International Journal of Steel Structures Improving seismic behavior of MRFs by U-shaped hysteretic damper along diagonal brace --Manuscript Draft-Manuscript Number:
SSIJ-D-18-00092R2
Full Title:
Improving seismic behavior of MRFs by U-shaped hysteretic damper along diagonal brace
Article Type:
Practical application
Corresponding Author:
Seyed Mehdi Zahrai, Professor University of Tehran Tehran, IRAN, ISLAMIC REPUBLIC OF
Corresponding Author Secondary Information: Corresponding Author's Institution:
University of Tehran
Corresponding Author's Secondary Institution: First Author:
Seyed Mehdi Zahrai
First Author Secondary Information: Order of Authors:
Seyed Mehdi Zahrai Mohammad Froozanfar, Masters
Order of Authors Secondary Information: Funding Information: Abstract:
This paper presents seismic assessment of a U-shaped hysteretic damper as an enhancement system, in Moment Resisting Frames, MRFs. The proposed system consists of a damping box at the middle of a diagonal brace. The box includes Ushaped steel plates welded to the side plates. When a transverse loading, like earthquake, is exerted to the building, relative displacement between the stories forms and will be transmitted to the braces where energy dissipation will be achieved by adding a displacement-dependent U-shaped damper. For this purpose, the system is applied to a 2D 2-span 3-story frame to which by applying 3 different earthquake records, far-field, near-field and mid-field, seismic response are evaluated. The responses are the roof displacement, inter-story drifts, root mean squared of roof displacement and base shear. Result verification is carried out via calibrating characteristics of this damper with those obtained through experimental work on a somewhat similar device conducted at the University of Toronto. The results showed that by using this system, the roof maximum displacement decreased 36.7, 45.3 and 38.1% and the maximum base shear decreased 46.6, 12.2 and 45.5% respectively for near-field, mid-field and far-field records. Similar results were observed in inter-story drifts and roof displacement RMS.
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2nd Reply to Review Comments SSIJ-D-18-00092 Improving seismic behavior of MRFs by U-shaped hysteretic damper along diagonal brace
The authors have followed all the reviewers comments and accordingly revised the paper. All the changes are highlighted in yellow color in the revised manuscript. Reviewer #1 Comment 1- After first review, the English of the submission is acceptable although minor improvement is required, e.g., Page 2 line 37, "their RC wall" confuses reviewer. Proper changes were made to further improve the revised manuscript.
Comment 2- Through the whole paper, when author presents time-history figures, the same pattern is always used, i.e., Kobe (near-field), Northridge (mid-field) and Roudbar-Manjil (farfield). Reviewer would like to see other 5 also. In Figure 10, Kobe (near-filed), Kobe (Midfiled), Kobe (far-field) can be used instead since author try to prove the influence of epicenterdistance. The reason has been to see the epicentral distance and the time-history characteristic effects, simultaneously. As respected reviewer suggested, Figure 10 was changed in the revised manuscript to clearly see the epicentral distance effect.
Comment 3- Since the "present paper is to propose a new placement for the U-shaped device, far enough from brace-beam connection", author should include the reason why should it be far from brace-beam connection. The advantage? Will this arrangement makes braces violable from buckling? Almost all the U-shaped systems are used at the top of the chevron braces, between the apex of braces and the top beam. 1- There is always the risk of changing the order of the force-controlled and the displacement-controlled elements, as the beam is a part of load transmission and might 1
damage in the earthquake and though, must be designed precisely. But, in the diagonal damping system, this problem doesn’t occur. 2- Another danger is that one of the brace to the proposed damper or damper to beam connection sides must be welded at the site. If the brace is at the side frames located in perimeter axes (which happens often), it is hard to provide the quality welding, because of the spacing limits, but in the proposed diagonal damping system, all the connections are made in the factory with higher quality. 3- As the length of the brace is divided into 2 parts and as the slenderness has relation with length, the buckling of the brace is more secured now (k = 0.5).
Comment 4- Page 13, line 12-14. Author should explain how the teeth is changed while maintaining the reliability of the Yielding Brace System. The reliability of the result is secured, because: 1- All the conditions of the original system and the modified system are equal except for the dimensions of the teeth. 2- The force controlled parts of the proposed system remain in the elastic zone and only teeth experience inelastic deformations. 3- The hysteresis loop has similar shape as the original one, without any weakness. 4- Another verification was performed, by comparing the proposed yielding brace system hysteresis loop and the loop achieved from the SAP2000 with the same stress-strain ultimate limits.
