Damage detection of flexural structural systems using damage index method – Experimental approach

Alexandria Engineering Journal (2015) xxx, xxx–xxx

H O S T E D BY

Alexandria University

Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com

ORIGINAL ARTICLE

Damage detection of flexural structural systems using damage index method – Experimental approach Atef Eraky a, Ahmed M. Anwar b, Alaa Saad a, Ayman Abdo a b

a,*

Structural Eng. Dep., Faculty of Engineering, Zagazig University, Egypt Construction Research Institute, National Water Research Center, Egypt

Received 12 July 2014; revised 24 April 2015; accepted 23 May 2015

KEYWORDS Dynamics; Plates; Beams; Damage detection; Damage index

Abstract In the framework of structural health monitoring, continuous dynamic records are essential for good judgment of structures. Overall degradation of structures can be obtained with reasonable accuracy using various system identification techniques. It is however, challenging to obtain precisely the position and size of local damages. The current research focuses on Damage Index Method (DIM) as a tool for determining local damages occurred in flexural structural elements. The DIM technique depends on comparing modal strain energies of structures at different degradation stages. Self-made computer module was developed to encounter DIM for damage detection. First, the method was verified experimentally. Simply supported steel beam of 1500 mm (length), 50 mm (width) and 6 mm (thickness), in addition to steel plate of area 930 · 910 mm and 3 mm (thickness) was implemented in the experimental program. Both the beam and plate were subjected to different damage configurations. Collected acceleration time history was processed and used to verify the adequacy of DIM in identifying damages in the used physical models. Numerical parametric study was also conducted on a variety of beams and plates with various damage degrees and locations. It was noticed that both the experimental and numerical results showed good agreement in identifying damages in flexural structural elements. ª 2015 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction Occurrence of damage in existing civil structures causes reduction in their load carrying capacity and might end-up with catastrophic failure if not maintained at early stages.

* Corresponding author. Peer review under responsibility of Faculty of Engineering, Alexandria University.

Inaccessibility of portions of structures, presence of unseen hair cracks, as well as material deterioration of some parts of the structure can lead to whole structure failure or some of its elements. Early prediction of this damage could help in increasing their life time and prevent unexpected modes of failure. Therefore, health monitoring of vital structures by means of reliable non-destructive damage detection tools is crucial to maintain safety and integrity of these structures. Probably, damage detection is identified based on the comparison of the dynamic modal parameters of the structure

http://dx.doi.org/10.1016/j.aej.2015.05.015 1110-0168 ª 2015 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: A. Eraky et al., Damage detection of flexural structural systems using damage index method – Experimental approach, Alexandria Eng. J. (2015), http://dx.doi.org/10.1016/j.aej.2015.05.015

2 before and after damage occurrence. In practice, the referenced data might not always be available or difficult to be obtained. After a severe event, such as a strong earthquake, it may not be feasible to conduct vibration tests to obtain meaningful data for damage identification. Hence, it is desirable to adopt suitable analysis method capable of detecting structural damage based only on the vibration data measured during a severe event without a prior knowledge of the undamaged structure. Recently, many researchers are interested in developing methods to facilitate the identification of damage degree and location. Ratcliffe [1] introduced a finite difference approximation of Laplace’s differential operator which can be applied to mode shape of damaged beam for the purpose of damage detection. Damage locations for plate-type structures were identified based on the strain modal analysis of a damaged plate. Arau´jo dos Santos et al. [2] developed an algorithm based on the sensitivities of the orthogonality conditions of the mode shapes to identify damage of laminated plates. Moreover, the strain mode shapes were obtained by applying Rayleigh–Ritz approach, Li et al. [3]. Abdo and Hori [4] carried out study depend on comparison of the rotational mode shapes as a diagnostic tool in evaluating damage of plates. It was found that changes in the rotation of the mode shapes are more sensitive than the changes in the displacement mode shapes. Structural damages result in nonlinear dynamical signatures that can significantly enhance their detection, Marc Re´billatn et al. [5]. Experimental study was applied on reinforced concrete beams aiming to detect the cracks and their locations using dynamic system characteristics, Ndambi et al. [6]. Various damage detection methods based on mode shape changes and frequency response function were studied and compared. The mode shape difference method was not successfully able to identify the damage precisely, Maia et al. [7]. Kim et al. [8] formulated a damage index algorithm to estimate the severity of damage from monitoring changes in the modal strain energy. The sensitivity of mode shape to changes in mass or stiffness in structures was used as a base for damage assessment and localization, Parloo et al. [9]. The operational deflection shape and boundary effect evaluation method was used as a base for pinpointing crack location. The crack sizes were estimated by a local strain energy method Pai et al. [10]. The measured changes in the first three natural frequencies and corresponding amplitudes of the measured acceleration frequency response function were used as a damage detection scheme of beams, Owolabi et al. [11]. Furthermore, another technique, spatial wavelet based analysis, was introduced for prediction of crack depth and location in beams, Chang et al. [12]. Damage localization in laminated plates was determined based on mode shapes translation, rotation and curvature differences. The mode shapes translations are experimentally obtained using double pulse TV holography and an acoustic excitation, Arau´jo Dos Santos et al. [13]. Mode shape derivatives were used to determine the location of damages due to presence of single crack and honeycombs, Ismail et al. [14]. Story damage index was also introduced as a simple formula based on modal frequency and mode shape for earthquake damaged structures, Wang et al. [15]. The delaminating presence, location and size of laminated composite plates were investigated by measuring the modal parameters. Two different actuator–sensor measurement systems were used to extract the frequencies and modes shapes of the

