EVALUATION OF STRUCTURAL PERFORMANCE OF EXISTING TRADITIONAL TIMBER STRUCTURES IN JAPAN BY MICROTREMOR MEASUREMENTS

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1 EVALUATION OF STRUCTURAL ERFORMANCE OF EISTING TRADITIONAL TIMBER STRUCTURES IN JAAN B MICROTREMOR MEASUREMENTS Kazuki Chiba 1, Kaori Fujita ABSTRACT: This paper presents proposed the evaluation of the structural performance of traditional timber structures b microtremor measurements of the fundamental vibration characteristics of the structures, i.e., natural frequenc, vibration mode, and damping factor. The method is applied to gates of three temples in Kamakura. A temple gate is a simple structure that consists of column-beam joints and column-batten (Nuki) joints with timber sidewalls. The initial stiffness of the structure is determined b evaluating the horizontal load-resisting elements. The stiffness calculated from the natural frequenc and the building weight corresponds approximatel to the theoretical stiffness. Thus, the applicabilit of the proposed method for the performance evaluation of simple structures (column-beam and columnbatten joints) is verified. KEWORDS: Nondestructive Inspection Method, Seismic Diagnosis, Natural Frequenc, Damping Factor 1 INTRODUCTION 13 The structural integrit of the existing traditional timber structures (for instance, temples, shrines and folk dwellings) in Japan is maintained b the periodic maintenance and repairing after ever disaster. The evaluation of the structural performance is important to determine the necessit of repairing and maintenance. A nondestructive inspection method is required to evaluate traditional timber structures, to prevent an damage to these structures. The microtremor measurement method is a simple nondestructive inspection method used to evaluate the fundamental vibration characteristics of structures. Therefore, this method is expected to pla an effective role in the structural evaluation of the existing traditional timber structures. Numerous researchers have performed microtremor measurements of timber structures to investigate their fundamental vibration characteristics. In refs. [1,], the authors reported the results of previous microtremor measurements. It is necessar to clarif the relationship between the fundamental vibration characteristics of a structure and its structural performance, which includes 1 Kazuki Chiba, Assistant rofessor, Department of Architecture, Facult of Engineering, Toko Universit of Science, Kudan-kita, Chioda-ku, Toko, O 1-73, Japan. sennoha@rs.kagu.tus.ac.jp Kaori Fujita, Associate rofessor, Department of Architecture, Graduate School of Engineering, the Universit of Toko, Hongo, Bunko-ku, Toko, O , Japan. fujita@buildcon.arch.t.u-toko.ac.jp the initial stiffness, maximum strength, construction tpe, building configuration, wall specifications, and height and weight of the building. In recent ears, we have performed microtremor measurements and the structural surves for temples in Kamakura. This paper presents the results of microtremor measurements performed for the gate of three temples (,, and ), whose locations are shown in Figure 1. About 15 temples and shrines are located in Kamakura, which is a famous tourist region in Japan. The temple gate is a simple structure that consists of a column-beam joint, a column-batten (Nuki) joint, and a wooden sidewall. Therefore, the results of microtremor measurements are expected to determine the relationship between the fundamental vibration characteristics and the structural performance. Toko Kanagawa Kamakura Region ofuna kita-kamakura Figure 1: Map of Kamakura Region kamakura Japan Railwas Line National Route Surve oint 1 km

