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Assessing local-scale damage in reinforced concrete frame structures using dynamic measurements
Engineering Structures 79 (2014) 22–31
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Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Assessing local-scale damage in reinforced concrete frame structures using dynamic measurements Q.-B. Bui ⇑, M. Mommessin, P. Perrotin, J.-P. Plassiard, O. Plé Université de Savoie, LOCIE, CNRS, Polytech Annecy-Chambéry, F-73000 Chambéry, France
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Article history: Received 13 February 2014 Revised 25 July 2014 Accepted 28 July 2014 Available online xxxx Keywords: Dynamic measurement Reinforced concrete Frame Nondestructive testing
a b s t r a c t The applications of dynamic measurements on existing buildings are numerous: assessment of their seismic vulnerability, assessment of the structure’s capacities in post-earthquake situations or after changes in the vicinity, etc. At present, this type of measurement enables structural diagnosis on a global scale (the whole structure), while the identification and the assessment of local damage (each element of the structure) remains to be explored. Herein, diagnosis at the local scale was studied in the laboratory on an instrumented reinforced concrete structure consisting of two columns and one beam. It was loaded in the central part of the beam in several stages corresponding to different damage states. Displacements were measured simultaneously using displacement sensors and image correlation. After each load/ unload cycle, dynamic measurements were taken using accelerometers. In the first part of this paper, the observations from the experiment were presented, with the appearance of damage and the decrease in natural frequencies that occurred simultaneously with stiffness reduction. Thereafter, the technique characterizing damage that was developed taking into account the semi-rigid connections of the frame was presented. The stiffness of the connections was identified by calibrating the dynamic responses of the structure with respect to a model. The fixity factors were used to assess the loss of stiffness in the semi-rigid connections. The validity of the identified fixity factors was evaluated using the static experimental results. This study shows that dynamic measurement coupled with finite element analysis can provide a fast and effective method to assess the quality of connections of reinforced concrete structures. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Dynamic in-situ measurements are tests, most often nondestructive, achieved directly on real structures [4,11,32,33]. Dynamic measurements on existing building structures can be applied in numerous situations: verification of the seismic vulnerability of structures that were built before the development of seismic regulations [3]; assessment of the structures in postearthquake situations or after changes in the vicinity (e.g., digging of a tunnel, demolition of neighboring buildings); and the study of the behavior of unusual structure [5,6,32]. At present, this kind of measurement makes it possible to diagnose a structure on a global scale (the whole structure), while the identification and the assessment of local damage (each element of the structure) remains to be explored. Herein, the diagnosis in the laboratory and at the local scale of an instrumented reinforced concrete (RC) structure consisting of two columns and one beam is studied, as part of the ⇑ Corresponding author. E-mail address: [email protected] (Q.-B. Bui). http://dx.doi.org/10.1016/j.engstruct.2014.07.038 0141-0296/Ó 2014 Elsevier Ltd. All rights reserved.
French national program for the re-assessment of existing structures. 2. Experiment on a reinforced concrete frame 2.1. Test set-up The instrumented RC structure (Fig. 1) was composed of two 2m-high columns (section, 20 25 cm2) and one beam spanning 2.27 m (section, 20 20 cm2), Fig. 2. It corresponds to a geometric scale of 0.4 comparing to current RC structures. The structure was manufactured by a RC company. Column ends were restrained by jaws. The structure was loaded in the central part of the beam in several stages to study different damage states (Fig. 3). Blue and white color was sprayed on the structure which enables to use an image correlation technique. Cylindrical concrete specimens (16 cm diameter and 32 cm height) were made and tested to characterize the concrete used. The mean values of the compressive strength and the Young modulus were, respectively, 22 MPa and 20 GPa. These results
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Wooden plates
Fig. 1. The reinforced concrete frame studied, at the maximal load.
are relatively low compared to the values usually obtained in the laboratory but come from an industrial manufacturing. In addition, after form removal, two shrinkage cracks were observed in the connections between the beam and the two columns. Steel used for reinforcement is S500B. Reinforcement in the columns was composed of four HA10 lengthwise bars and 17 HA6 stirrups spaced 12 cm apart. Reinforcement in the beams was composed of two upper lengthwise HA10 bars (with 40 cm of anchorage in each column), two HA12 lower lengthwise bars (with 12 cm of anchorage in each column), and 18 HA6 stirrups spaced 13 cm apart, Fig. 2.
Displacements were measured simultaneously by the press sensor, three displacement sensors positioned on the lower face of the beam, and image correlation. In image correlation technique, displacements field is generated by comparing two images which are taken at two different times (eg. before and after specimen is deformed) [31]. The dynamic characteristics of the structure were determined by means of four one-directional accelerometers: one was attached to a column to measure the horizontal accelerations and the others were put on the beam to measure vertical accelerations (see Fig. 5 for more details). The sensors were placed in the central axis of beam and column elements.
Fig. 2. Plan of reinforcement bars.
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ments (Fig. 3). So, natural frequencies and mode shapes were determined at different damage stages. At 62 kN, an important damage was observed and unloading was performed. 2.3. Dynamic results Dynamic measurement 2
Dynamic measurement 3 Dynamic measurement 1
Dynamic measurement 4
Fig. 3. Relationship between the loading force and the displacement at the middle of the beam.
2.2. Test sequence Before testing, dynamic measurements with a shock hammer were taken to characterize the structure’s initial state. Then the structure was loaded at the middle of the beam with an imposed displacement rate of 0.02 mm/s. After each loading (21 kN, 58 kN and 62 kN), the frame was unloaded to take dynamic measure-
Two data processing techniques were used: the FFT (fast Fourier transform) and the FDD (frequency domain decomposition [1]). FFT is a classical technique for dynamic data processing. The disadvantage of this method is that the data from each sensor are analyzed separately. There is no intercorrelation between the data of the different sensors. FDD is a more recent method that consists of factorization of the power spectral density (PSD) matrix of the response time histories such that the component modal responses are revealed at different frequencies using singular value decomposition (SVD). This method allows the data processing of several sensors at the same time. The intercorrelation between the various sensors is determined and so that the mode shapes can be determined. Fig. 4 shows that the modal frequencies determined by the two methods are similar. SV1 to SV4 are the singular values obtained from the decomposition of the four accelerometers’ signals. Fig. 5 presents two mode shapes at 73 and 195 Hz. In fact, there are only four accelerometers and the other values are obtained from the symmetry of the structure. To achieve the exact profile
Am plit ud e (ar bitr ery uni ts)
Am plit ud e (ar bitr ery uni ts)
Fig. 4. Frequencies identified by FFT (left) and FDD (right: singular values decomposed).
Fig. 5. Mode shapes obtained by dynamic measurements. Left: for 73 Hz; right: for 195 Hz.
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Fig. 6. Variation of the natural frequencies according to the loading levels.
of the mode shapes, it would be necessary to have a larger number of accelerometers available. However, it is obvious that the shapes correspond to the beam’s first and second bending modes [8]. This result will be confirmed by the numerical study presented in the following section. Fig. 6 (top) presents the decrease of the frequencies of the first five modes according to the previously exerted loading. It is important to note that, the next section (numerical simulation) show that frequencies 1, 2 and 4 correspond to the eigen modes of the RC structure, modes 3 and 5 correspond to vibrations due to the steel frame. As there is an interaction between the steel frame and the RC structure, accelerometers placed on the RC structure measure frequencies of the global system. Then with degradations in RC structure, frequencies of modes 3 and 5 measured by accelerometers decrease. The natural frequency decrease rate depending on the loading level is presented in Fig. 6 (bottom). The appearance of microcracks has induced a decrease in the stiffness of the structure. At 62 kN, the decrease in the first mode frequency is about 19% compared to the initial state. This result is similar with those reported in the literature [18] and will be discussed below.
