Theoretical-Experimental damage determination in prestressed concrete beams
Laboratorio de Estructuras
Universidad Nacional de Tucumán, Argentina.
- International Symposium on NDT Contribution to|
the Infrastructure Safety Systems, 1999 NOV 22-26 Torres,
published by UFSM, Santa Maria, RS, Brazil
The dynamic properties of engineering systems are modified by the presence of structural damage. Changes in a structure are made evident by modification of the modal parameters such as natural frequencies, modes of vibration and modal damping. All this parameters can be obtained from dynamic tests. Experimental results of a prestressed concrete beam are presented in this paper. Damage due to corrosion of the reinforcement was simulated by the progressive cut of the prestressing bars until 50% of them. The beam was tested under flexion exceeding the cracking load and, thus, concrete was also damaged. For each load step, natural frequencies and modes of vibration were measured. In based of these values, a correlation between changes in dynamic parameters and damage produced can be formulated. On the other hand, a numerical computational analysis was performed in order to validate frequencies and modes of vibration registered.
Keywords: Damage, natural frequencies, beams, prestressed concrete, tests.
Non destructive techniques for damage assessment in civil structures had a great development during the last years. Among the methods existent, a very interesting and reliable technique is that based in the proved physical fact that the dynamic properties of a system, like natural frequencies, modes of vibration and modal damping, are modified by the existence of damage (Salawu et al 1995, Salane et al 1990, Kato et al 1986 Cawley and Adams 1979, Hearn and Testa 1991, Gardner-Morse et al 1993). These parameters can be obtained from dynamic tests.
The changes in modal parameters may not be the same for each mode because they depend on the nature, location and severity of damage. Experimental results obtained from tests performed at different times bring the possibility of registering changes in structural conditions along time. Another advantage of measuring vibration responses is the global nature of natural frequencies in comparison with other damage detection methods based on local inspection. In this way measuring points are chosen according to the test situation, avoiding points of difficult access.
Modal parameters can be measured without mayor difficulties. The responses are obtained from transducers monitoring the structural response to artificially induced or ambient forces proper of the service condition of the structure. Low levels of input energy are required to produce measurable responses, since these responses are dynamically amplified by the structure.
Numerical and experimental results suggest that the lower modes of vibration are more appropriate for damage detection. However, in the opinion of other researchers, higher modes should be used to improve damage identification. Anyway, it must be taken into account that higher modes are very difficult to obtain from actual structures so that their use is not totally justified (Salawu et al 1997).
In reinforced and prestressed concrete beams, the existence of a crack in a section leads to a loss of flexional stiffness and, consequently, a reduction of natural flexional frequencies. However, according to Salawu et al (1997), it can be proved that, in the case of prestressed concrete structures, even a significant a loss of prestressing force (up to 50%) can not be detected by the changes of natural frequencies if the tests are performed with the structure unloaded. This is due to the fact that the prestressing force only modifies the cracking load and so, no changes in dynamic properties are registered under low levels of load. In opposition, in actual structures under load, when the prestressing tendons are subjected to stresses that exceed the yielding stress, a great decay in natural frequencies can be observed. By the other hand, the breakage of tensors by local corrosion may not be detectable since the changes in global stiffness that govern the changes in dynamic properties are very low.
Within the frame of a research project about corrosion effects in prestressed concrete structures (Cordero et al 1999), the simple supported prestressed concrete I beam of Fig. 2.1 was tested under static load. The test was performed in load steps of 5000, 10000, 15000, 20000 and 25000 N. After each load step, the beam was unloaded and natural frequencies were measured.
Originally, the beam had 20 prestressing bars. To simulate reinforcement damage due to corrosion they were cut, two by two, until reducing the prestressed reinforcement to a 50%. In each case, the beam was subjected to five load steps, progressively reducing the final load so as to produce no additional concrete damage.
Fig 2.1: Geometry and test setup
The dynamic measurement equipment was basically composed by acceleration transducers (600mV/V, 0-150 Hz), a dynamic amplifier (KYOWA , DPM-600) and a data acquisition equipment consistent in a computer with a differential eight channels card (PCM-DAS16/16, ComputerBoards). The data adquisition program was developed within the visual programming language HPVEE (Hewllet Packard 1998).
Acceleration transducers, numbered 1 to 4 in Fig.2.1, were located on the beam to measure dynamic response. The beam was excited with a hammer blow in the central section. The measurements were initiated a moment after so as to registered only free vibrations. As an example, accelerations registered by a transducer and the corresponding frequency spectrum are presented in Fig.2.2.