2 The primar purpose of this stud is to use microtremor measurements to reveal the fundamental vibration characteristics of temple gates. B comparing the present results with those of previous research, the validit of the present results is clarified. A secondar purpose of this stud is to estimate the relationship between the horizontal load and displacement for the temple gate. We compare the results of eigenvalue analsis, which depend on the initial stiffness as calculated b the horizontal-load-displacement relationship and the building weight with the fundamental vibration characteristics obtained from the microtremor measurement and b analzing the results of the stud, we verif the validit of microtremor measurements as a nondestructive inspection method. MICROTREMOR MEASUREMENTS OF TEMLE GATES.1 OUTLINE Microtremor measurements and forced-vibration tests were performed to clarif the fundamental vibration characteristics such as the natural frequenc, damping factor, and vibration mode. This section presents the temple gates that we investigated via microtremor measurements.. INVESTIGATED TEMLE GATES The characteristics of the temple gates that we investigated, which are all classified as Important Cultural roperties, are listed in Table 1. With their post and beam structures with timber sidewalls, these structures are examples of traditional timber two-storied gate structures constructed in the Edo eriod. Table 1: Characteristics of Investigated Temple Gates Frontage Side Frontage Side Frontage Side Exterior Elevation (mm) st Stor lan (mm) FRONTAGE 1318 FRONTAGE 19 FRONTAGE 1585 nd Stor lan (mm) Construction ear Assignment Wall Roof 1st Stor Area (m ) Total Weight (t) (Edo eriod) Important Cultural roperties (Nation Assignment) 18 Copper late (Edo eriod) Important Cultural roperties (refecture Assignment) Timber Siding Walls 187 (Edo eriod) Important Cultural roperties (refecture Assignment) Cla Tile

3 The roofs are either a half-hipped roof with copper plating ( and ) or cla tiles (koumoji). The roof of the temple gate has a gable on the frontage. The and temple gates have three spans and two spans, respectivel, and the temple gate has five spans and three spans. The Kenchoji temple gate is the highest among the three, and the temple gate is the largest scale plan among the three gates. The total building weight is calculated from the timber volume through a structural surve and ref. [3] (this estimation is explained in section.). The weight calculations for the and temple gates are currentl under examination because the information from drawings and size of members is insufficient to make an estimate. The temple gate was damaged b the 193 Kanto Earthquake; the roof, which was thatched with reed, collapsed, and the record repaired in 198 has been left. In 1951 and 197, the roof was covered with copper plates [3]. The record damaged b earthquake has not been left for the and temple gates [,5]. Z 1_ 1_ Section of Central Ridge Line Top of Column on nd Stor Beam on Attic Space of 1st Stor Bottom of Column on 1st Stor.3 EERIMENTAL METHOD lan of Bottom of Column on 1st Stor Thirteen velocimeters were used for the microtremor measurements. As a representative example, of the microtremor measurement of the temple gate is shown in Figure. This program is able to simultaneousl determine vertical motion modes, torsional modes, and the vibration characteristics of ground motion. First, a microtremor measurement was conducted to identif the natural frequenc in the first mode. Second, a forced-vibration test in the first mode was performed b simple human power (i.e., a person pushed the column). The sampling frequenc was Hz, which was estimated from the velocit and displacement. For the forced-vibration test, the data were measured b displacement. The recording time was 3 s for the microtremor measurement and 6 s for the forced-vibration test. Z 1_ 1_ lan of Attic Space on 1st Stor Top of Column on nd Stor. WAVE ANALSIS METHOD The natural frequenc is determined b the predominant frequenc of the transfer function and vibration modes. The concept of the wave analsis method is shown in Figure 3 and the transfer function was calculated using Equation (1): H ( i) S ( i) S ( i) S S ( i) E( * ( i ) E( ) (1) * ) where and * are a complex-conjugate pair, E( ) is the ensemble average function, S (iω) is the power spectrum, and S (iω) is the cross spectrum. x(t) denotes the results of microtremor measurement on the ground, and (t) denotes the response of the building. Figure : Representative Example of Microtremor Measurement of Temple Gate Building Measurement oint Grand Measurement oint (t) FFT Analsis x(t) N(t) N(t) (N : Frequenc of analsis in analtical section) Microtremor Figure 3: Concept of Wave Analsis Method

