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COMPUTATIONAL MECHANICS WCCM VI in conjunction with APCOM’04, Sept. 5-10, 2004, Beijing, China 2004 Tsinghua University Press & Springer-Verlag Theoretical and Experimental Analysis of Brick Chimneys, Tokoname, Japan T. Aoki 1*, D. Sabia2 1 Graduate School of Design and Architecture, Nagoya City University, kitachikusa 2-1-10, Chikusa-ku, 464-0083 Nagoya, Japan 2 Department of Structural and Geotechnical Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy e-mail: aoki@sda.nagoya-cu.ac.jp, donato.sabia@polito.it Abstract For the purpose of obtaining the data concerning static and dynamic structural properties of brick chimneys in Tokoname, a series of material test, dynamic test and static collapse test of the existing two brick chimneys are carried out. From the material tests, Young’s modulus and compressive strength of the brick used for these chimneys are estimated 3200MPa and 7.5MPa, respectively. The results of static collapse test of the existing two brick chimneys are discussed here comparing with the results obtained by FEA (Finite Element analysis). From the results of dynamic tests, the fundamental frequencies of Howa and Iwata brick chimneys are estimated to be about 2.79 Hz and 2.93 Hz, respectively. Their natural modes and damping factors are identified by ARMAV (Auto Regressive Moving Average) model. On the basis of the static and dynamic experimental tests, numerical model has been prepared. According to the elastic transient dynamic analysis, these brick chimneys seem to be vulnerable to earthquakes with 0.24 to 0.30 g. Key words: brick chimney, dynamic test, static collapse test, ARMAV, Identification INTRODUCTION Tokoname City, Aichi Prefecture, is located in the center of the west coast of the Chita Peninsula, facing Ise Bay to the west and hilly terrain extends to the east. Tokoname has long been noted for its production of ceramic ware, and its history dates back to nearly 1,000 years ago. Along with Seto, Shigaraki, Echizen, Tanba, and Bizen, Tokoname is included in the Rokkoyo (the nation’s six oldest ceramic producing districts). And Tokoname is said to be the oldest and largest kiln site of them all. Even today, Ceramics is one of the major industries in Tokoname where the tradition and the culture of Tokoname ware are still alive. On the offshore waters of Tokoname City, the construction of the Central Japan International Airport is now underway aiming to begin its operation in 2005 [1]. Pottery has been a drastically growing industry since the Meiji period as ceramic pipes started to be used as a piping material for drainage. In these days, industrial materials or products for business use such as sanitary wares and ceramic tiles are eagerly produced. “Tokoname ware” has a wide range of products from tea-things, flower vases, bonsai pots, and ceramic ornaments to a new series of products such as “handmade tableware” which meets the demands of the present age while preserving the tradition [1]. Until the first half of the Showa period, there were over 300 chimneys in Tokoname. Some of them were destroyed by typhoon and/or earthquake. Unfortunately, according to the vulnerability for typhoon and/or earthquake, chimneys which were not used were pulled down, or they were made half height, and now, the number of chimneys is decreasing to 119 (Figure 1). According to the results of an investigation on a history of earthquakes, it is the interval of about 100 to 150 years in the Tokai - Nankai area until now, and there is rising concern that earthquake of magnitude 8 class will occur in the first half of this century. The purpose of this paper is to obtain the data concerning static and dynamic structural properties of brick chimneys in Tokoname to preserve them. CHIMNEYS IN TOKONAME According to an investigation of chimneys conducted by T. Kakita in August 1995, there were 152 chimneys including 55 perfect brick ones. Unfortunately, the number of Chimneys is decreasing to 119 including 45 perfect brick ones in January 2003 [2, 3]. Howa and Iwata brick chimneys were destroyed due to construction of the access road to the Central Japan International Airport in January 2003 (Figures 2 and 3). But fortunately the chance of investigation relating to these two brick chimneys