A. Eraky et al. plates, Qiao et al. [16]. Two damage indexes (DIs) were proposed. The first DI was built as the ratio of the energy contained in the nonlinear part of an output versus the energy contained in its linear part. The second DI was the angle between the subspaces obtained from the nonlinear parts of two sets of outputs after a principal component analysis, Marc et al. [17]. Extending the notion of transmissibility functions to nonlinear systems was described by Volterraseries [18], Lang etal. [19] where the decrease of linearity generated by a nonlinear damage was quantified and thus to effectively detect and locate the damage. However, as such approaches are focusing on the loss of linearity, they do not seem to be able to deal with systems that are nonlinear in their healthy states, a fact that is quite common in real life. Hu et al. [20] proposed a modal strain energy based scanning damage index method for damage detection of circular hollow cylinder. However, most of the above methods depends on mode shapes or FRFs, which is time consuming and less accurate in practice. The current research adopted the damage index method (DIM) where the modal strain energy with the aid of stochastic analyses was utilized to detect damage in beams and plates. Time histories of damaged and undamaged beams and plates, with different crack configurations, were processed and analyzed. Numerical and physical models were performed to validate the DIM. 2. Modal strain energy The modal strain energy based on DIM uses the change in modal strain of the undamaged and damaged structure to detect and locate damage in structure. The strain energy ‘U’ stored in an elastic body for a general state of stress is expressed by: ZZZ 1 U¼ ðrx ex þ ry ey þ rz ez þ sxy cxy þ sxz cxz 2 v þ syz cyz Þdxdydz

ð1Þ

where r and e are the normal stress and corresponding strain components at a point in a body respectively, V is the volume of the three dimensional body in a coordinate system (x, y and z-axis). By equating the total strain energy of damaged and undamaged structures, one can obtain the position of damages. The damage indicator (DI) which was introduced by Ugural [21] was used in beams, plates and truss elements to locate the damage. 2.1. Beam elements The strain energy stored in a beam due to pure bending is given as follows:  2 Z EI d2 y U¼ dx ð2Þ 2 dx2 where x is the distance measured along the length of the beam, y is the vertical deflection, and EI is the flexural rigidity of the cross section. The change in strain energy ‘DU’ DU ¼ Ud  Uu

ð3Þ

Please cite this article in press as: A. Eraky et al., Damage detection of flexural structural systems using damage index method – Experimental approach, Alexandria Eng. J. (2015), http://dx.doi.org/10.1016/j.aej.2015.05.015

Damage detection of flexural structural systems

3

where ‘d’ and ‘u’ refers to damaged and undamaged state, where the ‘Ud ’ and ‘Uu ’ are the damaged and undamaged strain energy, respectively [22]. Equating the external ‘WE ’ and internal work ‘WI ’; WE ¼ WI

ð4Þ

WE ¼ Ki d2i

ðAssume the logarithmic decrement ‘di ¼ 1’Þ ð5Þ

WI ¼

Z

L

ð6Þ

MðxÞdh 0

where M dh d2 / ¼ ¼ ¼ /00 ðxÞ EI dx dx2

ð7Þ

and /(x) represents the normalized modal vectors The ith modal stiffness Ki of the beam is given by: Z L    Ki ¼ kðxÞ/00i ðxÞ /00i ðxÞdx where kðxÞ ¼ EI

ð8Þ

0

Ki ¼

Z

L

U¼

h i kðxÞ/00i ðxÞ2 dx

ð9Þ

0

The contribution of the jth member of the ith modal stiffness, Cij, is given by Z  00 2 Cij ¼ kj /i ðxÞ dx ð10Þ j

where kj is the stiffness of the jth member The fraction of the modal stiffness ‘Fij’ (element sensitivity) of the ith mode that is concentrated in jth member and is given by

