Cross-story installation of viscous dampers in timber frame houses for earthquake damage reduction

Timber frame structures are commonly used in housing construction that use squared-off timber beams, columns, and walls as lateral load-bearing members. A small-size viscous damper can be applied to timber frame houses to reduce damage caused by major earthquakes. Dampers are normally installed inter-story (between adjacent floors) to absorb vibration energy and reduce seismic response. Another method is the cross-story installation wherein a damper is installed between the rooftop and base of the structure across intermediate floors. This study investigated the effectiveness of cross-story installation of a viscous damper by conducting eigenvalue analyses of 2DOF models and earthquake response analyses of a two-story timber frame house subjected to the 2016 Kumamoto earthquake and other major earthquakes. We compared the damping factors and response reduction effects of the cross-story installation with those of conventional inter-story installations. The results showed that the cross-story installation of dampers was more effective than the inter-story installation in terms of reducing story drift. Furthermore, the cross-story installation reduced the number of dampers required for preventing severe damage by half. Finally, the cross-story installation allowed the viscous damper in the first story to absorb vibration energy nearly twice as much as that of the inter-story installation. Therefore, while the cross-story damper is typically installed on an outer frame fixed to the house, our results conclude that it can be applied to an existing house as a seismic retrofitting measure.

Introduction

The passive control method has been widely used in buildings where various dampers have been installed inter-story onto structural frames to dissipate seismic energy and reduce earthquake damage to buildings. In Japan, the application of dampers to structures has increased considerably since the 1995 Kobe earthquake (Kasai et al., 2008; Kasai et al., 2009). According to the Japan Society of Seismic Isolation (JSSI), as of 2020, the total number of buildings with dampers was 1,600 in Japan. Metallic hysteretic, fluid viscous (oil), and viscous liquid dampers accounted for 36%, 21%, and 18% of all dampers, respectively (Manual for Design and Construction, 2013; Design of Seismic Isolation and Response Control, 2016; MENSHIN, 2022). Design manuals for passive building control have been published in Japan in 2013 and 2016.

Since the 1990s, viscous dampers have been studied for building applications, mainly based on mechanical engineering (Constantinou and Symans, 1992; Constantinou and Symans, 1993; Taylor and Constantinou, 1995; Seleemah and Constantinou, 1997; Soong and Dargush, 1997; Fu and Kasai, 1998). In the last 2 decades, several studies have been conducted on device development, seismic performances, applications in tall buildings, response analyses, and experiments (Lee and Taylor, 2001; Lin and Chopra, 2002; Soong and Spencer, 2002; McNamara and Taylor, 2003; Sorace and Terenzi, 2008; Liang et al., 2012; Seo et al., 2014; Tubaldi et al., 2014; Dong et al., 2016). Viscous dampers have been installed inter-story (between adjacent floors) in the same manner as other dampers to absorb vibration energy.

Furthermore, viscous dampers have been used for seismic enhancement and retrofitting (Uriz and Whittaker, 2001; Martinez-Rodrigo and Romero, 2003; Sorace and Terenzi, 2009; Rama Raju et al., 2014; Lavan, 2015; Pollini et al., 2016, 2017; Impollonia and Palmeri, 2018; Aydin et al., 2019; Tabar et al., 2021). Design procedures and optimum design methods have been studied for use of supplemental dampers in structures (Tsuji and Nakamura T, 1996; Uetani et al., 2003; Lavan and Levy, 2005; Lavan and Levy, 2006; Silvestri and Trombetti, 2007; Hwang et al., 2008; Takewaki, 2009; Hao and Zhang, 2016; Kawamoto et al., 2016; Parcianello et al., 2017; Wang and Mahin, 2018; De Domenico et al., 2019; De Domenico and Ricciardi, 2019; Idels and Lavan, 2020; De Domenico and Hajirasouliha, 2021; Wani et al., 2022). While previous studies have investigated high-rise buildings, slender towers, and long-span bridges that may suffer severe damage due to seismic excitations or wind loads, no research had been conducted on low-story houses until small-size viscous dampers were developed and applied to housing structures.

