structural performance evaluation of arch type long span...

Indian Journal of Engineering & Materials Sciences Vol. 23, April & June 2016, pp. 188-202

Structural performance evaluation of arch type long span highway bridge

Ahmet Can Altunişik* & Alemdar Bayraktar Karadeniz Technical University, Department of Civil Engineering, 61080, Trabzon, Turkey

Received 11 September 2014; accepted 16 October 2015

This paper describes an arch type long span highway bridge, its finite element modeling, experimental measurements, finite element model updating using some uncertain parameters, and structural performance evaluation before and after model updating. For this purpose, Birecik Highway Bridge located on the 81st km of Şanlıurfa-Gaziantep state highway over Fırat River in Turkey is selected as a numerical example. The bridge consist of five arches, each of arch has a 55 m main span. The total bridge length is 300 m and width of bridge is 10 m.The initial finite element model of the arch type long span highway bridge is modelled using SAP2000 program to extract the analytical dynamic characteristics. Operational modal analysis method is used to extract dynamic characteristics using enhanced frequency domain decomposition method. Obtained dynamic characteristics are compared with each other and finite element model of the bridge is updated to reduce the differences by changing of some uncertain parameters such as section properties, damages, boundary conditions and material properties. At the end of the study, structural performance of the highway bridge is determined under dead load, live load, and dynamic loads before and after model updating to specify the updating effect. Displacements, internal forces and stresses are used as comparison parameters. From the study, it is seen that the ambient vibration measurements are enough to identify the most significant modes of long span highway bridges. Maximum differences between the natural frequencies are reduced averagely from 49.1% to 0.6% by model updating. A good harmony is found between mode shapes after finite element model updating. It is demonstrated that finite element model updating has an important effect on the structural performance of the arch type long span highway bridge. Maximum displacements, axial forces, bending moments and compressive stresses are reduced 35.7%, 38.9%, 47.05%, and 29.6%, respectively.

Keywords: Birecik highway bridge, Dynamic characteristics, Enhanced frequency domain decomposition, Finite element model updating, Long span highway bridge, Operational modal analysis, Structural performance evaluation.

Birecik arch type long span highway bridge located on the 81st km of Şanlıurfa-Gaziantep state highway over Fırat River in Turkey. Because of the fact that the bridge is the sole in this part of Fırat, it has a major logistical importance. The construction of the bridge was started in June 1951 and the bridge was opened the traffic in April 1956. The bridge is the longest concrete highway bridge of Turkey considering the construction date. The bridge consist of five arches, each of arch has a 55 m main span. The total bridge length is 300 m and width of bridge is 10 m. The bridge arches have rigid connectivity at middle spans and side supports. But, right and left side of the middle points of slabs are constructed using joints. Columns, beams, arches, decks and foundations were constructed as reinforced concrete. Some views of general appearance, joints and support types of the bridge are given in Fig. 1.

Among all types of civil engineering structures, long span highway bridges attract the greatest interest

for studies of structural performance1. To achieve this purpose, dynamic testing under operational conditions called as non-destructive experimental technique is steadily increasing in popularity nowadays. To determine the static, dynamic, linear and nonlinear structural performance of this type of the structures more accurately, finite element models must be reflected of real conditions as soon as possible. But as is known, it is usual to make simplifying assumptions in the development of finite element models. Because, the finite element models are constructed on the basis of highly idealized engineering blueprints and designs that may or may not truly represent all the physical aspects of an actual structure. When experimental measurement tests are performed to validate the analytical model commonly natural frequencies and mode shapes, do not coincide with the expected results from the finite element model. These discrepancies originate from the uncertainties in simplifying assumptions of structural geometry, materials, as well as inaccurate boundary conditions2. So, analytical dynamic

—————— *Corresponding author (E-mail: [email protected])

mailto:[email protected])

ALTUNISIK & BAYRAKTAR: ARCH TYPE LONG HIGHWAY BRIDGE

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Fig. 1—Some views of general appearance, joints and support types of the Birecik arch type long span highway bridge

characteristics must be approved by experimental techniques and finite element model of the structures must be updated to eliminate the differences.

