THE STRUCTURAL DESIGN OF TALL AND SPECIAL BUILDINGS

Struct. Design Tall Spec. Build. 13, 1–8 (2004)

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

STRUCTURAL DAMAGE ASSESSMENT OF BUILDING

STRUCTURES USING DYNAMIC EXPERIMENTAL DATA

HEUNG-SIK KIM1 AND YOUNG-SOO CHUN2*

1

2

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

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 inspection opportunity for the structures. In addition, in the case of large-scale 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.

1.

INTRODUCTION

The trend of constructing bigger and higher buildings demands greater safety caution for these structures. 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 assessing 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 necessary 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

* 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.

Copyright © 2004 John Wiley & Sons, Ltd.

Received October 2002

Accepted November 2002

2

H.-S. KIM AND Y.-S. CHUN

identification of structural damage or quantification of such damage. However, up to now, no method

has been able to provide this function reliably for large structures, and it is more so for the case of

building structures. It is reasoned that this is perhaps due to restrictions on the experiment, incorrect

method, and lack of inspection opportunity for the structures. In addition, for the case of large-scale

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.

2.

DAMAGE DETECTION ALGORITHM

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 measured 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 stiffnesses 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).

NL

Ki* = Â a i Ki

(1)

i =1

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

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. ai can 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):

( K - l j M )f j = 0

(2)

Here, lj is the eigenvalue (= wj2) of the jth vibration mode, and fj is the corresponding natural mode

shape of the system. Equation (2) can then be rewritten as

[K ]{f j } = w 2j [ M ]{f j }

(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

[K *]{f *j } = w *j 2 [ M ]{f *j }

(4)

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

[K *]{f *j } = [ D*][K ]{a i }

Copyright © 2004 John Wiley & Sons, Ltd.

(5)

Struct. Design Tall Spec. Build. 13, 1–8 (2004)

DAMAGE ASSESSMENT USING DYNAMIC EXPERIMENTAL DATA

3

where

Èf1*jf 2*j ◊ ◊ ◊ ◊ ◊ ◊ f *N

0 ◊◊◊◊◊◊ 0

Í

*

Í f1*j ◊ ◊ ◊ ◊ ◊ ◊ 0 f2*jf3*j ◊ ◊ ◊ f Nj

Í

[ D*] = Í

f1*j ◊ ◊ ◊ 0

f2*j ◊ ◊ ◊ 0

Í

O M

O M

Í

*

ÍÎ

f1 j

f2*j

È K1

ÍK

Í 1

ÍM

Í

Í0

Í0

[K] = Í

Í0

ÍM

Í

Í0

Í0

Í

ÍÎ 0

K2

- K2

M

0

K2

0

M

0

0

0

0

0

M

0

- K3

- K3

M

0

0

0

◊◊◊ 0 ˘

˙

◊◊◊ 0 ˙

˙

◊◊◊ 0 ˙

OM ˙

˙

* ˚˙

f Nj

(6)

◊◊◊◊◊◊

◊◊◊◊◊◊

O

0 ˘

0 ˙

˙

M ˙

˙

0 ˙

◊◊◊◊◊◊

0 ˙

˙

◊◊◊◊◊◊

0 ˙

O

M ˙

˙

K N -2 K N -1 ˙

- K N -1 ˙

0

˙

K N ˙˚

0

{a i } = {a 1 , a 2 , a 3 , ◊ ◊ ◊ ◊ ◊ ◊ , a N }

T

(7)

(8)

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

a i = w *j [ A][ M ]{f *j }

(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.

3.

DAMAGE DETECTION PROCESS AND NUMERICAL EXAMPLE

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 verified 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.

Copyright © 2004 John Wiley & Sons, Ltd.

Struct. Design Tall Spec. Build. 13, 1–8 (2004)

4

H.-S. KIM AND Y.-S. CHUN

(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 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 massspring system and the actual structure, system identification is performed.

First, full-scale measurements are carried out for the building, and by applying the random decrement 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.

Copyright © 2004 John Wiley & Sons, Ltd.

Struct. Design Tall Spec. Build. 13, 1–8 (2004)

5

DAMAGE ASSESSMENT USING DYNAMIC EXPERIMENTAL DATA

Table 1. Damage scenarios

Classification

Case 1

Case 2

Case 3

Case 4

Damage element

Degree of damage

Vibration mode used

2-storey

10-storey

17-storey

5-storey, 15-storey

20% decrease in stiffness

20% decrease in stiffness

20% decrease in stiffness

20% decrease in stiffness

First mode

First mode

First mode

First mode

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 characteristics 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 unrealistically 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.