Various studies have investigated the effectiveness of a small-size viscous damper installed in a timber frame house to reduce damage caused by earthquakes. Conventionally, timber frame structures are used in housing construction in Japan, and their seismic performance can be secured by the load-bearing capacity of erected braces and walls. However, major earthquakes of the past, such as the 2016 Kumamoto earthquake, have caused severe damage to earthquake-resistant timber frame houses (Yamada et al., 2017). Previous studies on small-size viscous dampers (Matsuno et al., 1999; Matsuno et al., 2000) have conducted shaking table tests and simulation analyses on a one-story timber test structure subjected to the 1995 Kobe earthquake. In addition, earthquake response analyses of a full-scale two-story timber frame house with small-size viscous dampers against the 2016 Kumamoto earthquake have been conducted (Nakamura and Fujii, 2021). These studies showed that the small-size viscous dampers effectively reduced the story drift and prevented severe damage.

Cross-story installation is another method wherein a damper is installed between the roof top and base of the structure across intermediate floors to enhance the response reduction effects. Recent studies on the cross-story installation of dampers conducted earthquake response analyses on super high-rise reinforced-concrete buildings installed with cross-story buckling restrained braces (Maida et al., 2015; Ueno and Ikenaga, 2018) and on steel buildings installed with cross-story viscous dampers (Ueno et al., 2020). The effects of tuned viscous mass dampers installed across multiple stories have been investigated through earthquake response analyses of tall buildings (Ogino et al., 2014; Fujise and Ikenaga, 2021; Lim and Ikenaga, 2021). These studies concluded that the cross-story installation of dampers effectively reduced the earthquake response of buildings. However, no research has been conducted on the cross-story installation of dampers in timber frame houses.

This study investigates the cross-story installation of a small-size viscous damper in a two-story timber frame house to demonstrate its advantage over the conventional inter-story installation, where a damper is installed between adjacent floors. Eigenvalue analyses of 2DOF mass-spring-dashpot models and earthquake response analyses of a two-story timber frame house installed with small-size viscous dampers are performed to investigate the effectiveness of the cross-story installation of a damper. Compared to inter-story installation, the cross-story installation of dampers effectively reduced the story drift and the number of dampers required for preventing severe damage by half. The results of the study demonstrated that a cross-story damper can effectively enhance the seismic resistance of timber frame houses.

Eigenvalue analyses of 2DOF dashpot models

The small-size viscous damper shown in Figure 1 was developed based on a general-type viscous damper, which is used mainly in timber frame houses in Japan to reduce damage caused by earthquakes (Matsuno et al., 1999; Matsuno et al., 2000). Similarly, the small-size viscous damper is installed inter-story, which induces a damping force proportional to the relative velocity of the piston rod.

FIGURE 1

FIGURE 1. Small-size viscous damper for timber frame houses.

We considered 2DOF mass-spring-dashpot models, where a dashpot was installed between floors as a damping element. Figures 2A, B show the conventional inter-story and cross-story dashpot installation where each dashpot was installed between adjacent floors and between the roof top and base of the building, respectively. No structural damping was assumed, and the dashpots represented the installed dampers. The connection member was assumed to be rigid. The free vibration of a two-story shear building can be expressed as

$\mathit{M}\ddot{\mathit{x}}+{\mathit{C}}_D\dot{\mathit{x}}+\mathit{K}\mathit{x}=\mathbf{0}(1)$

$\mathit{M}=\left[\begin{array}{cc}{m}_1& 0\\ 0& m_2\end{array}\right],(2)$

$\mathit{K}=\left[\begin{array}{cc}{k}_1+k_2& {-k}_2\\ {-k}_2& k_2\end{array}\right],(3)$

$\mathit{x}=\left\{\begin{array}{c}{x}_1\\ x_2\end{array}\right\}(4)$

${\mathit{C}}_D=\begin{array}{cc}\left[\begin{array}{cc}{c}_1+c_2& {-c}_2\\ {-c}_2& c_2\end{array}\right]& \mathrm{f}\mathrm{o}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}-\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{y}\mathrm{i}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\end{array}(5)$

${\mathit{C}}_D=\begin{array}{cc}\left[\begin{array}{cc}0& 0\\ 0& c_S\end{array}\right]& \mathrm{f}\mathrm{o}\mathrm{r}\mathrm{c}\mathrm{r}\mathrm{o}\mathrm{s}\mathrm{s}-\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{y}\mathrm{i}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\end{array}(6)$

where m₁ and m₂ are the first and second story masses, respectively; k₁ and k₂ are the first and second story shear stiffnesses, respectively; c₁ and c₂ are the damping coefficients of the first and second inter-story dashpots, respectively; and c_s is the damping coefficient of the cross-story dashpot.

FIGURE 2

FIGURE 2. 2DOF mass-spring-dashpot models. (A) Inter-story dashpot installation (B) Cross-story dashpot installation.