3. Validation of the dynamic results with a 2D finite element model A 2D (plane stress) finite element model was carried out to check the dynamic results presented above, in particular the influence of the steel frame on the modes of the RC structure. Since the dynamic tests were performed in small strains (after the unloading), an elastic model could be used here. To be able to take into account the influence of the steel frame on the behavior of the RC frame, the model includes the two frames (Fig. 7). The steel frame is fixed to the floor by bolts and these connections are modeled as embedded connections. The model ensures the compatibility of the displacements between the steel frame and the RC structure. Cracks generated during the experiment are introduced in the model. Their lengths are the same as those of the real cracks measured. Following observations during the test, when the cracking occurred, residual strains had been noted after the unloading. So discontinuities in concrete at cracked sections could be assumed. Therefore, in the model, the crack size
Steel frame
RC frame
Fig. 7. FE model of steel frame and RC structure.
should be wide enough to ensure that no contact could occur in the cracked section of the concrete; but it should also be small enough so that the deleted mass does not influence the eigen frequencies. The width of the cracks in the model is taken equal to 2 mm. The reinforcement are represented by springs (Fig. 8) whose stiffness is calculated by ksteel = Esteel Ssteel/Lsteel [20], where Esteel and Ssteel are the Young’s modulus and the section of the reinforcement bars, respectively. The determination of Lsteel can be obtained following the procedure proposed in [14]. This procedure is detailed for the complete study of the plastic hinging behavior. However, in the structural diagnosis, which requires fast and simple calculation, it is not necessary to follow the entire procedure: by simplification, Haskett et al. [13] propose to take Lsteel equal to the steel active length which corresponds to the interface bond slip capacity of the reinforcing bar, typically a value of 15 mm. Figs. 9–11 show the mode shapes and the values of the natural frequencies obtained with the model. The concordance between the experimental mode shape and that of the numerical model is checked by the MAC (Modal Assurance Criterion) coefficient:
2 MAC Unum ; Uexp ¼ UTnum Uexp =jUnum j2 jUexp j2
ð1Þ
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crack steel Fig. 8. Simplified modeling of the cracks [20].
These results confirm that modes 3 and 5 are vibration modes of the steel frame. Fig. 12 presents the comparison of displacements achieved by the experiments and the FE model. It should be noted that since the model used is an elastic model, the residual strains resulting from the previous loading/unloading cycles could not be simulated. However, the model correctly represents the load–displacements relationship corresponding to the unloading–reloading cycles (without residual strains), excepted for the first loading cycle where the experimental data are not reliable (due to initial conditions which is difficult to carry out). Then the use of an elastic model was acceptable.
4. A method for damage characterization 4.1. State of the art of existing methods Currently, the strategy commonly used in monitoring of structures by dynamic measurements is the identification of the
60,87 Hz
changes in the dynamic characteristics. The most widely used indicator is the change in the natural frequencies. The natural frequencies are relative to the structural stiffness, so a change in a structure’s stiffness leads to changes in the natural frequencies [21,22,29]. The disadvantage of this approach is that damage cannot be localized. This shortcoming is overcome by proposing mode shapes to verify whether the damage also leads to changes in the mode shapes [9,24]. Another strategy to localize damage is identifying the changes in the structure’s flexibility matrix [19,25,34]. Ideally, the flexibility matrix of the actual structure is compared to that of the initial (undamaged) structure. This approach is interesting in theoretical cases, but its application in practice presents limitations, especially in the case of reinforced concrete structures. Firstly, the dimensions of structures in civil engineering are not ‘‘perfect’’ and the in-situ conditions (temperature, wind,. . .) may influence the measurements [7,10]. Secondly, information on the initial state of the structure is not always accessible and therefore determining the variation in the structure’s characteristics is difficult. To overcome this, some studies consider that precise numerical modeling (materials and connections) is sufficient to represent the structure in its initial state [17,10]. This hypothesis is obviously questionable. Information relative to the reinforcing steel of existing structures is usually unknown and therefore it is difficult to take the reinforcement into account in the numerical model to define the damage criteria for a diagnostic. This is why identifying the structure’s characteristics in its actual state is more adequate because information on the structure’s history is not necessary. Actually, for RC structures, this approach can be carried out on the global scale (entire structure) by assuming that the overall dynamic behavior of the structure is known: it is a shear beam, a flexion beam, or a Timoshenko beam
83.10 Hz
188,70 Hz
Fig. 9. Mode shapes corresponding to the state after loading at 62 kN.
Fig. 10. Mode shapes of the steel frame at 152 Hz (left) and 218 Hz (right).
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Fig. 11. Comparison of the natural frequencies obtained by the FE model and experiments (MAC > 0.97 for all presented modes).
and after the loaded state (Fig. 13a, left). When the connection is not rigid (cracking, etc.), a rotation hc is added in the connection rotation (Fig. 13a, right). The structure can be modeled by semirigid connections (Fig. 13b) of stiffness kc, with kc = Mc/hc; where Mc is the moment at the connection. The fixity factor p is introduced, which has a value between 0 and 1 (0 for a hinge and 1 for a rigid connection). The relationship between p and kc is [28]:
p ¼ 1=½1 þ 3EI=ðkc LÞ
ð2Þ
where E is the Young modulus; I the inertia moment and L is the element’s length Using p facilitates the quantification of the decrease in stiffness of a connection compared to its initial rigid state.
Fig. 12. Displacements achieved by the experiments and the FE model.
[3,11,15,23]. However, identification of the damage at the local scale (structural elements) remains more complex. On one hand, the global dynamic behavior influences the internal forces in the structural elements. On the other hand, the redistribution of the internal forces in the elements may also change the global behavior of the structure. There are few investigations that take into account the semirigid connections in their model to characterize existing structures. This approach has been successfully applied to steel structures in the study reported by Katkhuda et al. [16] and Turker et al. [30]. To our knowledge, this principle has not yet been used to characterize RC structures. The present investigation studied the possibility of applying semi-rigid connections (rotational springs) and the fixity factors to the assessment of damage of RC frames at the local scale, which is more complex than that of steel structures [12,26]. 4.2. Fixity factor and the approach proposed 4.2.1. Fixity factor In the case of a rigid connection, stiffness is assumed to be infinity. The angle between the beam and the column is constant before
4.2.2. Approach proposed We hypothesize that damage is mainly located at the two ends and the middle point of a beam and at the two ends of a column (Fig. 14) because the bending moments and the shear forces are usually the greatest at these points [27]. Indeed, mid-span point usually has the greatest bending moment in the case of vertical loads; ends of column and beam generally have the greatest bending moment in the case of horizontal loads. Actually, damage can be located anywhere on the structure, but the above-mentioned zones are the most solicited that should be monitored. Therefore, these important zones are modeled by semi-rigid connections (Fig. 14a). The actual stiffness values of the connections are the unknowns to be identified. When the stiffness values are identified, the fixity factors will be used to assess the state of the connections more accurately. 5. Assessing the approach proposed 5.1. Application of the approach proposed to the experimental frame The previous sections have shown that the steel frame had an influence on the dynamic behavior of the RC structure. Therefore the steel frame must be introduced into the numerical model (Fig. 15). The steel frame + the RC structure system is modeled by beam elements that have an elastic-linear behavior and semi-rigid con-
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Fig. 13. (a) Rigid connection (left) and semi-rigid connection (right); (b) modeling a semi-rigid connection [28].