4.

EXPERIMENTAL VERIFICATION

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 fck = 300 kgf/cm2, and 5 kgf of

Copyright © 2004 John Wiley & Sons, Ltd.

Struct. Design Tall Spec. Build. 13, 1–8 (2004)

6

H.-S. KIM AND Y.-S. CHUN

Table 2. Modal data of numerical example

Classification

Case 1

Case 2

Case 3

Case 4

Frequency

(rad/s)

First mode 1·0000 0·9943

shape

0·7008 0·6447

Frequency

(rad/s)

First mode 1·0000 0·9942

shape

0·6842 0·6276

Frequency

(rad/s)

First mode 1·0000 0·9941

shape

0·6906 0·6336

Frequency

(rad/s)

First mode 1·0000 0·9943

shape

0·6936 0·6379

2·622

0·9828 0·9658

0·5850 0·5219

0·9432 0·9152

0·4558 0·3871

0·8820 0·8437

0·3162 0·2435

0·8005 0·7528

0·1694 0·0755

0·8805 0·8418

0·2974 0·2245

0·7982 0·7499

0·1504 0·0754

0·8751 0·8361

0·3005 0·2269

0·7921 0·7435

0·1520 0·0762

0·8739 0·8357

0·2941 0·2220

0·7928 0·7453

0·1487 0·0746

2·638

0·9826 0·9654

0·5674 0·5039

0·9425 0·9142

0·4374 0·3685

2·652

0·9824 0·9606

0·5730 0·5089

0·9376 0·9089

0·4419 0·3723

2·619

0·9829 0·9658

0·5785 0·5159

0·9433 0·9154

0·4503 0·3821

Table 3. Damage index of numerical examples

Storey number

Classification

Case 1

Predicted value

Actual value

Case 2

Predicted value

Actual value

Case 3

Predicted value

Actual value

Case 4

Predicted value

Actual value

1

11

2

12

3

13

4

14

5

15

6

16

7

17

8

18

9

19

10

20

1·004

1·032

1·0

1·0

0·799

1·015

0·8

1·0

0·991

1·135

1·0

1·0

0·993

1·006

1·0

1·0

0·997

1·026

1·0

1·0

0·986

1·055

1·0

1·0

0·981

1·000

1·0

1·0

0·999

0·998

1·0

1·0

0·971

0·986

1·0

1·0

1·003

0·999

1·0

1·0

0·993

1·003

1·0

1·0

0·996

0·986

1·0

1·0

0·999

0·999

1·0

1·0

0·999

0·995

1·0

1·0

1·000

1·003

1·0

1·0

1·008

1·013

1·0

1·0

1·018

1·000

1·0

1·0

1·009

1·002

1·0

1·0

0·986

1·003

1·0

1·0

0·8123

1·032

0·8

1·0

0·999

1·000

1·0

1·0

0·992

1·005

1·0

1·0

0·998

0·998

1·0

1·0

0·997

0·999

1·0

1·0

0·999

0·989

1·0

1·0

1·002

0·992

1·0

1·0

1·012

0·799

1·0

0·8

1·006

0·998

1·0

1·0

1·080

0·979

1·0

1·0

1·002

0·991

1·0

1·0

1·000

1·023

1·0

1·0

1·002

1·008

1·0

1·0

1·001

1·000

1·0

1·0

0·999

1·016

1·0

1·0

0·811

0·808

0·8

0·8

0·998

0·999

1·0

1·0

0·999

0·999

1·0

1·0

0·989

0·998

1·0

1·0

0·999

1·000

1·0

1·0

1·003

1·003

1·0

1·0

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.

Copyright © 2004 John Wiley & Sons, Ltd.

Struct. Design Tall Spec. Build. 13, 1–8 (2004)

DAMAGE ASSESSMENT USING DYNAMIC EXPERIMENTAL DATA

7

Figure 2. Experimental model

Table 4. Modal data of experimental model

Classification

Case 5

Frequency (rad/s)

First mode shape

1·0

628·42

0·79

0·93

0·60

0·25

Table 5. Damage index of experimental example

Storey number

Classification

Actual value

Predicted value

Error (%)

1

2

3

4

5

1·0

0·99832

-70·17

0·8

0·8225

+2·8

1·0

1·0132

+1·3

1·0

0·9798

-2·02

1·0

1·0602

+6·0

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 conventional modal testing technique was applied to determine the experimental modal data. In traditional

modal analysis, the modal data are found by fitting a model to the frequency response function relating excitation forces and vibration response.

