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Experimental study on seismic performance of RC frames with Energy-Dissipative Rocking Column system
Engineering Structures 194 (2019) 406–419
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Experimental study on seismic performance of RC frames with EnergyDissipative Rocking Column system
T
Yan-Wen Lia, Guo-Qiang Lib, , Jian Jiangc, Yan-Bo Wanga ⁎
a
Department of Structural Engineering, Tongji University, Shanghai 200092, China State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China c School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China b
ARTICLE INFO
ABSTRACT
Keywords: Reinforced concrete moment resisting frame Energy-Dissipative Rocking Column Soft story failure Pseudo-dynamic test Inter-story drift
The conventional reinforced concrete Moment Resisting Frames (MRFs) have suffered from soft story failure during major earthquake events. A novel system of steel Energy-Dissipative Rocking Column (EDRC) is proposed to mitigate seismic responses of MRFs. Pseudo-dynamic tests are conducted on large-scale two-story and two-bay reinforced concrete frames, with and without EDRC, respectively. The post-earthquake behavior of these two systems is also compared through quasi-static cyclic tests. The experimental results show that the presence of EDRC can effectively mitigate the maximum value, residual value and inhomogeneous distribution of inter-story drifts, and thus prevent the soft story failure of MRFs. It is found that the maximum and residual inter-story drift of combined MRF and EDRC systems is reduced by 26.0% and 82.0%, respectively, compared to pure MRFs. The inhomogeneous degree of inter-story drifts can be reduced by 25.0% and 11.0%, respectively, in the pseudodynamic and quasi-static tests.
1. Introduction Reinforced Concrete Moment Resisting Frame (hereinafter referred to as MRF) is one of the most common lateral load resisting systems for low-rise to mid-rise structures in earthquake regions. However, conventional MRFs have suffered from severe damage such as soft story failure during major earthquake events [1,2], although they are normally designed with ductile detailing and strong column-weak beam (SCWB) criterion in accordance with current seismic design provisions [3–5]. Due to soft story mechanism, plastic hinges are mainly distributed at the ends of columns on a single story. Large residual drift and concentrated damage may bring difficulties in the reparability and fast resilience of MRFs after earthquakes [6,7]. From point view of structural strength, some researchers proposed the theory of plastic mechanism control that prevent undesired failure modes such as soft story mechanism by evaluating the total plastic moments of the columns required at each story [8,9]. Since metal energy-dissipative devices can provide strength as well as energy-dissipation capacity for the structures, some other researchers developed a number of novel metal energy-dissipative devices [10–13] for the framed structures. In recent decades, many efforts have been put in investigating the effect of vertical continuous stiffness on mitigating damage concentration along the height of a structure. These include ⁎
studies on the relationship of damage concentration and stiffness of the continuous columns in steel concentrically braced frames [14,15]. The effect of increasing flexural stiffness of continuous columns on mitigating inter-story drift ratio concentration was examined by analytical and nonlinear time history analysis. As an effective solution to avoid soft/weak-story failure of framed structures, rocking walls with much larger flexural stiffness than individual columns were proposed [16–21], and have been applied for retrofit projects [22,23]. However, conventional rocking walls have negligible lateral resisting stiffness and energy dissipation capacity, which limits their application in new constructions. As an alternative, a novel system of Energy-Dissipative Rocking Column (EDRC) has been proposed by the authors [24–26], as shown in Fig. 1. The EDRC system is a combination of rocking components and metal energy-dissipative components. It consists of two steel column branches with pinned supports which are connected by distributed strip dampers. In a combined MRF and Energy-Dissipative Rocking Column dual system (hereinafter referred to as EDRC-F), the framing beams are simply connected to the column branches of EDRC where the moment transfer is negligible, as illustrated in Fig. 1. Under frequent earthquakes, the EDRC is designed to stay in an elastic state, providing lateral resisting stiffness for the structure system. Under rare earthquakes, the steel strips are designed to yield and dissipate seismic energy, while
Corresponding author. E-mail address: [email protected] (G.-Q. Li).
https://doi.org/10.1016/j.engstruct.2019.05.052 Received 3 February 2019; Received in revised form 15 May 2019; Accepted 18 May 2019 Available online 30 May 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.
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Frame beam
In this paper, a pseudo-dynamic testing program was developed to investigate the nonlinear dynamic response of EDRC-F system under earthquakes with different intensity levels. This test program includes low-intensity and high-intensity pseudo-dynamic tests to represent frequent earthquakes and rare earthquakes, respectively. A comparison of seismic responses between MRF and EDRC-F systems was made. The post-earthquake behavior of these two systems was also investigated by conducting quasi-static cyclic tests. The key responses such as maximum, residual and inhomogeneous distribution of inter-story drift ratios were output to quantify the effect of EDRC on mitigating the seismic responses of reinforced concrete structures.
Rigid link Strip dampers
B-B
B-B
Hinge
2. Test setup
Column branches
2.1. Layout of specimens
C-C
C-C
A conventional MRF and an EDRC-F were selected from a six-story prototype building designed with ductile detailing in Chinese seismic design code [4], except strong column-weak beam criterion. The prototype building is located in a site with seismic design intensity of 7 (the maximum spectrum acceleration is 0.15 g for 63% probability of exceedance in 50 years) and site classification of III. As shown in Fig. 3, the prototype building has four spans in the X-direction and two spans in the Y-direction. The ground story is 4.0 m in height and the upper stories are 3.0 m in height. The dead load and live load on the floor are 5.0 and 2.0 kN/m2, respectively. These loads produce a load ratio of about 40% and 68% for the exterior and interior columns on the ground story, respectively. The load ratio is defined as the ratio between applied load and the design column axial load capacity. The concrete grade is C35 in Chinese standard for the beams and columns, with a cubic compressive strength of 35 MPa [27]. The steel grades of the longitudinal and transverse reinforcements are HRB400 and HRB300, with a nominal yield strength of 400 MPa and 300 MPa, respectively. The cross-sectional dimensions of the beams and columns are 600 mm × 300 mm and 360 mm × 360 mm, respectively. A scaled two-span and two-story substructures (dashed block in Fig. 3) was selected from the prototype building as the tested frame. The scaling ratio is 1:1.5. The selection of two-story substructures is because that soft ground story collapse was normally observed in the post-earthquake field investigation, while the upper stories often remained undamaged or even in elastic range. The selection is also to consider the cost effectiveness of tests and limitations of the loading
Fig. 1. Schematic of Energy-Dissipative Rocking Column (EDRC) system.
Plastic hinge
EDRC
Fig. 2. Comparison of failure modes between MRF and EDRC-F under earthquakes.