 2 2  2 2  2  2  @ w @ w @ w @ w þ þ 2t 2 2 @x @y @x2 @y2 0 0  2 2 ! @ w dxdy þ 2ð1  tÞ @x@y D 2

Z

b

Z

a

ð16Þ

where D is the bending stiffness of the plate, w is the transverse displacement of the plate, @ 2 w=@x2 and @ 2 w=@y2 are the bending curvatures, and 2@ 2 w=@x@y is the twisting curvature of the plate Cornwell et al. [23]. For a particular mode shape /i ðx; yÞ of the undamaged structure, the strain energy Ui associated with that mode shapes is  2 2  2 2  2  2  Z Z D b a @ /i @ /i @ /i @ /i Ui ¼ þ þ 2t @x2 @y2 @x2 @y2 2 0 0 !  2 2 @ /i þ 2ð1  tÞ dxdy ð17Þ @x@y where @ 2 /=@x2 and @ 2 /=@y2 are the curvatures of the flexural mode shape, and 2@ 2 /=@x@y is the twisting mode shape curvature for the ith mode of the plate. If the plate is subdivided into Nx subdivisions in the x direction and Ny subdivisions in the y direction, then the energy Uijk associated with sub-region jk for the ith mode is given by  2 2  2 2 Z Z Djk bkþ1 ajþ1 @ /i @ /i Uijk ¼ þ 2 2 bk @x @y2 aj  2  2   2 2 ! @ /i @ /i @ /i dxdy ð18Þ þ 2ð1  tÞ þ 2t @x2 @y2 @x@y

Ui ¼

and

Ny X Nx X Uijx

ð19Þ

K¼1 j¼1

Fij ¼ Cij =Ki

ð11Þ

The fractional energy at location ‘jk’ is defined as:

for the damaged structure, Fij ¼ Cij =Ki

ð12Þ C*ij,

Fijk ¼

Uijk Ui

and

Ny X Nx X Fijx ¼ 1

ð20Þ

K¼1 j¼1

Utilizing the expressions for Cij and Eq. (12) is transformed to [22]: R  RL RL 2 2   2 kj j ½/00i ðxÞ þ k1 0 k ½/00i ðxÞ dx kðxÞ 0 ½/00i ðxÞ dx j  1 ffi R RL RL 2 2 2  kj j ½/00i ðxÞ þ k1j 0 k½/00i ðxÞ dx k ðxÞ 0 ½/00i ðxÞ dx

Similar expressions can be written using the modes of the damaged structure /i ; where the subscript * indicates damaged state. A ratio of parameters can be determined which is indicative of the change of stiffness in the structure as follow:

ð13Þ

ð21Þ

by approximating kðxÞ ffi k ðxÞ R R RL 2 2   2 L ½/00i ðxÞ þ 0 ½/00i ðxÞ dx 0 ½/00i ðxÞ dx j kj R DIj ¼  ¼ R RL 2 2 2  L kj ½/00i ðxÞ þ 0 ½/00i ðxÞ dx 0 ½/00i ðxÞ dx j h PNM 00 2 ihPNM 00 2 i 2 ð/00 ji Þ þ i¼1 ð/ji Þ i¼1 ð/ji Þ kj ihP i DIj ¼  ¼ h P 2 NM 00 2 00 2 kj ð/ Þ ð/ Þ ð/00ji Þ þ NM ji ji i¼1 i¼1 where NM is the number of modes 2.2. Plate structures The strain energy U for a plate of size b · a is given by:

 Djk fijk ¼ Djk fijk

where ð14Þ

 R bkþ1 R ajþ1 @ 2 /i 2

 2  2   2 2  @ /i @ /i @ /i þ 2t dxdy þ 2ð1  tÞ 2 2 bk aj @x @y @x@y      fijk ¼       2 2 R b R a @ 2 /i 2 2 2 2 @ 2 /i þ @@y/2i þ 2t @@x/2i @@y/2i þ 2ð1  tÞ @x@y dxdy 0 0 @x2 @x2

þ



@ 2 /i @y2

2

ð22Þ

ð15Þ

fijk

and an analogous term can be defined using the damaged mode shapes. In order to account for all measured modes, the following formulation for the damage index, for subregion ‘jk’ is used: Pm  i¼1 fijk bji ¼ Pm ð23Þ i¼1 fijk

Please cite this article in press as: A. Eraky et al., Damage detection of flexural structural systems using damage index method – Experimental approach, Alexandria Eng. J. (2015), http://dx.doi.org/10.1016/j.aej.2015.05.015

