Seismic Response Comparison of Full-Scale Moment-Resisting Timber Frame and Joint Test Result

In Japanese seismic code, two-phase design has usually been required since 1981 (MLIT 2008). The first-phase design is based on allowable stress design (ASD), and how the structure responds elastically during a moderate earthquake. The second-phase design is to ensure the life safety against a severe earthquake, which is considered the maximum earthquake in limit state design (LSD). For 2-story residential houses, a prescribed amount of shear wall per square meter is required [Notification 1100 of the Ministry of Construction (2007)] because most houses in Japan are made of a wooden frame construction with shear walls and the seismic performance depends mostly on the amount of shear walls. On the other hand, for a wooden house with moment-resisting connections that are main seismic elements, calculation is required as subsequently explained. The small-size and low-rise structure dealt with in this study has to only obey to ASD not LSD in law. From the trend of performance-based seismic design, it is a key issue to prevent the collapse against an expected earthquake. The objective of the first-phase design is preventing structural damage under frequent loading conditions. Concretely, the stresses at structural members were calculated by a linear elastic analysis under the seismic forces that are within their allowable stress.

The design shear force of each story is calculated using Eq. (1) according to the Japanese standardwhere $C_0$ is the base shear coefficient; $A_i$ is the vertical distribution factor; $W_i$ is the weight of $i$ story; seismic zone factor $Z$ and vibration characteristic factor $R_t$ were set as 1.0; $T$ is the natural period (for timber structure, $T=0.03\mathit{H}$, where H is the total height); $n$ is the the number of stories above base; and $i$ is the story number.

While $C_0$ is usually set as 0.2 for ASD, to design the specimen with the Earthquake Resistance Grade 3 based on ASD, we defined $C_0$ is $0.2\times 1.5=0.3$ in this study. The analysis model as described in the next section was used and the design was carried out according to the following:

The allowable value for members is defined of two-thirds of the nominal strength. The capacity of the joint will be assigned the 95% lower limit of capacity based on experiments in the design of specimen. The results of ASD will be mentioned after the explanation of the specimen.

Figs. 1–3 show the photo, plan views, and elevations of the specimen, respectively. The specimen is 3.64 m long in both directions. The test specimen is a 2-story box-type timber construction with the joint’s rotational resistance as the main seismic element in the excited direction (direction 1). Shear walls were installed in the perpendicular (direction 2) to direction 1. The contribution of the shear walls is quite small, and we intended that the seismic performance of this specimen depends on the moment-resistance of joints in direction 1. Fig. 1 shows elevations of MRTF and shear walls. Figs. 2 and 3 also show the section size of each member. The section size of the continuous column in the corner was $120\times 360\mathrm{mm}$, and the material is Glued Laminated Timber (Glulam) composed of Scotch pine (Pinus sylvestris, E95-F315), compliant with Japanese Agricultural Standard [JAS, Notification 1152 of the Ministry of Agriculture, Forestry, and Fisheries (2013)]. Accordingly, the mean value of elastic modulus of all layers is greater than $9.5\mathrm{kN}/{\mathrm{mm}}^2$. The material of beams is Glulam composed Scotch pine (Pinus sylvestris, E105–F300), and the mean value of elastic modulus of all layers is greater than $10.5\mathrm{kN}/{\mathrm{mm}}^2$. JAS has no regulation for the upper limit in these values such as elastic modulus. However, if the timber has more large strength and elastic modulus, the grade will be ranked higher.

The details of connectors and joints are shown in Figs. 4 and 5, respectively. Beam–column joints had lag screw bolts and a joist hanger, and the column was fixed to the foundation by column leg hardware and anchor bolts. Lag screws, shown in Fig. 5, have benefits of minimal loosing and slippage during the initial application of loads and are increasingly used to join timber members. The tensile stiffness of a lag screw bolt is higher than the normal bolt due to the meshing between the bolt and timber. The joist hanger at the edge of the beam is fixed by the lag screw bolts to the column. This installation method is very easy on-site, which is one of advantages of this connection system. Joist hangers indicated in Fig. 5(b) were used to connect the beam and column and column leg hardware indicated in Fig. 5(c) was used to fix the column to the foundation. Photos in Fig. 6 show details of the joints in the stories and foundation.