Copyright © 2004 John Wiley & Sons, Ltd.

Struct. Design Tall Spec. Build. 13, 1–8 (2004)

8

H.-S. KIM AND Y.-S. CHUN

The damage index, ai, is then computed. Table 5 demonstrates that the proposed damage detection

method enables damage detection for each storey using only the first natural frequency and mode

shape. The error is due to an inaccuracy of the modal data obtained from the experiment, and such

error can be reduced by optimization if modal data on several modes can be obtained.

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 inaccuracy of the experimental data can be reduced by increasing the number of modes used and optimization. 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 modelling for each storey is possible.

REFERENCES

Bicanic N, Chen HP. 1997. Damage identification in framed structures using natural frequencies. International

Journal for Numerical Methods in Engineering 40: 4451–4468.

Clough RW, Penzien J. 1993. Dynamics of Structures. McGraw-Hill: New York.

Goh CG, See LM, Balendra T. 1995. Damage detection of buildings: numerical and experimental studies. Journal

of Structural Engineering 121(ST8): 1155–1160.

Guyan RJ. 1965. Reduction of stiffness and mass matrices. AIAA Journal 3(2): 380.

Hassiotis S, Jeong GD. 1993. Assessment of structural damage from natural frequency measurements. Computers and Structures 49: 679–691.

Hassiotis S. 2000. Identification of damage using natual frequencies and Markov parameters. Computers and

Structures 74: 365–373.

Li GQ, Hao KC, Lu Y, Chen SW. 1999. A flexibility approach for damage identification of cantilever-type structures with bending and shear deformation. Computers and Structures 73: 565–572.

Liu PL. 1995. Identification and damage detection of trusses using modal data. Journal of Structural Engineering 121: 599–606.

Stephens JE, Yao JTP. 1987. Damage assessment using response measurements. Journal of Structural Engineering 113(ST4): 787–801.

Copyright © 2004 John Wiley & Sons, Ltd.

Struct. Design Tall Spec. Build. 13, 1–8 (2004)

Struct. Design Tall Spec. Build. 13, 1–8 (2004)

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

STRUCTURAL DAMAGE ASSESSMENT OF BUILDING

STRUCTURES USING DYNAMIC EXPERIMENTAL DATA

HEUNG-SIK KIM1 AND YOUNG-SOO CHUN2*

1

2

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

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 inspection opportunity for the structures. In addition, in the case of large-scale 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.

1.

INTRODUCTION

The trend of constructing bigger and higher buildings demands greater safety caution for these structures. 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 assessing 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 necessary 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

* 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.

Copyright © 2004 John Wiley & Sons, Ltd.

Received October 2002

Accepted November 2002

2

H.-S. KIM AND Y.-S. CHUN

identification of structural damage or quantification of such damage. However, up to now, no method

has been able to provide this function reliably for large structures, and it is more so for the case of

building structures. It is reasoned that this is perhaps due to restrictions on the experiment, incorrect

method, and lack of inspection opportunity for the structures. In addition, for the case of large-scale

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.

2.

DAMAGE DETECTION ALGORITHM

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 measured 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 stiffnesses 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).

NL

Ki* = Â a i Ki

(1)

i =1

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

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. ai can 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):

( K - l j M )f j = 0

(2)

Here, lj is the eigenvalue (= wj2) of the jth vibration mode, and fj is the corresponding natural mode

shape of the system. Equation (2) can then be rewritten as

[K ]{f j } = w 2j [ M ]{f j }

(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

[K *]{f *j } = w *j 2 [ M ]{f *j }

(4)

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

[K *]{f *j } = [ D*][K ]{a i }

Copyright © 2004 John Wiley & Sons, Ltd.