[email protected]
the steel column branches are to stay in elastic and rock to re-distribute seismic forces along the structural height and to mitigate inter-story drift concentration. Benefiting from the advantages of vertical continuous column branches and energy dissipation characteristic of steel strip dampers in EDRC, the EDRC-F dual system tends to form a global plasticity failure mode rather than a local plasticity one of MRF, as shown in Fig. 2.
Y
4.0m
Test frame
X
2@ 6.0m
(a) Plane view
(b) Elevation view
Fig. 3. Schematic of the prototype building.
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200 2000
2870
240
3760
1250
550 6@75
1
1
1260
2
2660 2 6@135
1250
1250
3
3
550 6@75
240
3760
550 6@75
1250
1260
1
2
3
1
2 2660
6@135
3
550 6@75
C
C
650
615 6@75
1460 6@135
1190 6@75
995 810 6@135 6@75
240
400
4000
4000
8800
400
(a) Dimension of MRF 4 14(corner), 4 12 6@75/135
2 12,1 12
2 12
2 12,1 10
2 12,1 10
1-1(3-3)
2-2 (b) Reinforcement layout
C-C
Fig. 4. Layout of the MRF specimen.
facilities. The purpose of this experiment is to study the effect of EDRC on mitigating the soft story collapse of reinforced concrete structures. Since the prototype building had a relatively large span, the beams were designed with a relative deep section which was stronger than columns in flexural capacity. This type of MRF was observed in the seismic region and vulnerable to the seismic action [2]. The following two subsections presented the details of MRF and EDRC-F specimens, respectively.
diameter of 6 mm and spacing distance of 135 mm was used, which was anchored using 135-degree hooks. The spacing of stirrups in the end region of beams and columns was reduced to 75 mm to ensure the ductile details, and the column stirrups were continuous in the beam-tocolumn joints. The concrete bases of the specimens were anchored to the concrete floor by pre-stressed high strength rods in a diameter of 120 mm. 2.1.2. Design of EDRC component As reported in the previous studies [24], the presence of EDRC in RC moment resisting frame can mitigate seismic response significantly, such as the maximum inter-story drift and inter-story drift concentration. The most effective EDRC stiffness ratio for mitigating seismic response of RC moment resisting frames fell in the range of less than 0.2. In this study, a design EDRC stiffness ratio of 0.1 is adopted. For simplification, the ith story stiffness of RC moment resisting frame can be estimated as,
2.1.1. MRF specimen As shown in Fig. 4(a), the scaled MRF specimen has a total height of 5.72 m, total width of 8.8 m, and span of 4.0 m. The story height of the ground and second story is 2 m and 1.67 m, respectively. The cross section of the columns and beams is 240 mm × 240 mm and 400 mm × 200 mm, respectively. The column section has four longitudinal reinforcing bars in a diameter of 14 mm (at corner) and four bars in a diameter of 12 mm (at mid-span), as shown in Fig. 4(b). This results in a reinforcement ratio of about 1.6%. Longitudinal reinforcement in the columns was extended to the concrete base by a embedment depth of 650 mm. The beam section at the mid-span and end has five and six longitudinal reinforcing bars, respectively. For the stirrups in the middle region of both columns and beams, reinforcement with a
m
KMi = j=1
12Ec Ic, ij hi3
(1)
where Ec is the elastic modulus of concrete, Ic, ij is the jth column section
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200 2000
1460 6@135
240
3760
1250
550 6@75
1260
1
1
2
2660 2 6@135
3600
1250
1250
3
3
550 6@75
550 6@75
150 260 150
4
5
4
5 2190
6@135
660 6@75
C
C
650
615 6@75
2870
1190 6@75
995 810 6@135 6@75
240
400
4000
8800
800
3600
(a) Dimension of EDRC-F 2 12,1 12
2 12
2 12,1 10
2 12,1 10
4-4
(b) Reinforcement layout
5-5
Fig. 5. Layout of the EDRC-F specimen.
moment of inertia in ith story, and hi is the ith story height. Then, the overall elastic stiffness of the bare RC moment resisting frame under concentrated lateral load can be expressed as,
KMRF =
n i=1
1 1/ KMi
branches, respectively. Ai , Ii (i = 1, 2) are the gross section area and moment of inertia of the two column branches, respectively, Ie is the summation of moment of inertia of all the shear links. Note that several iterations may need to obtain desired EDRC parameters, and this process can be easy with help of the widely used Excel software. Finally, the section HW150 × 150 × 7 × 10 in Chinese standard [28] is adopted as the column branch section. The clear distance between dual column branches is 260 mm. The length and thickness of dumbbell-shaped steel links are 260 mm and 16 mm, respectively. A total of 18 shear links are distributed along the EDRC height. The EDRC system is designed to yield at an inter-story drift ratio of 1/300, thus the Q225 steel with nominal yield strength of 225 MPa is adopted for the shear links. It is noteworthy that due to the coupling effect between EDRC and the concrete frame, the overall elastic stiffness of EDRC-F dual system may larger than the pure MRF, this can be solved by minor reducing the beam or column section size in the concrete frame.
(2)
where n is the number of stories. The elastic stiffness of the EDRC component can be determined as [24],
KEDRC =
(3)
k KMRF
where k is the design elastic stiffness ratio of EDRC system, 0.1 is adopted in this study. When the elastic stiffness demand on EDRC is determined, the cross section of column branches and dimensions of the steel shear links can be roughly estimated by the EDRC stiffness formula [26],
KEDRC =
2
1 Hl2 EI (k )2
+
k 2 1 H2l k2 12EIe
+
k2 1 H3 k 2 3EI
12I l 4 AI l3 = 3 c , k2 = 1 + , I = I1 + I2, Ie = 2 b hI A1 A2 l 12E
(4)
2.1.3. EDRC-F specimen The layout of EDRC-F specimen is shown in Fig. 5(a). The left span of EDRC-F has the same dimension of beams and columns as MRF, while the cross section of beams connected to EDRC in the right span was adjusted to 320 mm × 200 mm, as shown in Fig. 5(b). This arrangement is to maintain the same elastic stiffness of EDRC-F as MRF. This specimen design was validated against pre-test measurement of the
ki, A = A1 + A2
where E is the elastic modulus of steel material, H is the height of EDRCs, h is the distance between shear links from center to center, b and l are the clear and center-to-center distances between column
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150
260
150
260 45 170 45
Hinge 55 70 65
D
D
16
20 83 55 83 20
250
10
100
200
110 100 110
320
4M20 21.5,10.9
220
25 78 55 78 25
welding
D-D 560
(c) Configuration of EDRC joint
Cover plate
650
Base plate
Bolt nuts
A
Dscrew
16 16
27 mm
8@120
H150 150 7 10 8@120
A
A-A
800 (d) Configuration of EDRC foundation Fig. 5. (continued)
recorded. The measured elastic stiffness of MRF and EDRC-F are 1363.6 kN/m and 1481.6 kN/m, respectively, with a difference of 0.8%. This means that the two specimens have nearly the same elastic stiffness. A pinned beam-to-EDRC connection was designed in the EDRC-F system where the concrete beam was connected to the steel column through a bolted steel connector, as shown in Fig. 5(c). The connector consists of two spliced end plates, which were connected in the web by four high strength bolts to resist shear force. To ensure reliable axial force transmission, the longitudinal bars in the concrete beam and four additional shear studs were welded to the connector, and the connector was welded to the flange of the steel column in EDRC. For EDRC, the dumbbell-shaped steel strip dampers were used and connected to the steel column branches by welding. The steel column has a cross section of H150 × 150 × 7 × 10 (mm). At the floor level,
Table 1 Material properties of steel. Steel members
fy (MPa)
fu (MPa)
δ (%)
Rebar Φ10 Rebar Φ12 Rebar Φ14 Steel column Steel strip plate
437 423 439 403 283
593 640 594 550 437
31 33 29 36 34
Note: fy = yield strength; fu = ultimate strength; δ = elongation at fracture.