4 (iω) and (iω) were taken from the Fourier spectrum calculated b the FFT analsis of response wave of velocit. The FFT analsis was performed b moving half in analtical section and analzing 9.6 s in analtical section for 3 s in measurement time. The vibration mode is determined from the phase difference and amplitude of the transfer function. The damping factor is calculated from the logarithmic decrement of the free-vibration waveform (Equation (), Figure ) and the half-power method of the transfer function is calculated b the formula for the amplification ratio (Equation (5), Figure 5). Finall, the natural frequenc f is obtained using Equation (). Amplitude Frequenc (Hz) Figure 6: Transfer Function ( Temple Gate) (3) m m h loge 1 log e m m _ 1 _ f ( x ) n 1 xn () (xn, n) Amplitude (xn+1, n+1) x Frequenc (Hz) Figure 7: Transfer Function ( Temple Gate) Figure : Logarithmic Decrement of Free-Vibration Waveform Amax Amax / h / (5) Δω ω1 ω ω Transfer Function Frequenc Figure 5: Half-ower Method for Calculation of Damping Factor from Results of Microtremor Measurements.5 RESULTS OF EERIMENTS Figures 6, 7, and 8 show the transfer functions of the investigated temple gates. The measuring instruments were set up at the center of the given building (1_, 1_, _, _). Hereinafter, is the ridge direction and is the span direction of the building row. Some predominant frequencies of each temple gate are determined from the transfer functions. Amplitude _ 1 _ Frequenc (Hz) Figure 8: Transfer Function ( Temple Gate) The natural frequencies of vibration in the first and second modes were confirmed from each transfer function. The transfer functions for the and temple gates appear reasonable. The transfer function of the temple gate exhibits a different tendenc for the fundamental vibration characteristics. Three points in the transfer function confirm the distinctive predominant frequenc of temple gate. The natural frequencies of vibration and the damping factors are shown in Table, which also shows the results of the forced-vibration tests. The results of the forced-vibration tests given in Table are the mean value of three individual tests. The column heading Disp. in Table indicates the maximum displacement of the response wave. For the forced-vibration test, Disp. indicates the maximum value in the analtical section.

5 The natural frequenc of vibration of the first mode in the direction ranges from about 1.9 to 1.59 Hz, and for the direction the range is from about 1. to 1.3 Hz. The first natural frequenc in the direction is slightl larger than in the direction, and the same tendenc is found for the natural frequenc of vibration of the second mode. The damping factor ranges from 1. to 1.5 % except for the temple gate. The accurac of the analtical results for the temple gate is thought to be low because the wind was high on the da of the measurement. The relationship between the first natural frequenc and the maximum displacement is shown in Figure 9. Except for the temple gate in the direction, the nonlinear dependence of the first natural frequenc in response displacement is confirmed. 3 COMARISON WITH REVIOUS RESEARCHES 3.1 OUTLINE The fundamental vibration characteristics determined b microtremor measurements of traditional timber structures have been accumulated from previous research [1,]. In this section, we compare these results with the results of our microtremor measurements. 3. INFLUENCE OF CONSTRUCTION EAR The relationship between the first natural frequenc and the construction ear is shown in Figure 1, which shows average frequencies for the ridge and span directions. The construction ears in Figure 1 were estimated if the precise ear was unknown. From the comparison with previous research, it appears that the results of microtremor measurements performed b the authors lie among the temples and Shrines, and agodas. However, because of the small number of results that we have for temple gates, it is not possible to find a clear tendenc in the results for temple gates. Thus, it is necessar to accumulate more results of microtremor measurements of temple gates in future research. 