(5)

Struct. Design Tall Spec. Build. 13, 1–8 (2004)

DAMAGE ASSESSMENT USING DYNAMIC EXPERIMENTAL DATA

3

where

Èf1*jf 2*j ◊ ◊ ◊ ◊ ◊ ◊ f *N

0 ◊◊◊◊◊◊ 0

Í

*

Í f1*j ◊ ◊ ◊ ◊ ◊ ◊ 0 f2*jf3*j ◊ ◊ ◊ f Nj

Í

[ D*] = Í

f1*j ◊ ◊ ◊ 0

f2*j ◊ ◊ ◊ 0

Í

O M

O M

Í

*

ÍÎ

f1 j

f2*j

È K1

ÍK

Í 1

ÍM

Í

Í0

Í0

[K] = Í

Í0

ÍM

Í

Í0

Í0

Í

ÍÎ 0

K2

- K2

M

0

K2

0

M

0

0

0

0

0

M

0

- K3

- K3

M

0

0

0

◊◊◊ 0 ˘

˙

◊◊◊ 0 ˙

˙

◊◊◊ 0 ˙

OM ˙

˙

* ˚˙

f Nj

(6)

◊◊◊◊◊◊

◊◊◊◊◊◊

O

0 ˘

0 ˙

˙

M ˙

˙

0 ˙

◊◊◊◊◊◊

0 ˙

˙

◊◊◊◊◊◊

0 ˙

O

M ˙

˙

K N -2 K N -1 ˙

- K N -1 ˙

0

˙

K N ˙˚

0

{a i } = {a 1 , a 2 , a 3 , ◊ ◊ ◊ ◊ ◊ ◊ , a N }

T

(7)

(8)

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

a i = w *j [ A][ M ]{f *j }

(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.

3.

DAMAGE DETECTION PROCESS AND NUMERICAL EXAMPLE

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 verified 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.

Copyright © 2004 John Wiley & Sons, Ltd.

Struct. Design Tall Spec. Build. 13, 1–8 (2004)

4

H.-S. KIM AND Y.-S. CHUN

(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 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 massspring system and the actual structure, system identification is performed.

First, full-scale measurements are carried out for the building, and by applying the random decrement 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.

Copyright © 2004 John Wiley & Sons, Ltd.

Struct. Design Tall Spec. Build. 13, 1–8 (2004)

5

DAMAGE ASSESSMENT USING DYNAMIC EXPERIMENTAL DATA

Table 1. Damage scenarios

Classification

Case 1

Case 2

Case 3

Case 4

Damage element

Degree of damage

Vibration mode used

2-storey

10-storey

17-storey

5-storey, 15-storey

20% decrease in stiffness

20% decrease in stiffness

20% decrease in stiffness

20% decrease in stiffness

First mode

First mode

First mode

First mode

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 characteristics 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 unrealistically 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.

4.

EXPERIMENTAL VERIFICATION

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 fck = 300 kgf/cm2, and 5 kgf of

Copyright © 2004 John Wiley & Sons, Ltd.

Struct. Design Tall Spec. Build. 13, 1–8 (2004)

6

H.-S. KIM AND Y.-S. CHUN

Table 2. Modal data of numerical example

Classification

Case 1

Case 2

Case 3

Case 4

Frequency

(rad/s)

First mode 1·0000 0·9943

shape

0·7008 0·6447

Frequency

(rad/s)

First mode 1·0000 0·9942

shape

0·6842 0·6276

Frequency

(rad/s)

First mode 1·0000 0·9941

shape

0·6906 0·6336

Frequency

(rad/s)

