Experimental and numerical modal analyses of a historical masonry palace

Construction and Building Materials 25 (2011) 81–91

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Experimental and numerical modal analyses of a historical masonry palace F. Aras a,*, L. Krstevska b, G. Altay c, L. Tashkov b a

Civil Engineering Department, Anadolu University, 26555 Eskisßehir, Turkey Institute of Earthquake Engineering and Engineering Seismology, University ‘‘Ss. Cyril and Methodius, Skopje, Macedonia c Civil Engineering Department, Bog˘aziçi University, 34342 Istanbul, Turkey b

a r t i c l e

i n f o

Article history: Received 24 February 2010 Received in revised form 27 April 2010 Accepted 19 June 2010 Available online 13 July 2010 Keywords: Historical structures Dynamic investigation Ambient vibration survey Modal tuning

a b s t r a c t This study presents the determination of modal properties of a historical masonry palace built between 1861 and 1865 in Istanbul. Both an experimental and a numerical study have been performed. The experimental study was based on ambient vibration survey while numerical analysis was based on finite element analysis of the structure. The results of the experimental study were used to tune the numerical model of the structure. As the most doubtful parameter, the modulus of elasticity of the masonry was adjusted to achieve the experimental results with numerical model by simple operations. Obtaining good consistency between the experimental and numerical analysis, the study revealed the dynamic properties of the palace. Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction This study was developed within the PROHITECH (Earthquake protection of historical structures by reversible mixed technologies) project [1] and aims to present the dynamic identification of Beylerbeyi Palace, constructed between 1861 and 1865 on the Asian shore of the Bosporus in Istanbul. Due to many uncertainties associated with the construction systems, material properties, modelling techniques, analysis methods and soil interactions, evaluation of a historical structure is indeed a difficult task. However, sophisticated measurement techniques on the real structure enable engineers to track the real behaviour of the structure and calibrate the numerical models to use in further assessments [2]. Because of the historical importance of Beylerbeyi Palace and the known difficulties, both experimental and numerical analyses were seen essential. Modal properties of a structure can be experimentally determined by forced or ambient vibration tests using modal identification methods [3–7]. Ambient vibration survey has been preferred in this study because it works in natural conditions and no excitation is required, hence, the test implies a minimum interference with normal use of the structure. Furthermore, ambient vibration testing has recently become the main experimental method for assessing the dynamic behaviour of full-scale structures and it

_ Eylül Kampüsü, Ins _ ßaat * Corresponding author. Address: Anadolu Universitesi, Iki Mühendislig˘i Böülümü, 26555 Eskisßehir, Turkey. Tel.: +90 222 3213550x6600. E-mail address: [email protected] (F. Aras). 0950-0618/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2010.06.054

has generally been preferred for testing historic structures [8]. The obtained data are important but can provide more meaningful results if they are used to update a finite element model of the building, which is potentially able to estimate important mechanical properties [9–12]. In the numerical part of this study, a 3D finite element model, based on the geometric survey of the building, was developed. For the material properties laboratory based investigation was performed and required parameters for the masonry were determined [2]. In this laboratory based experimental investigation, test specimens were created by freshly prepared lime mortar and clay burnt brick since even non destructive tests were allowed by the authorities. Under these conditions numerical model of the structure was updated based on the experimental modal data. The aim was to correct young modulus of the material in the initial FE model through a model tuning procedure to catch the same dynamic characteristics obtained by the experimental study. Before the experimental and the numerical part of the study, brief information about structural system of the palace would be useful to understand the performed analyses. 2. Beylerbeyi Palace The three-storey main structure is consisted of a basement and two ordinary floors with a 72 m length along the shore (longitudinal direction) and 48 m in the perpendicular direction (transversal direction). The storey heights of the basement floor change between 1.5 and 2.5 m and that floor is partially underground while

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in the ordinary floors they vary between 7 m and 9 m. Fig. 1 shows a general view of the palace and the architectural plan lay-outs for the basement, first floor and second floor. The structure is mainly made of masonry walls and timber slabs. On the basement floor the masonry walls are composed of stone and lime mortar. Thicknesses of the walls are changing be-