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Improving seismic behavior of MRFs by U-shaped hysteretic damper along diagonal brace Seyed M. Zahraia and Mohammad Froozanfarb Center of excellence for Engineering and Management of civil Infrastructures, School of Civil Engineering, the University of Tehran, P.O. Box 11155-4563, Tehran, Iran
Abstract: This paper presents seismic assessment of a U-shaped hysteretic damper as an enhancement system, in Moment Resisting Frames, MRFs. The proposed system is consisted of a damping box at the middle of a diagonal brace. The box includes U-shaped steel plates welded to the side plates. When a transverse load, like earthquake, is exerted to the building, relative displacement between the stories forms and will be transmitted to the braces where energy dissipation will be achieved by adding a displacement-dependent U-shaped damper. For this purpose, the system is applied to a 2D 2-span 3story frame to which by applying 8 different earthquake records, far-field, near-field and mid-field, seismic response are evaluated. The responses are the roof displacement, inter-story drifts, root mean squared of roof displacement and base shear. Result verification is carried out via calibrating characteristics of this damper with an experimental work on a somewhat similar device conducted at the University of Toronto. The results showed that by using this system, the roof maximum displacement decreased 38.9, 40.0 and 37.1% and the maximum base shear decreased 36.5, 28.5 and 39.5% respectively for near-field, mid-field and far-field records, averagely. Similar results observed in interstory drifts and roof displacement RMS.
Keywords: seismic behaviour; U-shaped hysteretic damper; energy dissipation; near-field and far-field earthquakes; diagonal brace
1. Introduction With the lack of certainty and knowledge about the performance of structures against earthquakes, any structure is susceptible to damages even in moderate ground motions. So, every structural element is in danger, even vital elements which guarantee the stability of the
a
Corresponding to: Seyed M. Zahrai, Center of excellence for Engineering and Management of civil Infrastructures, School of Civil Engineering, the University of Tehran, P.O. Box 11155-4563, Tehran, Iran Tel: +982161112226 E-mail:
[email protected] b Master student: Mohammad Froozanfar E-mail:
[email protected] 1
structure. The idea of a pre-defined fuse came up just to prevent the mentioned probable 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
damage. When the seismic demand is going to exceed a certain range, the fuse element will yield and dissipate values of energy by its pre-defined mechanism as well as limiting the incoming seismic demand. Instead of repairing the whole structure which is sometimes impossible, just the fuse element needs to be exchanged after the earthquake. As an example, the work done by Calado et al. (2013) on dissipative welded fuses for earthquake resistant composite steel and concrete frames can be mentioned. They used cyclic and monotonic tests to evaluate the seismic performance of such repairable fuses. Hysteretic or Metallic-yielding dampers were invented to play the role of the aforementioned fuse by enduring the inelastic strains, generating a hysteretic damping in addition to the inherent damping of the structure. First concepts of exerting such a system to the buildings get back to Japan in late 1960s and also to New Zealand in early 1970s. Kelly et al. (1972) made some conceptual and experimental efforts with the goal of achieving earthquake resistant structures. Two years later, Skinner et al. (1974) conducted a research with the same goal. They proposed some types of hysteretic dampers, among them U-shaped plates. The concept of the U-shaped plates was just as the concept of a bulldozer truck. In their proposed system, parallel relative motions of the RC walls cause desired flexure, providing energy dissipation through inelastic flexural deformations. Two important benefits of hysteretic dampers transfigured them to an important issue in controlling systems: first, their perceptible concept and second, their easy mechanism which helps them to be used with the minimum requirements. Tyler (1978) presented a tapered steel energy dissipater which was later used in a 29-story steel frame. In recent 50 years, many devices have been proposed and widely used by researchers and engineers. Among them, X-shaped Added Damping And Stiffness (ADAS) plates developed by Whittaker et al. (1989) and also Triangular Added Damping And Stiffness (TADAS)
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system presented by Tsai et al. (1993) are well known and widely used. They can be added to 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