was obtained. The profile of Howa and Iwata brick chimneys are listed in Table 1. Figure 4 shows the proportion of the existing chimneys in Tokoname. As shown in Figure 4, the proportion of these two brick chimneys is standard one in Tokoname. As for Howa brick chimney, four iron angles of 75mm x 75mm x 6mm at corners are fastened by 12 series of iron ties of φ 16mm. On the other hand, four iron angles of 40mm x 40mm x 3mm at corners are fastened by 6 series of iron ties of φ 9mm in Iwata brick chimney. Electromagnetic Radar is applied in order to estimate the thickness of chimneys. The thickness of Howa brick chimney is changed four times from the top to the bottom, that is, 0.21m, 0.315m, 0.42m, and 0.53m. On the other hand, the thickness of Iwata brick chimney is changed 0.11m at the top and 0.21m at the bottom (Figure 3). Fig. 1 Landscape of Tokoname City (offered by K. Sughie) (a) Howa (b) Iwata Fig. 2 Brick Chimneys 3.0 2.5 Bottom width [m] 2.0 1.5 1.0 ● Brick □ Clay pipe 0.5 × Steel pipe ○ Partial collapse 0.0 10 0 5 15 20 25 (a) Howa (b) Iwata Height [m] Fig. 3 Plan and Section Fig. 4 Proportion of Chimneys in Tokoname Table 1. Profile of Howa and Iwata Brick Chimneys (m) Height Bottom width Top width Bottom thickness Top thickness Howa 15.0 1.96 1.06 0.53 0.21 Iwata 8.2 1.16 0.68 0.21 0.11 MATERIAL TESTS In order to estimate Young’s modulus and compressive strength of the brick used for these brick chimneys, core sampling tests are carried out. The diameter and height of the brick specimens are about 33mm and 50mm, respectively. From the material tests, Young’s modulus and compressive strength of the brick are estimated 3200 MPa and 7.5 MPa, respectively [2, 3]. The specific gravity of the brick is determined about 16.5 kN/m3. STATIC COLLAPSE TEST For the purpose of obtaining the data concerning static structural properties of brick chimneys in Tokoname to preserve them, pull down test of Howa and Iwata brick chimneys are carried out (Figures 5 and 6). Upper part of the brick chimneys, wire rope was set and it was pulled by a derrick car until their collapse. During the static collapse test, horizontal load and deformation at the top of the brick chimneys are measured by means of load cell and laser range finder, respectively. Ultimate horizontal load of Howa and Iwata brick chimneys are 32.15 kN (horizontal component is 29.13 kN) and 4.40 kN (horizontal component is 4.25 kN), respectively. Collapse mode is different among Howa and Iwata brick chimneys. In case of Howa brick chimney, collapse occurs at the middle height of the chimney, that is 8m height from ground level which is shown in Figure 5. On the other hand, as shown in Figure 6, collapse of Iwata brick chimney occurs at the base of the chimney. (a) Crack at the middle height (b) Collapse Fig. 5 Static Collapse Test of Howa Brick Chimney (a) Crack at the base (b) Collapse Fig. 6 Static Collapse Test of Iwata Brick Chimney Figure 7 shows relationship between height of 15 Howa brick chimney and bending moment and its admissible based on static equilibrium. From this 12 Admissible Figure, it is to note that collapse of Howa brick Static Height [m] chimney occurs at the middle height of the chimney, 9 that is 8m height from ground level. From static equilibrium, tensile strength of the brick chimney is 6 estimated to be 0.37 MPa. As shown in Figures 10 and 11, analytical model is 3 composed of 9-node isoparametric Heterosis shell elements which is consists of eight layers. The FEM (Finite Element Method) based on isoparametric 0 0 10 20 30 40 50 60 degenerated shell elements is adopted for the Bending moment [kN m] numerical analysis [4, 5]. The selective integration rule is adopted for numerical integration. Total Fig. 7 Relationship between Height and Bending number of nodes and elements are 1476 and 320, Moment (Howa Brick Chimney) respectively. The yielding surface, given by Equation (1), for the FEM analysis is drown in Figure 8. The yielding condition of bi-axial compressive masonry is expressed on the basis of the Duruker-Prager yielding condition. The yielding function depends the mean normal stress I1 and the second stress invariant J2 as follows, f ( I 1 , J 2 ) = [β (3J 2 ) + αI 1 ] 1/ 2 =σ (1) where α=0.355 σ and β=1.355 are adopted based on the experimental data by Kupfer