General view

First floor

tween 2 m and 1 m and it is often 1.4 m on that floor. These walls are also forming the foundation system of the palace. On the other hand, brick and lime mortar were used on the first and second floor. The thickness of the walls in the first storey is generally 80 cm while it is 60 cm in the second floor. Cast iron clamps were also used within the walls to increase the out of plane stability of

Basement floor

Second floor

Fig. 1. Beylerbeyi Palace and the architectural plans of its floors.

Fig. 2. Structural walls and timber slab on the basement and the roof of the palace.

Fig. 3. Examples from the interior decoration of Beylerbeyi Palace.

F. Aras et al. / Construction and Building Materials 25 (2011) 81–91

the structure but the oxidation caused that material to lose its function in many walls [2]. For this reason the contribution of the metal clamps to the stability of the masonry walls is doubtful. The exterior face of the structure was covered by ‘‘küfeki” stone. Fig. 2 illustrates the structural walls on the basement and the roof of the palace. The palace is used as a museum and attracting many people because of its historical importance and charming architectural features. It is decorated with fascinating furniture and curtains. The walls have been covered with timber, stucco and normal plaster (Fig. 3). It is under the protection of Regional Directorate of National Palaces in Turkey. In order to investigate the earthquake safety of the palace the permission was taken from the state agency but it was limited to visual inspections, length measurements and ambient vibration measurements. As a result, architectural drawings of the palace have been prepared, structural system has been investigated, a laboratory based material identification has been performed over reproduced test specimens to obtain the mechanical properties of the masonry [2] and ambient vibration survey has been carried out [13]. 3. Ambient vibration survey The ambient vibration testing method is widely applied and it is a popular full-scale testing method for experimental definition of structural dynamic characteristics. This fast and relatively simple procedure has been accepted by the regional directorate of the national palaces since it was applied to Beylerbeyi Palace without disturbing the structure’s normal function. The ambient vibration testing procedure is consisted of real time recording of the vibrations and processing of the records.

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The initial test is the dynamic calibration test. During this test all sensors (seismometers) are placed on the same position in the same direction and the signals are recorded simultaneously and Fourier spectra are obtained. The differences between the spectrum amplitudes (at a particular frequency on recorded amplitude spectra for each signal) have to be taken into account for definition of the mode shapes later. Resonant frequencies of the structure can be preliminary defined using the dynamic calibration tests, but the final definition of the natural frequencies is possible after obtaining the mode shapes of vibration. After this test, the seismometers are placed at different levels and different points of the structure, but in the same direction, for simultaneous recording. This is necessary for obtaining the mode shapes of vibration. One level (point) is chosen as a reference one (usually at the top level). The duration of the recording should be long enough to eliminate the influence of possible non-stochastic excitations which may occur during the test [13]. During the ambient vibration measurements of the Beylerbeyi Palace, three Ranger type, Kinemetrics product seismometers were used and the measured signal was amplified by four-channel Signal Conditioner of a Kinemetrics product. The amplified and filtered signals from the seismometers were then collected by high-speed data acquisition system which transforms the analogue signals to digital. Special software for on-line data processing has been used to plot time history and Fourier amplitude spectra of the response at any recorded point. 3.1. Experimental results For definition of the dynamic characteristics of the Beylerbeyi Palace, ambient vibration measurements were performed at 24

Fig. 4. Disposition of the measuring points and position of the reference point T1.

Fig. 5. Seismometers in the dynamic calibration test on T2 and on the reference point T1.

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points of the structure, namely at six points on four different levels – basement, first level, second level and level of the roof. The geometry built by the measurement points, their respective location on the structure and the terminology used for the explanation

Fig. 6. Fourier amplitude spectrum recorded at the reference point, transversal direction.

