Damage Detection Tests of Five-Story Steel Frame with Simulated Damages

Koichi Morita*a, Masaomi Teshigawaraa, Hiroshi Isodaa, Takuji Hamamoto**b, Akira Mita***c

a Building Research Institute, MLIT, Tsukuba, Japan, 305-0802

b Musashi Institute of Technology, Tokyo, Japan, 158-8557 c Keio University, Yokohama, Japan, 223-8522

ABSTRACT

This paper presents damage detection tests of five-story steel frame with simulated damages. We discuss pre-analytical study and results of experiments. Fiber brag grating (FBG) sensors, accelerometers, strain gauges and laser displacement meters are installed in this test frame. We assume damages by removing studs from only one story, loosening bolts of beams, cutting part of beams and extracting braces from only one story. From the results of pre-analytical study, we can estimate which story is damaged from the change of natural period and mode shape to some extent. We applied flexibility method which is one of a damage identification methods using modal properties. We also apply flexibility method to results of experiments. In some cases we can estimate which story is damaged, and in other cases we cannot. We also applied a method using multiple natural frequency shifts. Making use of the change in five natural frequencies due to damage, the location of damaged stories can be pinpointed. In both methods, we cannot identify damaged story in some cases. Some methods other than methods using modal properties have to be tried to apply in such cases.

Keywords: Smart structure, Health monitoring, Damage detection, Identification techniques

1. INTRODUCTION If we have to reduce life cycle costs of a building from construction to maintenance, it is very effective to monitor structural health of a building. However, the research on healt h monitoring of buildings is rare, and health monitoring technique of a building is not still establishing. We had damage detection tests of five-story steel frame with simulated damages using smart sensors, as fiber optics. In this paper, we show results of pre-analysis and results of experiments. We try to identify damage by using change of modal properties, and we also use a method using multiple natural frequency shifts.

2. OUTLINE OF TEST FRAME AND EXPERIMENTS Test frame is five-story steel structure shown as figure 1 and figure 2. Dimension of test structure is shown as table 1. Floor height is 1m, total height is 5m and floor plan is 2m*3m. The cross section of members is following. column : H148*100*6/9(SS400) beam : H148*100*6/9(SS400) stud : H100*50*5/7(SS400) We put a weight of 2 ton on each story. There are two test cases, tests with studs shown as figure 1 1) and tests without stud shown as figure 1 2). Braces can be installed, when studs are removed. First natural period is almost 0.3 - 0.4 seconds. Test frame is set up on shaking table at BRI, and excitation tests using a vibration exciter are also carried out, if we need to excite higher modes, and we also have microtremor observation. Sensors are put on each floor and installed at beam edges. Fiber brag grating (FBG) sensors for acceleration , FBG sensors for stain, accelerometers, strain gauges and laser displacement meters are installed. Installed sensors are shown as table 2. In addition, ultrasonic measurements are carried out. Settings of simulated damages are as fellow. *morita@kenken.go.jp; phone +81-298-79-0668; fax +81-298-64-6773; Building Research Institute, MLIT; 1 Tatehara Tsukuba, Japan, 305-0802; **hamamoto@ipc.musashi-tech.ac.jp ; phone +81-3-3703-3111,3058;fax +81-3-5707-2197; Musashi Institute of Technology, Tokyo, Japan, 158-8557; ***mita@sd.keio.ac.jp; phone +81-45-566-1776; fax +81-45-566-1720; Keio University, Yokohama-shi, Japan, 223-8522

+Studs or braces are extracted only from one story. +Part of flanges of beams or columns is cut off. (See figure 3) +Bolts of beams or columns are loosened. etc. The following tests from i) to vii) are carried out in order to the number. i) Normal sound test structure with studs ii) Removing studs from only one story iii) Normal sound test structure without stud iv) Loosening bolts of beams of test structure without stud v) Exchanging sound beam for damaged beam vi) Extracting braces from only one story vii) Cutting of part of column