4

A. Eraky et al.

3. Experimental setup

3.2. Test procedure

3.1. Materials and methods

3.2.1. Beam

In the current research, steel beam and steel plate were used for the purpose of damage detection. The beam cross-sectional dimensions were (Width · Depth) equal to 50 · 6 mm. The beam was simply supported over an effective span of 1500 mm. The plate was of dimensions (Length · Width) equal to (930 · 910 mm) and 3 mm thickness. The four sides of the plate were fully supported onto a rigid steel frame by means of continuous weld. The elastic steel properties were determined experimentally by means of static tests. The unit mass and elastic modulus of steel were 7.85 t/m3, and 2e7 t/m2, respectively. Figs. 1 and 2 show general layouts for the beam and plate, respectively. The beam was divided into six equal spaces and mounted with five light weight accelerometers. Whereas, the plate was divided into eight cross seven mid-field divisions. Due to insufficient number of accelerometers, a total of twelve accelerometers were distributed eventually into one quarter of the plate at once. The same procedure was repeated after shifting the accelerometers to another quarter, i.e., to record a complete set of reading, the data were collected in four stages. Acceleration–Time histories were collected by means of strain type and piezoelectric accelerometers. The data were collected using a sampling rate of 200 Hz. This frequency was selected to capture up to the third mode for both beam and plate. In order to obtain high quality signals and decrease the low frequency noise, all records were subjected to a high pass filter of cut-off frequency of 5 Hz. The collected data were analyzed and modal parameters were obtained.

Firstly, the beam was examined in its sound state and kept for comparison with its state after subjecting to damage. The beam was degraded twice by means of making hand saw cuts along the beam. For the same station, two cuts were applied from both edges of the beam to keep its symmetric setting. The cut created a groove from both sides of the beam of dimensions of 8 mm width and 2 mm thickness. The first damage was represented by cut created at the beam mid-span while the second damage was represented by adding another cut at 250 mm right hand sided to the first crack. The beam in the three conditions was subjected to light impact at its midpoint and then left to vibrate freely. The collected data at each stage were obtained and formal modal analysis was conducted. Fast Fourier Transformation (FFT) was calculated for each case. Fig. 3 shows the beam with the mounted accelerometers. Fig. 4a and b shows the acceleration time history with the corresponding FFT plot for sound beam. The cracked beams are shown in Fig. 5a and b. The detail of the crack is shown in Fig. 5c. The FFT plots for the two cracked beams are shown in Fig. 6a and b.

6 mm CH1 250 mm

CH2

CH3

CH4

CH5

1500 mm Figure 3 Undamaged beam showing position of mounted accelerometers.

(a)

Figure 1

Examined beam with mounted accelerometers.

Acceleration (g)

5

0

-5 0

0.5

1

1.5

(b)

3

Amplitude

Time (sec)

2

10.5 Hz

1

0

0

20

40

60

80

100

Frequency (Hz)

Figure 2

Plate divisions showing monitoring points.

Figure 4 FFT.

(a) Acceleration time history, and (b) Corresponding

Please cite this article in press as: A. Eraky et al., Damage detection of flexural structural systems using damage index method – Experimental approach, Alexandria Eng. J. (2015), http://dx.doi.org/10.1016/j.aej.2015.05.015

Damage detection of flexural structural systems

5

Detail A 6 mm CH 1

CH 2 750 mm

CH 3

CH 4

6 mm CH 2 CH 1 750 mm

CH 5

1500 mm

CH 3 CH 4 250 mm

CH 5

1500 mm

(a)

(b)

8mm 50mm 6mm (c)

3 2

Cracked beam (a) damage I, (b) damage II, and (C) detail A representing the damage shape.

(a)

10.25 Hz

1 0

0

20

40

60

80

100

(b)

2

10.156 Hz Amplitude

1

2

3

4

5

6

7

8

9

10

11 12 Detail B

115 mm

Frequency (Hz)

930 mm

(a) Amplitude

Figure 5

1

130 mm 910 mm

0

0

20

40

60

80

100

Frequency (Hz)

Figure 6

(b)

FFT for damaged condition (a) D1, and (b) DII.

50 mm 3 mm 3 mm

Secondly, the plate was examined in its healthy state and kept for comparison with the damaged plate. The same plate was then subjected to a mechanical saw cut at its center. The cut created a groove of dimensions 50 · 3 · 3 mm in plan. Fig. 7a and b shows the plate and the detail of the cut, respectively. The plate in the two conditions was subjected to light impact at its center point and then left to vibrate freely. The collected data at each stage were obtained and formal modal analysis was conducted. Fast Fourier Transformation (FFT) was calculated for each case. Figs. 8 and 9 show the FFT plots for the sound and cracked plates, respectively.