Fig. 7. Fourier amplitude spectrum recorded at the reference point, longitudinal direction.

of the modes and the operations in this study are illustrated in Fig. 4. The dynamic calibration test was performed at point 20 (T2) at the roof. After that test, two seismometers were placed at the reference point 19 (T1), to measure the vibrations in transversal direction (TD) and longitudinal direction (LD), while the third Ranger seismometer was moved in all other measuring points. Fig. 5 shows the position of the seismometers on T1 and T2. The signals were collected by a high-speed data acquisition system and on-line processed for obtaining the time histories and Fourier amplitude spectra. Figs. 6 and 7 are the Fourier amplitude spectra obtained for the reference point T1, for transversal and longitudinal vibrations, respectively, while dominant frequencies are given in Table 1. For the post-processing and analysis of the recorded vibrations on all measuring points, ARTeMIS software was used. That software is based on the Peak Picking technique and Frequency Domain decomposition and provides good graphical presentation of the obtained data. Fig. 8 shows the obtained results by the analysis, with values of the resonant frequencies and damping coefficients while Fig. 9 presents the mode shapes. As can be seen from the obtained data, the first natural frequencies for both orthogonal directions are well separated: for transversal vibration 2.7 Hz and for longitudinal vibration 3.6 Hz. The obtained mode shapes are showing complex vibration of the structure, although it has a regular and symmetric shape in plan and in elevation. This complexity is probably caused by non-uniform material properties of the walls. Secondly, it is obvious that timber slab system of the palace does not provide horizontally rigid diaphragm action. Thereby the partial movements form the mode shapes like in the first and third mode. The results also indicated that the structure may be assumed as fixed supported [13].

4. Numerical dynamic identification Table 1 Dominant frequencies of the palace recorded at the reference point. Direction

Transversal Longitudinal

4.1. Numerical model of the palace

Dominant frequencies (Hz) F1

F2

F3

F4

F5

F6

2.8 3.6

4.2 4.8

5.2 8.2

8.0 9.0

10.8 10.0

14.6 –

Mode Frequency (Hz) Period (s) Damping ration (%)

Reflecting the determined architecture, structural carrying system and identified material properties [2] a three-dimensional finite element model has been prepared. The masonry walls were modelled by shell elements and frame elements were used for

Mode 1

Mode 2

Mode 3

Mode 4

Mode 5

Mode 6

Mode 7

Mode 8

2.697

3.593

4.147

5.208

7.927

8.339

10.56

14.55

0.371

0.278

0.241

0.192

0.126

0.120

0.095

0.069

2.653

2.6

1.937

2.516

2.542

2.397

1.045

2.549

Fig. 8. Peak-picking of the dominant frequencies, performed by ARTeMIS Extractor and modal properties of the palace.

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Mode 1: Movement of the left side along with the TD

Mode 2: Body movement of the structure along with the LD

Mode 3: Movement of the land side-middle part along with the TD

Mode 4: Movement of the left and right side together along with the TD

Mode 5: Slight body movement along with the LD except searight side corner.

Mode 6: Movement of the middle part, including sea and land side, along with the TD

Fig. 9. Obtained mode shapes by ARTeMIS Extractor [13].

Fig. 10. Three dimensional model of the palace with timber slab.

the column and timber slab members. Although there are advanced analytical techniques based on the theories of micromodelling, macromodelling and the theory of composites [14–16] for masonry, they were not used in the numerical model of Beylerbeyi Palace due to the complex geometry and big size of the structure. In the light of the results of AVS the structure was assumed to have fixed support at the base. Mode shapes obtained from the experimental study have shown that; although the timber slabs do not supply rigid diaphragm action on the storey level, it may be effective to connect the masonry walls. In this respect, they must be included in the numerical model. On the other hand their inclusion increases the size of the computer model very much. In order to decrease the size of the model 20  40 cm2 timber beams with one meter spacing were used instead of 8  40 cm2 timber beams with 40 spacing. Thereby, the planer dimension of a shell element was increased to one meter. Secondly, in order to eliminate the simple modes which contain the movement of only timber members, zero mass was assigned to those members. The mass was transferred to the walls directly. Finally, the numerical model was constructed with the stone masonry (modulus of elasticity, E = 50,000 MPa, unit weight, c = 26.5 kN/m3) [17], brick masonry (modulus of elasticity, E = 2500 MPa, unit weight, c = 22.4 kN/m3) [2], oak cushion beams (modulus of elasticity, E = 12,500 MPa, unit weight, c = 7.2 kN/m3) and fir slab beams (modulus of elasticity,