elastic stiffness of MRF and EDRC-F through monotonic loading tests on the second story of the frame. Both specimens were loaded to a roof drift ratio of 1/800, and the reaction force and roof displacement were
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(a) MRF
(b) EDRC-F
Fig. 6. Instrumentation and loading systems.
0.6
3 Input record GB50011-2010
Acceleration Spectra (g)
Acceleration (g)
0.3
0.0
-0.3
-0.6
0
40
80 Time (s)
120
2
1
0
160
0
1
(a) Shifang ground motion record
2 Period (s)
3
4
(b) acceleration spectra
Fig. 7. Ground motion inputs. Table 2 List of three loading schemes. Loading schemes Test 1 Test 2 Test 3
Description
Peak acceleration (drift ratio)
Low-intensity pseudo-dynamic test High-intensity pseudo-dynamic test Quasi-static cyclic test for post-earthquake behavior
0.065 g (0.637 m/s ) 0.550 g (5.390 m/s2) Roof drift ratio amplitudes of 1/100, 1/50 and 1/30
PGA=0.065g
0 -0.04 -0.08
5
10
Time (sec)
15
20
Acceleration (g)
0.6
-0.3 5
10
3
4
5
6
-1/50
the dual columns of EDRC were pinned connected by a rigid link to transfer the lateral force and coordinate the deformation. As shown in Fig. 5(d), the column foot of EDRC was designed as a hinge support. The base plate with an H-type shear connector and the anchorage screw were embedded into the concrete base to transfer the compression and shear force from the steel column. The bottom of columns was welded with anti-pulling stiffeners, and thus the tension force in the steel
0
0
2
Fig. 9. Loading histories of quasi-static cyclic Test 3.
PGA=0.550g
0.3
1
-1/30
(a) Test 1: low-intensity pseudo-dynamic test
-0.6
1/50 1/100
-1/100
0
Fall in the frequent earthquake level Exceed the rare earthquake level 2-cycle were repeated for each amplitude
1/30
0.04
Roof drift ratio
Acceleration (g)
0.08
Remarks
2
15
Time (sec) (b) Test 2: high-intensity pseudo-dynamic test
20
Fig. 8. Acceleration time histories of pseudo-dynamic tests.
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DH2
DH2
DH1
DH1
: Displacement transducer DH0
DH0
(a) MRF
(b) EDRC-F Fig. 10. Layout of measurements.
strength (fu), and elongation at fracture (δ). The reinforcement has an average yield and ultimate strength of 433 MPa and 609 MPa, respectively. The steel column has a yield strength of 403 MPa and ultimate strength of 550 MPa. The yield and ultimate strength of steel strip plates are 283 MPa and 437 MPa, respectively. 2.3. Loading system Fig. 6 shows the instrumentation and loading system for both MRF and EDRC-F. A gravity load of 385 kN and 654 kN was imposed on the two exterior columns and one interior column, respectively, using posttension rods attached to a cap beam over the top of the columns. The rods were anchored to the strong floor using hinge supports, and thus the gravity loading device allowed free sway of the specimen frame. Two steel portal frames were constructed in each span of the frame to restrict the out of plane displacement, as shown in Fig. 6. A limit slot was placed at mid-span of the second story beam with an adequate gap from the beam, which enabled the test frame to experience in-plane displacements without any artificial restraint. The lateral loads of the frame was imposed by a computer-controlled actuator on the second story of the frame, as shown in Fig. 6. The frame beam was connected to the actuator by two pre-stressed high strength rods with a diameter of 24 mm at both sides of the beam. This beam-to-actuator connection was used to pull back the tested frame. The reason for laterally loading on the second story is explained as follows. The bottom two stories of the 6-story prototype building were physically tested in this study by using sub-structuring techniques. The seismic forces on the structure were assumed to follow an inverted triangular pattern (i.e. 6:5:4:3:2:1 from the sixth to first story). Since only the bottom two stories were tested, the seismic forces sustained by the upper four stories were added to the second story. Therefore, the seismic forces ratio between the second and first story is about 20:1, indicating that the seismic force at the first story is far less than the second story. It is thus acceptable to only exert all the seismic force at the second story without strictly satisfying the prescribed force profile, which makes the test control much simpler [29]. Finally, the single actuator loading scheme (Fig. 6) was adopted. It is noteworthy that this simplification process would not change the potential soft story collapse failure mode of the prototype structure.
Fig. 11. Comparison of inter-story drift ratios in pseudo- dynamic Test 1.
Fig. 12. Comparison of hysteretic curves in pseudo-dynamic Test 1.
column can be transferred to the concrete base through the cover plates and the bolt nuts. 2.2. Material properties The compressive strength of concrete was determined through standard cubic compressive tests. The compressive cube strength (fcu) was found to be 36.99 MPa for MRF, while fcu was found to be 37.40 MPa for EDRC-F. The material properties of reinforcement, steel columns and steel strip plates in EDRC were measured by tensile coupon tests. Table 1 lists the results of yield strength (fy), ultimate
2.4. Loading scheme The continuous pseudo-dynamic testing method proposed by Molina et al. [30] was adopted in this test. The loading process was
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Table 3 Comparison of crack distribution in the interior column in Test 2. Location
Extent and distribution of cracking damage MRF
EDRC-F
No crack
Limited cracks, less than 2.0 mm
Several cross diagonal cracks in the panel zone, greater than 1.0 mm; a number of flexural cracks at the beam end, greater than 1.0 mm.