the end of the chevron bracings, where the braces connect to the upper floor beam. The relative displacement between two stories generates two inverse forces which makes a bending moment through the mentioned plates. When the strain passes the yielding limit, the plates begin to absorb energy via inelastic flexural displacements. The ADAS plates due to the uniform curvature through the plate are widely used with rigid connections at the bottom and top. Improved forms of TADAS and ADAS plates were the result of work conducted by Gao and Ye (1995) in another research on diagonal braces. Beside large amount of experimental and numerical research, remarkable applications of energy dissipation devices have been reported all over the world. Metallic-yielding damper was utilized for the first time in New Zealand, leading to reduction in structural responses which proved its efficiency in a real structure. Implementation of U-shaped steel plate damper in the government building in New Zealand in 1980 is the first instance of applying such a device in a real structure. Many of the well-known hysteretic devices were first, applied in a base isolation system and then distributed in the braced frames. Third millennium was accompanied with the advent of much more numerical and experimental research studies as well as implementation of the energy dissipation devices in real structures. Research projects conducted by some researchers are reviewed here. MartinezRueda (2002) reviewed the evolution of hysteretic dampers and described their relevant past applications. Xing and Guo (2003) investigated the performance of new type of steel damper, voided lozenge steel plates with simultaneous yielding. Li et al. (2004) conducted full scale tests on mild steel damper, controlling the vibration of steel frame structures. They used a three-layer structure for this purpose. Seismic response analysis of structures and their pseudo-dynamic testing demonstrated satisfactory results. In the recent five years, the studies on metallic yielding devices have been continued. Di
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Cesare et al. (2012) worked on the experimental and numerical model of energy dissipation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
devices in braced frames. The device was added to the end of inverted-V bracings and the frame was constructed with appropriate scale, representative of a full scale structure. Seismic behavior of the device was investigated through shaking table test. Bayat and Bayat (2014) studied on Special Moment Resisting Frames, SMRFs with different number of energy dissipating ADAS devices, and investigated its behavior under near-field ground motions. Aghlara et al. (2015) compared eight metallic yielding dampers through their four key variables. The relationship between the mechanism of devices and equivalent viscous damping was obtained. Sahoo et al. (2015) studied on three shear-and-flexural devices by varying the size of shear and flexure plates, to evaluate their cyclic behavior. Also, Garivani et al. (2016) introduced a new type of metallic yielding damper, called comb-teeth. In their study, acceptable hysteresis loop was achieved without any significant strength loss. Experimental and numerical studies with the goal of achieving a new biaxial elasto-plastic device were conducted by Dolce et al. (1996) for the passive control of structures. Their work was on a circular arrangement of U-shaped plates which were used in 1995 in Italy as seismic isolators. Since then, many samples have been implemented with the same aim. The work done by Sang-Hoon et al. (2012), that used the U-shaped hysteretic damper in a base isolated system, can be mentioned. Also, Bagheri et al. (2015) evaluated seismic behavior of U-shaped metallic yielding damper in building structures, using a uniaxial damper at the connection of chevron brace and the top floor beam. They also proposed a biaxial U-shaped metallicyielding damper with circular arrangement, at the same location as the uniaxial one. Deng et al. (2015) worked on shape optimization of U-shaped damper to improve its bi-directional performance under cyclic loading. They used finite element model in ABAQUS to reach their aim. After four levels of optimization, they could improve the bi-directional behavior significantly.
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U-shaped devices can be easily used by adding them just where the brace connects to the 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
beam. But there is a shortcoming on this arrangement. The behavior of the connections is not absolutely well-known during an earthquake and that may cause the danger of spoiling the sequence, between the displacement-controlled and force-controlled elements. In other words, in traditional braced frames that the bracing must act as the fuse element and other elements such as columns must stay in elastic range, there is a risk for occurrence of an unexpected behavior. In the past decades, there has been some research mostly conducted on separate elements such as beams, columns and braces, but there is still lack of work on the connections and their behavior through an earthquake. The aim of the present paper is to propose a new placement for the U-shaped device, far enough from the brace-beam connections, avoiding any undesired behavior in elements and also to present a special form of these devices to attain a logical set that can be used easier than before, without previously reported implementation difficulties. 2. Designing the damper The U-shaped hysteretic damper is assumed to be made of steel plates with the yielding strength of 240 MPa and the yielding limit strain of 0.00115. Also the ultimate values of stress and strain are 370 MPa and 0.2, respectively, as shown in Fig. 1. The density of the steel is supposed to be 7850 kg/m3. The damage of the steel due to great displacements is also considered. Table 1 shows mechanical properties of the assumed steel.