E = 9700 MPa, unit weight, c = 7.2 kN/m3) [18,19]. The model resulted in a total of 15,662 nodes, 3808 frames and 13,749 shell elements. The construction of the numerical model is illustrated in Fig. 10. Table 2 Dynamic parameters of the numerical model. Total mass Mass Mode Period Mass (s) participation participation participation ratio in LD ratio in TD ratio in LD

Total mass participation ratio in TD

1 2 3 4 5 6 7 8 9 10 11 12 13 – 58 59 60

0.120 0.230 0.240 0.240 0.310 0.310 0.310 0.330 0.330 0.330 0.330 0.340 0.340 – 0.710 0.710 0.920

0.361 0.317 0.301 0.282 0.277 0.276 0.249 0.242 0.236 0.229 0.227 0.224 0.221 – 0.019 0.009 0.009

0.000 0.003 0.100 0.120 0.000 0.074 0.073 0.000 0.003 0.000 0.014 0.001 0.000 – 0.054 0.210 0.000

0.120 0.120 0.005 0.001 0.075 0.002 0.000 0.012 0.000 0.000 0.002 0.011 0.000 – 0.000 0.000 0.200

0.000 0.003 0.110 0.220 0.220 0.300 0.370 0.370 0.370 0.370 0.390 0.390 0.390 – 0.710 0.920 0.920

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Mode 1

Mode 2

Mode 3

(T=0.361 sec, MPR=0.12-TD) Mode 7

(T=0.317 sec, MPR=0.12-TD) Mode 13

(T=0.301 sec, MPR=0.10-LD) Mode 59

(T=0.249 sec, MPR=0.07-LD)

(T=0.221 sec, MPR=0.0005-Vertical )

(T=0.009 sec, MPR=0.21-LD)

Fig. 11. Important modal parameters obtained from numerical model.

4.2. Modal analysis of the structure For the dynamic analysis of Beylerbeyi Palace, Ritz-vector analysis was performed. In order to catch 90% mass participation ratio at least 60 modes should be accounted, because many modes have small mass participation and they represent local movement in the palace due to lack of rigid floors. Table 2 summarizes the dynamic data of the analysis. The dynamic properties and mode shapes of the structure, illustrated in Fig. 11, have revealed important characteristics of the structural behaviour. These characteristics, as ordered below, distinguish Beylerbeyi Palace from a regular and basic structure.  Timber slabs could not provide diaphragm behaviour to the structure. For this reason local modes were observed (Fig. 11).  Due to small mass gathered on the storey levels, lumped mass behaviour was not observed.  Although it was tried to suppress by assigning zero mass to the timber members, they were effectuating the modes themselves (Mode 13 in Fig. 11).  Due to the high modulus of elasticity and thick cross-section, participation of the basement floor into the dynamic behaviour of the structure has been observed in the higher modes. (59th mode in Fig. 11). 5. Adjustment of the numerical model Several identification methods are available to determine modal properties of the structures. While several applications are reported in the literature for reinforced concrete or steel buildings, less is known about masonry buildings [4,5,8,9]. The methods aim to minimize the difference between theoretical and experimental modal properties. In present study instead of using one of the identification algorithms, the numerical model (NM) of Beylerbeyi Palace is updated by compare-alter-check based iterative solutions. The general modal and structural characteristics of the palace, such as high number of degree of freedom, possible vari-