The damping matrix, C_D in Eq. 3 represents non-proportional damping, and the eigenvalue problem of Eq. 1 can be solved using Foss’s method (Foss, 1958) as

$\left(\lambda \mathit{A}+\mathit{B}\right)\mathit{X}=\mathbf{0}(7)$

$\mathit{A}=\left[\begin{array}{cc}\mathbf{0}& \mathit{M}\\ \mathit{M}& {\mathit{C}}_D\end{array}\right],(8)$

$\mathit{B}=\left[\begin{array}{cc}-\mathit{M}& \mathbf{0}\\ \mathbf{0}& \mathit{K}\end{array}\right],(9)$

$\mathit{X}=\left\{\begin{array}{c}\lambda \mathit{u}\\ \mathit{u}\end{array}\right\}(10)$

Equation 7 yields two pairs of complex conjugate eigenvalues, {λ}, and their corresponding eigenvectors, {u}, for damped vibration; {λ} can be expressed as

$\lambda =\left\{{\lambda }_R^{\left(1\right)}-{i\lambda }_I^{\left(1\right)},{\lambda }_R^{\left(1\right)}+{i\lambda }_I^{\left(1\right)},{\lambda }_R^{\left(2\right)}-{i\lambda }_I^{\left(2\right)},{\lambda }_R^{\left(2\right)}+{i\lambda }_I^{\left(2\right)}\right\}(11)$

The natural circular frequencies, ω₁ and ω₂, and the damping factors, h₁ and h₂, of the first and second modes, respectively, are expressed as

${\omega }_j=\sqrt{{\lambda }_R^{{\left(j\right)}^2}+{\lambda }_I^{{\left(j\right)}^2}},h_j=-\frac{{\lambda }_R^{\left(j\right)}}{{\omega }_j}=-\frac{{\lambda }_R^{\left(j\right)}}{\sqrt{{\lambda }_R^{{\left(j\right)}^2}+{\lambda }_I^{{\left(j\right)}^2}}}\left(\mathrm{j}=\mathrm{1,2}\right)(12)$

When m₁ = m₂ = m, k₁ = k₂ = k, and c₁ = c₂ = c_s = c, the characteristic equation of the eigenvalue problem of Eq. 7 can be expressed as a quartic equation of λ, given as for inter-story installation,

$m^4{\lambda }^4+3c{m}^3{\lambda }^3+\left(c^2{m}^2+3k{m}^3\right){\lambda }^2+2ck{m}^2\lambda +k^2{m}^2=0(13)$

for cross-story installation,

$m^4{\lambda }^4+c{m}^3{\lambda }^3+3k{m}^3{\lambda }^2+2ck{m}^2\lambda +k^2{m}^2=0(14)$

By solving Eqs 13, 14 numerically for a specified set of {m, k, c}, two pairs of complex conjugate eigenvalues, {λ}, can be obtained, and the modal circular frequencies, ω₁ and ω₂, as well as the damping factors, h₁ and h₂, can be obtained by Eq. 12. Figure 3 shows the relationship between the damping coefficient, c, and the damping factors, h₁ and h₂, for m = 10 $\mathrm{k}\mathrm{N}\bullet {\mathrm{s}}^2/\mathrm{m}$ and k = 4,000 $\mathrm{k}\mathrm{N}/\mathrm{m}$ . The natural periods were insensitive to the damping coefficient, c, and the fundamental period, T₁ $=\left(2\pi /{\omega }_1\right)$ , was 0.51 s, whereas the second mode period, $T_2=\left(2\pi /{\omega }_2\right)$ , was 0.19 s. The damping factors, h₁ and h₂, increased linearly depending on the damping coefficient c. Figure 3A shows that the single cross-story dashpot multiplied h₁ twice as much as the two inter-story dashpots. However, Figure 3B shows that the cross-story dashpot installation had little effect on h₂. Considering that the first-mode oscillation of a building dominates the earthquake response, the cross-story damper installation can effectively upgrade the earthquake-proof performance of the structure.

FIGURE 3

FIGURE 3. Damping factors of 2DOF mass-spring-dashpot models. (A) Relationship between the first damping factor and the damping coefficient (B) Relationship between the second damping factor and the damping coefficient.