Minor diagonal cracks in the panel zone, less than 1.0 mm; several flexural cracks at the beam end, less than 1.0 mm.
Many cracks greater than 2.0 mm and minor spalling of concrete
Many flexural cracks less than 2.0 mm, no spalling of concrete
conducted by solving the general dynamic equation,
mx¨ + cx + fs (x) =
mx¨ g
components to facilitate the loading process, as illustrated in the dash block in Fig. 7(a). Two pseudo-dynamic tests with different levels of seismic intensities and one quasi-static test were conducted in this study, as listed in Table 2. The pseudo-dynamic tests include low-intensity seismic test (Test 1) and high-intensity seismic test (Test 2), which aim to investigate the linear elastic and elasto-plastic responses of the specimens. The peak acceleration value of these pseudo-dynamic tests are 0.065 g (0.637 m/s2) and 0.550 g (5.390 m/s2), respectively, which falls in the frequent earthquake level and exceeds the rare earthquake level in Chinese seismic design code [4], respectively. The acceleration time histories of low-intensity and high-intensity pseudo-dynamics tests are shown in Fig. 8. To better understand the post-earthquake behavior of the specimens, quasi-static roof drift ratio histories were imposed on the test specimens after the pseudo-dynamic tests, as shown in Fig. 9. The roof drift ratio amplitudes of 1/100, 1/50 and 1/30 were adopted, and two cycles were repeated for each amplitude.
(5)
where m is the mass matrix, c is the viscous damping matrix, fs(x) is the restoring force vector, x, x and x¨ are the nodal displacement, velocity, and acceleration, respectively. x¨ g is the input ground motion vector. To make the periods of the specimens consistent with the prototype structure, a lumped mass of 52980 kg was assigned in Eq. (5). The inherent damping was assumed to be 344.9 kN s/m, which was obtained based on the model period, 0.55 s, and 5% of equivalent damping ratio. The general dynamic equation was solved by central difference time integration, and the corresponding displacement at each time step was sent to the actuator. The Shifang ground motion record in 2008 Wenchuan Earthquake in China was adopted in the pseudo-dynamic test. As shown in Fig. 7(a), the ground motion duration exceeds 160 s. The acceleration spectra of the selected ground motion is shown in Fig. 7(b). The maximum earthquake design spectra considered in Chinese seismic design code [4] is also illustrated in the figure. Since the duration of original ground motion record is over 160 s, this experiment intercepted the 15–30 s record which contain the peak acceleration and main frequency
2.5. Layout of measurements The displacements of the test frames at the base, first and second floors were recorded during both pseudo-dynamic and quasi-static tests.
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Table 4 Comparison of crack distribution in the exterior column in Test 2. Location
Extent and distribution of cracking damage MRF
EDRC-F
No crack
Minor flexural cracks, less than 1.0 mm
A number of flexural cracks less than 2.0 mm, a wide crack about 4.0 mm formed at the beam end
Minor flexural cracks at the beam end, less than 2.0 mm
Many flexural cracks greater than 2.0 mm and minor spalling of concrete
Many flexural cracks less than 2.0 mm, no spalling of concrete
Fig. 14. Comparison of hysteretic curves in pseudo-dynamic Test 2. Fig. 13. Comparison of inter-story drift ratios between MRF and EDRC-F in pseudo-dynamic Test 2.
3. Test results 3.1. Results of pseudo-dynamic Test 1
As shown in Fig. 10, three displacement transducers were arranged at each floor level to measure the floor displacement of the specimens. The inter-story drift ratio was obtained as the ratio of displacement difference between top and bottom of current story to the story height.
Fig. 11 shows a comparison of inter-story drift ratios (IDRs) on the first and second story of MRF and EDRC-F in pseudo-dynamic Test 1, respectively. In general, the IDRs response was quite similar for the two specimens. Although the maximum inter-story drift ratios (IDRmax) of both specimens were quite small, the IDRmax value in the first story of MRF was much higher than that of EDRC-F. It is noteworthy that no crack was observed on the MRF or EDRC-F specimen after test 1. Fig. 12 414
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no spalling of concrete appeared for EDRC-F. Significant cracks were observed in the first-story beam-to-column joint of MRF, and particularly a wide crack through the whole section was found in the beam end. While only minor cracks were observed in the first-story beam-tocolumn joint of EDRC-F. For both specimens, no significant crack was observed at the second-story beam-to-column joint where connected to the actuator. The natural periods of specimens were calculated with free vibration method, using the 15–20 sec drift time history record. After Test 2, the natural periods of MRF and EDRC-F are 0.987 sec and 0.830 sec, respectively. It indicates that both specimens experienced significant stiffness degradation in Test 2. Specifically, the stiffness degradation of MRF is more severe than that of EDRC-F. Fig. 13 shows a comparison of inter-story drift ratios (IDRs) on the first and second story of MRF and EDRC-F, respectively. In general, the IDRs and residual drift ratio of MRF were significantly larger than those of EDRC-F. Fig. 14 shows the story shear v.s. inter-story drift ratio response for MRF and EDRC-F in Test 2, respectively. The hysteretic curves indicted that the two specimens experienced significant elastoplastic deformation, and this phenomenon is consistent with the direct observation. Fig. 15 and Table 5 show the maximum and residual interstory drift ratio distribution of MRF and EDRC-F. For the conventional MRF, the maximum inter-story drift ratio (IDRmax) and residual drift ratio (Res) at the first story were 2.21% and 0.35%, respectively. While the IDRmax and Res values at the second story were 1.60% and 0.24%, respectively. For the EDRC-F, the IDRmax and Res values at the first story were 1.56% and 0.01%, respectively, while the IDRmax and Res values at the second story were 1.62% and 0.06%, respectively. It indicates that the maximum inter-story drift ratio tended to concentrate in the first story for MRF, while EDRC-F was capable of achieving relatively more uniform inter-story drift ratios and much smaller residual inter-story drift ratios. To quantify the efficiency of EDRC, a reduction rate was defined as the ratio of difference in response values between MRF and EDRC-F to the response values of MRF, given as
Fig. 15. Comparison of maximum and residual inter-story drift ratios in pseudo-dynamic Test 2. Table 5 Comparison of maximum and residual inter-story drift ratios between MRF and EDRC-F in Test 2. Parameter
MRF
EDRC-F
Reduction rate (%)
Maximum drift ratio at first story (%) Maximum drift ratio at second story (%) Maximum drift ratio (%) Inhomogeneous coefficient Residual drift ratio at first story (%) Residual drift ratio at second story (%) Maximum residual drift ratio (%)
2.21 1.60 2.21 1.38 0.35 0.24 0.35
1.56 1.62 1.62 1.04 0.01 0.06 0.06
29.17 −1.38 26.59 24.64 97.15 73.97 82.05
shows the story shear v.s. inter-story drift ratio response for MRF and EDRC-F in Test 1, respectively. The hysteretic curves indicated that the two specimens only experienced elastic deformation. The natural periods of specimens were calculated with free vibration method, using the 15–20 sec drift time history record. After Test 1, the natural periods of MRF and EDRC-F are 0.560 sec and 0.559 sec, respectively. It indicates that both specimens had no significant stiffness degradation in Test 1.