First mode 1·0000 0·9943

shape

0·6936 0·6379

2·622

0·9828 0·9658

0·5850 0·5219

0·9432 0·9152

0·4558 0·3871

0·8820 0·8437

0·3162 0·2435

0·8005 0·7528

0·1694 0·0755

0·8805 0·8418

0·2974 0·2245

0·7982 0·7499

0·1504 0·0754

0·8751 0·8361

0·3005 0·2269

0·7921 0·7435

0·1520 0·0762

0·8739 0·8357

0·2941 0·2220

0·7928 0·7453

0·1487 0·0746

2·638

0·9826 0·9654

0·5674 0·5039

0·9425 0·9142

0·4374 0·3685

2·652

0·9824 0·9606

0·5730 0·5089

0·9376 0·9089

0·4419 0·3723

2·619

0·9829 0·9658

0·5785 0·5159

0·9433 0·9154

0·4503 0·3821

Table 3. Damage index of numerical examples

Storey number

Classification

Case 1

Predicted value

Actual value

Case 2

Predicted value

Actual value

Case 3

Predicted value

Actual value

Case 4

Predicted value

Actual value

1

11

2

12

3

13

4

14

5

15

6

16

7

17

8

18

9

19

10

20

1·004

1·032

1·0

1·0

0·799

1·015

0·8

1·0

0·991

1·135

1·0

1·0

0·993

1·006

1·0

1·0

0·997

1·026

1·0

1·0

0·986

1·055

1·0

1·0

0·981

1·000

1·0

1·0

0·999

0·998

1·0

1·0

0·971

0·986

1·0

1·0

1·003

0·999

1·0

1·0

0·993

1·003

1·0

1·0

0·996

0·986

1·0

1·0

0·999

0·999

1·0

1·0

0·999

0·995

1·0

1·0

1·000

1·003

1·0

1·0

1·008

1·013

1·0

1·0

1·018

1·000

1·0

1·0

1·009

1·002

1·0

1·0

0·986

1·003

1·0

1·0

0·8123

1·032

0·8

1·0

0·999

1·000

1·0

1·0

0·992

1·005

1·0

1·0

0·998

0·998

1·0

1·0

0·997

0·999

1·0

1·0

0·999

0·989

1·0

1·0

1·002

0·992

1·0

1·0

1·012

0·799

1·0

0·8

1·006

0·998

1·0

1·0

1·080

0·979

1·0

1·0

1·002

0·991

1·0

1·0

1·000

1·023

1·0

1·0

1·002

1·008

1·0

1·0

1·001

1·000

1·0

1·0

0·999

1·016

1·0

1·0

0·811

0·808

0·8

0·8

0·998

0·999

1·0

1·0

0·999

0·999

1·0

1·0

0·989

0·998

1·0

1·0

0·999

1·000

1·0

1·0

1·003

1·003

1·0

1·0

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.

Copyright © 2004 John Wiley & Sons, Ltd.

Struct. Design Tall Spec. Build. 13, 1–8 (2004)

DAMAGE ASSESSMENT USING DYNAMIC EXPERIMENTAL DATA

7

Figure 2. Experimental model

Table 4. Modal data of experimental model

Classification

Case 5

Frequency (rad/s)

First mode shape

1·0

628·42

0·79

0·93

0·60

0·25

Table 5. Damage index of experimental example

Storey number

Classification

Actual value

Predicted value

Error (%)

1

2

3

4

5

1·0

0·99832

-70·17

0·8

0·8225

+2·8

1·0

1·0132

+1·3

1·0

0·9798

-2·02

1·0

1·0602

+6·0

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 conventional modal testing technique was applied to determine the experimental modal data. In traditional

modal analysis, the modal data are found by fitting a model to the frequency response function relating excitation forces and vibration response.

Copyright © 2004 John Wiley & Sons, Ltd.

Struct. Design Tall Spec. Build. 13, 1–8 (2004)

8

H.-S. KIM AND Y.-S. CHUN

The damage index, ai, is then computed. Table 5 demonstrates that the proposed damage detection

method enables damage detection for each storey using only the first natural frequency and mode

shape. The error is due to an inaccuracy of the modal data obtained from the experiment, and such

error can be reduced by optimization if modal data on several modes can be obtained.

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 inaccuracy of the experimental data can be reduced by increasing the number of modes used and optimization. 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 modelling for each storey is possible.

REFERENCES

Bicanic N, Chen HP. 1997. Damage identification in framed structures using natural frequencies. International

Journal for Numerical Methods in Engineering 40: 4451–4468.

Clough RW, Penzien J. 1993. Dynamics of Structures. McGraw-Hill: New York.

Goh CG, See LM, Balendra T. 1995. Damage detection of buildings: numerical and experimental studies. Journal

of Structural Engineering 121(ST8): 1155–1160.

Guyan RJ. 1965. Reduction of stiffness and mass matrices. AIAA Journal 3(2): 380.

Hassiotis S, Jeong GD. 1993. Assessment of structural damage from natural frequency measurements. Computers and Structures 49: 679–691.

Hassiotis S. 2000. Identification of damage using natual frequencies and Markov parameters. Computers and

Structures 74: 365–373.

Li GQ, Hao KC, Lu Y, Chen SW. 1999. A flexibility approach for damage identification of cantilever-type structures with bending and shear deformation. Computers and Structures 73: 565–572.

Liu PL. 1995. Identification and damage detection of trusses using modal data. Journal of Structural Engineering 121: 599–606.

Stephens JE, Yao JTP. 1987. Damage assessment using response measurements. Journal of Structural Engineering 113(ST4): 787–801.

Copyright © 2004 John Wiley & Sons, Ltd.

Struct. Design Tall Spec. Build. 13, 1–8 (2004)

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