Static and Dynamic Indicators for Composite Bridges Naida Ademovic(&) Faculty of Civil Engineering, Department of Structures and Materials, University of Sarajevo, Sarajevo, Bosnia and Herzegovina
[email protected]
Abstract. Standard non destructive static and dynamic testing of bridges after their reconstruction serves as indicators regarding the capacity of the structure and their durability. Several steel concrete composite girder bridges were investigated and compared. Measurement from the static tests were used to make some correlation between the stiffness of the structure and dynamic properties. From the investigations it was clear that different truck weight has a direct influence of the dynamic characteristics, requiring a standardization of testing vehicle. Temperature influence was more than indicative. Keywords: Composite steel concrete Girder bridges Dynamic properties Stiffness Frequency Deflection Temperature effects on natural frequencies
1 Introduction Nondestructive load testing is an effective approach to measure the structural response of a bridge under various loading conditions and to determine its structural integrity. This load-test program integrates an optical surveying system, a sensor dilatation measurement on steel and concrete parts of the structure and deflection analysis by the use of Inductive Displacement Transducer. The bridge is exposed to static and dynamic loading in order to evaluate the behavior of the bridge. The actual response of a bridge to loads is usually better than what the theory dictates [1]. Factors that contribute to the load capacity difference include unintended composite action, load distribution effects, participation of parapets, railings, curbs, and utilities, material property differences, unintended continuity, participation of secondary members, effects of skew, portion of load carried by deck, and unintended arching action due to frozen bearings [1, 3]. Load testing in Bosnia and Herzegovina is defined by [2] and represents as an “effective means of evaluating the structural response of a bridge.” The purpose of conducting load testing on existing bridges is to evaluate their structural response without causing damages. In this respect, as load testing is usually conducted in a non-destructive manner resulting that it may be defined as such [3]. Every testing procedure is in one segment the same and in the other specific for each bridge. For each bridge a clear program needs to be set with clear testing objectives and load configurations, selection and placement of instrumentation, analysis technique, evaluation and comparison of test results and analytical results [3]. © Springer International Publishing AG 2018 M. Hadžikadić and S. Avdaković (eds.), Advanced Technologies, Systems, and Applications II, Lecture Notes in Networks and Systems 28, https://doi.org/10.1007/978-3-319-71321-2_59
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2 Static and Dynamic Tests Static load testing of bridges is conducted by the utilization of the trucks of certain weigh depending on the span and width of the bridge. In testing a bridge various structural elements need to be examined. Strain or deflection-transducer gages are placed at critical locations in order to measure the deflection of the bridge upon which the strength of these elements can be determined. Survey instruments are used to measure the deflection on the asphalt layer, while deflection of the composite steel concrete girders is done by Inductive Displacement Transducer positioned underneath the girder. Stresses in the steel and concrete elements of the superstructure are obtained from the strain gages measurements glued on the structure elements. For static testing the bridge was incrementally loaded up to the design live load in order to induce maximum effects. Previously analytical model was done in order to compare the experimental results with the calculations at each conducted load step. At the final stage the measured data (deformations, strains-calculated stresses) was compared with the obtained analytical results and adequate conclusions and recommendations were given. Dynamic load testing is performed by exciting the vibration of the bridge and by measuring its properties after the excitation has ceased. There are several ways to excite the bridge: eccentric rotating masses, impact of a heavy weight and passage of a loaded truck. The most realistic is the movement of the vehicles. By the dynamic loading tests controlling parameters of the dynamic behavior of the bridges are determined (the fundamental vibration frequency, the dynamic amplification factor and the logarithmic decrement). These quantities are relatively easy to obtain experimentally, and can give valuable information for the exploitation and maintenance of the bridge (Burdet and Corthay 1995). For dynamic loading one truck passed over a plank of 5 cm thick with different speeds. This plank is used to represent the effect of deterioration of the pavement and in this way it causes the excitation of the bridge. By varying the speed of the truck on the bridge, the full range of traffic speeds was investigated. Additionally, different trucks were used, which indicated the change in the dynamic characteristics of the bridge. This clearly indicated the influence of the truck structure interaction, connected to the different weight of the trucks. This is one of the elements that has to be taken into account during the calculations as well as the need for standardized trucks for dynamic testing is required in order to eliminate this influence. The influence of the temperature on the dynamic characteristics was investigated as well indicating a clear dependency of frequency upon temperature.
3 Conducted Experimental Tests 3.1
Comparison of Static Values
Static and dynamic analysis was conducted on five composite steel concrete bridges. Detailed comparison of the analytical and experimental results is given in the
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individual reports of each bridge [4–6]. The bridges composed of either one or several simple beams from 11 to 36.75 m. Modeling of all bridges was done with the application of the program Tower [7]. All the bridges were modeled as 3D structures, static and dynamic calculations were done, giving internal forces, stresses and deflections for symmetric and nonsymmetrical loading phases and comparison was done with the measured values on the site [4–6]. Characteristic cross section of only two the bridges is illustrated in (Fig. 1) for Bridge over Krivaja and in (Fig. 2) for the bridge over Sapna river. Details regarding other bridges can be found in [4–6].