Fig. 14. Positions of the semi-rigid connections in a RC frame.
nections at the ends. The structure was modeled using center-line to center-line dimensions. These semi-rigid connections have an elastic-linear behavior in rotation. Four fixity factors were added: p1, p2, p3 and p4. Other p factors were not added in the column (at the connection with the beam) to have a reasonable number of degree of freedom for the optimization process. This will be presented and discussed in the next sections. The RC structure is discretized by placing the nodes at the positions of the accelerometers of the experiment, making it possible to compare the mode shapes obtained by the model and the experiment. The elastic modulus and the density used for the RC frame are 20 GPa and 2500 kg/m3, respectively. The steel frame is composed of HEB 400 and UUPN 400 beams. The corresponding elastic modulus and density are 200 GPa and 7850 kg/m3, respectively. The steel frame is assumed embedded to the soil at the supports’ positions. Indeed embedment could be defined as partial fixity, but the steel frame’ modes were not the aim of this study. So other p factors were not added. To identify the fixity factors p1, p2, p3, p4, which reproduce the experimental dynamic response, a process is carried out with MATLABÒ. This process makes it possible to find a combination of the
Steel frame
RC structure
Fig. 15. Discretization of the steel frame and the RC structure.
Q.-B. Bui et al. / Engineering Structures 79 (2014) 22–31 Table 1 Fixity factors identified. F (kN)
p1
p2
p3
p4
0 20 58 62
0.8 0.8 0.8 0.8
0.8 0.72 0.56 0.48
1 1 0.6 0.4
0 0 0 0
fixity factors p1, p2, p3, p4, which give a minimized difference between the three first frequencies found by the model and that of the experimental results. Then the concordance between the experimental mode shape and that of the numerical model is checked by the MAC coefficient. If MAC > 0.9, the mode shapes can be considered correlated [7], but in reality, the modes identified had MAC > 0.95. Table 1 presents the optimal pi values, which are identified by the program. The relevance of these values will be assessed in the following section. Fig. 16 presents the corresponding mode shapes. The numerical results displayed in Table 1 show that at the initial state, the connections were not perfectly rigid (p1 = p2 = 0.8). The value of p1 can be explained because the RC frame was fixed to the steel frame using wooden elements (Fig. 1). The value of p2 is not really surprising because the shrinkage cracks were visible at the connections before the test. The zero value of p4, different to p1, can be explained because the top of columns was principally
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fixed in the horizontal direction, there was not any vertical support as the base of columns. Then, after 20 kN, the two ends of the beam began to lose their stiffness (p2 = 0.72). After 58 kN, the stiffness of the connections continued to decrease (p2 = 0.56) and a plastic hinge appeared at the middle of the beam (p3 = 0.6). When the loading increased, the cracking at the middle of the beam continued and a redistribution of the internal forces can be observed. After 62 kN, as the damage increased, these hinges lost their stiffness (p2 = 0.48 and p3 = 0.4). These numerical results are coherent with the cracking observed during the experiment. Following these results, at post-peak situation, the two ends and the middle of the beam lost 52% and 60%, respectively, of their stiffness compared to the theoretical perfectly rigid state (pi = 1).
5.2. Validation of the numerical values obtained The fixity factors obtained can be experimentally found by determining the experimental stiffness of the semi-rigid springs. By definition, the stiffness k of a semi-rigid spring can be calculated from experimental data:
K exp ¼ M=hexp where:
1st and 2nd modes
modes of the steel frame (3rd and 5th)
4th mode Fig. 16. Mode shapes obtained by the simplified model, for F = 62 kN.
ð3Þ
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Fig. 17. Determining the position of the neutral axis, at a loaded state.
6. Towards a damage criterion
Fig. 18. Comparison of the fixity factors at the beam’s middle, obtained by the experiments and the model.
hexp is the experimental rotation, which can be determined from the displacement of the point at the beam’s middle, at the bottom fiber; and the position of the neutral axis. These parameters are determined from the image correlation (an example is presented in Fig. 17). M is the experimental moment, which can be determined by a classical calculation on a RC section (strain and stress diagrams), by using: the steel rods’ strains, which are measured by the gages placed on these rods; the position of the neutral axis. The moment M was calculated for a loaded state. The equivalent rectangle-parabolic diagram was used for compressive stress of concrete. In the case of this study, for loads greater than 20 kN, the use of this conventional diagram can be acceptable. By replacing hexp and M in Eq. (1), the experimental stiffness and then the corresponding fixity factors are determined. Fig. 18 presents the comparison of the fixity factors at the mid-span of the beam, obtained by the experiments and the model. This figure shows a good correspondence between the values obtained. Table 2 Synthesis of the decrease in the structures’ stiffness (post-peak). Studies
First natural frequency decrease (global)
Local stiffness decrease (structural elements)
Hans et al. [11] Fang et al. [10] Masi and Vona [21] Maas et al. [18] Antunes et al. [2] Present study
18% N.D. 15–25% 15% N.D. 19%
N.D. 38% 40–50% N.D. 32–48% 50–60%
Table 2 presents the synthesis of the results in the literature on the stiffness decrease of the RC structures after severe damage (post-peak). The second column corresponds to the decrease in the first natural frequency which was measured on a whole structure or an assemblage of several structural elements. Theoretically, this decrease is proportional to the global stiffness decrease. For the works of Masi and Vona [21], Antunes et al. [2], the local stiffness decrease is linked to the decrease in the first natural frequency which was measured on a structural element. Although these results were obtained from different investigations on different structures, they present the same order of magnitude. Following these results, if a structure loses approximately 20% of its initial stiffness, it should be verified at the local scale (structural elements). If a structural element loses 30–60% of its stiffness (p < 0.7), it is seriously damaged and should be repaired. The fixity factor is a function of the rotational stiffness, so it is a function of the plastic hinge’s rotation. Following the formula mentioned above, the rotation is a function of the cracked section’s properties and the bond between the steel and concrete. Therefore, the fixity factor can represent the overall behavior of a cracked section (concrete + steel), which explains the reproduction of the model’s results using the rotational springs. Currently in seismic RC codes and design guidelines, plastic hinge rotations can be used as a damage indicator. The advantage of using fixity factor instead of plastic rotation is that when the load is removed the frame returns in a damaged elastic state that can be identified using experimental modal analysis. This remark suggests that the fixity factor may be a criterion to assess the performance of RC structures. If this point is confirmed, it is very important because in most cases of structural monitoring, information on steel rods is not available, so using a simple criterion relative to stiffness is useful. However, a greater number of experiments is necessary to confirm this result.
7. Conclusions and prospects The present investigation has studied the feasibility of using dynamic measurements to auscultate the structural health of RC frames. An experiment was carried out on a RC frame, H-form. Dynamic and static measurements were taken. Dynamic measurements were used to identify the plastic hinges’ properties. Static measurements obtained from image correlation were used to check the relevancy of the simple model proposed.