There are many studies in the literature including finite element analyses, experimental investigations

and finite element model updating procedures of long span highway bridges. Huang et al.3 carried out the finite element analyses, dynamic tests and finite element model updating of long span highway bridges based on the ambient vibrations. Hiatt et al.4 studied about the extraction of

INDIAN J. ENG. MATER. SCI., APRIL 2016

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experimental dynamic characteristics of PSC girder bridges for finite element model updating. Altunışık et al.5 performed the ambient vibration based seismic evaluation of isolated highway bridges. Magalhaes et al.6 realized the ambient and free vibration tests of the Millau Viaduct. The viaduct is the tallest vehicular bridge in the world, with the top of a pylon rising at 343 m above the river level, and due to its total length of 2460 m. Zhou et al.7 aimed to determine the structural behaviour of deteriorated reinforced concrete highway bridges. Ubertini et al.8 practiced about the automated modal identification of engineering structures in operational conditions. Also, this procedure is applied to bridge structures as a case study. Mosavi et al.9 calibrated a high-fidelity finite element model of a highway bridge using a multi-variable sensitivity-based optimization approach. It can be seen from the literature that there is no enough studies about structural performance of long span highway bridge before and after model updating under dead load, live load and dynamic loads.

The objective of this study is to investigate the structural performance of a long span highway bridge before and after finite element model updating. Birecik Highway Bridge located on the Şanlıurfa-Gaziantep state highway is chosen as an application. The initial finite element model of the bridge is modelled using SAP2000. Operational modal analysis method is used to extract dynamic characteristics. Finite element model of the bridge is updated to reduce the differences by changing of some uncertain parameters such as section properties, damages, boundary conditions and material properties. Structural performance of the highway bridge is determined under dead load, live load, and dynamic loads before and after model updating to specify the updating effect. Formulation

Ambient excitation does not lend itself to frequency response function (FRFs) or impulse response function (IRFs) calculations because the input force is not measured in an ambient vibration test. Therefore, a modal identification procedure will need to base itself on output-only data10. There are several modal parameter identification methods available. These methods are developed by improvements in computing capacity and signal processing procedures. In this study, Enhanced

frequency domain decomposition (EFDD) in the frequency domain is used for modal parameter extraction.

EFDD method is an extension to FDD method which is a basic technique that is easy to use. In this method, modes are simply picked locating the peaks in singular value decomposition plots calculated from the spectral density spectra of the responses. As FDD method is based on using a single frequency line from the Fast Fourier Transform analysis, the accuracy of the estimated natural frequency depends on the FFT resolution and no modal damping is calculated. However, EFDD gives an improved estimating of both the natural frequencies and the mode shapes and also includes damping11.

In EFDD, the single degree of freedom (SDOF) power spectral density (PSD) function, identified around a peak of resonance, is taken back to the time domain using the inverse discrete fourier transform. The natural frequency is obtained by determining the number of zero-crossing as a function of time, and the damping by the logarithmic decrement of the corresponding SDOF normalized auto correlation function11. In EFDD method, the relationship between unknown input and measured responses can be expressed as11,12:

Txxyy HGHG )()()()( * … (1)

where Gxx is the rxr PSD matrix of the input, r is the number of inputs, Gyy is the mxm PSD matrix of the responses, m is the number of responses, H(ω) is the mxr frequency response function (FRF) matrix, and * and superscript T denote complex conjugate and transpose, respectively. Solution of the Eq. (1) is given in detail elsewhere13-15. Finite Element Analysis

3D finite element model of the bridge is modeled using building survey drawings by SAP2000 software16. Arches, columns and beams are modeled by frame elements having three translational DOFs and three rotational DOFs at each node. Also, deck and side walls are modeled by shell elements. Expansion joints are modeled using restricted boundary conditions using very rigidity springs. Material and soil properties obtained from the laboratory tests are given in Table 1.