3.3 INFLUENCE OF BUILDING HEIGHT The relationship between of the first natural frequenc and the building height is shown in Figure 11, which shows average frequencies in the ridge and span directions. The curve in Figure 11 and the first natural frequenc for design b Building Standards Law in Japan are calculated b Equation (6): f 1/. 3h (6) where f is the first natural frequenc and h is the building height. The results show a good correlation between the first natural frequenc and the building height and these results confirm the tendenc found in previous research. Table : The Results of Microtremor Measurements Microtremor Measurement Free Vibration Test Natural Frequenc Damping Natural Damping Disp. Factor Frequenc Factor 1st nd Disp. (Hz) (%) (mm) (Hz) (%) (mm) st Freq. (Hz) Engaku_ji_ koumo-ji_ Disp. (mm) Figure 9: Relationship between First Natural Frequenc and Maximum Response Displacement 1st Freq. (Hz) Temples, Shirines Temple Gates agodas Construction ear Figure 1: Relationship between First Natural Frequenc and Construction ear 1st Freq. (Hz) Height of Building (m) Temples, Shrines agoda Temple Gates Eq. (6) Figure 11: Relationship between First Natural Frequenc and Height of Building

6 STRUCTURE ANALSIS.1 OUTLINE In this section, we discuss the structure analsis of the temple gate, which we take as a representative example. The output of the structure analsis is the loaddisplacement relationship. Once this is determined, an eigenvalue analsis is performed from the initial stiffness and building weight. To clarif the relationship between the microtremor measurements and structural performance, the results of the eigenvalue analsis are compared to the fundamental vibration characteristics obtained b microtremor measurements.. ESTIMATION OF BUILDING WEIGHT The weight of the temple gate is estimated from the timber volume and the roof load and evaluated using the results of a structure surve and ref. [3]. The results of the estimation are listed in Table 3. In the estimation,.69 t/m 3 was used as the specific gravit of the Zelkova serrata timber. The contribution of copper roof plating was estimated from its area densit (8.8 kg/m ). The total weight of the temple gate is 157 t of which 76 t is attributed the first stor and 77 t to the second stor..3 EVALUATION OF STIFFNESS In evaluating the theoretical stiffness of the structure the horizontal load-resisting elements considered are the moment resistance of column-beam and the columnbatten semi-rigid joints and the overturning resistance of the columns. Each evaluation method is explained below..3.1 Column-beam and column-batten (Nuki) joints The stiffness of the semi-rigid column-beam and column-batten joints are calculated on the basis of the theoretical stiffness of the timber perpendicular to the grain reported b Inaama [6]. Figure 1 shows the method used to calculate the timber stiffness in the direction perpendicular to the grain. The quantit E in the equations associated with Figure 1 is the oung modulus of transverse compression, and is about E/5, where E is the oung modulus (adopted E = 8. kn/mm from ref. [7], which is the value for Zelkova timber). The quantit fm is the elasticit limit of the compressive stress inclined to the grain, which is about. times the allowable stress for sustained loading (adopted fm = 8.6 N/mm from ref. [7], which is the value for Zelkova timber). The quantit n is the estimated substitutive multipling factor in the expression that relates the fiber direction and the perpendicular direction (adopted n = 7 in the present stud). The stiffness of the semi-rigid column-beam and column-batten joints is modeled as the bilinear function shown in Figure 1. Table 3: Estimated Weight of Temple Gate 1st Stor nd Stor x1 M Estimated Member