Experimental modal analysis of a cable-stayed bridge

P. Clemente, A. Manuli, F. Saitta

Research output: Contribution to conferencePaper


The identification of the dynamic characteristics of civil structures, such as bridges are usually performed by means of forced vibration testing or ambient vibration testing. In the first method the structure is excited by shakers and it is also possible to record free vibrations subsequently an imposed displacement. With ambient vibration testing, the response of structures to actions such as wind, traffic, or seismic micro-tremors, is considered. Better results can be obtained when the ambient unknown action is a broad band signal, which guaranties the excitation of a wide range of frequency components. In traditional modal analysis the dynamic parameters of the structure are obtained in the frequency domain by Frequency Response Functions (FRF), that are the ratio between output and input Fourier transforms. Obviously, the input must be known. However for very-long and high-rise structures, such as bridges and tall buildings, it is more convenient to measure the natural ambient response to unknown excitations, because testing is cheap, fast, and not interfere with the operation of the structure. Nevertheless, responses are small, and often covered in noise. So the analysis becomes more difficult then a traditional modal analysis. A large number of methods for the extraction of modal parameters, working some in the time domain, some in the frequency domain, has been proposed. The simplest way to estimate the resonant frequencies of structures, using only output measurements, is the peak-picking method, based on the calculation of the Power Spectral Densities of the recorded signals, through use of Discrete Fourier Transform (DFT). The coherence function computed for two simultaneously recorded output signals has values close to one at the resonant frequencies and phase angle closes to zero. Mode shapes can be obtained from FRFs, evaluated, in the context of ambient testing, as the ratio between the response measured in a point of the structure and the response measured in the reference point. In this method the dynamic response at resonance is assume to be dependent only on one mode; this assumption is almost true when modes are well separated and damping is low. The identification in the frequency domain from ambient vibrations can be also pursued by means of the Frequency Domain Decomposition, which is a technique closely related to the classical approach. In the hypotheses of white noise exciting force and of lightly damped structures, through a singular value decomposition of power spectral density function matrix, we obtain a set of auto power spectral density functions, each of them corresponding to a single degree of freedom system. This technique is very suitable to identify close modes. Furthermore the singular vectors are estimates of the modal shapes. Another way to estimate modal parameters from ambient vibration testing, always by making the assumption of structure excited by a stationary random white noise (or by a filtered white noise), is to operate in the time domain. In the above mentioned case it has been shown that correlation functions between recorded signals can be expressed as a sum of decaying exponential of complex quantities. It is therefore possible to apply time domain methods using impulse response function as input, such as Polyreference Last Square Complex Exponential (LSCE), Eigensystem Realization Algorithm (ERA), Ibrahim Time Domain (ITD). In this work the results of the experimental investigations on the Indiano cable stayed bridge are explained together with the numerical elaborations of the picked data. The Indiano cable-stayed Bridge over the Arno River in Florence was completed and opened to the traffic in 1977. The 189.1 m span girder of the bridge is simply supported by two piers, which are structurally independent of the other parts of the structure. In the central portion of the girder, whose length is 128.1 m, two boxes spaced of 6.0 m compose the cross-section. They are linked one to another, at the upper and lower levels, by means of truss structures. As a result, the beam is characterized by large torsional stiffness. The boxes have a width of 4.0 m and a height variable from 2.6 m to 1.6 m. Cantilever beams start from the boxes to support the external portion of the road. In the zones near the ends the cross-section becomes a three boxes cross-section. The girder is suspended by six couples of fan-shaped stays, starting at the tops of two steel towers. Cables are regularly spread along the deck and are 3.0 m spaced from the centre line, therefore their contribution in supporting the beam torsion is very low. Six cables constrained to an external gravity anchoring compose each anchor cable. The pylons have steel box cross-section and a height of about 55.0 m from the ground. They are fully constrained at their foundations, which are founded on large piles, and linked to the cable anchoring by means of a pre-stressed concrete trass, which is supposed to support horizontal component of the tower stress. A footbridge is suspended to the girder. The experimental set up was composed by eight Kinemetrics SS1 seismometers, an HP3566A signal conditioner and a laptop. The synchronized signals from several seismometers were recorded by the acquisition system and analysed in real time in order to have a first glance at the experimental data. Based on measured data a preliminary analysis in frequency domain has been performed, in order to determine auto and cross power spectral density functions. With MATLAB routines, Welch periodogram method has been used for this analysis. In order to minimize leakage a Hanning time window function has been used. Several peaks have been observed in the spectra. The final vertical and torsional mode shapes have been obtained by assembling the results obtained from three tests with different sensors locations; a reference location has been used. In the same way another test has been used to derive lateral mode shapes of the bridge deck. This choice was related to the very few number of instruments used on the bridge deck. The experimental frequencies and mode shapes have been derived by using a simple program on purpose developed and tested for MATLAB, based on Frequency Domain Decomposition method. The results have been compared with those obtained by means of a 3D finite element model, developed using SAP2000. Experimentally and analytical mode shapes have been object of comparison for by MAC modal indicator. Thus, six modes were correct identified. In spite of the few measurement locations used a good agreement between numerical and experimental modes was obtained. This can be viewed as a further confirmation of the validity of FDD method in the identification of modal parameters of civil structures subjected to ambient vibrations and for output-only measures. © 2006 Taylor & Francis Group.
Original languageEnglish
Publication statusPublished - 2006
Externally publishedYes
Event3rd International Conference on Bridge Maintenance, Safety and Management - Bridge Maintenance, Safety, Management, Life-Cycle Performance and Cost - , Portugal
Duration: 1 Jan 2006 → …


Conference3rd International Conference on Bridge Maintenance, Safety and Management - Bridge Maintenance, Safety, Management, Life-Cycle Performance and Cost
Period1/1/06 → …


All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • Safety, Risk, Reliability and Quality

Cite this

Clemente, P., Manuli, A., & Saitta, F. (2006). Experimental modal analysis of a cable-stayed bridge. Paper presented at 3rd International Conference on Bridge Maintenance, Safety and Management - Bridge Maintenance, Safety, Management, Life-Cycle Performance and Cost, Portugal.