To determine the structural behavior of the bridge arches as soon as possible and to compare the analytical results with experimental results for the aim


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of model updating, experimental measurements were separately conducted on the each bridge arches. At the end of the experimental measurements, it is seen that frequency span of each bridge arches were parallel to each other. For this reason, initial finite element model of the bridge was constituted for one bridge arch. Improvements to be made at the arches according to the experimental measurements applied to other bridge arches and all bridge model was obtained. The arch-foundation interaction points were assumed as a rigid and fully fixed in the initial finite element model. Expansion joints between each arch were modeled using spring and link elements which have longitudinal, transverse and vertical displacements stiffness. Figure 2 shows three dimensional initial finite element model of the bridge arch.

The first five mode shapes obtained from analytical solutions of the bridge are shown in Fig. 3. From the modal analysis, a total of five natural frequencies

are attained analytically, which range between 3.940 - 9.530 Hz. The analytical mode shapes can be classified into vertical and transverse modes. Experimental Measurements

There are two basically different methods available to experimentally identify the dynamic characteristics of a structure (of any kind, including long span highway bridge): Experimental modal analysis and operational modal analysis. In the experimental modal analysis, the structure is excited by known input force (such as impulse hammers, drop weights and electrodynamics shakers) and response of the structure is measured. In the operational modal analysis, the structure is excited by unknown input force (ambient vibrations such as traffic load, wind and wave) and response of the structure is measured. Some heavy forced excitations become very expensive and sometimes may cause the possible damage to the structure and traffic congestion/be pedestrianized. But, ambient excitations such as traffic, wave, wind, earthquake and their combination are environmental or natural excitations. Therefore, the system identification techniques through ambient vibration measurements become very attractive. In this case only response data of ambient vibrations are measurable while actual loading conditions are unknown. A system identification procedure will therefore need to base itself on output-only data. In this study, operational modal analysis procedure is used to determine the dynamic characteristics of the arch type long span highway bridge.

Fig. 2—Three dimensional initial finite element model of the bridge arch

Table 1—Material properties considered in finite element analyses

Material Properties Elements Modulus of Elasticity (N/m2)

Poisson Ratio

Density (kg/m3)

Arch 3.2E10 0.2 2450 Deck 3.2E10 0.2 2450

Column 3.2E10 0.2 2450 Beam 3.2E10 0.2 2450

Foundation 3.2E10 0.2 2450 Rebar 2.0E11 0.3 7850


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Fig. 3—Analytically identified the first five mode shapes

Birecik Highway Bridge located on the 81st km of Şanlıurfa-Gaziantep state highway over Fırat River in Turkey. Because of the fact that the bridge is the sole in this part of Fırat, it has a major logistical importance. During the experimental measurements, it was seen that different type of the vehicles such as car, truck, bus, long vehicle etc. passed. But, the dimensions, weights, loads and different other parameters are not important. These are used only the vibration source. The test vehicles are not used.

Experimental measurements are performed to increase the knowledge and understanding of the behavior of a structure. This is accomplished by observing the response of a structure to a set of known conditions. In the experimental measurements, the response of the arch is measured by using B&K 8340 type uni-axial accelerometers. The minimum

frequency span and sensitivity of these accelerometers are 0.1-1000 Hz and 10 v/g. The signals are acquired in the B&K 3560 type data acquisition system and then transferred into the PULSE Lapshop software17. For parameter estimation from the Ambient Vibration Survey data, the operational modal analysis software is used18. Some views of the experimental measurements and traffic density are shown in Fig. 4.

Normal traffic over the bridge was used as a source of ambient vibration during the tests. Since input force was not measured, the use of operational modal analysis to identify modal parameters was indispensable. Three ambient vibration tests were carried out during one hour on the bridge deck. Due to the limited availability of accelerometers and data acquisition equipment, maximum 11 accelerometers for each test step could be monitored simultaneously.


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Fig. 4—Some views of the experimental measurements and traffic density

Among these accelerometers, a uni-axial was used as reference accelerometer and its location unchanged throughout the test. The others were used as roving accelerometers and were moved in order to cover all accelerometer locations at the vertical and transverse directions. Explanation of the selected measurements points are given in Fig. 5.