3. PRE-ANALYSIS 3.1 Change of modal properties by setting damage We examine how natural periods and modal shapes change when damages are set at part of beams or columns. Some cases are examined, and all results tend to be same. Here, only the case in which damages are set at beam edge of test structure without stud is explained. Damage at beam is assumed as a pin in analysis. Table 3 shows that natural periods of test structure, in which damages at beam edge are assumed, are compared. First natural periods greatly change, when damages at lower story are assumed. Higher (third) natural periods greatly change, when damages at upper story are assumed. Figure 4 shows similar results of mode shapes. First mode shapes also greatly change, when damages are assumed at lower story. Higher (third) mode shapes gre atly change, when damages are assumed at upper story. From these results, it is effective to examine higher mode when there seem to be damages at upper story. We can estimate which story is damaged from the change of natural period and mode shape to some extent. 3.2 Damage identification by use of change of modal properties We make simulation waves calculated as results of same models used in 3.1 with white noise for input. Identification technique1 using the change of flexibility is applied to this simulation waves. Damaged location is estimated by comparison of sound modal properties and damaged modal properties. We show here results of the case setting damages at beam edge of 1st, 3rd, 5th story in figure 5 (a) - (c). Each figure shows the frame in case of figure 1 2). Y direction is height direction and dark line shows that damage index is large. That is to say, if the color of lines is dark, there should be damage. In figure 4 (assumed damages at lower story), the color of lower story is dark. In figure 5 (assumed damages at intermediate story), the color of intermediate story is dark. In figure 6 (assumed damages at upper story), the color of upper story is dark. From these figures, damage identification seems to be difficult when damage at upper story is assumed. And we can estimate which story is damaged when damages exist at lower story.

4. RESULTS OF EXPERIMENTS

4.1 Pinpoint of damaged stories using multiple natural frequency shifts In this experiment, five natural frequencies that range from the 1st to 5th translational mode were clearly observed as shown in figure 6. Making use of the change in five natural frequencies due to damage, the location of damaged stories can be pinpointed. Usually, natural frequencies are used to catch the mere occurrence of structural damage, because natural frequencies are a global measure of structural characteristics. Generally speaking, each natural frequency shift cannot provide the spatial information of structural damage. However, multiple natural frequency shifts can provide the spatial information on the location of damaged stories, because the change in structural condition at different locations cause different combinations of the change in natural frequencies. The squared natural frequency in the i-th mode is give as

}]{[}{

}]{[}{2

iT

i

iT

i

i

ii

M

K

M

K

φφφφ

ω == , (1)

in which iK and iM are the i-th generalized stiffness and generalized mass, respectively, ][K and ][M are global stiffness

and mass matrices, respectively, and }{ iφ is the i-th mode shape. Assuming that the global mass matrix is not changed during a damage event, the change in the i-th squared natural frequency due to damage can be expressed as

}]{[}{

}]{[}{2

iT

i

iT

ii

M

K

φφφφ

ω∆

=∆ , (2)

in which ][ K∆ is the change in global stiffness matrix.

When structural damage concentrates on the j-th story of the building structure, the change in global stiffness may be replaced by the change in the j-th story stiffness as

}]{[}{

}]{[}{2

iT

i

ijjT

iji

M

K

φφ

φφω

∆=∆ , (3)

in which ][ jK∆ is the change in the j-th story stiffness matrix and }{ ijφ is the j-th story deformation that are computed by

the i-th mode shape. The change in the j-th story stiffness matrix may be expressed as

jjj KK α][][ 0=∆ , (4)

in which ][ 0 jK is the j-th story stiffness matrix in the undamaged state and jα is the stiffness reduction ratio in the j-th

story. Incorporating Eq. (4) into Eq. (3) and dividing both sides in the resulting equation by the i-th squared natural frequency,

20iω , in the undamaged state yields

ji

ijj

ii

ijjT

ijj

iT

ii

ijjT

ij

i

i

S

S

K

K

M

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αφφω

φφ

ωω

00

0

20

0

20

2

}]{}[{

}]{[}{

}]{[}.{

}]{[}{===

∆, (5)

in which ][ 0K is the global stiffness matrix in the undamaged state, iS0 is the total strain energy in the i-th mode and ijS is

the j-th story strain energy in the i-th mode. The i-th modal strain energy ratio in the j-th story is defined as

i

ijij S

S

0

=λ . (6)

Eq. (5) may be rewritten as

jiji

i αλωω

=∆

20

2

. (7)

