Structural damage assessment of building structures using dynamic experimental data (p 1 8)

Detection of damage to structures has recently received considerable attention from the viewpoint of maintenance and safety assessment. In this respect, the vibration characteristics of buildings have been applied consistently to obtain a damage index of the whole building, but it has not been established as a practical method until now. It is reasoned that this is perhaps due to restrictions on the experiment, use of improper method, and lack of inspection opportunity for the structures. In addition, in the case of largescale structures such as buildings, many variables to be considered for the analysis contribute to a large number of degrees of freedom, and this can also be a considerable problem for the analysis. A practical method for the detection of structural damage using the first natural frequency and mode shape of building is proposed in this paper. The effectiveness of the proposed method is verified by numerical analysis and experimental tests. From the results, it is observed that the severity and location of the damage can be estimated with a relatively small error by using modal properties of building. Copyright © 2004 John Wiley Sons, Ltd.

STRUCTURAL DAMAGE ASSESSMENT OF BUILDING

STRUCTURES USING DYNAMIC EXPERIMENTAL DATA

HEUNG-SIK KIM 1

AND YOUNG-SOO CHUN 2

*

1 Department of Architecture, Honam University, Kwang-ju, Korea

2 Department of Structural Eng., Korea National Housing Corporation, Kyeonggi-do, Korea

SUMMARY Detection of damage to structures has recently received considerable attention from the viewpoint of maintenance and safety assessment In this respect, the vibration characteristics of buildings have been applied consistently to obtain a damage index of the whole building, but it has not been established as a practical method until now It

is reasoned that this is perhaps due to restrictions on the experiment, use of improper method, and lack of inspec-tion opportunity for the structures In addiinspec-tion, in the case of large-scale structures such as buildings, many vari-ables to be considered for the analysis contribute to a large number of degrees of freedom, and this can also be

a considerable problem for the analysis A practical method for the detection of structural damage using the first natural frequency and mode shape of building is proposed in this paper The effectiveness of the proposed method

is verified by numerical analysis and experimental tests From the results, it is observed that the severity and loca-tion of the damage can be estimated with a relatively small error by using modal properties of building Copy-right © 2004 John Wiley & Sons, Ltd.

The trend of constructing bigger and higher buildings demands greater safety caution for these struc-tures A diagnosis of structural integrity of these buildings involves an assessment of whether they can serve safely, and its current assessment techniques rely on a visual inspection or localized destructive and non-destructive tests In this case, the quality of the assessment is influenced by the experience and knowledge of each investigator Furthermore, the investigators are faced with problems in assess-ing an unapproachable element and in an area where direct visual inspection is difficult In addition, the result of a localized inspection does not represent the condition in whole structures, and it is nec-essary to inspect a considerable area to represent the condition of the building at large After all, these constraints imply that current assessment techniques are time-consuming, labour-intensive, and costly These problematic issues have stimulated a search for a better method, and recently many research attempts to accomplish this purpose have been continuing using dynamic characteristics of vibration

tests of the building (Goh et al., 1995; Li et al., 1999; Hassiotis and Jeong, 1993).

Structural damage to buildings can occur due to cracking, ageing of materials etc and is indicated

by a change in physical and modal parameters of structural system These parameters can be used as

an index of such damage detection This concept has recently been applied in many research studies

for damage detection of various structures (Stephens and Yao, 1987; Goh et al., 1995; Liu, 1995; Bicanic and Chen, 1997; Li et al., 1999; Hassiotis, 2000) In this case, most of these methods require

limited information on measured modal parameters such as natural frequency or mode shape for the

Published online in Wiley Interscience (www.interscience.wiley.com) DOI:10.1002/tal.227

* Correspondence to: Young-Soo Chun, Department of Structural Engineering Korea National Housing Corporation, 175 Kumi-dong, Pundang-gu, Sungnam-shi, Kyonggi-do, 463-500 Korea.

structures such as buildings, many variables to be considered for the analysis contribute to a large number of degrees of freedom (DOFs), and this can also be a considerable problem for the analysis Thus, this study, as an attempt at such analysis, takes a practical approach to use only first modal vibration characteristics of buildings to overcome the difficulties of the field experiment, proposes a method for damage detection by simple modelling of the buildings for each storey, and verifies its usefulness

The damage detection algorithm used in this research is a method to detect local damage using the change of stiffness of each storey of a multi-storied building based on the modal information as mea-sured and obtained in the field It requires first natural frequency and mode shape only as the input data Here, local damage refers to not each element level but each storey level, and structural damage

is indicated by the decrease in stiffness of each storey due to damage to each element Thus, it is assumed that any change in storey stiffness is solely due to change in the sum of column or wall stiff-nesses at that storey, and the stiffness of each storey of the damaged building can be represented by the product of a damage index and stiffness of each storey of the undamaged building as shown in Equation (1)