ability in the material properties of masonry and limited number of measurements for AVS prevent the use of those algorithms. In the iteration, the mode shapes and the frequencies (or periods) of the structure, obtained by experimental and numerical surveys would be compared and the young modulus of masonry in required part would be altered. The Young’s modulus of the material was obtained from laboratory tests on reproduced (not original) specimens and did not account the metal clamps used within the masonry walls in the palace [2]. For this reason it can show great diversity in the model. Finally the effect of the alteration was checked if the mode of numerical model fitted the AVS mode or not. The calibration process is explained below as a bunch of steps. In each step, mode shapes of AVS and NM are shown, calibration process is summarized and the results of the calibration are explained. It should be noted that; after each step of calibration the model was updated and next steps’ dynamic parameters were obtained from the altered model. 5.1. First step in calibration The first modes of both AVS and NM exhibit the same type of movement as shown in Fig. 12. This similarity also shows that a well constructed NM exists. On the other hand, there is a small difference between the period values. The first calibration aims to conceal the discrepancy between the periods. The calibration coefficient is calculated as the square of the ratio of the periods due to the fact that [20,21];

T ¼2p  C¼

T1 T2

rffiffiffiffiffi m K

2

Modulus of elasticity of the structure, E was decreased to 0.947  2500 = 2367 MPa in order to obtain the first mode period as 0.371 s.

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First Mode: T=0.361 sec

First Mode: T=0.371 sec

Material legend in the palace

2

⎛ 0,361 ⎞ Calibration Coefficient, c = ⎜ ⎟ = 0.947 ⎝ 0,371 ⎠

Young modulus, E1=2367 MPa

Fig. 12. First modes of AVS and NM.

Fourth Mode: T=0.192 sec

Second Mode: T=0.325 sec

After the calibration step

2

⎛ 0,325 ⎞ Calibration Coefficient, c = ⎜ ⎟ = 2.865 , ⎝ 0,192 ⎠

E1=2367 MPa,

E2=6781 MPa

Fig. 13. Fourth mode of AVS, second mode of NM and the result of calibration.

5.2. Second step in calibration As can be seen in Figs. 9 and 11, second mode shapes are totally different for NM and AVS results. In the NM the second mode is the movement of the right hand side while it is the longitudinal movement in AVS. For this reason, in NM this mode should be shifted to higher modes. This can be achieved by increasing the E of the moving part. Since the movement is in the transverse direction, only the wall along with that direction will be altered. AVS results indicate that the movement of the right hand side in transverse direction belongs to fourth mode. In this respect, a calibration should be performed between the second mode of the NM and fourth mode of the AVS as illustrated in Fig. 13. It aims to shift the second mode of NM to the fourth mode of AVS. Value of E of the wall in the transverse direction of the right hand side of the structure is increased by 2.87 and new E is calculated as 2.865  2367 = 6781 MPa. This alteration has caused to have the second mode shape of the structure as the movement of the sea side along with longitudinal direction and the third mode as the movement of the left side along with longitudinal direction. Moreover, the fourth mode is the movement of the mid part in transverse direction, fifth mode is the movement of the land side in longitudinal direction, sixth mode is the out of plane movement of the entrance wall in the left part and finally seventh mode is the movement of the right part in the transverse direction. These modes represent the movements in the first four modes of AVS. In other words, second, third and fifth modes are forming the second mode of the AVS, the fourth mode is the third mode of AVS and

finally seventh mode belongs to the fourth mode of AVS. Since no measurement has been taken from the entrance wall, on the left side, it is impossible to detect the sixth mode (see mode 7 in Fig. 11 and note that no measurement had been taken from the active wall segment). 5.3. Third step in calibration Third calibration is based on fitting the second mode of the NM to AVS. For this reason modulus of elasticity of the exterior walls, on the sea side of the palace along the longitudinal direction, is increased (Fig. 14). E of the wall in the longitudinal direction of the sea side of the structure is increased by 1.235 and new E is calculated as 1.235  2367 = 2923 MPa. This alteration did not change the mode shapes. 5.4. Fourth step in calibration The next calibration aims to change the order of the fourth and fifth modes of the model in order to make three consecutive modes to form the second AVS mode. If this can be achieved, the third mode of AVS will appear directly. For this reason the active walls in the fourth mode of NM will have bigger modulus of elasticity and this mode will be shifted to a higher mode. For this aim, the calculated modulus of elasticity from the third step is used. Fig. 15 shows the active mass in the fourth mode of model, its respective mode in AVS and result of the fourth step in calibration.