et al. [6, 7]. The masonry is assumed to yield in compression when the equivalent stress σ reaches to 30% of uni-axial compressive strength, and the flow rule proposed by Prandtl-Reuss is applied to the masonry in the plastic phase. The hardening rule of masonry is assumed based on the equivalent uni-axial stress-strain relation defined by the conventional Madrid parabola. Figure 9 shows the stress-strain relationship of concrete characterizing the element. The crush of masonry is judged by equivalent strain. The function is defined by replacing the stress components of the yield function with the strain components. The masonry is assumed to crush when the equivalent strain ε reaches the ultimate strain ε u , and the analysis is performed under a condition that the stiffness after this strain is to be zero (Figure 9(a)). (a) (b) Fig. 8 Yielding Condition for Fig. 9 Stress-strain Relationship for Concrete Constitutive Model Concrete Constitutive Model The crack of masonry is assumed to occur when the tensile principal stress exceeds the tensile ultimate strength shown in Figure 9(b). Cracks are assumed to form in planes perpendicular to the direction of maximum principal tensile stress which reaches the specified tensile strength. The cracked masonry is anisotropic and smeared crack model is adopted. After cracking, for the sake of the expediency to achieve numerical efficiency, a small amount of tension stiffening is assumed in uni-axial stress-strain relationships represented as follows, σ i = α ⋅ f t ' ⋅ (1 − ε i / ε m ), εt ≤ εi ≤ εm (i = 1,2) (2) σt’ is reduced in the region of tension-compression as follows. σ t ' = f t ' 1 + σ 2 / f c'( ) (3) where σt’ denotes the cracking stress. σ2 and ft’ is the compressive stress perpendicular to the tensile stress and the uni-axial tensile strength, respectively. Structural characteristics of the brick chimneys are considered through material and geometrical non-linear analyses. Material constants used in the analysis are Young’s modulus E = 3200 MPa, Poisson’s ratio ν = 0.15, weight per unit volume γ = 16.5 kN/m3, ultimate tensile strength ft’ = 0.37 MPa derived by static collapse test, ultimate compressive strength fc’ = 7.5 MPa, ultimate compressive strain εc = 0.003, tension stiffening parameter εm = 0.002 and α = 0.5 (Figure 9). (a) Deformation (b) Crack pattern (a) Deformation (b) Crack pattern Fig. 10 Result of FEA of Howa Brick Chimney Fig. 11 Result of FEA of Iwata Brick Chimney 35 5 30 Ultimate experimental load Ultimate experimental load Horizontal Load [kN] Horizontal Load [kN] 4 25 20 3 15 2 10 FEA 1 FEA 5 Experimental Experimental 0 0 0 10 20 30 40 50 60 0 10 20 30 40 50 60 70 80 Displacement [mm] Displacement [mm] (a) Howa (b) Iwata Fig. 12 Relationship between Horizontal Load and Displacement Figure 10 shows deformation and crack pattern of Howa brick chimney. From FEA (Finite Element Analysis) result, as shown in Figure 10(b), collapse occurs at the middle height of the chimney. This collapse mechanism corresponds well to that of experimental result (Figure 5 (b)). On the other hand, deformation and crack pattern of Iwata brick chimney are shown in Figure 11. Collapse occurs at the base of the chimney which corresponds well to that of experimental result (Figure 6 (b)). Figure 12 shows relationship between horizontal load and displacement of Howa and Iwata brick chimneys obtained by FEA comparing with those of experimental results. From these Figures, ultimate horizontal loads obtained by FEA correspond well to their ultimate experimental horizontal ones. MICROTREMOR MEASUREMENT 0.05 For the purpose of obtaining the data concerning N-S dynamic structural properties of Howa brick 0.04 E-W chimney, as a first phase of dynamic test, Vertical [cm/sec sec] microtremor by ambient vibrations are measured at 0.03 the top. Smoothed spectra by Parzen’s spectral window of 0.5 Hz are given in Figure 13. In Figure 0.02 13, bold solid line, bold dotted line and fine soli d line show the spectra of north-south, east-west and 0.01 vertical directions, respectively. According to the observation of microtremor measurement, the 0.00 fundamental frequencies of Howa brick chimney are 0 5 10 15 20 estimated to be 2.95 Hz and 2.67 Hz in north-south [Hz] and east-west directions, respectively. There is