Timber frame house model

The framework of an actual timber frame house, designed and built for sustaining seismic grade 3 (the highest grade) using the latest Japanese standards, used in this study is shown in Figure 4. The columns were made of Japanese cedar, each having dimensions of 12 cm × 12 cm; the beams were made of Douglas Fir. Young’s modulus and bending yield stress of the columns and beams were 7,500 N/mm² and 24 N/mm², respectively. The weights of the second story and rooftop were 198 kN and 158 kN, respectively.

FIGURE 4

FIGURE 4. Timber frame house for earthquake analyses (A) Framework of the timber frame house (B) Column and wall layout.

Figure 4B shows the wall layout and ratio (Supplementary Appendix S1) of each wall of the timber frame house. The walls were spaced uniformly on each floor. Table 1 shows the existing wall length L_E and necessary wall length L_N for seismic grade 3 for each floor and direction. Every L_E/L_N ratio was greater than one, indicating that the timber frame house was suitable for seismic grade 3.

TABLE 1

TABLE 1. Existing and necessary wall lengths and their ratios.

A beam and column were connected by a tenon joint or joint metals, such as “CP-T″ and “Hold-Down (HD)” joints, as shown in Figure 5A. Figure 5B shows the joint layout of the timber frame house. For conducting the earthquake response analyses, each beam-column joint was represented as an axial spring and a rotational spring with trilinear elastoplastic properties (Supplementary Appendix S2). Each timber beam or column was represented as an elastic bar element with rotational springs at both ends (Supplementary Appendix S3).

FIGURE 5

FIGURE 5. Joints of the timber frame house (A) Beam-column joints (B) Joint layout.

Kumamoto earthquake of 2016

The 2016 Kumamoto earthquake occurred beneath Kumamoto City of Kumamoto Prefecture in the Kyushu region of Japan. It comprised a series of earthquakes: a foreshock earthquake on April 14, and a main earthquake on 16 April 2016. Earthquakes exceeding the JMA seismic intensity of seven occurred twice with a maximum magnitude of 7.3. The earthquake resulted in 273 deaths, and 2,809 people were injured. Numerous structures had either collapsed or suffered severe damage (Yamada et al., 2017), including the Great Aso Bridge, Kumamoto Castle, and Aso Shrine. Over 8,500 houses collapsed, and 35,000 houses were partly destroyed. Even timber frame houses that were designed according to the latest quake-proof standards and built after the year 2000 were destroyed.

The records of the foreshock earthquake observed in Mashiki Town in Kumamoto Prefecture, as shown in Figure 6A, were used for the response analyses. The displacement and acceleration response spectra of the observed records are shown in Figures 6B, C, respectively.

FIGURE 6

FIGURE 6. Foreshock of the 2016 Kumamoto earthquake (14 April 2016) (A) Observed acceleration records (B) Displacement response spectra (C) Acceleration response spectra.

Earthquake response analyses

Response analysis program for timber structures

In this study, a collapse analysis program for timber structures, “wallstat”, was used for the earthquake response analyses. The “wallstat” program was developed to assess the damage status and likelihood of collapse of a timber structure when subjected to an earthquake motion (Nakagawa et al., 2010; Suzuki and Nakagawa, 2020). It is now widely used by housing makers to demonstrate the earthquake-proofing performance of timber frame houses at high seismic grades. The program utilizes the distinct element method, which is a non-continuum analysis method that can be applied to large deformation and collapse analyses.

The validity of the “wallstat” program was verified by comparing the simulation results and shaking table tests of full-size housing models (Nakagawa et al., 2006; Nakagawa et al., 2007; Fukumoto et al., 2008). Destructive damage of timber frame houses due to the 2016 Kumamoto earthquake was also analyzed using the “wallstat” program (Nakagawa, 2017; Namba et al., 2020).

A viscous damper can be represented by either the Maxwell model that connects a dashpot and spring in series or the Voigt model, which connects a dashpot and spring in parallel. The Maxwell model was used in this study.

Response analyses of a timber frame house

Figures 7A, B shows the 3D pictures of the response analysis and loci of the first-story drift angles, respectively, of the house model without dampers when subjected to 100% of the foreshock of the 2016 Kumamoto earthquake: The Y- and X-directions represent the N-S and the EW components, respectively. The first-story drift angle in the X-direction was dominant and exceeded 1/10, causing the house model without dampers to break down in the X-direction. Therefore, the dampers were placed in that direction to reduce the earthquake response and prevent severe damage.

FIGURE 7

FIGURE 7. Results of the earthquake response analyses of the timber frame house without dampers (100% of the foreshock of the 2016 Kumamoto earthquake) (A) 3D pictures of the earthquake response analyses (B) Loci of first-story drift angles.