50 mm

3.2.2. Plate

Figure 7 crack.

(a) Layout of the plate, and (b) dimension of artificial

4. Results and discussion Free vibration was conducted on the test specimen to obtain its dynamic characteristics including natural frequencies and

mode shapes. The following are the detailed damage assessment for the beam and plate, respectively.

Please cite this article in press as: A. Eraky et al., Damage detection of flexural structural systems using damage index method – Experimental approach, Alexandria Eng. J. (2015), http://dx.doi.org/10.1016/j.aej.2015.05.015

6

A. Eraky et al. 1.04

20.508 Hz

1.03

1

Damage Index

Amplitude

1.5

0.5

0

0

20

40

60

80

1.01 1

100

Frequency (Hz)

Figure 8

1.02

0.99

0

0.5

FFT for sound plate.

1

1.5

Length (m) 1.04

3

Damage Index

Amplitude

19.043 Hz 2

1

0

0

Figure 9

50

Frequency (Hz)

1.02

1

0.98

100 0.96

0

0.5

1

1.5

Length (m)

FFT for cracked plate.

Figure 10 Damage index for due to (a) damage (I), and (b) damage (II).

4.1. Damage assessment in beams The changes in the first three natural frequencies of beams were captured and shown in Table 1 for the damaged and undamaged beam. Numerical simulation for the beams was also adopted using the commercial finite element software (SAP2000 [24]). In experimental work, the damage reduced the first mode for the first and second cases of the first beam damage scenario with 2.32% and 3.27%, respectively as shown in Table 1. The change in the first mode of the second damaged beam was more than the first damaged beam as the presence of the second cut worked on extreme degradation of the beam stiffness. Also the change in the first mode obtained numerically for the first and second damaged beam were 0.15% and 0.66%, respectively. These values were decreased in the second mode because the influence of damage was much clear in the first mode. Fig. 10 a shows the damage index of the first cracked beam. It was demonstrated that, DI in each element was

Table 1 Mode No.

approximately ‘‘1’’ except the middle element in which the damage element exists. The error in damage detection was calculated as the absolute difference between detected and actual damage ratio. The change in the mode shape curvature appeared at damage location which affects the damage index calculations. Furthermore, Fig. 10b shows the damage index of the damaged beam with the second scenario. It was clear that the damage index has two spikes at the right position of existing damage due to the change in the mode shape curvature at the damaged points. The error in damage detection occurred because this method required a large number of readings in order to decrease the error and the available sensors are limited. The experimental damage index method gives a good indication of damage location. Fig. 11a and b shows the damage index of the first and second cracked beams when using the numerical finite element readings. It was shown that, the damage index in each element

First three natural frequencies of undamaged and damaged beams. Frequency (Hz) – (% change)* Numerical analysis

1st 2nd 3rd *

Experimental analysis

Undamaged beam

Damaged beam (I)

Damaged beam (II)

Undamaged Beam

Damaged beam (I)

Damaged beam (II)

10.7822 30.971 52.305

10.766 (0.15%) 31.002 (0.1%) 51.687 (1.18%)

10.711 (0.66%) 30.974 (.009%) 51.292 (1.93%)

10.5 31.006 52.73

10.254 (2.32%) 31.006 (0.0%) 51.27 (2.77%)

10.156 (3.27%) 31.25 (0.78%) 51.536 (2.26%)

%change (undamaged – damaged)/undamaged.

Please cite this article in press as: A. Eraky et al., Damage detection of flexural structural systems using damage index method – Experimental approach, Alexandria Eng. J. (2015), http://dx.doi.org/10.1016/j.aej.2015.05.015

Damage detection of flexural structural systems

7

1.04

(a)

Dmage Index

1.03

4

1.02

2

1.01

0 1

1

1

0.5 0.99

0

.25

.5

.75

1

1.25

0.5

Width

1.5

0 0

Length (m)

Length (m)

(b)

1.02

Damage Index

Experimental first mode shape of undamaged plate.

Figure 12

1.03

1.01

4

1 2

0.99 0.98

0

0.5

0 1

1.5

1

Length (m)

Figure 13

was approximately ‘‘1’’ except the damaged elements existing in both figures at which the curvature in the mode shapes occurred. The numerical results were very close to results obtained experimentally.