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Identifying the plastic hinges’ stiffness can be useful to develop a fast and efficient method in the structural monitoring of existing buildings. If the method is applied to a whole structure, the number of fixity factors to be identified quickly increases, so a more powerful optimization algorithm will be required, or methods of sub-structuring should be developed. In this investigation, the degradation of the connection stiffness following the loading increase was established. Following these results, a structural element loses its bearing capacity when it loses 30–60% of its stiffness, while a structure is totally damaged when it loses about 20% of its overall stiffness. This result is similar to what has been noted in the literature: this shows that the effect of the reinforcement was already taken into account in assessing the decrease in connection stiffness. Indeed, as a result of the bond between steel and concrete, the steel can limit the crack’s propagation in the RC structure. This is important because a criterion can be proposed to diagnose RC structures by assessing connection stiffness. This criterion makes simple diagnoses on RC structures possible, without needing to know the information about reinforced steel. A greater number of experiments will be conducted in the future to validate this. Tests at the building scale are also planned. References [1] Andersen P, Brincker R, Goursat M, Mevel L. Automated modal parameter estimation for operational modal analysis of large systems. In: Brincker R, Møller N, editors. Proceedings of the 2nd international operational modal analysis conference, Copenhagen, Denmark; 2007. p. 299–308. [2] Antunes P, Lima H, Varum H, André P. Optical fiber sensors for static and dynamic health monitoring of civil engineering infrastructures: adobe wall case study. Measurement 2012;45:1695–705. [3] Boutin C, Hans S, Ibraim E, Roussillon P. In situ experiments and seismic analysis of existing buildings. Part II: Seismic integrity threshold. Earthq Eng Struct Dyn 2005;34:1531–46. [4] Brownjohn JMW. Ambient vibration studies for system identification of tall building. Earthq Eng Struct Dyn 2003;32:71–95. [5] Bui QB, Morel JC, Hans S, Do AP. First exploratory study on dynamic characteristics of rammed earth buildings. Eng Struct 2011:3690–5. [6] Bui QB, Hans S, Boutin C. Dynamic behaviour of an asymmetric building: experimental and numerical studies. Case Stud Nondestruct Test Eval 2014;2(October):38–48. [7] Chang PC, Flatau A, Liu SC. Review paper: health monitoring of civil infrastructure. Struct Health Monit 2003;2:257–67. [8] Clough RW, Penzien J. Dynamics of structures. Berkeley: Computers & Structures Inc.; 1995. 746p. [9] Dutta A, Talukdar S. Damage detection in bridges using accurate modal parameters. Finite Elem Anal Des 2004;40:287–304. [10] Fang SE, Perera R, Roeck GD. Damage identification of a reinforced concrete frame by finite element model updating using damage parameterization. J Sound Vib 2008;313:544–59. [11] Hans S, Boutin C, Ibraim E, Roussillon P. In situ experiments and seismic analysis of existing buildings. Part I: Experimental investigations. Earthq Eng Struct Dyn 2005;34:1513–29. [12] Haselton CB, Liel AB, Lange ST, Deierlein GG. Beam-column element model calibrated for predicting flexural response leading to global collapse of RC frame buildings. PEER report 2007/03. Pacific Earthquake Engineering Research Center; May 2008.
31
[13] Haskett M, Oehlers DJ, Mohamed Ali MS. Local and global bond characteristics of steel reinforcing bars. Eng Struct 2008;30(2):376–83. [14] Haskett M, Oehlers DJ, Ali MSM, Wu C. Rigid body moment-rotation mechanism for reinforced concrete beam hinges. Eng Struct 2009;31:1032–41. [15] Hong LL, Huang LH, Jhou WY. Identification and variation of story lateral stiffness in buildings. Struct Contr Health Monit 2009;16:200–22. [16] Katkhuda HN, Dwairi HM, Shatarat N. System identification of steel framed structures with semi-rigid connections. Struct Eng Mech 2010;34(3):351–66. [17] Kudva J, Munir N, Tan P. Damage detection in smart structures using neural networks and finite element analysis. In: Proceedings of ADPA/AIAA/ASME/ SPIE conference on active materials and adaptive structures; 1991. p. 559–62. [18] Maas S, Zürbes A, Waldmann D, Waltering M, Bungard V, De Roeck G. Damage assessment of concrete structures through dynamic testing methods. Part 1 – Laboratory tests. Eng Struct 2012;34:351–62. [19] Mahowald J, Maas S, Waldmann D, Zuerbes A, Scherbaum F. Damage identification and localisation using changes in modal parameters for civil engineering structures. In: Proceedings of the international conference on noise and vibration engineering ISMA 2012, Leuven, Belgium; 2012. p. 1103– 17. [20] Massenzio M, Jacquelin E, Ovigne PA. Natural frequency evaluation of a cracked RC beam with or without composite strengthening for a damaged assessment. Mater Struct 2005;38:865–73. [21] Masi A, Vona M. Experimental and numerical evaluation of the fundamental period of undamaged and damaged RC framed buildings. Bull Earthq Eng 2010;8:643–56. [22] Massumi A, Moshtagh E. A new damage index for RC buildings based on variations of nonlinear fundamental period. Struct Des Tall Spec Build 2013;50–61. [23] Michel C, Guéguen P, Bard P-Y. Dynamic parameters of structures extracted from ambient vibration measurements: an aid for the seismic vulnerability assessment of existing buildings in moderate seismic hazard regions. Soil Dyn Earthq Eng 2008;28:593–604. [24] Nguyen VH, Golinval J-C. Damage localization in linear-form structures based on sensitivity investigation for principal component analysis. J Sound Vib 2010:4550–66. [25] Nguyen VH, Mahowald J, Golinval J-C, Maas S. Detection and localization of damage on industrially produced concrete slabs through time- and frequencydomain approaches. In: 6th ECCOMAS conference on smart structures and materials, Torino, Italy; 2013. [26] Sharma A, Eligehausen R, Reddy GR. A new model to simulate joint shear behavior of poorly detailed beam-column connections in RC structures under seismic loads, Part I: Exterior joints. Eng Struct 2011;33:1034–51. [27] Stafford Smith B, Coull A. Tall building structures – analysis and design. New York: Wiley; 1991. [28] Sucuoglu H. Effect of connection rigidity on seismic response of precast concrete frames. PCI J 1995:94–103. [29] Trifunac M, Todorovska M, Manic M, Bulajic B. Variability of the fixed-base and soil–structure system frequencies of a building – the case of Borik-2 building. Struct Contr Health Monit 2010;17(2):120–51. [30] Türker T, Kartal ME, Bayraktar A, Muvafik M. Assessment of semi-rigid connections in steel structures by modal testing. J Construct Steel Res 2009;65:1538–47. [31] Vacher P, Dumoulin S, Morestin F, Mguil-Touchal S. Bidimensional strain measurement using digital images. In: Proceedings of Instn Mech Engrs, vol. 213, Part C ImechE; 1999. p. 811–7. [32] Ventura CE, Finn WDL, Lord JF, Fujita N. Dynamic characteristics of a base isolated building from ambient vibration measurements and low level earthquake shaking. Soil Dyn Earthq Eng 2002;22:1159–67. [33] Volant Ph, Orbovic N, Dunand F. Seismic evaluation of existing nuclear facility using ambient vibration test to characterize dynamic behavior of the structure and microtremor measurements to characterize the soil: a case study. Soil Dyn Earthq Eng 2002;22:1159–67. [34] Yang AW, Liu JK. A coupled method for structural damage identification. J Sound Vib 2006;269:401–5.