Figures 8A, B show the inter-story and cross-story installation of the viscous dampers (Figure 1) in the timber frame house (Figure 4), respectively. Whether inter- or cross-story, viscous dampers are typically installed onto an outer frame fixed to the timber frame house so as not to block visibility and are placed uniformly in the X-direction at four, five, or six locations so as not to induce torsional oscillations (Figure 9). In the Maxwell model that was used to depict the viscous damper, the spring represented the stiffness of the connection member. For the dashpot, the relationship between the damping force and relative velocity was given by a bilinear model. The properties of the damper shown in Figure 9 were based on the performance tests of the manufactured small-size viscous damper (Figure 1).

FIGURE 8

FIGURE 8. Installation of viscous dampers in the timber frame house (A) Inter-story installation (B) Cross-story installation (C) Joint in outer-frame beams.

FIGURE 9

FIGURE 9. Layout of viscous dampers and damping property.

The target maximum story drift angle was specified as 1/30 given that a timber frame house would most likely be severely damaged or broken. Because the foreshock (Figure 6) was quite severe and the first-story drift angle in the X-direction was dominant, the timber house model with dampers was subjected to 70% of the E-W component of the foreshock in the X-direction. Figure 10A compares the resulting maximum first-story drift angles, γ_1max, in the X-direction between the house model without dampers and that installed with cross-story or inter-story dampers. Figure 10B shows the time histories of the first-story drift angles in the X-direction for the three cases: no dampers, 12 inter-story dampers (six in each story), and six cross-story dampers. For the model without dampers, γ_1max exceeded 1/26, and the structure was on the verge of collapse. Four cross-story and eight inter-story (four in each story) dampers reduced γ_1max to 1/30. The six cross-story dampers reduced γ_1max to 1/80, and the structure exhibited almost no damage. Therefore, the cross-story installation of dampers reduced the story drift more effectively than the inter-story installation while using half as many dampers.

FIGURE 10

FIGURE 10. Results of the earthquake response analyses of the timber frame house models with and without dampers (70% of the E-W component of the foreshock of the 2016 Kumamoto earthquake in X-dir.). (A) Maximum first-story drift angles in the X-direction (B) Time histories of the first-story drift angles in the X-direction.

Figure 11 compares γ_1max’s between the house model without dampers and that with six cross-story dampers or 12 inter-story dampers (six in each story) after being subjected to other major earthquakes in the X-direction. The peak velocity or input level of each earthquake was adjusted such that γ_1max of the house model without dampers was close to that of the model subjected to 70% of the E-W component of the foreshock of the 2016 Kumamoto earthquake. The mean and standard deviation of γ_1max’s for the three cases were also shown in the figure. The results showed that the reduction effects of the installed dampers differed among the earthquakes and that the six cross-story and 12 inter-story dampers (six in each story) reduced the story drift by almost equal amounts. Additionally, neither the cross-story nor inter-story dampers were able to reduce the γ_1max of the house model subjected to 70% of the N-S component of the 1995 Hyogo-ken Nanbu Earthquake (JMA Kobe). This may be because the JMA Kobe included an impulsive wave, and the peak response occurred before the dampers exhibited a damping effect.

FIGURE 11

FIGURE 11. Maximum first-story drift angles of the timber house model with and without dampers.

Note that the effects of installed dampers differed among the applied earthquake excitations and cannot be generalized from the results by small number of earthquake excitations. When the models installed with cross- or inter-story dampers in the X-direction were subjected to bilateral earthquake excitations, the first-story drift angles in the X-direction were reduced by the dampers in a similar manner as above. This is because the model had little eccentricities, and almost no torsional or rotational vibration occurred.

Dissipated energies of the inter-story and cross-story viscous dampers

The relationship between the damping force (induced by the viscous damper) and relative velocity was given by a bilinear model, where the gradient (i.e., the damping coefficient) changed when the velocity reached the relief velocity (Figure 9). Figure 12A shows the hysteresis loop of a cross-story viscous damper of the house model installed with six cross-story dampers subjected to 70% of the E-W component of the foreshock of the 2016 Kumamoto earthquake. Figure 12B shows the hysteresis loops of two inter-story viscous dampers in the first and second stories of the house model installed with 12 inter-story dampers (six in each story) for the same input. The induced damping force of every hysteresis loop in Figure 12 reached the same limit value of 4 kN (= C₁ $\times$ V₀ = 200 kN $\bullet$ s/m $\times$ 0.02 m/s), and every loop had a parallelogram-like shape. Moreover, the hysteresis loop of the cross-story viscous damper was larger than those of the inter-story ones, indicating that the former absorbed more vibration energy than the latter.