Singular values of spectral density matrices of the third test setup attained from vibration signals using EFDD method are shown in Fig. 6. The first five mode shapes obtained from the experimental measurements are given in Fig. 7. When the experimentally identified mode shaped compared with each other, it is seen that there is a good agreement between all results. So, only one measurement mode shapes are given with detail in Fig. 7.

Analytically and experimentally identified dynamic characteristics of the bridge are given in Table 2. When Figs 3 and 7 and Table 2 are compared with each other, it is seen that there is some differences between mode shapes and natural frequencies. The differences in the natural frequencies are obtained between 34.7% and 49.1%. Finite Element Model Updating

When the analytically and experimentally identified dynamic characteristics are compared with each other, it is seen that there is some differences between mode shapes and natural frequencies. So, finite element model of the bridge must be updated by changing of some uncertain parameters to eliminate these differences. Some deterioration was observed


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Fig. 5—The accelerometer locations for each experimental measurement

Fig. 6 – Singular values of spectral density matrices

during field investigations on the bridge such as: regional cracks at the arches and columns, deteriorations at the supports and expansion joints, foundation scouring, moisture, humidity and water infiltration, shell concrete failures due to the

Fig.7—Experimentally identified first eight mode shapes

Table 2—Comparison of the analytical and experimental dynamic characteristics

Natural frequency (Hz) Mod Number Analytical Experimental

Differences (%)

Damping ratios (%)

1 3.940 2.496 36.7 4.358 2 4.770 3.115 34.7 0.899 3 5.190 3.378 34.9 0.863 4 8.920 4.545 49.1 0.118 5 9.530 5.258 44.8 3.970

corrosions at some sections. Some views of the deteriorations explained in above can be seen in Fig. 8. According to these reasons, structural properties of all damaged sections were reduced. Also, semi rigid connections were designated at the foundations and expansion joints.

Comparison of the analytical and experimental dynamic characteristics of the bridge after finite element model updating is given in Table 3. According to Table 3, it is seen that maximum differences in the natural frequencies are reduced averagely from 49.1% to 0.60% and a good agreement is found between natural frequencies and mode shapes after model updating.

From the modal analysis of updated finite element model, a total of five natural frequencies are attained analytically, which range between 2.490-5.780 Hz. The first analytical five mode shapes obtained from analytical solutions after model updating can be classified into vertical, transverse and torsional modes. There is a good agreement is found between mode shapes after finite element model updating. It means that updated finite element model reflect the current behavior of Birecik arch type long span highway bridge more accurately.


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Table 3—Analytical and experimental dynamic characteristics after model updating

Natural frequency (Hz) Mod number Analytical Experimental

Differences (%)

Damping ratios (%)

1 2.490 2.496 0.60 4.358 2 3.050 3.115 2.08 0.899 3 3.950 3.378 14.4 0.863 4 4.300 4.545 5.39 0.118 5 5.780 5.258 9.09 3.970 The Birecik arch type long span highway bridge

consists of five arches. The regions between each arch were projected using expansion joint deck elements. The whole of the arch compartment of the bridge is constituted using updated finite element model of the one arch. Finite element model of the Birecik Highway Bridge can be seen in Fig. 9. In the finite element model, soil-structure interaction is taken into

account to determine the static and dynamic behaviour of the bridge more accurately. Structural Performance Evaluation

Finite element analyses are carried out to determine and compare the structural performance of the highway bridge before and after model updating. Finite element models of the bridge before and after model updating are constituted using SAP2000 software. The responses of the bridge are attained under deal loads, live loads and dynamic loads.

Structural performance of the bridge before finite element model updating

To determine the structural performance of the Birecik arch type highway bridge, displacements, internal forces (axial forces and bending moments) and stresses are selected as comparison parameters.