The acceleration time history response of the plate was recorded and analyzed. Formal modal analysis was consequently applied. In addition, finite element model of the steel plate was analyzed and the fundamental natural frequencies and the associated mode shapes were obtained and compared with the experimental work. The first three fundamental modes are shown in Table 2 for the damaged and undamaged cases. The damaged and undamaged first modes were also represented graphically and shown in Figs. 12 and 13, respectively. The changes in the first three modes were 7.14%, 1.27% and 0.0% for the experimental work, respectively. This was because; the contribution of the first mode was dominant in the vibration. Moreover the presence of the crack at the center Table 2 First three natural frequencies of undamaged and damaged plate. Frequency (Hz) – (% change)* Numerical analysis

Experimental analysis

Undamaged plate

Damaged plate

Undamaged plate

Damaged plate

1st

21.05

20.508

2nd

48.08

3rd

64.92

21.03 (0.09%) 48.07 (0.02%) 64.90 (0.03%)

19.043 (7.14%) 56.885 (1.27 %) 65.918 (0.0%)

*

57.617 65.918

%change (undamaged – damaged)/undamaged.

0

0

Length (m)

Experimental first mode shape of damaged plate.

1.015

Damage Index

4.2. Damage assessment in plate

0.5

Width

Figure 11 Damage index from numerical work for (a) damage (I), and (b) damage (II).

Mode No.

1

0.5

1.01 1.005 1 0.995 1 1 .5

L y (m)

.5 0 0

L x (m)

Figure 14 Modal strain energy based on damage index from the experimental work.

of the plate influences directly the first mode rather than any other mode. DI for experimental work is shown in Fig. 14. It was shown that; the damage index in each element was approximately one except the middle part in which the damaged element exists. This indicated that the probability of occurrence of damage at the center of the plate is high. The errors increased in plate model because the plate requires the availability of more sensors at once. Fig. 15 shows the damage index of the plate from the numerical work. It was also demonstrated that, the damage index was also very close to the result from experimental work. 5. Numerical results 5.1. Beams Further numerical simulation of steel beams with different statical systems as well as subjected to different damage

Please cite this article in press as: A. Eraky et al., Damage detection of flexural structural systems using damage index method – Experimental approach, Alexandria Eng. J. (2015), http://dx.doi.org/10.1016/j.aej.2015.05.015

8

A. Eraky et al. condition was examined. The beam cross-section was of dimensions (Width · Depth) equal to 50 · 20 mm. The beam was first examined in simply supported state with an effective span of 2.8 m. The beam was also examined as continuous beam by duplicating the span. Modal analysis was performed to obtain the natural frequencies and the associated mode shapes of the beam.

Damage index

1.015 1.01 1.005 1 0.995 1

Width (m)

0.5 0

Length (m)

0

Figure 15 Modal strain energy based on damage index from the FE software.

Damage Index

1.03 0.5

(a) 1.02 1.01 1 0

0.5

1

1.5

2

2.5

2

2.5

Length (m)

A B

Dimensions of cracks in beam. Length (mm) 100 100

1.03

Width (mm)

Depth (mm)

40 40

5 10

Damage Index

Table 3 Size

(b) 1.02 1.01 1 0

0.5

1

1.5

Length (m)

(a)

Size A

1.03

Damage Index

1 .4 m

Size B

(b) 1 .4 m

(c)

1.02 1.01 1

(c)

S iz e BA 0 .7 m

Figure 16

0

Size A

0.5

1

0 .7 m

2 .8 m

1.5

2

2.5

Length (m)

Damage cases for 1-span beam, (a) C1, (b) C2, (c) C3.

Figure 19 Modal strain energy based on damage index for 1span beam, (a) C1, (b) C2, (c) C3.

(a) Size A 1.4m

(b) Size A

Size B 1.4m

1.4m 2.8m

Figure 17

2.8m

Damage cases for 2-span beam, (a) C4, (b) C5.

100mm

100mm 20mm

(a)

5 mm Figure 18

20mm (b)

10 mm

Detail of crack (size A) simulated in FEM.

Please cite this article in press as: A. Eraky et al., Damage detection of flexural structural systems using damage index method – Experimental approach, Alexandria Eng. J. (2015), http://dx.doi.org/10.1016/j.aej.2015.05.015

Damage detection of flexural structural systems

9

(a)

(a)

1.15

1.01

Damage Index

Damage index

1.02

1 0

1

2

3

4

5

Length (m)

Damage index

1.02

1.1

C1

1.05 1 0.95 10

(b)

5

1.01

Ly (m)

0

2

0

8

6

4

Lx (m)

1 0

1

2

3

4

5

(b)

Length (m)

Table 4

Plate damage severity.

Damage case

Elastic modulus reduction ratio (%)

Damage A (DA) Damage B (DB) Damage C (DC)

30 50 80

Damage Index

1.15

Figure 20 Modal strain energy based on damage index for 2span beam, (a) C4, (b) C5.