Weight (t) (kn) Columns and Horizontal Members Bracket Complex Member Roof Frame Members Roofing Members Marginal Members Finishing Carpentr Members Subtotal Columns and Horizontal Members Bracket Complex Member Roof Frame Members Roofing Members Finishing Carpentr Members Subtotal Continuous Columns Total N xp θ Figure 1: Method for Calculation of Theoretical Stiffness of Timber erpendicular to Grain h 3 p x M b V V δ x pce 1 Cxd Z 3 x. 8x 1 p Cxd.5 Z Z x 1 x. 8x p Cx 1 1 Z Z Z n 1 n. 8nx p C 1 1 Z Z Z Z Z Cxm 1 Cm 1.8x p.8n p (a) Basic Method H 1 (a) (b) H H b V h a b V h θ h 1 x E p M M b p V a b b.9965e Z Z f m CxCCxmCm θ δ V θ θ (b) Method in Case of a < b H b1 Empirical Formula δ Figure 13: Method for Calculation of Theoretical Stiffness form Overturning Resistance of Columns

7 .3. Overturning resistance of columns A column is modeled as a rigid bod and the relationship between the horizontal displacement and the overturn resistance is modeled b an empirical formula based on the experiments and analsis of Kawai et al. and Ban et al. [8,9]. Figure 13 shows the method used to calculate the theoretical stiffness of the column-overturn resistance.. FORMULATION OF ANALSIS MODEL Figure 1 shows the arrangement of the columns and the plane tpes. The structural planes are labeled from A to D. The coordinate pairs 1 and 3,, 1 and, and and 3 are assumed to belong to the same plane of the structure in the analsis models. Therefore, we formulated a forth tpe of analsis model. As representative examples, we show analsis models B and C in Figures 15 and 16. The analsis models are formulated b a two-dimensional framed-structure model. The rotational stiffness of beam and batten joints are modeled b considering the timber perpendicular to the grain. The rotational stiffness calculated when a lateral load is exerted from the left side is shown near the mark of joint stiffness in Figures 15 and 16. The bottoms of the columns are modeled taking into consideration the rotational stiffness and overturning resistance of the columns. The parameters used to calculate the overturning resistance of the columns are listed in Table. Because the columns are modeled as a rigid bod, bend deformation is not considered. Table : arameters Used to Calculate Overturning Resistance of Columns 1st Stor nd Stor Column Size Number Diameter Capital Height Column Vertical Load H Cal. Tpe Restoring Force b a h V H H Nc Nc (mm) (mm) (mm) (t) (kn) (kn) (a) (b) (a) (b) (a) (a) (b) (a) (b) (a) RESULTS OF STRUCTURE ANALSIS Table 5 lists the stor stiffness calculated from the stiffness of semi-rigid joints. The stor stiffness is computed b multipling the lateral stiffness estimated for each structure plane b the number of planes in each direction, and the total stiffness is estimated b summing the stor stiffness in each direction. The ield deformation angle is determined from the smallest ield deformation angle of all the joint parts. Continuous Column (φ595 ) Stand Column (φ56 ) Stand Column (φ595 ) C D D C Figure 1: Tpe of lanes and Columns of Structures Rotational Stiffness (1^3 kn*m/rad.) (b Overturning Column) Beam Beam Batten 595 Column Batten Batten Beam Column Batten A B A Rotational Stiffness (1^3 kn*m/rad.) (b Timber erpendicular to the Grain) The Area of Same Displacement Figure 15: Analsis Models (B lane of Structure) Beam Batten Batten Beam 5 5 Column Beam Batten Batten 56 Column Figure 16: Analsis Models (C lane of Structure)

8 The relationship between load and the estimated deformation angle are shown in Figures 17, 18, and 19. The deformation angle data for Figures 17, 18, and 19 were estimated b the stiffness of semi-rigid joints, the stiffness of column overturn resistance, and b the sum of these two, respectivel. For the first stor, the maximum strength of the Kenchoji temple gate in the direction is estimated to be 931 kn (CB =.6, where CB is the base shear coefficient). For the same stor, the maximum strength in the direction is estimated to be 836 kn (CB =.56). The maximum strength in both directions are filled with CB =.. The strength of each member and the