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Second Mode: T=0.278 sec

After the calibration step

Second Mode: T=0.309 sec 2

⎛ 0,309 ⎞ Calibration Coefficient, c = ⎜ ⎟ = 1.235 , E1=2367 MPa, E2=6781 MPa, E3=2923 MPa ⎝ 0,278 ⎠ Fig. 14. Second mode of NM and AVS and the result of calibration.

After the calibration step

E1=2367 MPa, E2=6781 MPa, E3=2923 MPa Fig. 15. Third mode of AVS and fourth mode of NM and the result of calibration.

Final alteration gave the desired order of mode shapes. According to that order, the first mode shapes of NM and AVS are exactly the same, second mode of AVS was formed by second, third and fourth modes of NM, third mode of AVS is the fifth mode of NM and finally the fourth mode of AVS is formed by seventh and eighth modes of the NM. The sixth mode of the NM is the movement of the entrance, on the left side, in the longitudinal direction. This movement is a local movement and can not be included in AVS since there is no measurement at that location.

5.5. Fifth step in calibration Although rigid diaphragm action is out of question for the structure, the walls are interconnected to each other by timber elements. For this reason alteration of modulus of elasticity is effective on not only the modal period of the wall itself but also the overall structural modes. In that respect, a final revision should be made to catch the appropriate periods with three different moduli of elasticity. The final values are; E1 = 2315 MPa, E2 = 8000 MPa

Table 3 Dynamic parameters of the calibrated numerical model.

Fig. 16. Determined modulus of elasticity.

Total mass Mass Mode Period Mass (s) participation participation participation ratio in LD ratio in TD ratio in LD

Total mass participation ratio in TD

1 2 3 4 5 6 7 8 9 10 11 12 13 – 58 59 60

0.120 0.120 0120 0.130 0.210 0.210 0.220 0.340 0.340 0.350 0.350 0.350 0.360 – 0.710 0.740 0.920

0.371 0.289 0281 0.270 0.260 0.253 0.231 0.230 0.229 0.225 0.221 0.217 0.207 – 0.018 0.009 0.009

0.000 0.005 0120 0.190 0.002 0.034 0.003 0.005 0.000 0.062 0.000 0.000 0.001 – 0.046 0.180 0.026

0.120 0.000 0001 0.005 0.083 0.000 0.009 0.120 0.000 0.010 0.000 0.005 0.008 – 0.013 0.026 0.180

0.000 0.005 0130 0.310 0.310 0.350 0.350 0.360 0.360 0.420 0.420 0.420 0.420 – 0.720 0.900 0..920

F. Aras et al. / Construction and Building Materials 25 (2011) 81–91

Mode 1: Movement of the left side along with the transversal direction

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Mode 1: Movement of the left side along with the transversal direction

Fig. 17. The first mode of CNM is exactly the same as the first mode of AVS.

Mode 2: Movement of the left side along with the longitudinal direction

. Mode 3: Movement of the sea side along with the longitudinal direction

Mode 4: Movement of the land side along with the longitudinal direction

Mode 2: Body movement of the structure along with the longitudinal direction

Fig. 18. Three consecutive modes (second, third and fourth modes) of CNM form the second mode of AVS.

and E3 = 3100 MPa. At the end of this final revision Calibrated Numerical Model (CNM) is obtained with three different moduli of elasticity (Fig. 16). Dynamic parameters of this calibrated model are summarized in Table 3. 5.6. Results of calibration process Calibrated model’s mode shapes and respective AVS modes are summarized through Figs. 17–20. In the calibration process the most important challenge is that; one mode of the AVS can be formed by one or more consecutive modes of the CNM. In this study it is determined that, the first mode of the CNM is exactly the same as the first mode of AVS, the second, third and fourth modes of CNM are forming the second mode of AVS, the fifth mode of CNM is the third mode of AVS and finally the fourth mode of AVS is the combination of the seventh and the eighth modes of CNM. The sixth mode of the CNM is a local mode (7th mode in Fig. 11) and it could not detected by AVS measurements.