C2

1.1 1.05 1 0.95 10 5

Ly (m)

0

4

2

0

8

6

Lx (m)

(c) (b)

DB

5.0m

5.0m

(a)

DB

Damage Index

1.15

1.05 1

5.0m

5.0m

4.0m

4.0m

Ly (m)

4.0m

DC 4.0m

4.0m

4.0m

5.0m

5.0m

DC

Damage Index

DB

0

1.15

DB 5.0m

DA

5 0

2

8

6

4

Lx (m)

(d)

(d)

(c) 5.0m

1.1

0.95 10

DB

4.0m

C3

1.05 1 0.95 10

Ly (m)

4.0m

Figure 21 Different damage conditions for plate, (a) C1, (b) C2, (c) C3, and (d) C4.

C4

1.1

Figure 22 (d) C4.

5 0

0

2

4

6

8

Lx (m)

Damage index for 2-span, (a) C1, (b) C2, (c) C3, and

Please cite this article in press as: A. Eraky et al., Damage detection of flexural structural systems using damage index method – Experimental approach, Alexandria Eng. J. (2015), http://dx.doi.org/10.1016/j.aej.2015.05.015

10 Five damage cases were investigated with two different sizes of cracks as listed in Table 3, in which crack size B represents larger damage than crack size ‘A’. Fig. 16a –c shows three different scenarios for cracked single span beams. Moreover, Fig. 17a and b shows additional two scenarios for continuous cracked beams. Fig. 18 shows the details of crack size ‘A’ and ‘B’ simulated in the FE model. The first mode and their corresponding curvatures obtained from the results of the FE analysis were used to calculate the modal strain energy based on damage index of beams. The plot of damage index along the beam for all damage cases is shown in Fig. 19(a–c) and (Fig. 20a and b). The spikes with magnitudes greater than ‘‘1’’ indicated the location of damaged elements. Comparison of figures shows that the peak in the damage index increased by increasing the severity of damage. From the results of all cases, it is evident that the damage index based on the modal strain energy method was able to correctly locate the damage in beams in all damage cases. The increase of DI spike values was also proportional to the damage size. 5.2. Plates A typical rectangular concrete slab 5000 mm in length, 4000 mm in width and 250 mm in thickness was chosen for the numerical analysis. Rectangular array of 2 · 2 for the typical slab module was set for examination. The whole plate was simply supported on its four corners. The whole plate was discretized into 320 equal plate elements. Damage was simulated by weakening the elastic modulus (E) of some elements by 30%, 50%, and 80% as shown in Table 4. Fig. 21a–d, shows four damage scenarios for the plates with different damage configurations. DI was calculated and the values greater than unity identified the damage location. DI was represented by contour and shown in Fig. 22a–d. Comparison of the results shows that the DI based on the modal strain energy method is able to correctly locate the damage in plates in all damage scenarios. It was also shown that the higher the DI peak value obtained, the more severity in damage can be expected. 6. Conclusion In the current research, dynamic computer simulation techniques were used to develop non-destructive damage detection methodology for beam and plate structures. The proposed procedure was based on comparison of modal strain energy for different structure conditions from which damage index (DI) can be calculated. Analysis from free vibration records of undamaged and damaged finite element models was used to locate the position of damage throughout the beams and plates. In addition, experimental verification to validate the efficiency of the proposed method was conducted. The experimental data obtained from the dynamic tests were compared with those predicted from the finite element models. It was shown that DI method was able to correctly locate the damage in plates and beams for all damage cases. The main findings of the paper can be summarized as follow: 1. For beam with mid-point damage, one single peak appeared in plotting the DI at the mid-span of the beam. Single peak indicated the presence of single crack.

A. Eraky et al. 2. For beam with multiple cracks, DI plot with multiple peaks corresponding to each crack position was observed. 3. For plates, the DI was represented by a contour with peak value located exactly at the damage place. 4. Good agreement between numerical and experimental results was observed. Therefore, it provides confidence for using the adopted self-made computer module for further investigation towards establishing the proposed multicriteria damage detection method.