Fig. 8 – Some views of the deteriorations obtained from the field investigation


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Fig. 9—Finite element model of the Birecik arch type long span highway bridge

The maximum vertical displacements of the bridge before model updating under dead load are shown in Fig. 10. It is seen from the Fig. 10 that displacements have an increasing trend along to the joints located on the right and left side of the middle points of deck. The maximum displacements are attained as 12.2 mm. Also, vibrations and concussions were observed on these points bypassing of heavy vehicles during experimental measurements and field investigations. Finite element analyses results clearly revealed this event. Distribution of maximum internal forces such as axial forces and bending moments, and compressive strengths before model updating under dead load are given in Fig. 11. It is seen from Fig. 11 that maximum axial forces formed on the vertical structures between deck and arches as 180 kN, maximum bending moments taken place on the beams which carry the deck elements as 89 kNm, and maximum compressive strengths are obtained from the arches as 2 MPa, respectively.

The maximum vertical displacements of the bridge before model updating under increased live loads are shown in Fig. 12. It is seen from the Fig. 12 that displacements have an increasing trend along to the joints located on the right and left side of the middle

points of deck. The maximum displacements are attained as 18.2 mm. Distribution of maximum internal forces such as axial forces and bending moments, and compressive strengths before model updating under increased live loads are given in Fig. 13. It is seen from Fig. 13 that maximum axial forces formed on the vertical structures between deck and arches as 450 kN, maximum bending moments taken placed on the beams which carry the deck elements as 192 kNm, and maximum compressive strengths are obtained from the arches as 5.4 MPa, respectively.

Earthquake behaviour of Birecik arch type long span highway bridge before finite element model updating is performed using ERZ/EW component of 1992 Erzincan earthquake ground motion (Fig. 14). This earthquake occurred near the bridge region and has a magnitude value as 6.9 (M=6.9).

The maximum vertical displacements of the bridge before model updating under dynamic loads are shown in Fig. 15. It is seen from Fig. 15 that displacements have an increasing trend along to the key points of the arches and joints located on the right and left side of the middle points of deck. The


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Fig. 10—The maximum vertical displacements of the bridge before model updating under dead load

Fig. 11—Distribution of maximum internal forces before model updating under dead load


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Fig. 12—The maximum vertical displacements of the bridge before model updating under increased live load

Fig. 13 – Distribution of maximum internal forces before model updating under increased live load


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maximum displacements are attained as 26.4 mm ignoring the dead and live loads.

Distribution of maximum internal forces such as axial forces and bending moments, and compressive strengths before model updating under dynamic loads (ignoring the dead and live loads) are given in Fig. 16. It is seen from Fig. 16 that maximum axial forces formed on the vertical structures between deck and arches as 680 kN, maximum bending moments taken place on the beams which carry the deck elements as 425 kNm, and maximum compressive strengths are obtained from the arches as 7.2 MPa, respectively.

Structural performance of the bridge after finite element model updating

The structural performance of the bridge is determined after finite element model updating under dead, increased live and dynamic loads. The displacements, internal forces (axial forces and bending moments) and stresses are obtained with detail and they are used to compare the results with before finite element model updating. The results show that the distributions don’t change significantly. So, the results are given as numerical values and compared with each other by giving more specific tables to avoid the repetitions.

The maximum displacements are attained as 9.75 mm under dead loads. Maximum axial forces formed on the vertical structures between deck and arches as 110 kN, maximum bending moments taken placed on the beams which carry the deck elements as 54 kNm, and maximum compressive strengths are obtained from the arches as 1.6 MPa, respectively.

The maximum displacements are attained as 11.7 mm under increased live loads. Maximum axial forces formed on the vertical structures between deck and

Fig. 15—The maximum vertical displacements of the bridge before model updating under dynamic load

Fig. 14—Time history of ground motion acceleration of 1992 Erzincan earthquake


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Fig. 16—Distribution of maximum internal forces before model updating under dynamic load

arches as 330 kN, maximum bending moments taken placed on the beams which carry the deck elements as 103 kNm, and maximum compressive strengths are obtained from the arches as 3.8 MPa, respectively.

The maximum displacements under dynamic loads are attained as 20.8 mm ignoring the dead and live loads. Maximum axial forces formed on the vertical structures between deck and arches as 420 kN, maximum bending moments taken place on the beams which carry the deck elements as 225 kNm, and maximum compressive strengths are obtained from the arches as 5.1 MPa, respectively.