Fig. 1. Stress-Strain diagram of the steel utilized in this research
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Table 1. Mechanical properties of the steel, assumed for designing the damper elements, including the U-shaped plates, stiffener plates and the main plates
Material type
Young Modulus (N/m2)
Poisson Ratio
Density (kg/m3)
Isotropic
209e9
0.3
7850
The damper consists of 2 rectangular plates, perpendicular to the longitudinal axis of diagonal bracings, 8 triangular plates and also 4 U-shaped steel plates (see Fig. 2). In the series of load transferring, perpendicular plates act as the force-controlled elements which their stress must never reach the yielding limit. The triangular plates play the role of stiffeners for the rectangular plates, preventing them from local buckling and bending. Finally, the Ushaped plates act as the displacement-controlled elements. Designers are interested in achieving two important behaviors in structures: First, achieving the desired stiffness in order to resist the imposed forces such that the displacements of the structure remain in allowable range and second, achieving the desired ductility, reaching some states of dissipating the imposed energy due to the dynamic loads. So, from this concept, the dimensions of the U-shaped plates are designed to secure both behaviors. When the dynamic load is exerted, internal loads in the brace and the U-shaped plates will be mobilized. The force will cause a bending moment in any section of the Ushaped plates. As the force increases, the moment increases as well. This will continue until the stresses in some parts of the U-shaped plates reach the yielding value. The hysteresis loop will form and there will be some amounts of hysteresis damping besides the inherent damping of the structure. Due to aesthetic reasons in some cases in which the system is exposed and also for the ease of welding, the whole elements of the damper such as the three kinds of the defined plates, will be manufactured in factory. The dimensions required for any certain building will be designed and the damper will only be carried to the site and practically just a 4-side welding, CJP in Fig. 2 or a pretentioned bolted connection is needed. This completely obtains a 6
suitable condition to attain a prequalified mechanism and system, since more than 90% of the 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
welding connections will be done in fabrication shop (see Fig. 2).
(a) Side view
(b) Top view Fig. 2. U-shaped hysteretic damper and the dimension (in cm) of different plates used to fabricate the damper at the middle of a diagonal brace
In the literature, many of the U-shaped systems are used at the top of the chevron braces, between the braces and the top beam. The proposed system has some advantages: 1- There is always the risk of changing the order of the force-controlled and the displacement-controlled elements, as the beam is a part of load transmission and might damage in the earthquake and though, must be designed precisely. But, in the diagonal damping system, this problem doesn’t occur. 2- Another problem is that one connection (the brace to the proposed damper or damper to beam) must be welded at the site. If the brace is at the side frames located in perimeter axes (which often happens), it is hard to provide the quality welding, because of the
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spacing limits, but in the proposed diagonal damping system, all the connections are made in 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
the factory with higher quality. 3- As the length of the brace is divided into 2 parts and as the slenderness has relation with length, the buckling of the brace is more secured now (k = 0.5).
3. Analytical model In order to evaluate the performance of the introduced damper against seismic demand, an analytical model has been formed. The 2D model is made of a 3-story, 2-bay moment frame with rigid connections. The height of each story is 3.5 m with a total height of 10.5 m for the structure. Also, the length of all bays is 5 m (Fig. 3). In the first step, the model of the bare frame, i.e. the frame without any damper, was designed in SAP2000 (2008) and the drift ratios and other controlling criteria were checked.
Fig. 3. Moment frame used in this paper to evaluate the performance of the proposed damper
Then, totally 8 acceleration time-histories were chosen from the past earthquakes. These records are: 3 records from the Kobe earthquake (Japan 1995), a far-field, a mid-field and a near-field, 3 records from the Northridge earthquake (USA 1994), a far-field, a mid-field and a near-field and 2 records from the Roudbar-Manjil earthquake (Iran 1990), a far-field and a record with characteristics of both mid-field and near-field. The characteristics of the earthquake records are shown in Table 2. The reason of considering different kinds of earthquake records (also see Fig. 4) was to investigate the effect of earthquake frequency
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content and the epicentral distance on the performance of the damper. For all eight records, 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
horizontal acceleration time history in H1 direction is considered. All the earthquake records are scaled to the peak acceleration of 0.35g, to be comparable.