The performed alteration is not unique and further alterations are possible to make modes of NM more similar to those of AVS. For example additional steps can be added to eliminate the discrepancy between the second, third and fourth modes of CNM. On the other hand, this visual elimination is very difficult and increases the modulus of elasticity. Furthermore, the limited number of AVS measurements prevents the fine tuning of numerical model. The AVS mode shapes were characterized by 24 points and most importantly the 6 points on the most top level were active through these modes. However, the numerical model of the palace was constructed by 13,749 shell elements. Under these conditions the finer tuning of the numerical model is not favoured. Finally, explained five steps of calibration are assessed as adequate to correct the numerical model. The second important parameter is the period of the modes, seen as separate modes in CNM. For the calculation of mutual period, each mode period and mass participation ratios were accounted since mass participation ratio refers to active mass in

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Mode 5: Movement of the middle part along with the transversal direction

Mode 3: Movement of the land side-middle part along with the transversal direction

Fig. 19. The fifth mode of the CNM is the same as the third mode of the AVS.

Mode 7: Movement of the left side along with the transversal direction

Mode 8: Movement of the right side along with the transversal direction

Mode 4: Movement of the left and right side along with the transversal direction

Fig. 20. Two consecutive modes (seventh and eighth modes) of CNM form the fourth mode of AVS.

Table 4 Obtained modes at the end of the calibration process. Ambient vibration survey

Numerical analysis

Mode

Period (s)

Definition of mode

Mode

Period (s)

Mass PF (%)

Combined mode

Period (s)

Mass PF (%)

1

0.371

Movement of the left hand side in TD

1

0.371

12-TD

1

0.371

12-TD

2

0.278

Movement of the structure in LD

2 3 4

0.289 0.281 0.270

0.5-LD 12-LD 19-LD

2

0.274

32-LD

3 –

0.241 –

Movement of the mid part in TD –

5 6

0.260 0.253

8-TD 3-LD

3

0.260

8-TD

4

0.192

Movement of the left and right part in TD

7 8

0.231 0.230

1-TD 12-TD

4

0.230

13-TD

the mode. The period was obtained by weighted average as shown below:

Ta ¼

  T 1  PF 1 þ T 2  PF 2 þ    þ T n  PF n PF 1 þ PF 2 þ    þ PF n

As a result, Table 4 was constructed to show the modal parameters obtained from AVS and numerical analyses, before and after the calibration.

6. Conclusion The modal frequencies, damping ratios and mode shapes of historical Beylerbeyi Palace have been determined by ambient vibration survey. It is seen the modes are generally formed by partial movements except the second mode. The non-uniform material

properties and the lack of rigid floor diaphragm are grasped as the main reasons of this modal behaviour. The numerical modal analysis of the palace with a uniform material property has also shown that the modal behaviour is characterized by local modes. By using the results of experimental study a more accurate numerical model is tried to be achieved. Step by step modulus of elasticity of the masonry has been altered and after five steps of alteration results similar to experimental ones have been obtained by numerical model. The alteration process showed that, one mode of AVS can be seen as one or more separate modes of numerical analysis. The first four modes of the AVS were obtained. The general dynamic properties, such as, lack of rigid floors, distributed mass through the height, local modes, and small mass participation ratios, for modes of the calibrated model were the same as those of the initial model. At least 60 modes were required to have 90% mass participation in longitudinal and transverse direction.