The shear walls of 9 mm thick in the first and second layers were nailed with CN50 according to Japanese Industrial Standard (JIS) at nail spacing of 50 and 100 mm, respectively. The floor material was plywood with a thickness of 28 mm and nailed with CN75 according to JIS at a nail spacing of 150 mm. To simulate the mass condition corresponding to a 2-story structure, the design weight of each floor was calculated in consideration of the dead load and live load, and additional seismic masses of 30 kN and 20 kN were placed on the second floor and the roof floor, respectively.

The capacity of the moment-resisting joint (Ma) was defined by the results of the tensile and bending experiments. When the force 1.5 times as strong as the force generated by a moderate earthquake was considered, the ratios of the moment (M) and moment capacity of the joint (Ma) in the specimen was below 0.50 according to the calculation. Table 1 summarizes results of the linear analysis in ASD for the specimen. The shear tests for the walls were also conducted, and these results were used to construct the analysis model. The interstory drift of the first and second stories were 15.39 and 16.33 mm (0.05%), respectively. These results are discussed with experimental results in next section.

The excitation of the test is produced by a unidirectional full-scale shaking table using three ground motions conducted in the laboratories of the National Institute for Earth Science and Disaster Prevention (NIED) in Tsukuba, Japan. Fig. 7 summarizes the input ground motion. In the tests, two types of waves were utilized for input ground motions. The first was the wave defined in the Japanese BSL, 17% of the wave (BSL17%) is equivalent to a moderate earthquake and 85% of the wave (BSL85%) is equivalent to a severe earthquake for a 2-story building in BSL. The maximum accelerations of the waves for the cases BSL17% and BSL85% are $0.11g$ and $0.54g$, respectively. In Japanese law, 100% of the wave shown in Fig. 8 was defined to design the mid- to high-rise building with more than 5 stories. When 100% of the wave was added in a 2-story building, shear force will be higher than those calculated using Eq. (1) in ASD. Reduction factor 17% and 85% are to make it equal to shear force in the ASD and seismic event. The second wave was the Japan Meteorological Agency (JMA) Kobe wave observed in the Osaka-Kobe Earthquake of 1995; this type of wave is often used to represent an extremely severe earthquake beyond the BSL for shaking table tests. The maximum acceleration of the 1995 JMA Kobe wave was $0.87g$. Before and after each shaking test, the specimen was subjected to white noise excitation to obtain natural frequency. We call test 1 “BSL17%,” test 2 “BSL85%,” and test 3 “JMAkobe100%.”

The accelerations and displacements of the specimen during the tests were measured. The accelerations of the floors and shake table were measured by eight accelerometers: two of them on the shake table, three at the second floor, and three on the roof floor.

The results from all white noise tests are provided in Table 2, where the natural frequency of the structure ranges from 2.78 to 1.27 Hz. The initial first natural frequency was 2.78 Hz. After BSL17% and BSL85%, the natural frequency decreased 2 and 35%, respectively. The reduction of after BSL17% is 2%, which means this specimen remained undamaged after the moderate earthquake but was slightly damaged after BSL 85%. After JMA Kobe, it decreased 54% and the reduction rate was the largest due the damage of the structure.

Fig. 8 represents the displacement profile of the specimen for each test, with the profile constructed using the average maximum displacement of the story relative to the shaking table. Fig. 9 shows the relationships of shear force and interstory drift of the first and second stories. Across all tests, primarily a first mode response was observed, with the peak interstory drift for each story occurring simultaneously to the peak displacement. After the first wave BSL17% was input to the specimen in test 1, the maximum interstory of the first and second stories were 7.92 and 8.62 mm, respectively. In other words, the maximum interstory drift was about 1/360 rad and within the damage limit deformation angle $1/120\mathrm{rad}$ for wooden house in a moderate earthquake according to the BSL. In test 2 (BSL 85%), the maximum interstory drift of the first and second stories were 50.81 and 51.08 mm, respectively. In other words, the maximum interstory drift was about $1/50\mathrm{rad}$ and within the safety limit deformation angle $1/30\mathrm{rad}$ for a wooden house in a severe earthquake according to the BSL. From the figure, a clear yield point was not observed, and the behavior was not plasticized. After the third wave JMA Kobe of intensity 100% was inputted to the specimen, the maximum interstory drift of the first and second stories were 130.78 and 138.00 mm in the test, respectively. In other words, the maximum interstory drift was about $1/20\mathrm{rad}$. In addition, the residual drifts of the entire building were very small in all tests.