Table 2. Eight earthquake records used in this paper (NF: Near-field, MF: Mid-field and FF: Far-field) Earthquake Name
Country
Kobe
Japan
Northridge
U.S.A.
Roudbar-Manjil
Iran
Year
1995
1994
1990
Magnitude (Richter)
6.9
6.69
Station
Distance to the fault (km)
Kobe University
0.9 (NF)
Fukushima
17.85 (MF)
HIK
95.7 (FF)
Arleta-Nordhoff fire St.
8.6 (NF)
Burbank-Howard Rd.
15.87 (MF)
Featherly Park
82.3 (FF)
Abbar
12.5 (NF or MF)
Qazvin
50 (FF)
7.37
(a) The Kobe University station record from the Kobe earthquake (near-field)
(b) The Burbank-Howard Rd. station record from the Northridge earthquake (mid-field)
(c) The Qazvin station record from the Roudbar-Manjil earthquake (far-field) Fig. 4. Three of eight earthquake records used in this work
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In the next step, important responses of the bare frame (frame without any damper), i.e., 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
roof displacement (related to the relative displacements and the drift ratios), inter-story drifts, roof displacement RMS time-history and base shear, were recorded. Then, the damper was modelled in program ABAQUS (2012) and a cyclic loading from diminished SAC loading protocol (2000) was applied to one side of the diagonal brace containing the damper, while other side was fixed. The reason for decreasing the number of SAC cycles was that it had no special effect on analysis results and the simplifying assumption saved time in remodelling the damper until it became appropriate. The load was increased in order that the elasto-plastic behaviour of the damper was secured. Total number of the cycles was 13 (see Fig. 5) which efficiently supported the desired behaviour. Also, the damage to the steel was considered, modelling the upper limits of the exerted load, like any other dampers. It was observed that the yielding starts at the middle of the U-shaped plates, and then propagates to the sides (Fig. 6).
Fig. 5. SAC 2000 loading protocol used in this paper
Fig. 6. Stress distribution in U-shaped hysteretic damper under the loading protocol
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In the next step, the damper was added to the described moment frame. For this purpose, 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
the damper was modeled by the “Plastic (Wen)” link in SAP2000. The specifications of the link such as effective stiffness, post yield stiffness ratio and yield strength were obtained from the ABAQUS model, in a way in which the force-displacement diagrams (diagram from ABAQUS and from SAP2000) fit and collaborate each other with an acceptable tolerance (see Fig. 7). A good collaboration between the results of ABAQUS and SAP2000 was observed. In addition to the SAC protocol, a protocol similar to the default protocol of SAP2000 was used to prove the correctness of link modeling in SAP2000, in a better way. The forcedisplacement diagram showed a desired behaviour, proved that some undesired deficiencies such as pinching behaviour did not occur. Then the eight time-histories were exerted to the frame with damper and like the previous bare frame, the responses were recorded.
Fig. 7. Hysteresis loops and the resiliency of loops from ABAQUS and SAP2000
4. Result verification As it was not possible to do an experimental work and make a prototype or a full scale specimen of the proposed damper in this research, in the beginning of the numerical research, there must be result verification via calibrating the assumptions of this proposed damper and a similar work conducted before. In order to correlate the numerical results to a similar numerical and experimental work, similar aspects and original assumptions have been observed and considered as presented in Gray et al. (2010, 2012a and b, 2014). 11
In recent years, researchers from the University of Toronto and McGill University have 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
worked on the enhancement systems for structures, mainly passive systems. Gray et al. (2010, 2012a and b, 2014) presented the system called “Yielding Connectors” which are modular, replaceable, standardized hysteretic fuses that provide enhanced ductility and improved performance in the retrofit of seismically deficient structures or for use in the seismic force resisting system of new structures. One of the new types of this kind of dampers is the “Yielding brace system” which is a device for enhancing the seismic behavior of concentrically braced frames, which has shown a perfect performance in retrofitting the existing frames. The system is made of a hysteretic element connected to the end of the diagonal brace, just before its connection to the gusset plate. Axial force in the brace is transferred to the lower beam-column joint through bending of triangular-shaped flexural yielding fingers as they yield and show an inelastic behavior and accordingly significant energy dissipation occurs. In that work, a numerical modeling and designing a prototype for preliminary iterations and also a full scale specimen has been made. The numerical and experimental results fit each other perfectly. There are some reasons why the U-shaped damper is calibrated to yielding brace system: 1. Both cases are metallic yielding dampers that absorb the input energy by hysteretic behavior. 2. In both dampers, the mechanism is the bending of steel plates and the related flexural inelastic behavior, while other parts of the damper remain elastic and are force controlled. 3. Loading protocols of both cases have almost equal values, where SAC protocol is chosen for the U-shaped damper and the loading protocol of yielding brace system is from appendix T of AISC 341. 4. Both dampers are added to the diagonal bracing in order to retrofit the frame. 5. In yielding brace system, besides numerical work, there has been experimental work where the hysteresis loops as well as other characteristics fit each other appropriately.