Fig. 1. Typical cross section of the bridge and elevation view of the bridge in Krivaja [4]
Fig. 2. Typical cross section of the bridge and elevation view of the bridge in Zvornik [6]
Figure 3 shows the static testing of the bridge. As the analyzed bridges have different spans, lengths and height of the superstructure and in that respect the maximum loading to which the structures were exposed was different. In order to be able to make adequate comparisons correction of the deflection was done in respect to the geometrical dimensions of the bridge and loading. The deflection was corrected utilizing the formula:
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Fig. 3. Static testing of the bridge in Zvornik [6]
vk ¼ where: v deflection F loading L span of the bridge B width of the bridge i index for real value k index for referent value
Fk L3k Bi Fi L3i Bk
ð1Þ
From the conducted comparison it is evident that for all the bridges the measured values are lower than the calculated ones indicating that the constructed bridge has a higher stiffness in respect to the calculated one, raising the safety factor to a certain amount. It is interesting as well to note that the stressed in concrete have not reached not even 50% of the calculated value. This is a clear indication that concrete is most probably made of a higher quality than what is taken in the calculation as per the design. This could be checked by taking out the concrete cylinders from the bridge and conducting compression tests, or better with the application of some Non-destructive tests like Schmidt rebound hammer test and the ultrasonic pulse velocity test. However, in conducting such analysis special care should be taken into account [8–10]. Combined NDT methods (also known as SonReb method) yield better estimations than single NDT methods. The results also show that the SVMs model is more accurate than
L/H
23.25 20.00 23.00
Bridge
Krivaja Zvornik Donja Bioča
Stresses in steel (MPa) Cal. Meas. 36.27 30.24 49.60 41.70 35.41 26.56 16.6 15.9 25.0
Difference (%)
Stresses in concrete (MPa) Cal. Meas. −1.29 −0.20 −0.98 −0.35 −0.88 −0.36 84.5 64.3 59.0
Difference (%)
Deflection v (mm) Cal. Meas. 13.98 12.81 14.55 13.69 7.52 7.15
Table 1. Comparison of calculated and measured static values of different bridges
8.4 5.9 4.9
Difference (%)
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the statistical regression model [10, 11]. Stress in the steel is lower in the average of around 19% indicating as well good mechanical characteristics of the steel. In general it can be stated that the constructed bridge has a higher stiffness and better mechanical characteristics compared to the designed values (Table 1). 3.2
Comparison of Dynamic Values
Theoretical dynamic analysis was conducted which consists of bridge modeling and determination of the theoretical dynamic parameters which are than compared with the measured values on the site [12]. The main dynamic characteristics being: frequency, the dynamic amplification factor and the logarithmic decrement. As well the modal parameters are often sensitive to changing environmental conditions such as temperature, humidity, or excitation amplitude. Environmental conditions can have as large an effect on the modal parameters as significant structural damage, so these effects should be accounted for before applying damage identification methods. This is something that should be monitored in the structural health monitoring systems. Examination of the natural frequency and temperature data from the continuous monitoring system revealed that natural frequency and temperature were strongly correlated and that the relationship was nonlinear [13]. In order to grasp this effect, the dynamic testing was done during different weather conditions, day and night, and at temperature of 5 and 22°C. Figure 4 shows the track passing over the 5 cm plank at Zvornik bridge and the position of the accelerometers. Figure 5 shows the vertical excitation of the bridge when the truck passed having the speed of 20 km/h is shown in Fig. 5a. Finally the calculated power spectra using the FFT is shown in Fig. 5b for different temperatures. Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) In practice, the response function {x(t)} is recorded for a finite time duration at {N} discrete points that are evenly spaced by the sampling scheme and digitized by the analogue-to-digital conversion process. Assuming the record is periodic about the length of the sample, the Fourier Transform can be estimated as a finite series with discrete points at (t = tk) and (k = 1, N) [14]. XN=2 or ðN1Þ=2 1 2pnk 2pnk þ bn sin Þ ðan cos x(tk Þ ðxk Þ¼ a0 þ N¼1 2 N N
ð2Þ
and the coefficients are defined by, an ¼
1 XN 2pnk x cos k¼1 k N N
ð3Þ
bn ¼
1 XN 2pnk x sin k¼1 k N N
ð4Þ
2 XN x k¼1 k N
ð5Þ
a0 ¼
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Fig. 4. a Dynamic testing of the bridge in Zvornik b position of the accelerometers [6]
(b) 0,1
Accelelogram-Verical excitation -speed20km/h
Acceleration [m/sec2]
2,00 1,50 1,00 0,50 0,00 0,00
5,00
10,00
15,00
20,00
25,00
30,00
35,00
-0,50 -1,00
40,00
45,00
Power spectra [m/sec2^2]
(a)
Power Spectra 3,35
0,09
3,61
0,08 0,07
2,06 2,19
0,06 0,05 0,04 0,03 0,02 0,01
-1,50
0
-2,00
0
Time [s]
Series1
5
10
15
20
25
Frequency [Hz]
ACC106
Temp 5C