The specimen was inspected for damage after each test. Because the specimen was designed to achieve the seismic performance for a moderate earthquake in the design, no visible damage was confirmed after test 1. After tests 2 and 3, the damage mainly occurred at the joints (Fig. 10). After test 2, only a minor crack starting from the drift pin occurred at the column leg (PB36), and the beam sunk into the column at the beam–column joints slightly without major damage. After test 3, the crack at the column leg became larger than that in test 2, and embedment of the beam to column progressed as indicated in Fig. 10(c). Figs. 10(d–g) compare the crack of the column legs (PB36) in four corners after test 3. The cracks were different in all corners. In corner 1, the crack was relatively large. On the other hand, there was no crack in corner 2. This phenomenon was considered due to the variations in materials and construction.

Table 3 compares the linear pushover analysis in the design and experimental results. Because the ground motion in test 1 was equivalent to a moderate earthquake, we compared the experimental results in test 1 and the linear analysis for a design shear force when $C_0$ is set as 0.2. As analytical results, the interstory drifts of first and second stories were 10.26 and 10.89 within the damage limit deformation angle $1/120\mathrm{rad}$, respectively. The ratios of experimental results and the results of analysis were 1.29 and 1.26, respectively, and the experimental values were almost 30% smaller than the those obtained in analysis. This indicates that the design tends to have a large margin to simulate the actual behavior in the seismic event to produce the conservative design of the structure. The analysis in the design should be conservative to ensure the seismic performance. This finding shows that the design method can ensure the seismic performance when $C_0$ is set as 0.2, which is equivalent to a moderate earthquake at least.

To analyze responses of the wooden structures, we developed and used the wallstat ver.4.3.11. The time-response analysis conducted in the wallstat was based on three-dimensional nonlinear time-history response analysis, as adopted from the extended distinct element method (EDEM) (Meguro and Hakuno 1991). This modeling approach is fundamentally based on a noncontinuum analysis method, the distinct-element method (Cundall 1971), which enables analyzing significant deformation of a fracture-developing process and simulating the three-dimensional seismic response, such as the collapse or rocking motion of a building (e.g., Nakagawa and Ohta 2003a, b; Nakagawa et al. 2013; Sumida et al. 2020). In the wallstat, the analysis model is composed of two primary components: beam–column elements and nonlinear lateral load–resisting shear wall elements. Fig. 11 shows the outline of the analytical model. The beams and columns were modeled as beam–column elements having an elastoplastic rotational spring at the end of the element. According to JAS, Young’s modulus was set to $9.5\mathrm{kN}/{\mathrm{mm}}^2$ for the $120\times 120\text{-}\mathrm{mm}$ column, the other members were set to $10.5\mathrm{kN}/{\mathrm{mm}}^2$, and the bending strength was set to $50\mathrm{N}/{\mathrm{mm}}^2$ in consideration of actual performance. Each joint is modeled as an elastoplastic tensile compressional spring. Hysteretic characteristics of the tensile and compressional springs are set as one side elastic and one side slip types, respectively. In preparation for determining the mechanical properties of tensile, rotational springs, and shear walls, the tensile and bending experiments of the joints and shearing tests for walls were conducted. Each joint’s hysteretic behavior can be characterized using the experimental results and we derived skeleton curves of the moment and the deformation angle relationship for each joint. Fig. 12 shows the outline of the slip backbone curves of the rotational spring. Fig. 13 and Table 4 indicate the rotational hysteretic parameters for each joint (standard backbone curve). Five parameters describe the hysteretic characteristics. Using the shearing test result, brace-replaced springs with tensile compression springs are modeled for each shear wall.

Measured acceleration at the center of the shaking table was input as ground motions in the numerical analysis. Instantaneous stiffness-proportional damping was used with a coefficient of 2.0% for analytical convenience. When instantaneous stiffness became negative, the damping coefficient was assumed to be zero. All dynamic time-history results were produced using the wallstat program using a time-integration step of ${10}^{-5}\mathrm{s}$. The model weights are set to equal the actual weights of the specimen in the full-scale shaking table test, including the weights of members and the weights of the first and second floors were set to 42.7 and 30.2 kN, respectively.

First, we conducted time-history analysis using the standard backbone based on the experimental results of the joints and walls. While the linear analysis in the design is a conservative method, to estimate the deformation in tests, we conducted the analysis based on experiments of the joints. In the design, capacities of the joints are set to be the 95% lower limit of capacity. In the analysis, we set average value as the capacity in the experiments of joints and backbone curves. Fig. 14 shows the results of the analysis of tests 1, 2, and 3. The stiffness was low compared with the experimental result in both the first and second stories in all tests. This problem was also seen in previous studies of MRTF structure [e.g., Nasu et al. (2007)]. To solve the problem, we conducted the data assimilation to get analytical parameters closer to the experimental results and analyze the mechanism.