difference between two directions due to the Fig. 13 Spectra observed in Microtremors (Howa) window in north side (Figure 3). ACCELERATION MEASUREMENT In the second phase of dynamic test, as for both Howa and Iwata brick chimneys, acceleration of 6 points is contemporaneously measured in north-south or east-west direction. One sensor is placed at the base of the chimney and another one is placed at the top. Other sensors are placed as equally spaced. Excitation is ground motion due to derrick car. DYNAMIC IDENTIFICATION The experimental dynamic parameters such as fundamental frequencies, modal shapes and damping factors are identified by analysis of the accelerations time-history by means of ARMAV (Auto Regressive Moving Average) techniques. THE ARMAV TECHNIQUE An ARMAV model [8, 9, 10] can be expressed in the state space according to the following expression (u and x are the input and output): {x [n]} = [a ]{x [n − 1]} + [b]{u [n]} (4) In these parametric models the system output x [n] is supposed to be caused by a white noise input u [n] and the algorithm estimates the parameters’ values that minimize the residual variance. The parameter estimation algorithm works as follows: a first ARV model, whose structure is p x [n] = ∑ A[k ]x [n − k ] + u [n] ˆ ˆ (5) k =1 is fitted to the data. Using the estimated autoregressive parameters A[k ] , the residual vector u [n] is ˆ ˆ computed and used as input for the ARMAV model: p q x [n] = ∑ A[k ]x [n − k ] + u [n] + ∑ B[k ]u [n − k ] ˆ ˆ ˆ ˆ (6) k =1 k =1 An iterative procedure can then be started, to alternately refine the estimated parameters A[k ] , B[k ] and ˆ ˆ the residual u [n] to minimize the residual variance. The procedure ends when the difference between the ˆ parameters A[k ] and B[k ] , estimated in two consecutive iterations, is smaller than a desired value. ˆ ˆ RESULTS OF DYNAMIC IDENTIFICATION In Figure 14, the frequency distributions of Howa and Iwata brick chimneys identified by the ARMAV model are depicted in east-west and north-south directions, considering the complete time record. Fundamental frequencies and damping factor identified by the ARMAV model are listed in Table 2. Figure 15 shows natural mode shape both two orthogonal directions identified by the ARMAV model. As for the mode shape, especially first mode shape, there is difference between Howa and Iwata brick chimneys due to boundary condition. The foundation of Howa brick chimney is made in reinforced concrete, and on the other hand, that of Itawa brick chimney is made in sand. 18 20 16 18 14 16 14 Frequency Density Frequency Density 12 12 10 10 8 8 6 6 4 4 2 2 0 0 0 5 10 15 20 25 0 5 10 15 20 25 Frequency [Hz] Frequency [Hz] (a) East-west Direction (Howa) (b) North-south Direction (Howa) 18 14 16 12 14 10 Frequency Density Frequency Density 12 10 8 8 6 6 4 4 2 2 0 0 0 5 10 15 20 25 0 5 10 15 20 25 Frequency [Hz] Frequency [Hz] (c) East-west Direction (Iwata) (d) North-south Direction (Iwata) Fig. 14 Frequency Distribution identified by ARMAV Model Table 2. Fundamental Frequencies and Damping Factors Natural Frequency (Hz) Damping factor (%) Direction Mode ARMAV FEA ARMAV 1st 3.0603 2.7572 7.953 North-Sout 2nd 9.9725 11.1547 4.187 h 3rd 22.3372 25.6448 5.372 Howa 1st 2.6918 2.6924 3.069 East-West 2nd 9.3494 10.9514 3.157 3rd 22.7584 25.4511 4.613 1st 2.9330 2.9547 4.739 North-Sout 2nd 14.4932 15.5084 7.370 h 3rd 21.8729 23.0881 3.882 Iwata 1st 2.9356 2.9547 6.984 East-West 2nd 13.7789 15.5084 6.750 3rd 19.9204 23.0881 9.061 1.0 1.0 N-S E-W N-S E-W 0.8 0.8 0.6 0.6 Hi/H Hi/H 0.4 0.4 0.2 0.2 0.0 0.0 1st 2nd 3rd 1st 2nd 3rd (a) Howa (b) Iwata Fig. 15 Natural Mode Shape identified by ARMAV Model 1st 2nd 3rd 4th 6th 7th Fig. 16 Natural Mode Shape determined by Eigenvalue Analysis (Howa) The finite element model is composed of 20-node isoparametric solid elements (Figure 16). As for Howa brick chimney, the boundary condition at the base of the chimney is assumed to be fixed and its rocking behavior is not taken into account. On the other hand, as for the boundary condition at the base of Iwata brick chimney, soil foundation is also taken into consideration. From the material tests, specific gravity and Young’s modulus used in FEA are assumed to be 16.5 kN/m3 and 3200 MPa, respectively. Total number of nodes and elements are 4416 and 