DAMAGE INDEX OF ANGLE BRACE BASED ON RESIDUAL DEFORMATION

Transcription

1 1NCEE Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 214 Anchorage, Alaska DAMAGE INDEX OF ANGLE BRACE BASED ON RESIDUAL DEFORMATION N. Tatsumi 1 and S. Kishiki 2 ABSTRACT Low-rise steel building structures are expected to accommodate disaster prevention activities after an earthquake. Hence these structures are required to maintain their seismic performance not only for a single seismic event, but also in the event of aftershocks. Therefore, it is very important to evaluate the residual seismic performance of the damaged steel structures by quick inspections. However, the damage degree of steel structures obtained only by visual inspection is not enough, although for reinforced concrete structures it is common practice to use the crack width and pattern of reinforced concrete members to evaluate the damage. Many encountered damage patterns of angle braces, which are widely used for seismic members in low rise steel structures, are described in reports about the past earthquakes. This paper focuses on the geometrical changes of the angle cross section and out-of-plane deformations due to flexural buckling, and describes how to estimate a damage index based on these residual deformations of the angle brace. In order to find the relation between the damage and the residual deformation, cyclic loading tests of a single angle brace were carried out. The main parameter in these tests is width-to-thickness ratio of angle section: L65x6 (length of leg x thickness), L75x6, L75x9, L75x12, L9x7 and L1x7. In addition, constant amplitude loading pattern at.5,.75, 1., 1.25, 1.5 and 1.75%, is selected to be a parameter of the test. The test results can be summarized as follows: (1) local buckling occurring at the middle under the cyclic loadings. After that, crack appears at one of the free edges and grows to reach fracture; (2) the residual out-of-plane deformation increases proportionally to the maximum amplitude of loading; (3) the geometrical changes of the angle cross section is increased due to the number of the loading cycles; (4) the maximum story drift and the cumulative damage to angle brace can be estimated from the out-of-plane residual deformation and the geometrical changes of angle cross section, respectively. Consequently, by combining the visual information it is possible to evaluate the residual seismic performance of an angle brace. 1 Graduate Student Researcher, Dept. of Architecture, Osaka Institute of Technology, , Omiya, Asahi-ku, Osaka-city, Osaka, , Japan, m1m1328@st.oit.ac.jp 2 Lecturer, Dept. of Architecture, Osaka Institute of Technology, , Omiya, Asahi-ku, Osaka-city, Osaka, , Japan, kishiki@archi.oit.ac.jp Tatsumi N, Kishiki S. Damage Index of Angle Brace Based on Residual Deformation. Proceedings of the 1th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 214.

2 1NCEE Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 214 Anchorage, Alaska Damage Index of Angle Brace Based on Residual Deformation N. Tatsumi 1 and S. Kishiki 2 ABSTRACT Low-rise steel building structures are expected to accommodate disaster prevention activities after an earthquake. Hence these structures are required to maintain their seismic performance not only for a single seismic event, but also in the event of aftershocks. Therefore, it is very important to evaluate the residual seismic performance of the damaged steel structures by quick inspections. However, the damage degree of steel structures obtained only by visual inspection is not enough, although for reinforced concrete structures it is common practice to use the crack width and pattern of reinforced concrete members to evaluate the damage. Many encountered damage patterns of angle braces, which are widely used for seismic members in low rise steel structures, are described in reports about the past earthquakes. This paper focuses on the geometrical changes of the angle cross section and out-of-plane deformations due to flexural buckling, and describes how to estimate a damage index based on these residual deformations of the angle brace. In order to find the relation between the damage and the residual deformation, cyclic loading tests of a single angle brace were carried out. The main parameter in these tests is width-to-thickness ratio of angle section: L65x6 (length of leg x thickness), L75x6, L75x9, L75x12, L9x7 and L1x7. In addition, constant amplitude loading pattern at.5,.75, 1., 1.25, 1.5 and 1.75%, is selected to be a parameter of the test. The test results can be summarized as follows: (1) local buckling occurring at the middle under the cyclic loadings. After that, crack appears at one of the free edges and grows to reach fracture; (2) the residual out-of-plane deformation increases proportionally to the maximum amplitude of loading; (3) the geometrical changes of the angle cross section is increased due to the number of the loading cycles; (4) the maximum story drift and the cumulative damage to angle brace can be estimated from the out-of-plane residual deformation and the geometrical changes of angle cross section, respectively. Consequently, by combining the visual information it is possible to evaluate the residual seismic performance of an angle brace. Introduction Low-rise steel building structures are expected to accommodate disaster prevention activities after an earthquake. Hence these structures are required to maintain their seismic performance not only for a single seismic event, but also in the event of aftershocks. Therefore, it is very important to evaluate the residual seismic performance of the damaged steel structures by quick inspections and to assess whether the structure is available for the disaster prevention activities. 1 Graduate Student Researcher, Dept. of Architecture, Osaka Institute of Technology, , Omiya, Asahi-ku, Osaka-city, Osaka, , Japan, m1m1328@st.oit.ac.jp 2 Lecturer, Dept. of Architecture, Osaka Institute of Technology, , Omiya, Asahi-ku, Osaka-city, Osaka, , Japan, kishiki@archi.oit.ac.jp Tatsumi N, Kishiki S. Damage Index of Angle Brace Based on Residual Deformation. Proceedings of the 1th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 214.