Fig. 15 provides an overview of the data assimilation using orthogonal arrays (OAs) suggested by Kado et al. (2021). We tried the data assimilation for all tests. First, various skeletal curves are created by multiplying the parameters that simulate elemental experiments by correction factors (1. Definition of the Parameters). These parameters are set as the backbone curves of the springs in the analysis model, and multiple analyses are conducted (2. Numerical Analysis). The results of the multiple analyses are compared with the experiments, and the correction factor range are analyzed (3. Comparison). Then, the factor ranges are narrowed down by reviewing the range (4. Narrowing Down the Factor Range). Data assimilation was attempted by repeating these cycles multiple times. In this study, we were able to obtain accurate results by repeating this process four times. The details of the flow are described as follows:

Figs. 19 and 20 are comparisons of the analytical and experimental results of all tests. We extracted the closest combination of the analytical parameters from 14,641 analysis cases based on the values calculated by Eq. (2) for JMAkobe100%. The stiffness became closer after the data assimilation, the analytical results have a more accurate prediction of the experimental results, and the curve fits better. However, some points have to be revised to get more accurate prediction. For example, for JMAkobe100%, after about 23 s, the deformation is larger than the experimental result. Isoda et al. (2021) compared some hysteretic rules and clarified that there is much difference after the structure experienced maximum deformation to reproduce the experimental behavior. This indicated that a more accurate simulation is expected to occur by development of the hysteretic rule after 23 s in JMAkobe100% and revision of the damping. On the other hand, in BSL17%, the stiffness in the analysis is higher than those in the test. These analytical results occurred to reproduce the behavior at large deformation, so the accuracy of analysis at small deformation should be revised to simulate accurately. Fig. 21 shows the time-history curves of the deformation angle of joints in the north corner. The deformation angle is matched well with the experiment before 23 s. As aforementioned, this also depends on the hysteretic rule.

Fig. 22 shows analytical parameters ranked in the top five from 14,641 cases in the ascending order of ${}_2{\mathrm{D}}_1$, which targets the interstory drift of the first story in JMAkobe100%. For J2_2FL and PB36, both stiffness and capacity are higher than those in the standard backbone curve. The stiffness of some obtained data was 1.0–1.5 times higher than the properties of the standard skeletal curves obtained from the bending tests. The causes may include dynamic effect or influence of the floor. In the analysis model, the floor was modeled to brace-replaced springs, and the out-plane resistance of the floor was ignored. Furthermore, although the floor and placed weights might hold down the rotational behavior of the joint, it was ignored. Although other factors might not have been considered in the analysis model, we confirmed that the analysis results approach the experimental results by increasing the properties of the rotational spring in the analysis model. Therefore, the result indicates that the moment resistance of the floor and joint was higher than expected in analysis before data assimilation. Sakata et al. (2003) studied the stressed-skin effect on the moment-resisting joint and proved that the effect heightened the stiffness and capacity. We can say that one of the causes is stressed-skin effect of the floor. This phenomenon will be useful to estimate the seismic performance of MRTF, and future studies on the structure should include a follow-up study to verify the phenomenon.

As for the Young’s modulus of the member, the top five parameters were all 2.0, as large as those before data assimilation, indicating that the correction factor tended to be larger than that before data assimilation. The timber is manufactured according to JAS standards, which guarantees a minimum Young’s modulus value. However, we can say that the actual performance is considered to be much higher than the law value. Comparison of the actual performance and the law value is also an issue for future study.

The data assimilation allowed us to inductively infer what problems existed in the analysis. These causes, which may not have been taken into account in the analytical model, will be verified in the future through comparison of the behavior of each part and static joint and member tests, and will lead to the prediction of the response of the specimen without experimental results.

In this study, the wave defined in the Japanese BSL and the JMA Kobe wave observed in the Osaka-Kobe Earthquake of 1995 that destroyed many wooden houses were utilized for input ground motions and clarified the performance as a first step. Japan is located in the subduction zone, but waves that were observed in the Hokkaido and Tohoku earthquakes were not used, and various waves also should be considered to the structure in future studies to clarify the behavior in analysis and experiment.