ratio of the strength to the total strength calculate for each deformation angle are listed in Table 6. With increasing deformation angle, the ratio of the strength borne b column-beam and column-batten semi-rigid joints is predominant. Table 5: Stor Stiffness Estimated from Semi-Rigid Joints 1st Stor nd Stor lane Number Total Stiffness Estimated b Semi Rrigid Joints Stor Stiffness ield Deformation Angle Np pkr pkr Np KR θ (kn/rad.) (kn/rad.) (kn/rad.) (rad.) A B C D A 6 9 B C D Table 6: Strength and Strength Ratio Calculated from Each Deformation Angle R (rad.) 1/ 1/1 1/5 1/ joints 191 (.6) 381 (.7) 76 (.86) 813 (.88) 1s_ columns 115 (.38) 131 (.6) 1 (.1) 111 (.1) stories joints 166 (.59) 333 (.7) 665 (.85) 71 (.87) 1s_ columns 113 (.1) 19 (.8) 118 (.15) 11 (.13) stories (kn) joints 3 (.6) 86 (.61) 137 (.75) 137 (.77) s_ columns 5 (.5) 5 (.39) 6 (.5) (.3) stories joints 5 (.5) 1 (.65) 16 (.78) 16 (.79) s_ columns 5 (.5) 53 (.35) 6 (.) (.1) stories EIGENVALUE ANALSIS To clarif the validit of the structute-analsis results, we perform an eigenvalue analsis using the initial structure stiffness and building weight. To perform this analsis, we formulate a lumped mass model. The initial stiffness is calculated using an inclination of 1/1 rad., 1/ rad., and 1/1 rad. for the deformation angle from Figure 19. Response displacement of microtremor measurement was about.1 mm (1/1 rad.) at the top of column of second floor. Lamped mass model and the parameters used are shown in Figure. The results of analsis and microtremor measurement are shown in Table 7. Load (kn) Load Displacement of Semi Rigid Joints 1s_ s_ 1s_ s_ Deformation Angle (rad.) Figure 17: Relationship between Load and Deformation Angle of Semi-Rigid Joints Load (kn) Load Displacement of Overturning Columns Deformation Angle (rad.) Figure 18: Relationship between Load and Deformation Angle obtained from Overturning Resistance of Columns Load (kn) Load Displacement of Temple gate CB=.6 (931kN) CB=.56 (836kN) CB= Deformation Angle (rad.) Figure 19: Relationship between Load and Deformation Angle of Temple Gate.6 6. (m) M M1 Weight Defomation Initial Stiffness Angle (t) (rad.) (kn/m) M1 76. K A 1/1 M 76.3 K B C K / K 31 K /1 K Figure : arameters used to Eigenvalue Analsis

9 Table 7: Results of Eigenvalue Analsis and Microtremor Measurement Defomation Angle Natural Frequenc (Hz) Model to Calculate Case the Initial Sstiffness 1st mode nd mode (rad.) Microtremor Measurements A 1/ (1.) (1.) Eigenvalue B 1/ Analsis (1.5) (1.3).8.6 C 1/ (1.7) (1.)..1 The first natural frequenc obtained from the eigenvalue analsis in case A is close to the results of the microtremor measurements. The second natural frequenc, however, does not correspond. With increasing deformation angle to calculate the initial stiffness, the difference between the results of the microtremor measurements and the results of eigenvalue analsis extend. The ratio of the natural first frequenc estimated from eigenvalue analsis and the results of microtremor measurements are shown below the first natural frequenc in Table 7. The ratio ranges from about 1. to 1.7. To evaluate the initial structure stiffness, these ratios ma use as modification coefficients. However, in order to clarif the validit of these ratios, it is necessar to perform the static lateral loading test. In future research, the relationship between microtremor measurements, structure analsis and static lateral loading test have to be clarified. We suggest that the initial stiffness is influenced b the timber sidewalls and the finishing carpentr, which ma influence the results of the microtremor measurements. The timber sidewalls and the finishing carpentr are not ordinaril considered as earthquake-resisting members. However, to adequatel evaluate the initial stiffness of the structure, it ma be necessar to estimate the structural performance of these nonstructural members. 