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In remodeling the yielding brace system, the entire original assumptions of the main 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
modeling such as: material considerations, boundary conditions, original shape of the damper, loading protocol, degrees of freedom in connection of different parts are considered to ensure the correct calibration (see Fig. 8). The original material model with ultimate stress of 367 MPa is used for triangular teeth and 345 MPa for other parts of damper such as the brace. The boundary conditions are ensured, i.e., one end of triangular teeth has no rotational degree of freedom and the other end has a rotational degree of freedom, perpendicular to the axis of bracing, in order to reduce the load bearing capacity of damper. The protocol of loading is also chosen from appendix T of AISC 341. Dimensions of the damper parts which are force controlled are the same as the original model. Only teeth plate dimensions were modified according to the requirements of U-shaped damper calibration. The reliability of the result is secured, because: 1- All conditions of the original system and the modified system are equal except for the dimensions of the teeth. 2- The force controlled parts of the modified system remained in the elastic zone and only teeth had inelastic deformations. 3- The hysteresis loop had similar shape as the original one, without any weakness. 4- Another verification was performed, by comparing the modified yielding brace system hysteresis loop and the loops achieved from the SAP2000 with the same stress-strain ultimate limits. The important aspects are the yielding load of the damper, the stiffness of the damper and the surface of hysteresis loop directly related to the dissipated energy showing equivalent viscous damping; so it is tried to get close to the three named aspects of the dampers. The most important goal in calibrating was that similar hysteresis loops for U-shaped damper and the yielding brace system be achieved; because in metallic yielding braces, the most important characteristic of the damper is its hysteresis loop. In this case, from one hand the new yielding brace system remodeled only by changes in dimensions of triangular teeth will have similar results in full scale specimen to the numerical results. On the other hand, the U-shaped
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damper has damping characteristics completely similar to the remodeled yielding brace 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
system. Combining these two sides, it is obvious that in a full scale specimen, the U-shaped damper will show similar results to the yielding brace system (see Fig. 9).
Fig. 8. Remodelling the yielding brace system with dimension appropriate to this paper’s requirements
Fig. 9. Similarity between the hysteresis characteristics of U-shaped damper and yielding brace system
5. Numerical results and discussion The responses of the frame to the seismic records are shown in Figs. 10-13, consisting of the bare frame (frame without damper) and the enhanced frame (frame with damper) responses. As the hysteresis loops of SAP2000 and ABAQUS fit each other appropriately, the results are trustworthy for the numerical values. As the earthquake records are representative of three different kinds of records, i.e. far-
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field, near-field and mid-field, one can declare about the effect of the epicentral distance on 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
the performance of the proposed U-shaped damper. At the end, an IDA analysis was done for the peak accelerations of 0.2g, 0.35g, 0.5g, 0.65g and 0.8g.
5.1. Roof Displacement The first response assessed was roof displacement. The roof displacement time-histories of three out of eight records are shown in Fig. 10 and for other records, the peak values in the frame with damper and without damper and the effect of the proposed system are discovered and showed in Table 3. From the results (see Fig. 10 and Table 3), it is obvious that the proposed damper was capable of decreasing the vibrations induced by the earthquake, through dissipating the input energy. The damper was able to decrease the roof displacement responses of both peak values and time-history values, desirably. As observed, despite many peaks in the response history of the frame to the records, the damper could dissipate and decrease many of these peaks, very well. It is obvious that the epicentral distance and the duration of the earthquake had no effect on the performance of the damper, however more records and more kinds of this damper must be considered, besides the practical studies, to reach a promising conclusion. One of the important aspects of this response control is that the nonstructural elements which are susceptible to the damage due to relative displacements are now in a safer mode.