360, respectively. Natural mode shapes of Howa brick chimney determined by eigenvalue analysis are shown in Figure 16. In FEA, torsional mode shape is appeared in fifth mode. Fundamental frequencies determined by FEA are listed in Table 2 comparing with the results identified by ARMAV model. DYNAMIC CHARACTERISTICS OF BRICK CHIMNEYS On the basis of the static and dynamic experimental tests, numerical model has been prepared. The bending vibrational analytical model based on multi lumped mass model is adopted here for the elastic transient dynamic analysis [11, 12]. The assumptions using our analysis are as follows; 1) the boundary condition at the base of Howa brick chimney is fixed. On the other hand, soil foundation of Iwata brick chimney is taken into consideration by modifying Young’s modulus of the first beam element, 2) the thickness of each block is constant, 3) Young’s modulus of the brick determined by material test is used here, and 4) damping factor is proportional to mass and 2 % is adopted. The over 0.02 g accelerations observed in Tokoname City from 1997 are used as an input acceleration, that is north-south and east-west directions of 980422 (April 22, 1998), 980821 (August 21, 1998), 991129 (November 29, 1999), 010411 (April 11, 2001), 010621 (June 21, 2001), 010927 (September 27, 2001), 030709 (July 9, 2003) and 040106 (January 6, 2004) [13]. The maximum acceleration of each earthquake wave is normalized to be 0.1 g. 1.0 1.0 0.8 0.8 0.6 0.6 Hi/H Hi/H 980422EW 980422EW 990821EW 990821EW 991129EW 991129EW 0.4 010411EW 0.4 010411EW 010621EW 010621EW 010927EW 010927EW 0.2 030709EW 0.2 030709EW 040106EW 040106EW 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 (a) Howa (b) Iwata Fig. 17 Maximum Shearing Coefficient Response 1.0 1.0 0.8 0.8 0.6 0.6 Hi/H Hi/H 0.4 0.4 Howa Howa 0.2 0.2 Iwata Iwata 0.0 0.0 0 100 200 300 400 500 600 700 800 0 5 10 15 20 25 [cm/sec2] [cm/sec] Fig. 18 Maximum Acceleration Response Fig. 19 Maximum Velocity Response 1.0 1.0 Howa 0.8 0.8 Iwata 0.6 0.6 Hi/H Hi/H 0.4 0.4 0.2 Howa 0.2 Iwata 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0 1 2 3 4 5 6 [cm] [tonf] Fig. 20 Maximum Displacement Response Fig. 21 Maximum Shear Force Response 1.0 1.0 Howa 0.8 0.8 Iwata 0.6 0.6 Hi/H Hi/H 0.4 0.4 Howa 0.2 0.2 Iwata 0.0 0.0 0.0 0.51.0 1.5 2.0 2.5 3.0 0.0 0.2 0.4 0.6 0.8 1.0 [x103tonf cm] Fig. 22 Maximum Bending Moment Response Fig. 23 Maximum Shear Coefficient Response 1.0 1.0 0.8 0.8 0.6 0.6 Hi/H Hi/H 0.4 0.4 Howa Howa 0.2 Iwata 0.2 Iwata 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Fig. 24 Distribution Of Shear Force(Qi/QB) Fig. 25 Distribution Of Bending Moment(Mi/MB) Figure 17 (a) and (b) shows the maximum shearing coefficient response of Howa and Iwata brick chimneys. There is a little different in the response between the upper part (1/3 height from the top) and the lower part of the chimneys. Figures 20 to 25 show the maximum acceleration response, the maximum velocity response, the maximum displacement response, the maximum shearing force response, the maximum bending moment response, and the maximum shearing coefficient response concerning Howa and Iwata brick chimneys as the average of 16 earthquake waves. From Figure 23, the base shearing coefficient is determined to be 0.15. The distribution of the shearing force and the bending moment are shown in Figures 24 and 25. As for the distribution of the bending moment, there is a little difference between those two brick chimneys. As the brick chimneys are statically determinate structures, we can safely assume that the collapse of them is caused by the tensile failure of the mortar between the bricks. When the tensile stress of each section of the brick chimneys reaches the tensile strength, σt = 0.37 MPa derived by static collapse test is assumed here, we defined the brick chimneys as collapse. We call the maximum acceleration of the input wave “the collapse minimum acceleration α” when the brick chimneys are collapsed. From the maximum bending moment response under the condition that the maximum acceleration is 0.1 g, α is determined by Equation (7). N 1 α = (σ t + )Z (7) A M (0.1) × 10 where α is the collapse minimum acceleration g, M(0.1) is the maximum bending moment response under the condition that the maximum acceleration of the input wave