References [1] C.P. Ratcliffe, Damage detection using a modified Laplacian operator on mode shape data, J.Sound Vibr. 204 (3) (1997) 505– 517. [2] J.V. Arau´jo dos Santos, C.M. Mota Soares, C.A. Mota Soares, H.L.G. Pina, Development of a numerical model for the damage identification on composite plate structures, Compos. Struct. 48 (1–3) (2000) 59–65. [3] Y.Y. Li, L. Cheng, L.H. Yam, W.O. Wong, Identification of damage locations for plate-like structures using damage sensitive indices: strain modal approach, Comput. Struct. 80 (25) (2002) 1881–1894. [4] M.A. Abdo, M. Hori, A numerical study of structural damage detection using changes in the rotation of mode shapes, J. Sound Vib. 251 (2) (2002) 227–239. [5] Marc Re´billatn, Rafik Hajrya, Nazih Mechbal, Nonlinear structural damage detection based on cascade of Hammerstein models, Mech. Syst. Signal Process. 48 (2014) 247–259. [6] J.M. Ndambi, J. Vantomme, K. Harri, Damage assessment in reinforced concrete beams using eigen frequencies and mode shape derivatives, Eng. Struct. 24 (4) (2002) 501–515. [7] N.M.M. Maia, J.M.M. Silva, E.A.M. Almas, R.P.C. Sampaio, Damage detection in structures: from mode shape to frequency response function methods, Mech. Syst. Signal Process. 17 (3) (2003) 489–498. [8] J.T. Kim, Y.S. Ryu, H.M. Cho, N. Stubbs, Damage identification in beam-type structures: frequency-based method vs mode-shape-based method, Eng. Struct. 25 (1) (2003) 57–67. [9] E. Parloo, P. Guillaume, M. Van Overmeire, Damage assessment using mode shape sensitivities, Mech. Syst. Signal 17 (3) (2003) 499–518. [10] P.F. Pai, L.G. Young, S.Y. Lee, A dynamics-based method for crack detection and estimation, Struct. Health Monitor. 2 (1) (2003) 5–25. [11] G.M. Owolabi, A.S.J. Swamidas, R. Seshadri, Crack detection in beams using changes in frequencies and amplitudes of frequency response functions, J. Sound Vib. 265 (1) (2003) 1–22. [12] C.C. Chang, L.W. Chen, Detection of the location and size of cracks in the multiple cracked beam by spatial wavelet based approach, Mech. Syst. Signal Process. 19 (1) (2005) 139–155. [13] J.V. Arau´jo, H.M.R. Lopes, M. Vaz, C.M. MotaSoares, C.A. MotaSoares, M.J.M. de Freitas, Damage localization in laminated composite plates using mode shapes measured by pulsed TV holography, Compos. Struct. 76 (3) (2006) 272–281. [14] Z. Ismail, H. Abdul Razak, A.G. Abdul Rahman, Determination of damage location in RC beams using mode shape derivatives, Eng. Struct. 28 (11) (2006) 1566–1573. [15] J. Wang, C. Lin, S. Yen, A story damage index of seismicallyexcited buildings based on modal frequency and mode shape, Eng. Struct. 29 (9) (2007) 2143–2157. [16] P. Qiao, K. Lu, W. Lestari, J. Wang, Curvature mode shapebased damage detection in composite laminated plates, Compos. Struct. 80 (3) (2007) 409–428.

Please cite this article in press as: A. Eraky et al., Damage detection of flexural structural systems using damage index method – Experimental approach, Alexandria Eng. J. (2015), http://dx.doi.org/10.1016/j.aej.2015.05.015

Damage detection of flexural structural systems [17] Marc Re´billat, Rafik Hajrya, Nazih Mechbal, Nonlinear structural damage detection based on cascade of Hammerstein models, Mech. Syst. Signal Process. 279 (2014) 119–139. [18] Z. Lang, G. Park, C.R. Farrar, M.D. Todd, Z. Mao, L. Zhao, K. Worden, Transmissibility of non-linear output frequency response functions with application in detection and location of damage in MDOF structural systems, Int. J. Non-linear Mech. 46 (6) (2011) 841–853. [19] J.S. Uribe, N. Mechbal, M. Re´billat, K. Bouamama, M. Pengov, Probabilistic decision trees using SVM form ulti-class classification, in: 2nd International Conference on Control and Fault-Tolerant Systems 2, 2013m, pp. 619–624.

11 [20] H.W. Hu, C.B. Wu, W.J. Lu, Damage detection of circular hollow cylinder using modal strain energy and scanning damage index methods, Comput. Struct. 89 (2011) 149–160. [21] A.C. Ugural, Stresses in Plates and Shells, 4th ed., McGrawHill, Singapore, 1999. [22] N. Stubbs, J.T. Kim, C.R. Farrar, Field verification of a non destructive damage localization and severity algorithm, Int. Modal Anal. Conf. 13 (1995) 210–218. [23] D. Coronelli, P.G. Gambarova, Structural assessment of corroding RC beams: modelling guidelines, J. Struct. Eng. 130 (8) (2004) 1214–1224. [24] SAP2000, 2009. CSi: Computers and Structures Inc, Version 14.1.0. Computer software.

Please cite this article in press as: A. Eraky et al., Damage detection of flexural structural systems using damage index method – Experimental approach, Alexandria Eng. J. (2015), http://dx.doi.org/10.1016/j.aej.2015.05.015