3 However, it is difficult to estimate the seismic damage of the steel structure because of the rack of the damage index obtaining from visual information. The past reconnaissance reports of the earthquake indicated that angle braces they are often used for seismic members in low-rise steel building structures have considerable visual information of residual deformations owing to flexural buckling and local buckling after the earthquake (see Fig. 1 1) ). In this paper, these residual deformations due to buckling are defined as the geometrical changes of cross section of angle (see in Fig. 1(a)) and the out-of-plane deformation (see in Fig. 1(b)). If the residual seismic performance of angle braces can be estimated by these two visualized damage indices, it makes possible the quick judgment of the suitability for the disaster prevention activities. (a) Geometrical change of cross section (b) Residual out-of-plane deformation Figure 1. Damage to angle braces after an earthquake In the past research 2), the results that the geometrical change of cross section of the angle brace progresses under the cyclic loading are reported. Further, in the research that carried out axial loading tests to turnbuckle braces 3), the relation between the plastic deformation and the residual out-of-plane deformation was confirmed. The purpose of this study is to establish the visualized damage index based on the two residual deformations of the angle brace. In this paper, the relation between the damage and the two residual deformations of the angle brace obtained from results of the cyclic loading test is shown. Test Program All of specimens are single angle braces of 4,3 mm length including connections made of JIS SS4 steel. All connections are designed in order to meet the condition of the joint with the load-carrying capacity. The detail of a specimen is shown in Fig. 2, and the list of test parameters is shown in Table 1. In addition, the material, the thickness and the shape of the gusset plate and hole size, the number and the pitch of the high strength bolts and so on are the same for all specimens. Six types of the angle sections with difference the width-to-thickness ratios (b/t) and six types of the loading amplitudes ( ) are selected as test parameters. The loading amplitude equals the maximum axial deformation divided by length L A. The definition of b and t is shown in Fig. 3. The slenderness ratio of angle brace equals the length of the brace including connections L B divided by the radius of gyration around the vertical axis that goes through the centroid of the angle section. The calculation method for the radius of gyration is based on the deformation which is perpendicular to the gusset plate (the direction of out-of-plane in Fig. 2) of the angle brace by the flexural buckling, and not in the direction of weak axis of angle section. In

4 this paper, test results of specimens with circles in Table 1 are reported. Axial direction 45 Out-of-plane direction 5-M16 4 PL16 (SM49) L A =4,3 L B =4,3 PL9 (SM49) Figure 2. The detail of test specimen Table 1. The list of test parameters Specimen Amplitude e Brace yield strength Connection strength Section Width-to-thickness ratio b/t Slenderness ratio l 1.75% 1.5% 1.25% 1.%.75%.5% P y [kn] P u [kn] L-65x65x L-75x75x L-75x75x L-75x75x L-9x9x L-1x1x t b Figure 3. Definition of b/t in cross section of angle The test setup is shown in Fig. 4. In these tests, the constant deformation amplitude is applied to the test specimen until the fracture. The axial force is measured by the built-in load cell in actuator, and the axial deformation of specimen is obtained as the difference of jigs from the difference between the two displacement transducers set at points shown as the arrows in Fig. 4. Actuator Specimen Linear sliders Figure 4. Displacement transducers for the measurement of axial deformation Test setup As mentioned previously, the out-of-plane deformation and the geometrical change of cross section of angle are selected as the visualized damage indices. The measuring systems of each deformation are shown in Fig. 5 and Fig. 6. For the measurement of the out-of-plane deformation, three wire displacement transducers are used. For the measurement of the geometrical change of

5 cross section, two wire displacement transducers and two targets at the center of the specimen are used. The geometrical change of cross section is obtained from the difference between wire A attached to target A via target B and wire B attached to target B (Fig. 6). Wire 1 Wire 2 Wire 3 Figure 5. (a) Before (b) After The measuring system for out-of-plane deformation of the brace Out-of-plane direction Center of length Target A Wire A Stud Figure 6. Target B Wire B (a) Before (b) After The measuring system for the geometrical change of cross section Outline of Test Results The results of material tests, the relation between load and deformation and the change of the maximum strength in every cycle are shown in Table 2, Fig. 7 and Fig. 8 respectively. The vertical axis (P) indicates the axial force and the horizontal axis ( ) represents the axial deformation in Fig. 7, and the horizontal axis (N) stands for the number of loading cycles. Further on, the yield strength (P y ) calculated from the yield stress of the Coupon test in Table 2 multiplied by the nominal cross section is shown by a broken line.