reduction
rate =
MRF
EDRC - F
× 100%
(6)
MRF
An inhomogeneous coefficient is defined as the ratio of the larger response value in the two stories to the smaller response value in the two stories for MRF and EDRC-F, respectively, as given
3.2. Results of pseudo-dynamic Test 2
Inhomogeneous
A comparison of damage distribution in the interior column of MRF and EDRC-F is shown in Table 3. It shows that there were cracks appeared at the column bottom of both MRF and EDRC-F. However, there was no spalling of concrete at the column bottom of EDRC-F, compared to minor concrete spalling for MRF. Several cross diagonal cracks, greater than 1.0 mm in width, were observed in the beam-to-column panel zone of the first story of MRF. A number of flexural cracks, greater than 1.0 mm in width, were observed at the beam end, outside of the panel zone. In contrast, only minor diagonal cracks, less than 1.0 mm in width, were observed in the beam-to-column panel zone of of the first story of EDRC-F. Several flexural cracks, less than 1.0 mm in width, were observed at the beam end, outside of the panel zone of EDRC-F. For the second-story beam-to-column joint, there was no crack for MRF, while some medium cracks were observed in the column of EDRC-F. This indicates that the inter-story drift ratio of MRF was concentrated at the first story, while the inter-story drift ratio concentration was not significant in EDRC-F. Table 4 shows the crack distribution of one exterior column of MRF and EDRC-F. A large number of cracks were observed at the column base of both MRF and EDRC-F. Similarly,
coefficient =
Larger Smaller
× 100%
(7)
By using EDRC, under rare earthquakes, the inhomogeneous coefficient of inter-story drift ratios reduced by 24.64%, the maximum inter-story drift ratio reduced by 26.59% and the residual drift ratio reduced by 82.05%. It indicates that the application of EDRC can effectively mitigate the soft story failure of reinforced concrete buildings. 3.3. Results of quasi-static cyclic Test 3 Table 6 shows the distribution of cracks in the interior column of MRF and EDRC-F after Test 3. A large number of cracks appeared at the column base of both MRF and EDRC-F. Also, many crossed diagonal cracks were observed in the beam-to-column joint at the first story of MRF, while only a small amount of diagonal cracks was observed in the same location of EDRC-F. Specifically, many cross diagonal cracks greater than 3.0 mm, as well as a certain amount of concrete spalling, were observed in the beam-to-column panel zone of the first story of MRF. A number of flexural cracks greater than 1.0 mm appeared at the beam end, outside of the panel zone. However, only minor diagonal
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Table 6 Comparison of crack distribution in the interior column in Test 3. Location
Extent and distribution of cracking damage MRF
EDRC-F
No crack
A number of cracks less than 2.0 mm, minor spalling of concrete
Many cross diagonal cracks in the panel zone, greater than 3.0 mm; a certain amount of concrete spalling; a number of flexural cracks at the beam end, greater than 1.0 mm.
Minor diagonal cracks in the panel zone, less than 2.0 mm; several flexural cracks at the beam end, less than 1.0 mm.
Complete spalling of cover concrete
Large cracks greater than 3.0 mm, no spalling of cover concrete
cracks less than 2.0 mm were observed in the beam-to-column panel zone of EDRC-F. Several flexural cracks less than 1.0 mm in width were observed at the beam end, outside of the panel zone. There was no crack at the second-story beam-to-column joint of MRF, while some medium cracks were observed in the second-story column of EDRC-F. This is again because that the inter-story drift ratio of MRF was concentrated on the first story, while the inter-story drift ratio concentration was not significant for EDRC-F. Table 7 shows the crack distribution of one exterior column of MRF and EDRC-F at failure. In general, the damage degree of the edge column was slighter than that of the middle column, since the axial load ratio of the edge column is much smaller than that of the middle column. A large number of cracks were observed at the column base of both MRF and EDRC-F. Significant cracks were found in the first-story joint of MRF, while minor cracks were observed in the first-story joint of EDRC-F. The hysteretic curves and skeleton curves of MRF and EDRC-F under static loading phase are shown in Figs. 16 and 17, respectively. As shown in Fig. 16, the inter-story drift ratio amplitude in first story of MRF was significantly larger than that of EDRC-F, so the hysteretic loop of MRF seemed even fuller than that of EDRC-F. However, this is at the cost of serious damage of concrete column end region for the MRF in the first story. In fact, under the same inter-story drift ratio amplitude,
the bearing capacity and hysteretic loop area of EDRC-F were significantly larger than that of MRF. The quantified results are listed in Table 8. For the conventional MRF, the inter-story drift ratio (IDR) at the first story ranged from −3.60% to 4.16%, while the IDR value at the second story ranged from −3.30% to 2.00%. For EDRC-F, the IDR values at the first and second story varied in a range of −2.80% to 3.14% and −3.53% to 2.80%, respectively. It indicates that the interstory drift ratio tended to concentrate in the first story for MRF, while EDRC-F was still capable of achieving relatively uniform inter-story drift ratios. Due to the presence of EDRC, the inhomogeneous coefficient of inter-story drift ratios reduced by 11.11% and the maximum inter-story drift ratio reduced by 15.14%. As shown in Fig. 17 and Table 8, the difference in stiffness between the MRF and EDRC-F was not significant at the loading amplitude of 1/ 100 roof drift ratio. While with the increment of loading amplitude, the stiffness of MRF degraded rapidly, compared to a low stiffness degradation of EDRC-F. The ultimate capacity of MRF and EDRC-F were 139.7 kN and 177.3 kN, respectively, resulting in an increment of ultimate capacity of 26.91% for EDRC-F. Fig. 18 and Table 9 show the comparison of energy dissipation between MRF and EDRC-F in static Test 3. As listed in Table 9, for the conventional MRF, seismic energy dissipated in the first story is
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Table 7 Comparison of crack distribution in the exterior column in Test 3. Location
Extent and distribution of cracking damage MRF
EDRC-F
No crack
Minor flexural cracks, less than 1.0 mm
Many flexural cracks less than 2.0 mm, a wide crack about 4.0 mm through the section, the middle bottom longitudinal rebar was fractured
A number of cracks at the beam-to-column joint, less than 2.0 mm
Many flexural cracks greater than 2.0 mm, some spalling of concrete
Many flexural cracks less than 2.0 mm, minor spalling of concrete
Fig. 17. Skeleton curves of the specimens in static cyclic Test 3.