The analyses results obtained from before and after finite element model updating of arch type long span highway bridge are summarized in Tables 4 and 5. According to the comparison of Tables 4 and 5, it is seen that maximum displacements are reduced averagely 20.10%, 35.7% and 21.2% after finite element model updating for dead load, live load and dynamic load, respectively. Axial forces are reduced averagely 38.90%, 26.7% and 38.2% after finite element model updating for dead load, live load and

Table 4—Displacements, internal forces and stresses obtained before model updating

Analyses cases Analyses Results Before model updating

DL* DL*+LL* DL*+LL*+DYL* Displacements 12.2 mm 18.2 mm 26.4 mm

Axial Forces 180 kN 450 kN 680 kN Internal Forces Bending moments 89 kNm 192 kNm 425 kNm Stress Compressive 2.0 MPa 5.4 MPa 7.2 MPa

*DL: Dead load *LL: Live Load *DYL: Dynamic load

Table 5—Displacements, internal forces and stresses obtained after model updating

Analyses Cases Analyses Results After model updating

DL* DL*+LL* DL*+LL*+DYL* Displacements 9.75 mm 11.7 mm 20.8 mm

Axial Forces 110 kN 330 kN 420 kN Internal Forces Bending moments 54 kNm 103 kNm 225 kNm Stress Compressive 1.6 MPa 3.8 MPa 5.1 MPa

*DL: Dead load *LL: Live load *DYL: Dynamic load


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dynamic load, respectively. Bending moments are reduced averagely 39.30%, 46.35% and 47.05% after finite element model updating for dead load, live load and dynamic load, respectively. Compressive stresses are reduced averagely 20.20%, 29.60% and 29.15% after finite element model updating for dead load, live load and dynamic load, respectively. Conclusions

Comparing the results of this study, the following observations can be made:

(i) Initial analytical natural frequencies of the bridge were attained at ranges between 3.940-9.530 Hz for the first five modes. These can be classified into vertical modes in the z direction and transverse modes in the y direction.

(ii) The first five experimental modes were estimated within ranges between 2.496-5.258 Hz. These can be classified into vertical modes in the z direction, transverse modes in the y direction and torsional mode.

(iii) It was seen that there was some differences between mode shapes and natural frequencies. The differences in the natural frequencies were obtained between 34.7 % and 49.1%.

(iv) Finite element model of the bridge was updated to eliminate these differences by changing of some uncertain parameters such as regional cracks at the arches and columns, deteriorations at the supports and expansion joints, foundation scouring, moisture, humidity and water infiltration, shell concrete failures due to the corrosions at some sections.

(v) The differences in the natural frequencies were reduced averagely from 49.1% to 0.60%.

(vi) Finite element analyses are carried out under dead load, live load and dynamic load to determine and compare the structural performance of the highway bridge before and after model updating.

(vii) The maximum displacements are attained as 20.8 mm ignoring the dead and live loads. Maximum axial forces formed on the vertical structures between deck and arches as 420 kN, maximum bending moments taken place on the beams which carry the deck elements as 225 kNm, and maximum compressive strengths are obtained from the arches as 5.1 MPa, respectively.

(viii) According to the comparison of analyses results, it is seen that maximum displacements

are reduced averagely 20.10%, 35.7% and 21.2% after finite element model updating for dead load, live load and dynamic load, respectively.

(ix) Axial forces are reduced averagely 38.90%, 26.7% and 38.2% after finite element model updating for dead load, live load and dynamic load, respectively.

(x) Bending moments are reduced averagely 39.30%, 46.35% and 47.05% after finite element model updating for dead load, live load and dynamic load, respectively.

(xi) Compressive stresses are reduced averagely 20.20%, 29.60% and 29.15% after finite element model updating for dead load, live load and dynamic load, respectively.

Acknowledgements

This research was supported by TUBITAK and Karadeniz Technical University (KTU) under Research Grant No. 106M038, 2006.112.001.1, respectively. Also, many thanks to Assistant Professor Temel Türkerto his help during the experimental measurements. References 1 Brownjohn J M W, Magalhaes F, Caetano E & Cunha A,

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