F. Aras et al. / Construction and Building Materials 25 (2011) 81–91

Calibrated numerical model has shown that the walls in the left hand side of the structure have smaller modulus of elasticity than the ones on the right hand side. The big difference may stem from the different use of the cast iron reinforcements within the masonry wall parts in the palace or the iron reinforcement of left hand side may be exposed to oxidation. Secondly, the existing damage in the structure may be a reason of weaker masonry on the left hand side. The interior faces of the rooms were decorated by timber carving. For this reason, the existing condition of the masonry could not be investigated. Deterioration or cracks may be the main reason for weaker material. References [1] PROHITECH, Earthquake Protection of Historical Structures by Reversible Mixed Technologies, Specific Targeted Research or Innovation Project; 2004. [2] Aras F. Earthquake protection of Beylerbeyi Place by reversible mixed technologies. Ph.D. Thesis, Bogazici University, Istanbul; 2007. [3] Beolchini GC, Vestroni F. Experimental and analytical study of dynamic behaviour of a bridge. J Struct Eng ASCE 1997;123(11):1506–11. [4] Vestroni F, Beolchini GC, Antonacci E, Modena C. Identification of dynamic characteristics of masonry buildings from forced vibration tests. In: Proceedings of the 11th world conference on earthquake engineering; 1996. [5] Genovese F, Vestroni F. Identification of dynamic characteristics of a masonry building. In: Proceedings of the 11th European conference on earthquake engineering; 1998. [6] Lus H, Betti R, Longman RW. Identification of linear structural systems using earthquake-induced vibration data. Earthquake Eng Struct Dynam 1999;28: 1449–67.

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[7] Benedetti D, Gentile C. Identification of modal quantities from two earthquake responses. Earthquake Eng Struct Dynam 1994;23(4):447–62. [8] Gentile G, Saisi A. Ambient vibration testing of historic masonry towers for structural identification and damage assessment. Constr Build Mater 2007;21: 1311–21. [9] De Sortis, Antonacci E, Vestroni F. Dynamic identification of a masonry building using forced vibration tests. Eng Struct 2005;27:155–65. [10] Ahmadian H, Gladwell GM, Ismail F. Finite element model identification using modal data. J Sound Vib 1994;172(5):657–69. [11] Mottershead JE, Friswell MI. Model updating in structural dynamics: a survey. J Sound Vib 1993;167(2):347–75. [12] Capecchi D, Vestroni F. Monitoring of structural systems by using frequency data. Earthquake Eng Struct Dynam 1999;28:447–61. [13] Krstevska L, Taskov L. Ambient vibration measurements of Beylerbeyi Palace. IZIIS report no. 2006-030, Skopje; 2006. [14] Lopez J, Oller S, Onate E, Lubliner J. A homogeneous constitutive model for masonry. Int J Numer Methods Eng 1999;46:1651–71. [15] Anthoine A. Derivation of the in-plane elastic characteristics of masonry through homogenization theory. J Solid Struct 1995;32(2):137–63. [16] Pietruszcak S, Niu X. A mathematical description of macroscopic behaviour of brick masonry. J Solid Struct 1992(29):531–46. [17] Yüzer E, Görür N, Gürdal E, Vardar M. Dolmabahçe sarayında kullanılan tasßların korunmusßluk durumlarının, ayrısßma nedenlerinin belirlenmesi ve koruma ve onarım yöntemlerinin saptanması. ITU Gelisßtirme Vakfı. Technical report no. 01-103 [in Turkish]. [18] Bozkurt AY, Göker Y. Fiziksel ve mekanik ag˘aç Teknolojisi. Istanbul: Istanbul University Press; 1996 [in Turkish]. [19] Bozkurt AY, Erdin N. Ag˘aç teknolojisi. Istanbul: Istanbul University Press; 1997 [in Turkish]. [20] Chopra A. Dynamics of structures. Upper Saddle River (NJ): Prentice Hall; 2001. [21] Hart GC, Wong K. Structural dynamics for structural engineers. New York: John Wiley & Sons, Inc.; 1999.