(1) Here, ai represents the damage index of ith storey, K i , K * is the contribution of the ith storey on the i

global stiffness matrix of the undamaged and damaged structure respectively, and NL is the number

of elements of the structures with n degrees of freedom.aican provide information not only on the location of the damage but also the severity of the damage The damage index, ai, is obtained using the following algorithm First, the eigenvalue problem of an undamped free vibration equation of

undamaged structure with n-DOF can be written as follows (Clough and Penzien, 1993):

(2) Here, ljis the eigenvalue (= wj

2

) of the jth vibration mode, and f jis the corresponding natural mode shape of the system Equation (2) can then be rewritten as

(3)

It is assumed that damage is not accompanied by a change in mass However, a change in stiffness produces changes in the eigenvalues and eigenvectors Therefore, the eigenvalue problem of the damaged structure is given by

(4) The left-head side of Equation (4) can be rewritten by substituting Equation (1) as in Equation (5):

(5)

*

K j D K i

K j j M j

K j j M j

K- j M j

K i i K i i

NL

* =

=

1

(6)

(7)

(8) Finally, Equation (9) for the solution of the damage index, aj, is obtained by

(9)

where [A] = {[D*][K]}-1

As shown in Equation (9), the proposed algorithm makes the damage detection of the structure

in each storey possible with data on only one minimum mode If information on several modes can be obtained by experiment, an expanded equation as shown in Equations (4) and (5) is possible An optimization problem can then be solved for improvement in the accuracy of damage detection

Based in the proposed algorithm and the definition of damage to structures, a detailed method and process for the detection of building damage is introduced and the usefulness of such a method is ver-ified using a numerical example

The example building chosen for the illustration of the proposed method is a residential building with shear-wall dominant systems, which is widely used in Southeast Asia and is a 20-storey straight linear flat apartment as shown in Figure 1(a) The story height is 2600 mm for all storeys For the sake

of simplification of the analysis, it is assumed that all walls in the building are uniform This example assumes that a perfect analysis model has been set for the building before damage occurs

The procedure for damage detection is straightforward and easy to implement, as described in the following

*

*

ai=wj[ ][ ]{ }A M fj

T

{ } ={ 1, 2, 3,◊ ◊ ◊ ◊ ◊ ◊, }

K

K K

K K

K

K K

N

N

[ ] =

◊ ◊ ◊ ◊ ◊ ◊

- ◊ ◊ ◊ ◊ ◊ ◊

- ◊ ◊ ◊ ◊ ◊ ◊

-È

Î

Í Í Í Í Í Í Í Í Í Í Í Í Í Í

˘

˚

˙

˙

˙

˙

˙

3

1

˙˙

˙

˙

˙

˙

˙

˙

˙

˙

D

*

◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊

◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊ ◊

È

Î

Í Í Í Í Í Í Í

˘

˚

˙

˙

˙

˙

1 2

˙

Step 1 First, according to the assumption previously introduced in Section 2, the sample building is converted into a simple n-DOF system corresponding to n storeys as shown in Figure 1(b).

In this numerical example, the stiffness of each storey can be obtained by applying a unit load at each storey But, in a real problem, static condensation is performed to eliminate all rotational DOFs

(Guyan, 1965) and then, to narrow the gap between the condensed model with n-DOF lumped

mass-spring system and the actual structure, system identification is performed

First, full-scale measurements are carried out for the building, and by applying the random decre-ment technique on a time window of acceleration responses at each floor of the building, output-only modal analysis is conducted Then, by using the damage detection approach in Section 2, the stiffness terms of the simple model are identified and then used to update the stiffness matrix of the complete model

(a)

(b) Figure 1 Example building and condensed model (a) Typical floor plan of the example building

(b) Condensed model (numbers indicate condensed DOFs)

Step 2 Parameters such as natural frequency and mode shape are needed for the damage detection

and are obtained by experiment

In this numerical example, the damage at a particular storey is introduced by decreasing the stiffness

of the finite element model, and the modal information of the building before and after damage is obtained by an eigenvalue analysis In this case, the change in modal information is assumed to be data measured from the field test, and the damage at a particular storey follows an assumed damage scenario

In this example, four damage scenarios were constructed to indicate a change in modal character-istics with respect to the severity of damage and the location of damage and to verify the usefulness

of the proposed detection method Generally, most previous research has used a case of severe damage

in order to make the usefulness of the proposed method more visible and also applied a very unreal-istically high mode for the natural frequency and mode shape Nevertheless, the internal damage of

an aged building can be much less in reality, and the detection of such damage is considered to be more useful in a practical sense In addition, the number of vibration modes that can be obtained by

an actual measurement is very limited in the case of a building, and the validity of such measurements

is also very restricted For those reasons, this example uses only the first mode and a lightly damaged structure Table 1 summarizes the damage scenario