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Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Assessing local-scale damage in reinforced concrete frame structures using dynamic measurements Q.-B. Bui ⇑, M. Mommessin, P. Perrotin, J.-P. Plassiard, O. Plé Université de Savoie, LOCIE, CNRS, Polytech Annecy-Chambéry, F-73000 Chambéry, France
a r t i c l e
i n f o
Article history: Received 13 February 2014 Revised 25 July 2014 Accepted 28 July 2014 Available online xxxx Keywords: Dynamic measurement Reinforced concrete Frame Nondestructive testing
a b s t r a c t The applications of dynamic measurements on existing buildings are numerous: assessment of their seismic vulnerability, assessment of the structure’s capacities in post-earthquake situations or after changes in the vicinity, etc. At present, this type of measurement enables structural diagnosis on a global scale (the whole structure), while the identification and the assessment of local damage (each element of the structure) remains to be explored. Herein, diagnosis at the local scale was studied in the laboratory on an instrumented reinforced concrete structure consisting of two columns and one beam. It was loaded in the central part of the beam in several stages corresponding to different damage states. Displacements were measured simultaneously using displacement sensors and image correlation. After each load/ unload cycle, dynamic measurements were taken using accelerometers. In the first part of this paper, the observations from the experiment were presented, with the appearance of damage and the decrease in natural frequencies that occurred simultaneously with stiffness reduction. Thereafter, the technique characterizing damage that was developed taking into account the semi-rigid connections of the frame was presented. The stiffness of the connections was identified by calibrating the dynamic responses of the structure with respect to a model. The fixity factors were used to assess the loss of stiffness in the semi-rigid connections. The validity of the identified fixity factors was evaluated using the static experimental results. This study shows that dynamic measurement coupled with finite element analysis can provide a fast and effective method to assess the quality of connections of reinforced concrete structures. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction Dynamic in-situ measurements are tests, most often nondestructive, achieved directly on real structures [4,11,32,33]. Dynamic measurements on existing building structures can be applied in numerous situations: verification of the seismic vulnerability of structures that were built before the development of seismic regulations [3]; assessment of the structures in postearthquake situations or after changes in the vicinity (e.g., digging of a tunnel, demolition of neighboring buildings); and the study of the behavior of unusual structure [5,6,32]. At present, this kind of measurement makes it possible to diagnose a structure on a global scale (the whole structure), while the identification and the assessment of local damage (each element of the structure) remains to be explored. Herein, the diagnosis in the laboratory and at the local scale of an instrumented reinforced concrete (RC) structure consisting of two columns and one beam is studied, as part of the ⇑ Corresponding author. E-mail address: [email protected] (Q.-B. Bui). http://dx.doi.org/10.1016/j.engstruct.2014.07.038 0141-0296/Ó 2014 Elsevier Ltd. All rights reserved.
French national program for the re-assessment of existing structures. 2. Experiment on a reinforced concrete frame 2.1. Test set-up The instrumented RC structure (Fig. 1) was composed of two 2m-high columns (section, 20 25 cm2) and one beam spanning 2.27 m (section, 20 20 cm2), Fig. 2. It corresponds to a geometric scale of 0.4 comparing to current RC structures. The structure was manufactured by a RC company. Column ends were restrained by jaws. The structure was loaded in the central part of the beam in several stages to study different damage states (Fig. 3). Blue and white color was sprayed on the structure which enables to use an image correlation technique. Cylindrical concrete specimens (16 cm diameter and 32 cm height) were made and tested to characterize the concrete used. The mean values of the compressive strength and the Young modulus were, respectively, 22 MPa and 20 GPa. These results
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Wooden plates
Fig. 1. The reinforced concrete frame studied, at the maximal load.
are relatively low compared to the values usually obtained in the laboratory but come from an industrial manufacturing. In addition, after form removal, two shrinkage cracks were observed in the connections between the beam and the two columns. Steel used for reinforcement is S500B. Reinforcement in the columns was composed of four HA10 lengthwise bars and 17 HA6 stirrups spaced 12 cm apart. Reinforcement in the beams was composed of two upper lengthwise HA10 bars (with 40 cm of anchorage in each column), two HA12 lower lengthwise bars (with 12 cm of anchorage in each column), and 18 HA6 stirrups spaced 13 cm apart, Fig. 2.
Displacements were measured simultaneously by the press sensor, three displacement sensors positioned on the lower face of the beam, and image correlation. In image correlation technique, displacements field is generated by comparing two images which are taken at two different times (eg. before and after specimen is deformed) [31]. The dynamic characteristics of the structure were determined by means of four one-directional accelerometers: one was attached to a column to measure the horizontal accelerations and the others were put on the beam to measure vertical accelerations (see Fig. 5 for more details). The sensors were placed in the central axis of beam and column elements.
Fig. 2. Plan of reinforcement bars.
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ments (Fig. 3). So, natural frequencies and mode shapes were determined at different damage stages. At 62 kN, an important damage was observed and unloading was performed. 2.3. Dynamic results Dynamic measurement 2
Dynamic measurement 3 Dynamic measurement 1
Dynamic measurement 4
Fig. 3. Relationship between the loading force and the displacement at the middle of the beam.
2.2. Test sequence Before testing, dynamic measurements with a shock hammer were taken to characterize the structure’s initial state. Then the structure was loaded at the middle of the beam with an imposed displacement rate of 0.02 mm/s. After each loading (21 kN, 58 kN and 62 kN), the frame was unloaded to take dynamic measure-
Two data processing techniques were used: the FFT (fast Fourier transform) and the FDD (frequency domain decomposition [1]). FFT is a classical technique for dynamic data processing. The disadvantage of this method is that the data from each sensor are analyzed separately. There is no intercorrelation between the data of the different sensors. FDD is a more recent method that consists of factorization of the power spectral density (PSD) matrix of the response time histories such that the component modal responses are revealed at different frequencies using singular value decomposition (SVD). This method allows the data processing of several sensors at the same time. The intercorrelation between the various sensors is determined and so that the mode shapes can be determined. Fig. 4 shows that the modal frequencies determined by the two methods are similar. SV1 to SV4 are the singular values obtained from the decomposition of the four accelerometers’ signals. Fig. 5 presents two mode shapes at 73 and 195 Hz. In fact, there are only four accelerometers and the other values are obtained from the symmetry of the structure. To achieve the exact profile
Am plit ud e (ar bitr ery uni ts)
Am plit ud e (ar bitr ery uni ts)
Fig. 4. Frequencies identified by FFT (left) and FDD (right: singular values decomposed).
Fig. 5. Mode shapes obtained by dynamic measurements. Left: for 73 Hz; right: for 195 Hz.
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Fig. 6. Variation of the natural frequencies according to the loading levels.
of the mode shapes, it would be necessary to have a larger number of accelerometers available. However, it is obvious that the shapes correspond to the beam’s first and second bending modes [8]. This result will be confirmed by the numerical study presented in the following section. Fig. 6 (top) presents the decrease of the frequencies of the first five modes according to the previously exerted loading. It is important to note that, the next section (numerical simulation) show that frequencies 1, 2 and 4 correspond to the eigen modes of the RC structure, modes 3 and 5 correspond to vibrations due to the steel frame. As there is an interaction between the steel frame and the RC structure, accelerometers placed on the RC structure measure frequencies of the global system. Then with degradations in RC structure, frequencies of modes 3 and 5 measured by accelerometers decrease. The natural frequency decrease rate depending on the loading level is presented in Fig. 6 (bottom). The appearance of microcracks has induced a decrease in the stiffness of the structure. At 62 kN, the decrease in the first mode frequency is about 19% compared to the initial state. This result is similar with those reported in the literature [18] and will be discussed below.