6 CONCLUSIONS Microtremor measurements of three temple gates were performed and new perceptions were accumulated. Comparing these results with previous results, we find good correlation, which suggests a relationship between the first natural frequenc and the building height. We also verif the relationship between the results of the microtremor measurements and the structural performance estimated b structural analsis using the stiffness of semi-rigid joints calculated from timber perpendicular to the grain and from the column-overturn resistance. We find that the maximum strength of the temple gate is about 931 kn (CB =.6). With increasing deformation angle, the ratio of the strength borne b the semi-rigid column-beam and column-batten joints is predominant. B comparing these results to those of the eigenvalue analsis and the microtremor measurements, we confirm the evaluation of the initial stiffness of the structure. However, because the second natural frequencies derived from the eigenvalue analsis and the microtremor measurements do not agree, we suggest that it ma be necessar to evaluate the structural performance of just the nonstructural members. We suggest that the ratio of the natural first frequenc estimated from eigenvalue analsis and the results of microtremor measurements ma be useful as modification coefficients. In the future research, a method to estimate the maximum strength of structures from the results of microtremor measurement should be clarified. The relationship between microtremor measurements, structure analsis and static lateral loading test should be clarified. In addition, the application of microtremor measurements to evaluate structural performances should be organized. ACKNOWLEDGEMENTS The authors express their gratitude to the administrator of the,, and temples for allowing them to carr out this investigation. The authors would like to express their sincere gratitude to Dr. Matsuda of Too Universit, Dr. Sato of Tokushima Universit, and Mr. Nakashima and Mr. Watabe of the Fujita Laborator, The Universit of Toko. The authors are also grateful to the staff of the Kurita Laborator, Toko Universit of Science, For their assistance in microtremor measurements and the structural surve. Author expresses appreciation to rofessor Kurita of Toko universit of Science for lending vibration measurement equipments and guidance ever da. This research was funded b a Grant-in-Aid for oung Scientists (Start-up) Japan. REFERENCES [1] Kazuki CHIBA, Kaori FUJITA, Hiromi SATO, Soutarou TAKAHASHI, Akiko BABA, Seismic Diagnosis and Structural erformance Evaluation of Existing Timber Houses in Toko art 5 Application of Microtremor Measurement, roceedings of Building Stock Activation 7, International Conference of 1 st Centur COE rogram of Toko Metropolitan Universit, Nov., 7 [] The Report of the Upgrading of Seismic Diagnosis Method, The Japan Building Disaster revention Association Mar., 9 (in Japanese) [3] The Repairing Report on the Temple Gate in, Edit: The Japanese Association for Conservation of Architectural Monuments, Issue: The Committee for Conservation and Repairing of Temple Gate in, Mar., 1996 (in Japanese) [] Mikio KOSHIHARA, Kaori FUJITA, oshimitsu OHASHI, Isao SAKAMOTO, A Stud on Damages of Traditional Wooden Buildings in Kamakura b The 193 Kanto Earthquake, Annual roceeding of the Architectural Institute of Japan, No.573, pp , Nov., 3 (in Japanese) [5] Mikio KOSHIHARA, A Stud on Damages of Temples and Shrines in Kamakura b The 193

10 Kanto Earthquake, Master s Thesis, The Universit of Toko, Feb., 199 (in Japanese) [6] Masahiro INAAMA, Theoretical Research on the Stiffness of Timber erpendicular to the Grain, Doctoral Thesis, The Universit of Toko, 199 (in Japanese) [7] Standard for Structural Design of Timber Structures, Architectural Institute of Japan, Dec., 6 (in Japanese) [8] Naohito KAWAI, A Series of Experiments on Restoring Force roduced b Rocking of Wooden Column, Annual meeting of Architectural Institute of Japan, pp.91-9, Sep., 1991 (in Japanese) [9] Shizuo BAN, Research on the Structural erformance of the Timber Frame used in Temples and Shrines art 1 Horizontal Load Resistance of the Column, Journal of the Annual meeting of Architectural Institute of Japan, pp.5-58, Apr., 191 (in Japanese)