(a) The Kobe University station from the Kobe earthquake (near-field)
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(b) The Fukushima station from the Kobe earthquake (mid-field)
(c) The HIK station from the Kobe earthquake (far-field) Fig. 10. Roof displacement response history of the frame for three of eight earthquake records Table 3. Max roof displacement values with and without damper (NF: Near-field, MF: Mid-field & FF: Far-field) Earthquake Name
Kobe
Northridge
Max Roof Max Roof Roof displacement displacement (cm) displacement (cm) reduction (%) (without damper) (with damper)
Station
Type
Kobe University
NF
20.7
13.1
36.7
Fukushima
MF
23.6
15.9
32.3
HIK
FF
20.4
14.2
32.6
Arleta-Nordhoff fire St.
NF
21.4
13.4
37.6
Burbank-Howard Rd.
MF
20.3
11.1
45.3
Featherly Park
FF
21.6
12.8
40.7
Abbar
NF or MF
17.2
9.9
42.4
Qazvin
FF
16.8
10.4
38.1
RoudbarManjil
5.2. Inter-story Drift The damper decreased the maximum inter-story drift ratios of all three stories, under all eight different earthquake records (see Fig. 11). The decrease of the maximum values was the most in story 3, in comparison with the other two stories. In the bare frame, the maximum values for inter-story drifts increased from the base to the roof, in a similar way for all the
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records. In the enhanced frame, the maximum values increased from the base to the story 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
and then decreased in story 3. In story 3, the maximum drift ratio is decreased even to 50 percent of the primary values in the bare frame, due to application of U-shaped damper. It is also obvious that the decrease is almost similar for all the records, proving no impact of the record characteristics on the performance of the system (See Table 4).
(a) The Kobe University Station (near-field)
(b) The Burbank-Howard Rd. station (mid-field)
(c) The Qazvin station (far-field) Fig. 11. Maximum inter-story drift ratios for three of eight records Table 4. Max inter-story drift ratios with and without damper (For the most decrease in the 3 stories) (NF: Near-field, MF: Mid-field and FF: Far-field) Earthquake Name
Kobe
Northridge
RoudbarManjil
Station
Type
Max drift ratio (without damper)
Max drift ratio (with damper)
Max drift ratio reduction (%)
Kobe University
NF
2.57
1.34
47.8
Fukushima
MF
2.86
1.63
43.0
HIK
FF
2.38
1.37
42.1
Arleta-Nordhoff fire St.
NF
2.23
1.06
52.3
Burbank-Howard Rd.
MF
2.56
1.09
57.4
Featherly Park
FF
2.17
1.04
51.7
Abbar
NF or MF
1.97
1.04
47.1
Qazvin
FF
2.00
1.11
44.5
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5.3. Roof Displacement RMS (Root Mean Squared) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
In an earthquake, a structure may sustain the first sharp peaks, but yield under the next shorter peaks, due to cyclic fatigue; especially it is important in time-histories in which there are several sharp peaks, like here in Burbank-Howard Rd. station. So, RMS of the results is also investigated. The results showed that the damper was successful in decreasing RMS (Root Mean Squared) of the roof displacement response history which directly relates to the low cycle fatigue of the structure during an earthquake (see Fig. 12). The results are the same for other records, not shown here for abbreviations.
(a) The Kobe University station (near-field)
(b) The Burbank- Howard Rd. station (mid-field)
(c) The Qazvin station (far-field) Fig. 12. Roof displacement RMS time-history for three of the eight records
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5.4. Base Shear 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Base shear of the frame has decreased under all different earthquake records, by applying the U-shaped damper (see Fig. 13). The damper decreased both the peak values and the response history values, proving its positive effect. Reduction of the peak values varies from 12.2% for the Burbank-Howard Rd. station record to 46.6% for the Kobe University record, not as stable as other responses (see Table 5). In the Burbank-Howard Rd. record, by the passage of time, the U-shaped damper gets more effective in the peak values domain, at the middle of the earthquake duration.