3. Validation of the dynamic results with a 2D finite element model A 2D (plane stress) finite element model was carried out to check the dynamic results presented above, in particular the influence of the steel frame on the modes of the RC structure. Since the dynamic tests were performed in small strains (after the unloading), an elastic model could be used here. To be able to take into account the influence of the steel frame on the behavior of the RC frame, the model includes the two frames (Fig. 7). The steel frame is fixed to the floor by bolts and these connections are modeled as embedded connections. The model ensures the compatibility of the displacements between the steel frame and the RC structure. Cracks generated during the experiment are introduced in the model. Their lengths are the same as those of the real cracks measured. Following observations during the test, when the cracking occurred, residual strains had been noted after the unloading. So discontinuities in concrete at cracked sections could be assumed. Therefore, in the model, the crack size
Steel frame
RC frame
Fig. 7. FE model of steel frame and RC structure.
should be wide enough to ensure that no contact could occur in the cracked section of the concrete; but it should also be small enough so that the deleted mass does not influence the eigen frequencies. The width of the cracks in the model is taken equal to 2 mm. The reinforcement are represented by springs (Fig. 8) whose stiffness is calculated by ksteel = Esteel Ssteel/Lsteel [20], where Esteel and Ssteel are the Young’s modulus and the section of the reinforcement bars, respectively. The determination of Lsteel can be obtained following the procedure proposed in [14]. This procedure is detailed for the complete study of the plastic hinging behavior. However, in the structural diagnosis, which requires fast and simple calculation, it is not necessary to follow the entire procedure: by simplification, Haskett et al. [13] propose to take Lsteel equal to the steel active length which corresponds to the interface bond slip capacity of the reinforcing bar, typically a value of 15 mm. Figs. 9–11 show the mode shapes and the values of the natural frequencies obtained with the model. The concordance between the experimental mode shape and that of the numerical model is checked by the MAC (Modal Assurance Criterion) coefficient:
2 MAC Unum ; Uexp ¼ UTnum Uexp =jUnum j2 jUexp j2
ð1Þ
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crack steel Fig. 8. Simplified modeling of the cracks [20].
These results confirm that modes 3 and 5 are vibration modes of the steel frame. Fig. 12 presents the comparison of displacements achieved by the experiments and the FE model. It should be noted that since the model used is an elastic model, the residual strains resulting from the previous loading/unloading cycles could not be simulated. However, the model correctly represents the load–displacements relationship corresponding to the unloading–reloading cycles (without residual strains), excepted for the first loading cycle where the experimental data are not reliable (due to initial conditions which is difficult to carry out). Then the use of an elastic model was acceptable.
4. A method for damage characterization 4.1. State of the art of existing methods Currently, the strategy commonly used in monitoring of structures by dynamic measurements is the identification of the
60,87 Hz
changes in the dynamic characteristics. The most widely used indicator is the change in the natural frequencies. The natural frequencies are relative to the structural stiffness, so a change in a structure’s stiffness leads to changes in the natural frequencies [21,22,29]. The disadvantage of this approach is that damage cannot be localized. This shortcoming is overcome by proposing mode shapes to verify whether the damage also leads to changes in the mode shapes [9,24]. Another strategy to localize damage is identifying the changes in the structure’s flexibility matrix [19,25,34]. Ideally, the flexibility matrix of the actual structure is compared to that of the initial (undamaged) structure. This approach is interesting in theoretical cases, but its application in practice presents limitations, especially in the case of reinforced concrete structures. Firstly, the dimensions of structures in civil engineering are not ‘‘perfect’’ and the in-situ conditions (temperature, wind,. . .) may influence the measurements [7,10]. Secondly, information on the initial state of the structure is not always accessible and therefore determining the variation in the structure’s characteristics is difficult. To overcome this, some studies consider that precise numerical modeling (materials and connections) is sufficient to represent the structure in its initial state [17,10]. This hypothesis is obviously questionable. Information relative to the reinforcing steel of existing structures is usually unknown and therefore it is difficult to take the reinforcement into account in the numerical model to define the damage criteria for a diagnostic. This is why identifying the structure’s characteristics in its actual state is more adequate because information on the structure’s history is not necessary. Actually, for RC structures, this approach can be carried out on the global scale (entire structure) by assuming that the overall dynamic behavior of the structure is known: it is a shear beam, a flexion beam, or a Timoshenko beam
83.10 Hz
188,70 Hz
Fig. 9. Mode shapes corresponding to the state after loading at 62 kN.
Fig. 10. Mode shapes of the steel frame at 152 Hz (left) and 218 Hz (right).
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Fig. 11. Comparison of the natural frequencies obtained by the FE model and experiments (MAC > 0.97 for all presented modes).
and after the loaded state (Fig. 13a, left). When the connection is not rigid (cracking, etc.), a rotation hc is added in the connection rotation (Fig. 13a, right). The structure can be modeled by semirigid connections (Fig. 13b) of stiffness kc, with kc = Mc/hc; where Mc is the moment at the connection. The fixity factor p is introduced, which has a value between 0 and 1 (0 for a hinge and 1 for a rigid connection). The relationship between p and kc is [28]:
p ¼ 1=½1 þ 3EI=ðkc LÞ
ð2Þ
where E is the Young modulus; I the inertia moment and L is the element’s length Using p facilitates the quantification of the decrease in stiffness of a connection compared to its initial rigid state.
Fig. 12. Displacements achieved by the experiments and the FE model.
[3,11,15,23]. However, identification of the damage at the local scale (structural elements) remains more complex. On one hand, the global dynamic behavior influences the internal forces in the structural elements. On the other hand, the redistribution of the internal forces in the elements may also change the global behavior of the structure. There are few investigations that take into account the semirigid connections in their model to characterize existing structures. This approach has been successfully applied to steel structures in the study reported by Katkhuda et al. [16] and Turker et al. [30]. To our knowledge, this principle has not yet been used to characterize RC structures. The present investigation studied the possibility of applying semi-rigid connections (rotational springs) and the fixity factors to the assessment of damage of RC frames at the local scale, which is more complex than that of steel structures [12,26]. 4.2. Fixity factor and the approach proposed 4.2.1. Fixity factor In the case of a rigid connection, stiffness is assumed to be infinity. The angle between the beam and the column is constant before
4.2.2. Approach proposed We hypothesize that damage is mainly located at the two ends and the middle point of a beam and at the two ends of a column (Fig. 14) because the bending moments and the shear forces are usually the greatest at these points [27]. Indeed, mid-span point usually has the greatest bending moment in the case of vertical loads; ends of column and beam generally have the greatest bending moment in the case of horizontal loads. Actually, damage can be located anywhere on the structure, but the above-mentioned zones are the most solicited that should be monitored. Therefore, these important zones are modeled by semi-rigid connections (Fig. 14a). The actual stiffness values of the connections are the unknowns to be identified. When the stiffness values are identified, the fixity factors will be used to assess the state of the connections more accurately. 5. Assessing the approach proposed 5.1. Application of the approach proposed to the experimental frame The previous sections have shown that the steel frame had an influence on the dynamic behavior of the RC structure. Therefore the steel frame must be introduced into the numerical model (Fig. 15). The steel frame + the RC structure system is modeled by beam elements that have an elastic-linear behavior and semi-rigid con-
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Fig. 13. (a) Rigid connection (left) and semi-rigid connection (right); (b) modeling a semi-rigid connection [28].