Fig. 16. Hysteretic curves of the specimens in quasi-static Test 3.
Table 8 Comparison of inter-story drift ratios in static Test 3.
5112 kN·m , while this value in the second story is 2517 kN·m . For the EDRC-F, the seismic energy dissipated in the first and second story are 4877 kN·m and 3922 kN·m , respectively. The total energy dissipation of MRF and EDRC-F are 7629 kN·m and 8799 kN·m , respectively. Similar to the inter-story drift response, seismic energy dissipation is tending to concentrate in the first story for the MRF, while the EDRC-F is still capable of achieving relatively uniform seismic energy dissipation distribution. By adopting the EDRC, the total energy dissipation increased by 15.34%. the inhomogeneous coefficient of story seismic energy dissipation reduced by 38.92%.
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Parameter
MRF
EDRC-F
Reduction rate (%)
Maximum drift ratio at first story (%) Maximum drift ratio at second story (%) Maximum drift ratio (%) Inhomogeneous coefficient Ultimate capacity (kN)
4.16 3.30 4.16 1.26 139.7
3.14 3.53 3.53 1.12 177.3
32.48 −6.97 15.14 11.11 −26.91
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Test 2. Corresponding uplift of the column branch flange is about 8 mm, as shown in Fig. 19(b). After Test 2, significant residual deformation of the cover plate was observed which indicated it was yield during the test, as shown in Fig. 19(c). In practical, the cover plate can be replaced after strong earthquakes due to the bolt connection. However, to test the reliability of this configuration, the cover plate was not replaced in this study. In static cyclic Test 3, the maximum inter-story drift ratio of EDRC-F is 3.53%. Corresponding uplift of the cover plate was about 14 mm, as shown in Fig. 20(a). After Test 3, a gap about 4 mm in width was observed between the cover plate and the stiffener of column flange, due to the plastic deformation of cover plate and elongation of the anchorage screw. This connection can be easy repaired after earthquakes. During the tests, two strain gauges were used to monitor the strain of steel strip dampers. One strain gauge was set on the steel strip at the top of the first story, the other strain gauge was set on the steel strip at the top of the second story. The strain of one edge of each steel strip is shown Fig. 21. According to the material test, the steel strips yield in tension at strain about 1400 µ , as illustrated in Fig. 21. Though the steel strips sustained both moment and shear forces, the tension yield strain can be adopted as a reference index. Obviously, the edge of each steel strip experienced yielding during the pseudo-dynamic Test 2. However, the strain gauges were failure during static cyclic Test 3, and the strain data was not recorded.
Fig. 18. Comparison of energy dissipation in static Test 3. Table 9 Comparison of energy dissipation in static Test 3. Parameter
MRF
EDRC-F
Reduction rate (%)
Energy dissipation 1F (kN·m ) Energy dissipation 2F (kN·m ) Inhomogeneous coefficient Total energy dissipation (kN·m )
5112 2517 2.03 7629
4877 3922 1.24 8799
4.60 −55.82 38.92 −15.34
(a)
Maximum column foot uplift
(b)
4. Conclusions
column foot after Test 2
This paper experimentally investigated the effect of steel EnergyDissipative Rocking Column (EDRC) system on the seismic behavior of reinforced concrete frames. A comparison of seismic responses of pure reinforced concrete moment resisting frame (MRF) and combined MRFEDRC system was made by conducting pseudo-dynamic tests. The postearthquake behavior of these two systems was also compared by conducting quasi-static cyclic tests. The following conclusions can be drawn based on the experimental results:
(c)
(1) The EDRC can effectively mitigate the inter-story drift ratio concentration and prevent soft story failure of conventional MRF under earthquakes. Compared to a conventional MRF, the presence of EDRC led to a reduction in the inter-story drift ratio inhomogeneous index of 25.0% and 11.0%, respectively, as found in the pseudodynamic and quasi-static test. (2) The combined MRF-EDRC system had stable lateral load resisting capacity and energy dissipation capacity. The results from the pseudo-dynamic tests showed that the maximum and residual interstory drift ratio of EDRC-F system was reduced by 26.0% and 82.0%, respectively, comparing to MRF. The quasi-static test results also showed that the ultimate capacity was increased by 27.0% comparing to MRF.
Maximum drift in Test 2
Fig. 19. Behavior of EDRC in Test 2.
3.4. Response of the Energy-Dissipative Rocking Column Acknowledgments
No significant response of the Energy-Dissipative Rocking Column (EDRC) was observed in low intensity pseudo-dynamic Test 1. However, the EDRC experienced rocking and yielding in the high intensity pseudo-dynamic Test 2 as well as in the static cyclic Test 3. Specifically, the bottom of steel column branches uplifted and triggered the rocking behavior of EDRC system, as shown in Figs. 19 and 20. The maximum inter-story drift ratio of EDRC-F is 1.62% in pseudo-dynamic
The work presented in this paper was supported by the National Key Research and Development Program of China (Project No. 2017YFC0703607). Ground motion for this study is provided by China Strong Motion Network Centre at Institute of Engineering Mechanics, China Earthquake Administration.
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Maximum column foot uplift in Test 3
column foot after Test 3
(a)
(b) Fig. 20. Behavior of EDRC column foot in Test 3.
y , strip
y , strip
(a) strip at the top of story 1
(b) strip at the top of story 2
Fig. 21. Strain of steel strips in Test 2.
References
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Experimental study on seismic performance of RC frames with EnergyDissipative Rocking Column system
T
Yan-Wen Lia, Guo-Qiang Lib, , Jian Jiangc, Yan-Bo Wanga ⁎
a
Department of Structural Engineering, Tongji University, Shanghai 200092, China State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China c School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China b
ARTICLE INFO
ABSTRACT
Keywords: Reinforced concrete moment resisting frame Energy-Dissipative Rocking Column Soft story failure Pseudo-dynamic test Inter-story drift
The conventional reinforced concrete Moment Resisting Frames (MRFs) have suffered from soft story failure during major earthquake events. A novel system of steel Energy-Dissipative Rocking Column (EDRC) is proposed to mitigate seismic responses of MRFs. Pseudo-dynamic tests are conducted on large-scale two-story and two-bay reinforced concrete frames, with and without EDRC, respectively. The post-earthquake behavior of these two systems is also compared through quasi-static cyclic tests. The experimental results show that the presence of EDRC can effectively mitigate the maximum value, residual value and inhomogeneous distribution of inter-story drifts, and thus prevent the soft story failure of MRFs. It is found that the maximum and residual inter-story drift of combined MRF and EDRC systems is reduced by 26.0% and 82.0%, respectively, compared to pure MRFs. The inhomogeneous degree of inter-story drifts can be reduced by 25.0% and 11.0%, respectively, in the pseudodynamic and quasi-static tests.