Fig 2.2: Accelerations and frequency spectrum
Test Results Analysis
In order to check and identify natural frequencies obtained from the tests, the undamaged beam was analyzed with a finite element (SAP2000 1995). 12 frame elements of I section with an equivalent Young modulus, obtained fitting the load displacement curve before cracking, were used in the analysis. The first ten modes of vibration obtained and their corresponding frequencies are presented in Table 3.1. All of them, except the last, are flexural modes.
|2 lat. |
|2 vert |
|3 vert |
|4 lat. |
|5 lat. |
|Table 3.1: Numerical natural frequencies|
In Table 3.2 frequencies registered in each one of the test stages are presented. Comparing the values for the uncracked beam with those presented in Table 3.1., it can be seen that the 3 first frequencies registered correspond to the 3 first vertical flexural modes. Due to the sensing direction of the transducers, lateral flexural modes were not measured. It can also be observed that, in agreement with the modal shape, the second vertical flexural mode was not detected by the transducers located in the central section of the beam. The fourth frequency identified in the test corresponds to the first torsional mode and according to that, was registered by transducer 2 that was laterally situated and not by transducer 1 located on the axis. By the other side, it can be seen that the values of frequencies registered in the test are always lower than those numerically obtained. For the first mode, the difference between them is low than 1% but it increases for higher modes.
|Table 3.2: Natural frequencies experimentally obtained|
Concerning the evolution of the frequencies with damage, it can be seen that the frequency that suffers more decay is that corresponding to the first vertical flexural mode. All vertical flexural frequencies are reduced as a consequence of concrete cracking in the region between loads. In opposition, torsional frequency is not altered by closed flexural cracks.
Even for the unloaded beam, changes in natural frequencies were detected when the reduction in prestressing reinforcement was equal or more than 30%. As the beam was initially cracked and with low reinforcement, a low excitation produces the opening of cracks and the flexural stiffness begins to depend strongly on the longitudinal reinforcement. The second vertical flexural frequency is no affected by the cut of the reinforcement because damage is in coincidence with a modal point. The first torsional frequency is not altered because torsional stiffness depends almost only on concrete section and not on longitudinal reinforcement, when there are not inclined torsional cracks.
The values of frequencies f/fo , obtained for the first and third vertical flexural modes, as functions of the square root of the relative stiffness obtained from load-displacement experimental curves (Cordero et al 1999) are presented in Fig.3.1. It can be seen that the first vertical flexural frequency varies almost linearly with the square root of the relative stiffness.
Fig 3.1: Variation of frequencies with stiffness
The results corresponding to frequency measurements in a prestressed concrete beam subjected to progressive damage were presented. From the analysis of them the following conclusions can be stated.
Frequency measurement is a reliable and relatively simple technique for damage identification in prestressed concrete beams.
In order to locate the transducers adequately, to be able to identify damage through changes in natural frequencies, it is strongly important to have a previous estimation of the modes and natural frequencies that are going to be measured.
The fact that a frequency is not affected by damage may indicate that damage is coincident with a nodal point or that the kind of damage existent has no influence on the corresponding stiffness. For this reason, it is recommended to locate an adequate number of sensors, so as to be able to identify and locate damage.
In beams subjected to flexion, the first flexural frequency suffers the highest decay with damage. This variation is almost proportional to the square root of the relative flexural stiffness.
Although the changes in higher frequencies are not so significant their evolution is very useful for the identification and location of damage.
Unlike others opinions, damage in presstressing reinforcement or loss of prestressing force in prestressed concrete beams can be identified through changes in natural frequencies of the unloaded structure, if it exhibits previous cracking and damage is more than, approximately, 30%.
The authors are greatly thanked to the engineers R. Benito and M. Cordero, who planned and performed the static test and to CONICET (Argentina) for the economical support.
/DB:Article /SO:NDTISS /AU:Ambrosini_D /AU:Luccioni_B /AU:Danesi_R /CN:AR /CT:NDT /CT:vibration /CT:civil /ED:2000-07
- Cawley, P. y Adams, R. D. "The location of defects in structures from measurements of natural frequencies", Journal of Strain Analysis, 4 (2), 49-57 (1979).
- Cordero M., Martel E., Benito R., Danesi R., "Efectos de la Corrosión en Elementos de Hormigón Pretensado", Mecánica Computacional, Asociación Argentina de Mécanica Computacional (AMCA), Vol. XIX, Tomo II, Septiembre 1999.
- Friswell, "A combined genetic and eigensensitivity algorithm for the location of damage in structures", Comput Struct, 1998.
- Gardner-Morse, M. Y Huston, D. "Modal identification of cable stayed pedestrian bridge", Journal of Structural Engineering, ASCE, 119 (11), 3384-3404 (1993).
- Hearn, G. Y Testa, R. B. "Modal analysis for damage detection in structures", Journal of Structural Engineering, ASCE, 117 (10), pp. 3042-3063 (1991).
- Hewllett-Packard. "Advanced Programming Techniques". HP VEE 5.0, Hewlett Packard. 1998.
- Kato, M. y Shimada, S. "Vibration of PC bridge during failure process", Journal of Structural Engineering, ASCE, 112 (7), 1692-1703 (1986.
- Masri, "A Method for non parametric damage detection through the use of neutral networks", Earthquake Engineering Structural Dynamic, 1998.
- Salane, H. J. Y Baldwin, J. W. "Identification of modal properties of bridges", Journal of Structural Engineering, ASCE, 116 (7), 2008-2021 (1990).
- Salawu, O.S. "Detection of structural damage through changes in frequency: a review. Engineering Structures, Vol. 19, pp. 718-723, 1997.
- Salawu, O. S. y Williams, C. "A review of full-scale dynamic testing of bridge structures", Engineering Structures, 17 (2), 113-121 (1995).
- SAP2000 Non Linear Version 6.11, Structural Analysis Program, Computer and Structures, Inc., University Ave., Berkeley, CA, 1995.