Fig. 14. Positions of the semi-rigid connections in a RC frame.
nections at the ends. The structure was modeled using center-line to center-line dimensions. These semi-rigid connections have an elastic-linear behavior in rotation. Four fixity factors were added: p1, p2, p3 and p4. Other p factors were not added in the column (at the connection with the beam) to have a reasonable number of degree of freedom for the optimization process. This will be presented and discussed in the next sections. The RC structure is discretized by placing the nodes at the positions of the accelerometers of the experiment, making it possible to compare the mode shapes obtained by the model and the experiment. The elastic modulus and the density used for the RC frame are 20 GPa and 2500 kg/m3, respectively. The steel frame is composed of HEB 400 and UUPN 400 beams. The corresponding elastic modulus and density are 200 GPa and 7850 kg/m3, respectively. The steel frame is assumed embedded to the soil at the supports’ positions. Indeed embedment could be defined as partial fixity, but the steel frame’ modes were not the aim of this study. So other p factors were not added. To identify the fixity factors p1, p2, p3, p4, which reproduce the experimental dynamic response, a process is carried out with MATLABÒ. This process makes it possible to find a combination of the
Steel frame
RC structure
Fig. 15. Discretization of the steel frame and the RC structure.
Q.-B. Bui et al. / Engineering Structures 79 (2014) 22–31 Table 1 Fixity factors identified. F (kN)
p1
p2
p3
p4
0 20 58 62
0.8 0.8 0.8 0.8
0.8 0.72 0.56 0.48
1 1 0.6 0.4
0 0 0 0
fixity factors p1, p2, p3, p4, which give a minimized difference between the three first frequencies found by the model and that of the experimental results. Then the concordance between the experimental mode shape and that of the numerical model is checked by the MAC coefficient. If MAC > 0.9, the mode shapes can be considered correlated [7], but in reality, the modes identified had MAC > 0.95. Table 1 presents the optimal pi values, which are identified by the program. The relevance of these values will be assessed in the following section. Fig. 16 presents the corresponding mode shapes. The numerical results displayed in Table 1 show that at the initial state, the connections were not perfectly rigid (p1 = p2 = 0.8). The value of p1 can be explained because the RC frame was fixed to the steel frame using wooden elements (Fig. 1). The value of p2 is not really surprising because the shrinkage cracks were visible at the connections before the test. The zero value of p4, different to p1, can be explained because the top of columns was principally
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fixed in the horizontal direction, there was not any vertical support as the base of columns. Then, after 20 kN, the two ends of the beam began to lose their stiffness (p2 = 0.72). After 58 kN, the stiffness of the connections continued to decrease (p2 = 0.56) and a plastic hinge appeared at the middle of the beam (p3 = 0.6). When the loading increased, the cracking at the middle of the beam continued and a redistribution of the internal forces can be observed. After 62 kN, as the damage increased, these hinges lost their stiffness (p2 = 0.48 and p3 = 0.4). These numerical results are coherent with the cracking observed during the experiment. Following these results, at post-peak situation, the two ends and the middle of the beam lost 52% and 60%, respectively, of their stiffness compared to the theoretical perfectly rigid state (pi = 1).
5.2. Validation of the numerical values obtained The fixity factors obtained can be experimentally found by determining the experimental stiffness of the semi-rigid springs. By definition, the stiffness k of a semi-rigid spring can be calculated from experimental data:
K exp ¼ M=hexp where:
1st and 2nd modes
modes of the steel frame (3rd and 5th)
4th mode Fig. 16. Mode shapes obtained by the simplified model, for F = 62 kN.
ð3Þ
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Fig. 17. Determining the position of the neutral axis, at a loaded state.
6. Towards a damage criterion
Fig. 18. Comparison of the fixity factors at the beam’s middle, obtained by the experiments and the model.
hexp is the experimental rotation, which can be determined from the displacement of the point at the beam’s middle, at the bottom fiber; and the position of the neutral axis. These parameters are determined from the image correlation (an example is presented in Fig. 17). M is the experimental moment, which can be determined by a classical calculation on a RC section (strain and stress diagrams), by using: the steel rods’ strains, which are measured by the gages placed on these rods; the position of the neutral axis. The moment M was calculated for a loaded state. The equivalent rectangle-parabolic diagram was used for compressive stress of concrete. In the case of this study, for loads greater than 20 kN, the use of this conventional diagram can be acceptable. By replacing hexp and M in Eq. (1), the experimental stiffness and then the corresponding fixity factors are determined. Fig. 18 presents the comparison of the fixity factors at the mid-span of the beam, obtained by the experiments and the model. This figure shows a good correspondence between the values obtained. Table 2 Synthesis of the decrease in the structures’ stiffness (post-peak). Studies
First natural frequency decrease (global)
Local stiffness decrease (structural elements)
Hans et al. [11] Fang et al. [10] Masi and Vona [21] Maas et al. [18] Antunes et al. [2] Present study
18% N.D. 15–25% 15% N.D. 19%
N.D. 38% 40–50% N.D. 32–48% 50–60%
Table 2 presents the synthesis of the results in the literature on the stiffness decrease of the RC structures after severe damage (post-peak). The second column corresponds to the decrease in the first natural frequency which was measured on a whole structure or an assemblage of several structural elements. Theoretically, this decrease is proportional to the global stiffness decrease. For the works of Masi and Vona [21], Antunes et al. [2], the local stiffness decrease is linked to the decrease in the first natural frequency which was measured on a structural element. Although these results were obtained from different investigations on different structures, they present the same order of magnitude. Following these results, if a structure loses approximately 20% of its initial stiffness, it should be verified at the local scale (structural elements). If a structural element loses 30–60% of its stiffness (p < 0.7), it is seriously damaged and should be repaired. The fixity factor is a function of the rotational stiffness, so it is a function of the plastic hinge’s rotation. Following the formula mentioned above, the rotation is a function of the cracked section’s properties and the bond between the steel and concrete. Therefore, the fixity factor can represent the overall behavior of a cracked section (concrete + steel), which explains the reproduction of the model’s results using the rotational springs. Currently in seismic RC codes and design guidelines, plastic hinge rotations can be used as a damage indicator. The advantage of using fixity factor instead of plastic rotation is that when the load is removed the frame returns in a damaged elastic state that can be identified using experimental modal analysis. This remark suggests that the fixity factor may be a criterion to assess the performance of RC structures. If this point is confirmed, it is very important because in most cases of structural monitoring, information on steel rods is not available, so using a simple criterion relative to stiffness is useful. However, a greater number of experiments is necessary to confirm this result.
7. Conclusions and prospects The present investigation has studied the feasibility of using dynamic measurements to auscultate the structural health of RC frames. An experiment was carried out on a RC frame, H-form. Dynamic and static measurements were taken. Dynamic measurements were used to identify the plastic hinges’ properties. Static measurements obtained from image correlation were used to check the relevancy of the simple model proposed.