FIGURE 12

FIGURE 12. Hysteresis loops of viscous dampers (A) Hysteresis loop of a cross-story viscous damper (B) Hysteresis loops of inter-story viscous dampers.

The energy dissipated by the viscous dampers was obtained by integrating the damping force along the deformation of the hysteresis loop. Figure 13 shows the dissipated energy of the cross-story damper of the house model installed with six cross-story dampers and those of two inter-story dampers in the first and second stories of the house model installed with 12 inter-story dampers (six in each story) when subjected to major earthquakes in the X-direction. The results showed that the energy dissipated by a single cross-story damper was larger than the sum of the dissipated energies of two inter-story dampers for all applied earthquake inputs. Therefore, the cross-story installation allowed the viscous damper in the first story to absorb vibration energy nearly twice as much as that of the inter-story installation. The volumes of dissipated energy differed among the earthquakes and were irrelevant to the response reduction effects of the dampers (Figure 11).

FIGURE 13

FIGURE 13. Dissipated energies of viscous dampers.

Conclusion

In this study, we investigated the effectiveness of the cross-story installation of a damper by performing eigenvalue analyses of 2DOF mass-spring-dashpot models and earthquake response analyses of a two-story timber frame house installed with small-size viscous dampers. The damping factors and response reduction effects of the cross-story installation of a damping device were compared with those of the conventional inter-story installation. The results showed that the single cross-story dashpot multiplied the first damping factor twice as much as the two inter-story dashpots. Moreover, although the cross-story dashpot effectively increased the first damping factor, it had little effect on the second damping factor.

The house models were subjected to 70% of the E-W component of the foreshock of the 2016 Kumamoto earthquake in the X-direction. The earthquake response analyses revealed that, without the dampers, the first-story drift angle exceeded 1/25, and the structure was on the verge of collapse. Four cross-story and eight inter-story (four in each story) dampers reduced the first-story drift angle to 1/30. The six cross-story dampers reduced the first-story drift angle to 1/80, and the structure experienced almost no damage. The cross-story installation of dampers was quite effective in reducing the story drift and also reduced the necessary number of dampers by half compared to the inter-story installation.

Earthquake response analyses of the house model subjected to other major earthquakes showed that the response reduction effects of the installed dampers differed among the earthquakes. The six cross-story and 12 inter-story (six in each story) dampers had almost equal effects on the story drift. However, owing to its impulsive wave, neither the cross-story nor inter-story dampers reduced the story drift of the house model subjected to the 1995 Hyogo-ken Nanbu Earthquake (JMA Kobe).

The hysteresis loop and dissipated energy of a cross-story viscous damper of the house model installed with six cross-story dampers were compared with those of the inter-story viscous dampers in the first and second stories of the house model installed with 12 inter-story dampers (six in each story). The energy dissipated by a single cross-story damper was larger than the sum of the dissipated energies of two inter-story dampers for all applied earthquake inputs. Furthermore, the cross-story installation allowed the viscous damper in the first story to absorb vibration energy nearly twice as much as that of the inter-story installation. The volumes of dissipated energy differed among earthquakes and were irrelevant to the response reduction effects of dampers.

Therefore, compared to the conventional inter-story installation, the cross-story installation of a viscous damper could upgrade the response reduction effects of the installed dampers and reduced the number of dampers necessary for preventing severe damage by half, although the effects varied with earthquake excitations and cannot be generalized. As a cross-story damper can be installed onto an outer frame fixed to the house, it can be used as a seismic retrofitting measure in an existing house. Further research will focus on the application of cross-story dampers to low-rise structures made of laminated wood members.

Data availability statement

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.

Author contributions

YN: eigenvalue analyses of the two-story shear building installed with dashpots. RM: time-history response analyses of the timber frame house models installed with viscous dampers.

Funding

This study has been supported by JSPS KAKENHI (grant number JP20K04792).

Acknowledgments

The authors would like to express their appreciation to Ichijo Co. Ltd. for providing the design documents of the timber frame house and to Edogawa Mokuzai Co. Ltd. for providing permission to use the pictures of the small-size viscous damper.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fbuil.2022.1037832/full#supplementary-material

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