6 Table 2. Section Yield stress [N/mm 2 ] The results of material tests Ultimate stress [N/mm 2 ] Yield ratio [%] Elongation [%] 65x65x x75x x75x x75x x9x x1x P y=267kn Crack 5 1~3 cycles at first 1~3 cycles before fracture N [ 回 ] Figure 7. Figure 8. P y=522kn Axial force and axial deformation relations N [ 回 ] P y=43kn (a) 75x75x6 Amplitude 1.% (b) 75x75x12 Amplitude 1.% (c) 9x9x7 Amplitude 1.% (d) 1x1x7 Amplitude 1.% Changes of the maximum strengths in each cycle The specimens in Fig. 7 demonstrate the maximum strength in the initial tension early and then the gradual decrease in the strength. The agreement between the maximum strengths and yield strengths is gathered from Fig. 7. Similar results were obtained in all specimens, not only those of 1.%. The flexural buckling occurs in compression immediately, and the specimen maintains almost constant strength. The maximum strength in each cycle is displayed in the maximum tensile deformation since the second cycle and the strength decreases gradually while the similar loop is shown. The maximum strength in each cycle gently declines under the cyclic loading. After the crack (shown as in Fig. 8) occurs, the strength drop is rapid and the development of this crack causes fracture (shown as in Fig. 8). Performance of Low-cycle Fatigue The list of test results on all specimens is shown in Table 3. N c indicates the number of cycles until the crack and N f stands for the number of cycles until the fracture. The relation between the number of cycles until the fracture N f and the strain of whole amplitude t is shown in Fig. 9. The vertical axis t in Fig. 9 shows the whole amplitude 2 divided by the length of angle steel L A. By N [ 回 ] Crack Crack Crack Fracture Fracture Fracture Fracture P y=458kn (a) 75x75x6 Amplitude 1.% (b) 75x75x12 Amplitude 1.% (c) 9x9x7 Amplitude 1.% (d) 1x1x7 Amplitude 1.% 5 N [ 回 ]

7 comparing with results at the same amplitudes, it is found that the lower the width-to-thickness ratio of the cross section, the larger are the low-cycle fatigue characteristics. Further, in the larger amplitudes, the effects of the width-to-thickness ratio on the low-cycle fatigue characteristics are more clear. In addition, it is understood that lower slenderness ratio causes the earlier fracture (compare L-75x75x6 with L-9x9x7 whose width-to-thickness ratios b/t are close). Table 3. The list of test results First stiffness K e Yield strength Slip strength Section Amplitude e [%] [N/mm] [kn] [kn] Tension Compression L-65x65x6 L-75x75x6 L-75x75x9 L-75x75x12 L-9x9x7 L-1x1x7 Specimen Maximum strength [kn] Crack N c [times] Fracture N f [times] Figure 9. t The curve of fatigue obtained from the past research 5) N f [ 回 ] Legend Section b /t l L-75x75x L-75x75x L-65x65x L-75x75x L-9x9x L-1x1x Red signs represent results of tests in which crack occurs at placement of stud welding. Low-cycle fatigue characteristics of the angle brace

8 In the past research 5), cyclic loading tests of the steel elements with the buckling restrained were carried out. The straight line in Fig. 9 indicates the fatigue curve obtained from the tests. Compared with this fatigue curve, it is found that there are many points of results in these tests above the straight line. Namely, the performance of low-cycle fatigue of the angle steel with the flexural buckling and the local buckling is greater than that of the steel material. Geometrical Change of Cross Section Visual information and hysteresis loop of the geometrical change of cross section until fracture are shown in Fig. 1 and Fig. 11 respectively. Fig. 1 shows pictures taken in no axial deformation of specimen. The vertical axis a in Fig. 11 represents the amount of change in the distance between both edges in angle section, and the horizontal axis ( ) stands for the axial deformation. The angle section at the center of the specimen opens in compression and returns to its original state in tension at the early stage of cyclic loading, but the flat part starts to be deformed out-of-plane also in tension during the repetition of loading. Eventually crack appears at the free edge in the direction of out-of-plane and it leads to fracture. In the research literature 6), tests of cyclic loading are carried out for flexural buckling to occur in the direction of the weak axis in angle section and the fracture behavior of angle steel is grasped. However, the flexural buckling in the direction of out-of-plane is dominant about the angle brace with gusset plate, and the fracture behavior in these tests is different from that in the literature 6). Before loading In 3 cycles In 5 cycles In 1 cycles In 15 cycles In 2 cycles In 25 cycles Fracture Figure 1. Process of geometrical change of cross section Figure cycles before fracture 1~5 cycles at first a Residual deformation Cyclic behavior of geometrical change of cross section