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Identifying the plastic hinges’ stiffness can be useful to develop a fast and efficient method in the structural monitoring of existing buildings. If the method is applied to a whole structure, the number of fixity factors to be identified quickly increases, so a more powerful optimization algorithm will be required, or methods of sub-structuring should be developed. In this investigation, the degradation of the connection stiffness following the loading increase was established. Following these results, a structural element loses its bearing capacity when it loses 30–60% of its stiffness, while a structure is totally damaged when it loses about 20% of its overall stiffness. This result is similar to what has been noted in the literature: this shows that the effect of the reinforcement was already taken into account in assessing the decrease in connection stiffness. Indeed, as a result of the bond between steel and concrete, the steel can limit the crack’s propagation in the RC structure. This is important because a criterion can be proposed to diagnose RC structures by assessing connection stiffness. This criterion makes simple diagnoses on RC structures possible, without needing to know the information about reinforced steel. A greater number of experiments will be conducted in the future to validate this. Tests at the building scale are also planned. References [1] Andersen P, Brincker R, Goursat M, Mevel L. Automated modal parameter estimation for operational modal analysis of large systems. In: Brincker R, Møller N, editors. Proceedings of the 2nd international operational modal analysis conference, Copenhagen, Denmark; 2007. p. 299–308. [2] Antunes P, Lima H, Varum H, André P. Optical fiber sensors for static and dynamic health monitoring of civil engineering infrastructures: adobe wall case study. Measurement 2012;45:1695–705. [3] Boutin C, Hans S, Ibraim E, Roussillon P. In situ experiments and seismic analysis of existing buildings. Part II: Seismic integrity threshold. Earthq Eng Struct Dyn 2005;34:1531–46. [4] Brownjohn JMW. Ambient vibration studies for system identification of tall building. Earthq Eng Struct Dyn 2003;32:71–95. [5] Bui QB, Morel JC, Hans S, Do AP. First exploratory study on dynamic characteristics of rammed earth buildings. Eng Struct 2011:3690–5. [6] Bui QB, Hans S, Boutin C. Dynamic behaviour of an asymmetric building: experimental and numerical studies. Case Stud Nondestruct Test Eval 2014;2(October):38–48. [7] Chang PC, Flatau A, Liu SC. Review paper: health monitoring of civil infrastructure. Struct Health Monit 2003;2:257–67. [8] Clough RW, Penzien J. Dynamics of structures. Berkeley: Computers & Structures Inc.; 1995. 746p. [9] Dutta A, Talukdar S. Damage detection in bridges using accurate modal parameters. Finite Elem Anal Des 2004;40:287–304. [10] Fang SE, Perera R, Roeck GD. Damage identification of a reinforced concrete frame by finite element model updating using damage parameterization. J Sound Vib 2008;313:544–59. [11] Hans S, Boutin C, Ibraim E, Roussillon P. In situ experiments and seismic analysis of existing buildings. Part I: Experimental investigations. Earthq Eng Struct Dyn 2005;34:1513–29. [12] Haselton CB, Liel AB, Lange ST, Deierlein GG. Beam-column element model calibrated for predicting flexural response leading to global collapse of RC frame buildings. PEER report 2007/03. Pacific Earthquake Engineering Research Center; May 2008.
31
[13] Haskett M, Oehlers DJ, Mohamed Ali MS. Local and global bond characteristics of steel reinforcing bars. Eng Struct 2008;30(2):376–83. [14] Haskett M, Oehlers DJ, Ali MSM, Wu C. Rigid body moment-rotation mechanism for reinforced concrete beam hinges. Eng Struct 2009;31:1032–41. [15] Hong LL, Huang LH, Jhou WY. Identification and variation of story lateral stiffness in buildings. Struct Contr Health Monit 2009;16:200–22. [16] Katkhuda HN, Dwairi HM, Shatarat N. System identification of steel framed structures with semi-rigid connections. Struct Eng Mech 2010;34(3):351–66. [17] Kudva J, Munir N, Tan P. Damage detection in smart structures using neural networks and finite element analysis. In: Proceedings of ADPA/AIAA/ASME/ SPIE conference on active materials and adaptive structures; 1991. p. 559–62. [18] Maas S, Zürbes A, Waldmann D, Waltering M, Bungard V, De Roeck G. Damage assessment of concrete structures through dynamic testing methods. Part 1 – Laboratory tests. Eng Struct 2012;34:351–62. [19] Mahowald J, Maas S, Waldmann D, Zuerbes A, Scherbaum F. Damage identification and localisation using changes in modal parameters for civil engineering structures. In: Proceedings of the international conference on noise and vibration engineering ISMA 2012, Leuven, Belgium; 2012. p. 1103– 17. [20] Massenzio M, Jacquelin E, Ovigne PA. Natural frequency evaluation of a cracked RC beam with or without composite strengthening for a damaged assessment. Mater Struct 2005;38:865–73. [21] Masi A, Vona M. Experimental and numerical evaluation of the fundamental period of undamaged and damaged RC framed buildings. Bull Earthq Eng 2010;8:643–56. [22] Massumi A, Moshtagh E. A new damage index for RC buildings based on variations of nonlinear fundamental period. Struct Des Tall Spec Build 2013;50–61. [23] Michel C, Guéguen P, Bard P-Y. Dynamic parameters of structures extracted from ambient vibration measurements: an aid for the seismic vulnerability assessment of existing buildings in moderate seismic hazard regions. Soil Dyn Earthq Eng 2008;28:593–604. [24] Nguyen VH, Golinval J-C. Damage localization in linear-form structures based on sensitivity investigation for principal component analysis. J Sound Vib 2010:4550–66. [25] Nguyen VH, Mahowald J, Golinval J-C, Maas S. Detection and localization of damage on industrially produced concrete slabs through time- and frequencydomain approaches. In: 6th ECCOMAS conference on smart structures and materials, Torino, Italy; 2013. [26] Sharma A, Eligehausen R, Reddy GR. A new model to simulate joint shear behavior of poorly detailed beam-column connections in RC structures under seismic loads, Part I: Exterior joints. Eng Struct 2011;33:1034–51. [27] Stafford Smith B, Coull A. Tall building structures – analysis and design. New York: Wiley; 1991. [28] Sucuoglu H. Effect of connection rigidity on seismic response of precast concrete frames. PCI J 1995:94–103. [29] Trifunac M, Todorovska M, Manic M, Bulajic B. Variability of the fixed-base and soil–structure system frequencies of a building – the case of Borik-2 building. Struct Contr Health Monit 2010;17(2):120–51. [30] Türker T, Kartal ME, Bayraktar A, Muvafik M. Assessment of semi-rigid connections in steel structures by modal testing. J Construct Steel Res 2009;65:1538–47. [31] Vacher P, Dumoulin S, Morestin F, Mguil-Touchal S. Bidimensional strain measurement using digital images. In: Proceedings of Instn Mech Engrs, vol. 213, Part C ImechE; 1999. p. 811–7. [32] Ventura CE, Finn WDL, Lord JF, Fujita N. Dynamic characteristics of a base isolated building from ambient vibration measurements and low level earthquake shaking. Soil Dyn Earthq Eng 2002;22:1159–67. [33] Volant Ph, Orbovic N, Dunand F. Seismic evaluation of existing nuclear facility using ambient vibration test to characterize dynamic behavior of the structure and microtremor measurements to characterize the soil: a case study. Soil Dyn Earthq Eng 2002;22:1159–67. [34] Yang AW, Liu JK. A coupled method for structural damage identification. J Sound Vib 2006;269:401–5.