1. Introduction Reinforced Concrete Moment Resisting Frame (hereinafter referred to as MRF) is one of the most common lateral load resisting systems for low-rise to mid-rise structures in earthquake regions. However, conventional MRFs have suffered from severe damage such as soft story failure during major earthquake events [1,2], although they are normally designed with ductile detailing and strong column-weak beam (SCWB) criterion in accordance with current seismic design provisions [3–5]. Due to soft story mechanism, plastic hinges are mainly distributed at the ends of columns on a single story. Large residual drift and concentrated damage may bring difficulties in the reparability and fast resilience of MRFs after earthquakes [6,7]. From point view of structural strength, some researchers proposed the theory of plastic mechanism control that prevent undesired failure modes such as soft story mechanism by evaluating the total plastic moments of the columns required at each story [8,9]. Since metal energy-dissipative devices can provide strength as well as energy-dissipation capacity for the structures, some other researchers developed a number of novel metal energy-dissipative devices [10–13] for the framed structures. In recent decades, many efforts have been put in investigating the effect of vertical continuous stiffness on mitigating damage concentration along the height of a structure. These include ⁎
studies on the relationship of damage concentration and stiffness of the continuous columns in steel concentrically braced frames [14,15]. The effect of increasing flexural stiffness of continuous columns on mitigating inter-story drift ratio concentration was examined by analytical and nonlinear time history analysis. As an effective solution to avoid soft/weak-story failure of framed structures, rocking walls with much larger flexural stiffness than individual columns were proposed [16–21], and have been applied for retrofit projects [22,23]. However, conventional rocking walls have negligible lateral resisting stiffness and energy dissipation capacity, which limits their application in new constructions. As an alternative, a novel system of Energy-Dissipative Rocking Column (EDRC) has been proposed by the authors [24–26], as shown in Fig. 1. The EDRC system is a combination of rocking components and metal energy-dissipative components. It consists of two steel column branches with pinned supports which are connected by distributed strip dampers. In a combined MRF and Energy-Dissipative Rocking Column dual system (hereinafter referred to as EDRC-F), the framing beams are simply connected to the column branches of EDRC where the moment transfer is negligible, as illustrated in Fig. 1. Under frequent earthquakes, the EDRC is designed to stay in an elastic state, providing lateral resisting stiffness for the structure system. Under rare earthquakes, the steel strips are designed to yield and dissipate seismic energy, while
Corresponding author. E-mail address: [email protected] (G.-Q. Li).
https://doi.org/10.1016/j.engstruct.2019.05.052 Received 3 February 2019; Received in revised form 15 May 2019; Accepted 18 May 2019 Available online 30 May 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.
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Frame beam
In this paper, a pseudo-dynamic testing program was developed to investigate the nonlinear dynamic response of EDRC-F system under earthquakes with different intensity levels. This test program includes low-intensity and high-intensity pseudo-dynamic tests to represent frequent earthquakes and rare earthquakes, respectively. A comparison of seismic responses between MRF and EDRC-F systems was made. The post-earthquake behavior of these two systems was also investigated by conducting quasi-static cyclic tests. The key responses such as maximum, residual and inhomogeneous distribution of inter-story drift ratios were output to quantify the effect of EDRC on mitigating the seismic responses of reinforced concrete structures.
Rigid link Strip dampers
B-B
B-B
Hinge
2. Test setup
Column branches
2.1. Layout of specimens
C-C
C-C
A conventional MRF and an EDRC-F were selected from a six-story prototype building designed with ductile detailing in Chinese seismic design code [4], except strong column-weak beam criterion. The prototype building is located in a site with seismic design intensity of 7 (the maximum spectrum acceleration is 0.15 g for 63% probability of exceedance in 50 years) and site classification of III. As shown in Fig. 3, the prototype building has four spans in the X-direction and two spans in the Y-direction. The ground story is 4.0 m in height and the upper stories are 3.0 m in height. The dead load and live load on the floor are 5.0 and 2.0 kN/m2, respectively. These loads produce a load ratio of about 40% and 68% for the exterior and interior columns on the ground story, respectively. The load ratio is defined as the ratio between applied load and the design column axial load capacity. The concrete grade is C35 in Chinese standard for the beams and columns, with a cubic compressive strength of 35 MPa [27]. The steel grades of the longitudinal and transverse reinforcements are HRB400 and HRB300, with a nominal yield strength of 400 MPa and 300 MPa, respectively. The cross-sectional dimensions of the beams and columns are 600 mm × 300 mm and 360 mm × 360 mm, respectively. A scaled two-span and two-story substructures (dashed block in Fig. 3) was selected from the prototype building as the tested frame. The scaling ratio is 1:1.5. The selection of two-story substructures is because that soft ground story collapse was normally observed in the post-earthquake field investigation, while the upper stories often remained undamaged or even in elastic range. The selection is also to consider the cost effectiveness of tests and limitations of the loading
Fig. 1. Schematic of Energy-Dissipative Rocking Column (EDRC) system.
Plastic hinge
EDRC
Fig. 2. Comparison of failure modes between MRF and EDRC-F under earthquakes.
[email protected]
the steel column branches are to stay in elastic and rock to re-distribute seismic forces along the structural height and to mitigate inter-story drift concentration. Benefiting from the advantages of vertical continuous column branches and energy dissipation characteristic of steel strip dampers in EDRC, the EDRC-F dual system tends to form a global plasticity failure mode rather than a local plasticity one of MRF, as shown in Fig. 2.
Y
4.0m
Test frame
X
2@ 6.0m
(a) Plane view
(b) Elevation view
Fig. 3. Schematic of the prototype building.
