wood material, the dissipation of seismic energy in timber structures is typically ensured through yielding of the mechanical connectors, where plastic deformations are developed in fasteners that have adequate ductility and cycle-fatigue strength. These structural components are denoted dissipative zones, whereas all other structural elements are assumed to behave elastically. Such elements are designated as non-dissipative zones and are designed with sufficient over-strength, to meet the requirements of capacity-based design (CD). Despite the general consensus that using the principle of CD could lead to safe buildings, where brittle failures are avoided, the applicability of such approach to light frame timber (LFT) and cross laminated timber (CLT) buildings has lacked analytical expressions that depend on the structural typology and failure mechanism. The current paper aims to fill this gap in knowledge by proposing an analytical approach that incorporates the CD philosophy to LFT and CLT buildings at the substructure (wall) and super-structure (building) levels. A simplified approach is adopted for structures with a low-to-medium energy dissipation capacity whereas a more rigorous approach is presented for structure with a high energy dissipation capacity. An experimental comparison and design example is included to present the applicability of the proposal.

Appendix

In this section, two design examples serve to illustrate the applicability of the proposed capacity-based design approach. The examples include a case with LFT structure, assuming medium or high ductility, and a case with multi-panel CLT wall assuming high ductility.

1.1 LFT SFRS in medium and high ductility classes

A two-storey building consisting of LFT SFRS composed of two walls with an inter-storey height h equal to 2.5 m and a length B equal to 5.0 m (index, i = 1) and 2.5 m (i = 2), respectively, is assumed, see Fig. 8. The nailed sheathing-to-framing connection (used on one side of the shear-wall) is characterized by a design strength r_c of 0.835 kN for each fastener. The two walls are anchored to the foundation by means of hold-downs, at each corner, as well as angle brackets that are uniformly distributed along the wall’s length. In DCM, by adopting a q-factor equal to 2.5, the design values of the lateral forces, F ⁱ _{Ed, j, DCM} , are calculated to be 48 kN and 24 kN for the 5 m and 2.5 m wall segments, respectively. When a non-dissipative global behaviour is assumed (i.e. q_ND = 1.5), the design forces, F ⁱ _{Ed, j, ND} , become equal to 80 kN and 40 kN for the 5 m and 2.5 m wall segments, respectively. In DCH, a q-factor equal to 4 is adopted and the design forces are equal to 30 kN for the 5 m wall segment and 15 kN for the 2.5 m wall segment. A uniform vertical load w equal to 5 kN/m, acting at each level, is assumed. The design shear loads on the sheathing-to-framing connections, hold-down and angle brackets are evaluated according to the methods presented in the previous sections. In this example, the shear strength of the wall related to the sheathing-to-framing connections and the tensile load on the hold-down are calculated according to Eurocode 5 (EN 1995-1 2014).

Fig. 8

LFT system

1.1.1 Medium ductility class

Adopting a nail spacing, s ⁱ _j , in the sheathing-to-framing connection of 0.05 m at the 1st storey and 0.10 m at the 2nd storey, the design shear strength of the walls related to the sheathing-to-framing connection V ⁱ _{Rd, sh, j} can be calculated according to EN 1995 (2014), as reported in Table 3.

Table 3 Design parameters for LFT walls in DCM

The design shear load, V ⁱ _{Ed, a, j} , on the angle brackets and the tensile load, T ⁱ _{Ed, b, j} , on the hold-down are calculated from the equilibrium (EN 1995-1 2014) by adopting the design forces F ⁱ _{Ed, j, DCM} , as reported in Table 3, according to Eqs. 47–49

$$V_{Ed,a,j}^{i} = \mathop \sum \limits_{j}^{2} F_{{Ed,{\text{j}},DCM}}^{\text{i}}$$

(47)

$$T_{Ed,b,2}^{i} = \frac{{F_{Ed,2,DCM}^{i} \cdot h}}{l} - \frac{w \cdot l}{2}$$

(48)

$$T_{Ed,b,1}^{i} = \frac{{F_{Ed,2,DCM}^{i} \cdot 2 \cdot h + F_{Ed,1,DCM}^{i} \cdot h}}{l} - \frac{2 \cdot w \cdot l}{2}.$$

(49)

The actions of all others brittle components (wood framing members, floor-to-wall connections, etc.) can be obtained from the design forces, F ⁱ _{Ed, j, ND} , where the non-dissipative behaviour is assumed.

1.1.2 LFT SFRS in high ductility class

The design shear load V ⁱ _{Ed, E, j} is equal to 60 kN and 30 kN at the first and second level of the 5 m wall. For the 2.5 m wall, the shear load V ⁱ _{Ed, E, j} is equal to 30 kN and 15 kN at the first and the second storey, respectively. Adopting a sheathing-to-framing nail spacing, s ⁱ _j , of 0.07 m at the 1st storey and 0.15 m at the 2nd storey, the design shear strengths of the wall related to the sheathing-to-framing connection V ⁱ _{Rd, sh, j} can be calculated according to EN 1995-4 (2014), as reported in Table 4.