Temp 22C
Fig. 5. a Accelelogram b frequency in dependence of temperature [6]
The Fast Fourier Transform (FFT) is and optimization of the DFT where the method requires N to be an integral power of two (2) thereby reducing the execution time to compute the DFT of the response time history. The modal parameters of the system are then estimated from Fourier spectra generated from these relationships. Here only the result form the Zvornik bridge will be given as the same trend is observed in the other two bridges as well. It was clearly see that the identified natural frequencies increase as temperatures decrease, which is in consistency with the experimental results done by other researchers [14–19]. The difference in the first frequency is from 5, 5–6, 2%, and the second frequency in the range form 7, 2–9, 4% (Fig. 5). No such temperature dependence was observed for the identified damping ratios or mode shapes. The concept of a dynamic amplification factor (DAF) is used to describe the ratio between the maximum load effect when a bridge is loaded dynamically, and the maximum load effect when the same load is applied statically to the bridge. As stated in [20] generalized DAF value was applied to the worst static load case for a given bridge. This is a conservative approach since DAF depends on the length of the bridge and ignores many significant bridge and truck dynamic characteristics. However, as this is
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currently enforced rule calculations were done obeying these rules. More complex calculations would be an advantage and this is planned to be done in the future [3]. Table 2 shows the valued of the dynamic characteristics of different bridges. It is interesting to note that the difference between the calculated and measured second frequency is higher in respect to the first mode. However, the calculated and experimental results are in a rather good agreement, indicating that there are no damages on
Table 2. Comparison of calculated and measured dynamic values of different bridges Bridge
Krivaja Zvornik Donja Bioča
Frequency 1 [Hz] Cal. 3.83 2.29 5.72
Difference [%]
Meas. 3.54 7.6 2.34 2.1 5.57 2.6
Frequency 2 [Hz]
Difference Dynamic [%] amplification factor (DAF) Cal. Meas. Cal. Meas. 4.51 4.13 8.4 1.11 1.095 3.32 3.81 12.9 1.176 1.16 6.78 6.05 10.8 1.24 1.20
Difference [%]
1.4 1.4 3.2
the structures. And the consistency between the stiffness and frequency are quite obvious. The first mode of all three bridges was of a pure flexural shape. During the testing of the bridge in different temperatures the modes did not change. The calculated modes of the three bridges are presented in Fig. 6.
Fig. 6. a Krivaja bridge b Zvornik bridge c Donja Bioča bridge [4–6]
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4 Conclusion This paper presents static and dynamic load testing of composite steel concrete girder bridges in Bosnia and Herzegovina. It is clear from the analysis of all bridges that the stiffness and material quality is of a higher degree in respect to the modeled structure where the data from the design of the bridge was taken into account. Stresses in the steel reached maximum 75% from the calculated values, while stresses in the concrete were rather low. Dynamic characteristics of the structure (frequency and DAF) showed excelled correlation between the experimental and numerical results. This all indicates that the bridges at the moment do not have any defects. Examination of the natural frequency and temperature data that natural frequency and temperature were correlated. No such temperature dependence was observed for the identified damping ratios or mode shapes.
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13. Moser, P., Moaveni, B.: Environmental effects on the identified natural frequencies of the dowling hall footbridge pp. 1–42. https://pdfs.semanticscholar.org/196b/2d3792ad9d1fbe 7c5c2462481c916ec93ce5.pdf 14. Ewins, D.J.: Modal Testing: theory, practice and application, 2nd edn. Research Studies Press Ltd (2000) 15. Cross, E., Worden, K., Koo, K.Y., Brownjohn, M.W.: Modelling environmental effects on the dynamic characteristics of the Tamar suspension bridge. In: Proceedings of the IMAC-XXVIII, pp. 21–33. Jacksonville, Florida, USA, 1–4 February 2010 16. Balmes, E., Corus, M., Siegert, D.: Modeling thermal effects on bridge dynamic responses, pp 1–8. http://www.sdtools.com/pdf/IMAC06_thermal.pdf 17. Farrar, C., Doebling, S., Cornwell, P., Straser, E.: Variability of modal parameters measured on the Alamosa Canyon Bridge. In: Proceedings of SPIE, The International Society for Optical Engineering, vol. 3089, pp. 257–263 (1997) 18. Alampalli, S.: Influence of in service environment on modal parameters. In: Proceedings of the 16th International Modal Analysis Conference, pp. 111–116. Santa Barbara, California (1998) 19. Hu, W.-H., Mountinho, C., Magalhaes, F., Caetano, E., Cunha, A.: Analysis and extraction of temperature effect on natural frequencies of a footbridge based on continuous dynamic monitoring. In: Proceedings of the 3rd International Operational Modal Analysis Conference, pp. 55–62. Portonovo, Italy (2009) 20. Rule book on technical normative for determination of the loads on bridges. Official Gazette, Belgrade (1991) (in Serbian language)