In Eq. (7), the change in squared natural frequencies due to damage is related to the modal strain energy ratio in the undamaged state. Consequently, if modal strain energy ratios are calculated at each story in advance, the location of damaged stories can be pinpointed by using the change in squared natural frequencies due to damage. Figure 7 shows the distribution of modal strain energy ratios at each story. Figure 8 shows the distribution of the change in squared natural frequencies for various damage situations that are set in this experiment. The distributions of the change in squared natural frequencies due to the j-th story damage are reasonably similar to the distribution of modal strain energy ratios in the j-th story except for a couple of damage situations. These exceptions are observed only when the change in natural frequencies due to a damage event is considerably small. This simple damage detection method that can pinpoint damaged stories by comparing the distribution patterns between modal strain energy ratios at each story in the undamaged state and the change in squared natural frequencies due to damage may be called a pattern matching method. The pattern matching method is especially useful if several natural frequencies are precisely identified and structural damage concentrates on a certain story. 4.2 Damage identification by use of change of modal properties We apply identification method to simulation waves in previous section. We apply same identification method to measured waves. Table 4 shows that natural periods of test structure are compared. First natural periods greatly change, when damages at 1st story exist. Higher (third) natural periods greatly change, when damages at 5th story exist. These results agree with results in case of pre-analysis. Figure 6 shows measured transfer function. This shows five clear peaks and we use 1st to 5th modal characteristics to identification. Identification technique1 using the change of flexibility is applied to the case of test frame with studs. Damaged location is estimated by comparison of sound modal properties and damaged modal properties. We show here results of the case of no stud in 1st, 3rd, 5th story in figure 9 (a) – (c). From figure 9 (a) and (c), we can identify which story is damaged when damage exist at lower story or upper story. But figure 9 (b) shows that it is difficult to identify middle story damages.

5. CONCLUSIONS

Outline of damage detection tests are shown here, and results of pre-analysis and results of experiments are reported. We applied damage identification method using modal analysis and method using multiple natural frequency shifts. In case of pre-analysis we can clearly estimate which story is damaged when damages exist at lower story and middle story. In case of experiments, we can clearly estimate which story is damaged when damages exist at lower story and upper story. We cannot clearly estimate which story is damaged when damages exist at middle story, but we can estimate to some extent. Damage detection method by comparing the distribution patterns between modal strain energy ratios at each story in the undamaged state and the change in squared natural frequencies due to damage can pinpoint damaged stories. In both methods, we cannot identify damaged story in some cases. Some methods other than methods using modal properties have to be tried to apply in such cases.

ACKNOWLEDGEMENTS The authors wish to thank the members of Structural Health Monitoring working group in the Sensor section of the Japan side of the project, “Smart Materials and Structural Systems” for their fruitful discussions.

REFERENCE 1. ”Damage Identification and Health Monitoring of Structural and Mechanical Systems from Changes in Their Vibration

Characteristics” : A Literature Review, Los Alamos National Laboratory Report, LA-13070-MS, 1996

Table 1 : Dimension of test structure

floor height 1m total height 5m floor plan 2m*3m column, beam H148*100*6/9(SS400) footing beam H250*250*9/14(SS400) weight of each floor 2.57ton

Table 2 : Installed sensors

number of sensors Installed at accelerometer 20 each floor strain gage 24 beam edges FBG sensors for acceleration 6 each floor FBG sensors for strain 17 beam edges Laser displacement meter 3 each floor

Table 3 : Comparison of Natural Periods [sec] (simulation)

1st 2nd 3rd Sound structure 0.366 0.120 0.0710

Damaged beam at 5th story 0.371 0.131 0.0786 Damaged beam at 4th story 0.385 0.141 0.0745 Damaged beam at 3rd story 0.409 0.132 0.0729 Damaged beam at 2nd story 0.431 0.120 0.0768 Damaged beam at 1st story 0.437 0.129 0.0716

Table 4 : Comparison of Natural Periods [sec] (measured)

1st 2nd 3rd Sound structure with studs 0.251 0.0837 0.0515 Damaged beam at 5th story 0.255 0.0911 0.0575 Damaged beam at 3rd story 0.267 0.0862 0.0563 Damaged beam at 1st story 0.278 0.0905 0.0539

Sound structure without studs 0.343 0.113 0.0678 Damaged beam at 5th story 0.343 0.114 0.0696 Damaged beam at 3rd story 0.352 0.117 0.0684 Damaged beam at 1st story 0.362 0.116 0.0679

Figure 1 : 1)Test frame with studs 2)Test frame without studs

Figure 2 : 1)Test frame with studs 2)Test frame without studs

Figure 4 : Comparison of mode shape without damages and mode shapes with damages

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mode mode mode

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mode Loosing 5F beam bolts

Figure 7 : Distribution of modal strain energy ratios for a reference model

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Figure 8: Changes in squared modal frequencies for various damage situations

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