Table 4 Design parameters for LFT walls in DCH

The over-capacity coefficients of the SFRS system C_sh,j at the jth storey are calculated according to Eq. 14 and yields values of 1.19 and 1.11 at the 2nd and 1st storey levels, respectively. In order to ensure a uniform energy dissipation along the height of the building, the condition of Eq. 15 has to be satisfied, as reported in Eq. 50

$$\frac{{max\left( {C_{sh,j} } \right)}}{{min\left( {C_{sh,j} } \right)}} = \frac{1.19}{1.11} = 1.07 \le 1.25.$$

(50)

Since in DCH, the hold-down and shear anchors are considered as non-dissipative zones, and are designed to behave elastically based on the CD approach, and according to Eq. 13. Adopting an over-strength factor $\gamma_{Rd}$ of 1.6 and the minimum over-capacity coefficient min(C_sh,j) equal to 1.11, the design shear load of the angle brackets V ⁱ _{Ed, a, j} and the tensile load of the hold-down T ⁱ _{Ed, b, j} can be calculated as:

$$V_{Ed,a,j}^{i} = \gamma_{Rd} \cdot min\left( {C_{sh,j} } \right) \cdot V_{Ed,E,j}^{i}$$

(51)

$$T_{Ed,b,j}^{i} = \gamma_{Rd} \cdot min\left( {C_{sh,j} } \right) \cdot T_{Ed,E,b,j}^{i} - T_{Ed,G,b,j}^{i}$$

(52)

where T ⁱ _{Ed, E, b, j} is the design tensile load due to seismic loads, calculated according the method reported in Eurocode 5 (EN 1995-1 2014) and $T_{Ed,G,b,j}^{i}$ is the stabilizing effect due to vertical load, as shown in, Eqs. 53–55:

$$T_{Ed,E,b,1}^{i} = \frac{{F_{{Ed,2,{\text{DCH}}}}^{\text{i}} \cdot 2 \cdot h + F_{{Ed,1,{\text{DCH}}}}^{\text{i}} \cdot h}}{l}$$

(53)

$$T_{Ed,E,b,2}^{i} = \frac{{F_{{Ed,2,{\text{DCH}}}}^{\text{i}} \cdot h}}{l}$$

(54)

$$T_{Ed,G,b,1}^{i} = \frac{2 \cdot w \cdot l}{2}$$

(55)

$$T_{Ed,G,b,2}^{i} = \frac{w \cdot l}{2}.$$

(56)

1.2 Multi-panel CLT wall in high ductility class

A two-storey 3-panel CLT wall (m = 3) with an individual panel length b equal to 1.25 m, a total length B = 3.75 m (b∙m), and a height h at each level equal to 3.0 m is considered. The wall is subjected to a design horizontal force F_Ed,E (derived from the design response spectrum) equal to 20 kN and 40 kN at the 1st and 2nd storey, respectively. The vertical joints are composed of n = 15 screws at the second level and n = 30 screws at the first level, see Fig. 9. A uniform vertical load, w, equal to 5 kN/m, acting at each level, is assumed. The hold-downs at the first and second level are characterized by an elastic stiffness equal to $k_{h,1} = 20000\frac{{\text{kN}}}{{\text{m}}};\, k_{h,2} = 15000\frac{{\text{kN}}}{{\text{m}}}$ with a strength equal to r_h,1 = 110 kN; r_h,2 = 55 kN, respectively. Each connector of the vertical joints is characterized by a stiffness equal to $k_{c} = 1500\,{\text{kN/m}}$ and a strength of r_c = 2.5 kN. An over-strength factor $\gamma_{Rd}$ equal to 1.6 is adopted.

Fig. 9

CLT wall in high ductility class

The design values of the rocking moment and the shear at each storey of the wall as well as the values of the design strength of the rocking moment, calculated according to Eq. 38, are reported in Table 5.

Table 5 Design parameters for the multipanel CLT wall

The over-capacity coefficients of the SFRS system C_sh,j at the jth storey are calculated according to Eq. 42, yielding values of 1.45 and 1.16 at the 2nd and 1st storey levels, respectively. In order to ensure a uniform energy dissipation along the height of the building, the condition of Eq. 14 has to be satisfied, as reported in Eq. 57

$$\frac{{max\left( {C_{sh,j} } \right)}}{{min\left( {C_{sh,j} } \right)}} = \frac{1.45}{1.16} = 1.25.$$

(57)

The relative stiffness of the hold-down at the first floor yields $\tilde{k} = \frac{20000}{30 \cdot 1500} = 0.44 < 1$, couple-panel behaviour including yielding of all vertical joints can be ensured by satisfying Eq. 35:

$$r_{h,1} = 110 kN > max\left[ {1.6 \cdot 30 \cdot 2.5 \cdot 0.44; 1.6 \cdot 30 \cdot 2.5 - 10 \cdot 1.25} \right] = 107.5 {\text{kN}}$$

(58)

The relative stiffness of the hold-down at the second floor yields $\tilde{k} = \frac{15000}{15 \cdot 1500} = 0.67 < 1$, couple-panel behaviour including yielding of all vertical joints can be ensured by satisfying Eq. 35:

$$r_{h,2} = 55 kN > max\left[ {1.6 \cdot 15 \cdot 2.5 \cdot 0.67; 1.6 \cdot 15 \cdot 2.5 - 5 \cdot 1.25} \right] = 54 {\text{kN}}$$

(59)

The design shear load acting on angle brackets V_Ed,a (when these are considered as non-dissipative) and on CLT panel V_Ed,wp are calculated according to Eqs. 60 and 61, as non-dissipative elements:

$$V_{Ed,wp,1} = n_{a} \cdot V_{Ed,a,1} = \gamma_{Rd} \cdot min\left( {C_{sh,j} } \right) \cdot V_{Ed,E,1} + V_{Ed,G,1} = 1.6 \cdot 1.16 \cdot 60 + 0 = 111\,{\text{kN}}$$

(60)

$$V_{Ed,wp,2} = n_{a} \cdot V_{Ed,a,2} = \gamma_{Rd} \cdot min\left( {C_{sh,j} } \right) \cdot V_{Ed,E,2} + V_{Ed,G,2} = 1.6 \cdot 1.16 \cdot 40 + 0 = 74\,{\text{kN}}$$

(61)

where V_Ed,E,1, V_Ed,E,2 and V_Ed,G,1.V_Ed,G,2 are the design shear loads due to the seismic load and the gravity load, respectively.