(a) The Kobe University station (near-field)
(b) The Burbank-Howard Rd. station (mid-field)
(c) The Qazvin station (far-field) Fig. 13 Base shear response history for three of the eight records
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Table 5. Base shears of the frame with and without damper (NF: Near-field, MF: Mid-field and FF: Far-field)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Earthquake Name
Station
Type
Base shear (kN) (without damper)
Base shear (kN) (with damper)
Base shear reduction (%)
Kobe University
NF
375
200
46.6
Fukushima
MF
363
227
37.3
HIK
FF
382
222
41.8
Arleta-Nordhoff fire St.
NF
354
259
26.7
Burbank-Howard Rd
MF
370
325
12.2
Featherly Park
FF
367
272
31.3
Abbar
NF or MF
396
253
36.1
Qazvin
FF
385
210
45.5
Kobe
Northridge
RoudbarManjil
5.5. IDA analysis An IDA analysis has been provided to see the earthquake magnitude and the PGA effect on the performance of the U-shaped hysteretic damping system. From the responses of the frames with and without damper, the inter-story drift ratio is chosen to be assessed. The record for this analysis is the Burbank-Howard Rd. station. The record has been scaled to the PGA of 0.2g, 0.35g, 0.5g, 0.65g and 0.8g, for this purpose. After scaling the PGA of the record to the defined accelerations, the frames with and without damper have been loaded with these 5 different records (PGA of 0.2g, 0.35g, 0.5g, 0.65g and 0.8g) (see Fig. 14).
Fig. 14. IDA analysis and the results for inter-story drift ratios, for the Burbank-Howard record, scaled to 5 different PGA values (0.2g, 0.35g, 0.5g, 0.65g and 0.8g)
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It was observed that the frame without any damper, from the acceleration of 0.5g on, 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
entered the inelastic domain and some plastic hinges were made, at the end of its beams, starting from the story 1 to the above. This has lowered the story stiffness, so one can see that the drift ratio values has increased more rapid for these PGA values, especially for stories 1 and 2. By adding the U-shaped damper, as the fuse has transmitted from the beams to the damper and as the majority of the stiffness of the frame is still due to the beams and columns and the rigid connection of them, it was obvious that even after inelastic behavior in the dampers, the frame stood stiff enough and the drift ratios didn’t increase rapidly. Also, it was observed that the difference between the drift ratios is less in the fame enhanced with damper, in comparison with the frame without any dampers. This diagram can be used by the users to guess and predefine the performance of the proposed system, in any PGA to which they are scaling the records (Surely after making this diagram for many other different earthquake records and many different types of such system with different characteristics and making an average of them). In the next parts of the research, a full scale U-shaped damper can be manufactured and cyclically tested in order to further make sure of the damper capability and design details. More studies must be done on this kind of system to reach optimum design. The U-shaped hysteretic damper can be used in the diagonal or the chevron bracings. They should be used in a symmetrical array, in which, some brace be exposed to tension and other to the compression, in each cycle. Also, the braces must be secured from the total and the local buckling, as well as the torsion. By achieving the seismic characteristics, such as the R, , 0, Cd and else, via the analytical and experimental studies, these systems can be taken to the seismic provisions and be widely used.
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6. Conclusion and summary 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65
Metallic yielding braces are one of the most important types of dampers with rich performance in decreasing the seismic induced vibrations of structures. Creating high performance, they also have a simple mechanism and can be replaced easily by another damper after the earthquake. One type of these dampers is U-shaped damper which works by adding such bent plates to the bracings. In common type of U-shaped dampers, they are added to where the brace connects to the gusset and where the behavior is often unknown. However, in this paper, the proposed placement is at the middle of the brace and also the mechanism changes from rolling mechanism to the bending mechanism. Adding the proposed U-shaped dampers to the moment frame systems, as a retrofit solution in order to improve their seismic performance was discussed in this paper showing great performance. It could decrease the important features of the seismic responses in a structure, i.e. the base shear and the roof displacement (related to relative displacement and drift ratio), effectively. The decrease was in peak values as well as the values in other ranges. Totally, hysteretic dampers due to two important features, i.e. accountable decrease in the values of seismic responses, and the damper’s low expenditure, has become a high revenue system to be used in retrofitting existing buildings or to enhance the performance of new buildings. Another important merit shown in this paper was that the damper could almost decrease the responses of all near-field, mid-field and far-field earthquakes almost similarly, which means that the epicentral distance does not have a logical effect on their performance.
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