9 The comparison of the geometrical change of cross section with some test parameters is shown in Fig. 12. The vertical axis (l / l ) indicates the ratio of the geometrical change of cross section and the horizontal axis (N / N c ) represents the damage index until the occurrence of crack. l is the original diagonal distance between the free edges of the cross section and l is that in the deformed cross section (l + a ). The residual deformation is defined at the zero axial deformation when the loading shifts from tension to compression. From the comparison among specimens with the same cross section, it is found that the higher the amplitude, the more widely the angle section opens. In addition to this, it is understood that the larger width-to-thickness ratio results in a larger ratio of geometrical change of cross section as compared with specimens at the same amplitude. Besides, for all the specimens, the progress of geometrical change of cross section becomes small when damage index (N / N c ) reaches around.2~ l / l Amplitude 1.75% Amplitude 1.5% l / l Amplitude 1.5% Amplitude 1.25% Amplitude 1.% Amplitude.75% Amplitude 1.% Amplitude.5% 1.5 Amplitude.5% 1.5 Figure N / N c Effects of the loading amplitude and width-to-thickness ratio on geometrical change of cross section Residual Out-of-plane Deformation The theoretical calculation model of the out-of-plane deformation is illustrated in Fig. 13 and the measurement result of the residual out-of-plane deformation in typical section is shown in Fig. 14. The length used for the theoretical formula in Fig. 13 is the length of brace including gusset plate (L B ). It is confirmed that the out-of-plane deformation is almost constant regardless of cumulative damage and changes according to the maximum axial deformation of angle brace. The straight line in Fig. 14 represents the calculation value of the residual out-of-plane deformation obtained from the formula in Fig. 13. Although there is a little difference between the measurement value and the calculation value, they agree with each other. Therefore, it is considered that the measurement of out-of-plane deformation makes possible the judgment of the maximum axial deformation of the angle brace. w 75x75x6 (b/t 12.5) L B - w out 1 N / N c x1x7 (b/t 14.3) L B : Length of angle brace : Ratio of plasticity w y : Yield deformation w : Axial deformation Figure 13. = ( 1) ( 1) The calculation model of the residual out-of-plane deformation

10 out Amplitude 1.5% Amplitude 1.% Amplitude.5% Figure 14. N / N c Residual out-of plane deformation of the brace Conclusion In this research, from focusing on the out-of-plane deformation and the geometrical change of cross section of angle braces, residual axial loading tests of angle braces are carried out to evaluate these deformations. Test results obtained in this paper are summarized as the following. [1] Regarding the angle brace with the gusset plate, the geometrical change of cross section due to the local buckling occurs at the free edge in the direction of out-of-plane, and the crack occurred at the free edge causes fracture of the brace. [2] The out-of-plane deformation and the geometrical change of cross section increase in proportion to the given amplitude. [3] The maximum axial deformation can be obtained from the residual out-of-plane deformation and the cumulative damage due to the cyclic loadings can be estimated from the residual geometrical change of cross section. Consequently, it is considered that the combination of the two of these residual deformations makes possible the evaluation of the damage of the angle brace. In future research, in the case of receiving different amplitudes, the influence which the combination of amplitudes and its turn give the low-cycle fatigue performance, the out-of-plane deformation and the geometrical change of cross section need to be considered. In addition, the evaluation of dynamical model which can explain the geometrical change of cross section is required. References 1) Architecture Institute of Japan. Research on Seismic Performance in Educational Institutions. AIJ: Tokyo, ) Takahashi O, Hirano M, Hodumi H, Kaneko S. Experimental Studies on the Collapse Behavior of Bracing under Cyclic Loadings. Summaries of Technical Papers of Annual Meeting of AIJ 1991; (C, Structures Ⅱ): ) Kishiki S, Saito S, Yamada S. Damage Index Based on Out-of-plane Residual Deformation of Tension Brace. Journal of Constructional Steel; 2: ) Yuko S, Kishiki S, Yamada S. Measurement Method in Full-scale Shaking Table Rest of Steel Building. Journal of Constructional Steel; 17: ) Yamada S, Jiao Y, Kishiki S, Shibata A. Plastic Deformation Capacity of Structural Steel under Various Axial Strain Histories. Journal of Structural and Construction Engineering; 75 (656): ) Iwai S, Park Y, Nonaka T, Kameda H. Very Low-cycle Fatigue Tests of Steel Angles. Journal of Structural and Construction Engineering; (445):