Step 3 As previously mentioned in Section 2, the decrease in stiffness is computed reversely In this

case, the accuracy of damage detection can vary according to the number of vibration modes used, the location and the severity of damage, etc Therefore, the usefulness of the proposed method can be examined with respect to the reversely computed amount of decrease in the stiffness

In order to find out the detection result with respect to the location of damage, a 20% decrease in the stiffness at the 2nd, 10th, 17th and 5–15th storeys was applied according to the damage scenario, and the location and severity of damage were computed following the proposed algorithm Table 2 exhibits the modal data for each model per the case scenario, and Table 3 depicts the damage detection result Table 3 shows the result of the simulation, that the proposed damage detection method can predict the damage at each storey of a building regardless of the damage location if the accuracy of the modal data obtained from the field test is assured

An experimental model was constructed as shown in Figure 2 in order to verify the usefulness of the proposed damage detection method experimentally The experimental model is a reduced model of the major structural member of the sample building as shown in Figure 1 The experimental model building has five storeys, and the size of wall of the model is 50 cm, 8 cm and 100 cm for the width,

thickness and height, respectively It was constructed using concrete of f ck= 300 kgf/cm2

, and 5 kgf of

Table 1 Damage scenarios

additional steel mass blocks at each storey was added to simulate the lumped mass on the floor of building The damage to the building was modelled by increasing the size of the opening to reduce the stiffness of the experimental model by 20% for the second storey only in order to model the case

of entirely known damage Table 4 shows the modal experimental data of the experimental model before and after the damage, and the damage detection result using this data is depicted in Table 5

(rad/s)

First mode 1·0000 0·9943 0·9828 0·9658 0·9432 0·9152 0·8820 0·8437 0·8005 0·7528 shape 0·7008 0·6447 0·5850 0·5219 0·4558 0·3871 0·3162 0·2435 0·1694 0·0755

(rad/s)

First mode 1·0000 0·9942 0·9826 0·9654 0·9425 0·9142 0·8805 0·8418 0·7982 0·7499 shape 0·6842 0·6276 0·5674 0·5039 0·4374 0·3685 0·2974 0·2245 0·1504 0·0754

(rad/s)

First mode 1·0000 0·9941 0·9824 0·9606 0·9376 0·9089 0·8751 0·8361 0·7921 0·7435 shape 0·6906 0·6336 0·5730 0·5089 0·4419 0·3723 0·3005 0·2269 0·1520 0·0762

(rad/s)

First mode 1·0000 0·9943 0·9829 0·9658 0·9433 0·9154 0·8739 0·8357 0·7928 0·7453 shape 0·6936 0·6379 0·5785 0·5159 0·4503 0·3821 0·2941 0·2220 0·1487 0·0746

Table 3 Damage index of numerical examples

Storey number

Case 1 Predicted value 1·004 0·799 0·991 0·993 0·997 0·986 0·981 0·999 0·971 1·003

1·032 1·015 1·135 1·006 1·026 1·055 1·000 0·998 0·986 0·999

Case 2 Predicted value 0·993 0·996 0·999 0·999 1·000 1·008 1·018 1·009 0·986 0·8123

1·003 0·986 0·999 0·995 1·003 1·013 1·000 1·002 1·003 1·032

Case 3 Predicted value 0·999 0·992 0·998 0·997 0·999 1·002 1·012 1·006 1·080 1·002

1·000 1·005 0·998 0·999 0·989 0·992 0·799 0·998 0·979 0·991

Case 4 Predicted value 1·000 1·002 1·001 0·999 0·811 0·998 0·999 0·989 0·999 1·003

1·023 1·008 1·000 1·016 0·808 0·999 0·999 0·998 1·000 1·003

As previously mentioned in the procedure in Section 2, the condensed model is constructed and each storey stiffness for the undamaged and damaged model building identified by experimental modal data A pre-damage test was therefore conducted on the undamaged model to identify the undamaged storey stiffness and, subsequently, the damage test is conducted on the damaged model A conven-tional modal testing technique was applied to determine the experimental modal data In tradiconven-tional modal analysis, the modal data are found by fitting a model to the frequency response function relat-ing excitation forces and vibration response

Table 5 Damage index of experimental example

Storey number

Predicted value 0·99832 0·8225 1·0132 0·9798 1·0602

Table 4 Modal data of experimental model Classification

First mode shape 1·0 0·93 0·79 0·60 0·25

Figure 2 Experimental model

5 CONCLUSION This investigation proposes a practical method for detecting damage per each storey of a building structure using measured vibration characteristics, and its usefulness is verified by a numerical example and model experiment The major contribution of the proposed method is that it is possible to detect damage using data of only one vibration mode at the minimum and the prediction error due to inac-curacy of the experimental data can be reduced by increasing the number of modes used and opti-mization The proposed method of this study is a method for detecting a change in stiffness at each storey, and it can be applied to all widely used cantilever-type building structures, for which a mod-elling for each storey is possible

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