is 0.1 g, σt is the tensile strength, N is the axial force (kN), A is the cross section (mm2), and Z is the section modulus (mm3). According to the elastic transient dynamic analysis in Figure 25 and Equation (7), those structures seem to be vulnerable to earthquakes with 0.157 and 0.123 g and the collapse occurs at the middle height of the brick chimneys. When material non-linearity is taken into consideration, the collapse minimum acceleration will be grater than those obtained here. If the multiple factor is assumed to be 1.5, the collapse minimum acceleration seems to be 0.236 and 0.184 g. When using the damping factor identified by ARMAV model, the collapse minimum acceleration seems to be 0.300 and 0.238 g. CONCLUDING REMARKS The following concluding remarks were obtained: 1) From the material tests, Young’s modulus and compressive strength of the brick used for these chimneys are estimated 3200MPa and 7.5MPa, respectively. 2) The results of static collapse test of the existing two brick chimneys are discussed here comparing with the results obtained by FEA. Ultimate horizontal loads obtained by FEA correspond well to their ultimate experimental horizontal ones. 3) From the results of dynamic tests, the fundamental frequencies of Howa and Iwata brick chimneys are estimated to be about 2.79 Hz and 2.93 Hz, respectively. Their natural modes and damping factors are identified by ARMAV model. 4) According to the elastic transient dynamic analysis, these brick chimneys seem to be vulnerable to earthquakes with 0.24 to 0.30 g. How to strengthening and preserving those brick chimneys is remaining problem. Acknowledgements The authors wish to appreciate the cooperation of Mr. Tomizou Kakita of Ex-director of INAX Kiln Plaza and Museum, Mr. Keizo Umehara of Tokoname City, and Mrs. Keiko Sugie of the representive of Tokoname hometown circle “Tsuchinoko”. Also, to KiK-net of National Research Institute for Earth Science and Disaster Prevention for earthquake waves. The financial supports were offered by Grants-in-Aid for Scientific Research (Kakenhi), The Hibi Research Grant, Tokai Academic Encouragement Grant and The Grant-in-Aid for Research in Nagoya City University. REFERENCES [1] Citation from http://www.city.tokoname.aichi.jp/html/intro_e/top.html [2] T. Aoki, Study on preservation and use of historical masonry structures, Report of The Hibi Science Foundation, 5, (2003), 83-133, (in Japanese). [3] T. Aoki, Brick Chimneys in Tokoname, Invitation to Design and Architecture VIII, Gifu Newspaper Inc., (2004), 1-33, (in Japanese). [4] E. Hinton, J. Owen, Finite element software for plates and shells, Pineridge Press, (1984). [5] T. Aoki, S. Kato, K. Ishikawa, K. Hidaka, M. Yorulmaz, F. Çili, Principle of structural restoration for Hagia Sophia dome, in Proc. of STREMAH Int. Symp., San Sebastian, (1997), pp. 467-476. [6] H. Kupfer, K. H. Hilsdorf, H. Rush, Behavior of Concrete Under Biaxial Stresses, in Proc. of ACI, 66(8), (1969), pp. 656-666. [7] H. Kupfer, K. H. Gerstle, Behavior of Concrete Under Biaxial Stresses, ASCE J. of the Eng. Mech. Div., 99(EM4), (1973), 853-866. [8] A. De Stefano, D. Sabia, L. Sabia, Structural identification using ARMAV models from noisy dynamic response under unknown random excitation, in Proc. of DAMAS Int. Conf, Sheffield, (1997), pp. 419-428. [9] A. De Stefano, R. Ceravolo, D. Sabia, Output only dynamic identification in time-frequency domain, in Proc. of American Control Conf., Arlington, (2001). [10] D. Sabia, E. Bonisoli, A. Fasana, L. Garibaldi, S. Marchesiello, Advances in identification and fault detection in bridge structures, in Proc. of DAMAS Int. Conf., Southampton, (2003), pp. 339-348. [11] T. Aoki, S. Kato, K. Ishikawa, M. Yorulmaz, F. Çili, Vibrational characteristics of Hagia Sophia and some related historical structures based on measurement of micro tremors, Journal of Structural Engineering, 40B, (1994), 87-98, (in Japanese). [12] T. Aoki, S. Kato, K. Ishikawa, M. Yorulmaz, F. Çili, Vibrational characteristics of the minarets in Hagia Sophia and Süleymaniye Mosque based on measurement of micro tremors, in Proc. of IASS Int. Symp., 2, (1995), pp. 1135-1142. [13] KiK-net, National Research Institute for Earth Science and Disaster Prevention, Japan.

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