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200 2000
2870
240
3760
1250
550 6@75
1
1
1260
2
2660 2 6@135
1250
1250
3
3
550 6@75
240
3760
550 6@75
1250
1260
1
2
3
1
2 2660
6@135
3
550 6@75
C
C
650
615 6@75
1460 6@135
1190 6@75
995 810 6@135 6@75
240
400
4000
4000
8800
400
(a) Dimension of MRF 4 14(corner), 4 12 6@75/135
2 12,1 12
2 12
2 12,1 10
2 12,1 10
1-1(3-3)
2-2 (b) Reinforcement layout
C-C
Fig. 4. Layout of the MRF specimen.
facilities. The purpose of this experiment is to study the effect of EDRC on mitigating the soft story collapse of reinforced concrete structures. Since the prototype building had a relatively large span, the beams were designed with a relative deep section which was stronger than columns in flexural capacity. This type of MRF was observed in the seismic region and vulnerable to the seismic action [2]. The following two subsections presented the details of MRF and EDRC-F specimens, respectively.
diameter of 6 mm and spacing distance of 135 mm was used, which was anchored using 135-degree hooks. The spacing of stirrups in the end region of beams and columns was reduced to 75 mm to ensure the ductile details, and the column stirrups were continuous in the beam-tocolumn joints. The concrete bases of the specimens were anchored to the concrete floor by pre-stressed high strength rods in a diameter of 120 mm. 2.1.2. Design of EDRC component As reported in the previous studies [24], the presence of EDRC in RC moment resisting frame can mitigate seismic response significantly, such as the maximum inter-story drift and inter-story drift concentration. The most effective EDRC stiffness ratio for mitigating seismic response of RC moment resisting frames fell in the range of less than 0.2. In this study, a design EDRC stiffness ratio of 0.1 is adopted. For simplification, the ith story stiffness of RC moment resisting frame can be estimated as,
2.1.1. MRF specimen As shown in Fig. 4(a), the scaled MRF specimen has a total height of 5.72 m, total width of 8.8 m, and span of 4.0 m. The story height of the ground and second story is 2 m and 1.67 m, respectively. The cross section of the columns and beams is 240 mm × 240 mm and 400 mm × 200 mm, respectively. The column section has four longitudinal reinforcing bars in a diameter of 14 mm (at corner) and four bars in a diameter of 12 mm (at mid-span), as shown in Fig. 4(b). This results in a reinforcement ratio of about 1.6%. Longitudinal reinforcement in the columns was extended to the concrete base by a embedment depth of 650 mm. The beam section at the mid-span and end has five and six longitudinal reinforcing bars, respectively. For the stirrups in the middle region of both columns and beams, reinforcement with a
m
KMi = j=1
12Ec Ic, ij hi3
(1)
where Ec is the elastic modulus of concrete, Ic, ij is the jth column section
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1460 6@135
240
3760
1250
550 6@75
1260
1
1
2
2660 2 6@135
3600
1250
1250
3
3
550 6@75
550 6@75
150 260 150
4
5
4
5 2190
6@135
660 6@75
C
C
650
615 6@75
2870
1190 6@75
995 810 6@135 6@75
240
400
4000
8800
800
3600
(a) Dimension of EDRC-F 2 12,1 12
2 12
2 12,1 10
2 12,1 10
4-4
(b) Reinforcement layout
5-5
Fig. 5. Layout of the EDRC-F specimen.
moment of inertia in ith story, and hi is the ith story height. Then, the overall elastic stiffness of the bare RC moment resisting frame under concentrated lateral load can be expressed as,
KMRF =
n i=1
1 1/ KMi
branches, respectively. Ai , Ii (i = 1, 2) are the gross section area and moment of inertia of the two column branches, respectively, Ie is the summation of moment of inertia of all the shear links. Note that several iterations may need to obtain desired EDRC parameters, and this process can be easy with help of the widely used Excel software. Finally, the section HW150 × 150 × 7 × 10 in Chinese standard [28] is adopted as the column branch section. The clear distance between dual column branches is 260 mm. The length and thickness of dumbbell-shaped steel links are 260 mm and 16 mm, respectively. A total of 18 shear links are distributed along the EDRC height. The EDRC system is designed to yield at an inter-story drift ratio of 1/300, thus the Q225 steel with nominal yield strength of 225 MPa is adopted for the shear links. It is noteworthy that due to the coupling effect between EDRC and the concrete frame, the overall elastic stiffness of EDRC-F dual system may larger than the pure MRF, this can be solved by minor reducing the beam or column section size in the concrete frame.
(2)
where n is the number of stories. The elastic stiffness of the EDRC component can be determined as [24],
KEDRC =
(3)
k KMRF
where k is the design elastic stiffness ratio of EDRC system, 0.1 is adopted in this study. When the elastic stiffness demand on EDRC is determined, the cross section of column branches and dimensions of the steel shear links can be roughly estimated by the EDRC stiffness formula [26],
KEDRC =
2
1 Hl2 EI (k )2
+
k 2 1 H2l k2 12EIe
+
k2 1 H3 k 2 3EI
12I l 4 AI l3 = 3 c , k2 = 1 + , I = I1 + I2, Ie = 2 b hI A1 A2 l 12E
(4)
2.1.3. EDRC-F specimen The layout of EDRC-F specimen is shown in Fig. 5(a). The left span of EDRC-F has the same dimension of beams and columns as MRF, while the cross section of beams connected to EDRC in the right span was adjusted to 320 mm × 200 mm, as shown in Fig. 5(b). This arrangement is to maintain the same elastic stiffness of EDRC-F as MRF. This specimen design was validated against pre-test measurement of the
ki, A = A1 + A2
where E is the elastic modulus of steel material, H is the height of EDRCs, h is the distance between shear links from center to center, b and l are the clear and center-to-center distances between column
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150
260
150
260 45 170 45
Hinge 55 70 65
D
D
16
20 83 55 83 20
250
10
100
200
110 100 110
320
4M20 21.5,10.9
220
25 78 55 78 25
welding
D-D 560
(c) Configuration of EDRC joint
Cover plate
650
Base plate
Bolt nuts
A
Dscrew
16 16
27 mm
8@120
H150 150 7 10 8@120
A
A-A
800 (d) Configuration of EDRC foundation Fig. 5. (continued)
recorded. The measured elastic stiffness of MRF and EDRC-F are 1363.6 kN/m and 1481.6 kN/m, respectively, with a difference of 0.8%. This means that the two specimens have nearly the same elastic stiffness. A pinned beam-to-EDRC connection was designed in the EDRC-F system where the concrete beam was connected to the steel column through a bolted steel connector, as shown in Fig. 5(c). The connector consists of two spliced end plates, which were connected in the web by four high strength bolts to resist shear force. To ensure reliable axial force transmission, the longitudinal bars in the concrete beam and four additional shear studs were welded to the connector, and the connector was welded to the flange of the steel column in EDRC. For EDRC, the dumbbell-shaped steel strip dampers were used and connected to the steel column branches by welding. The steel column has a cross section of H150 × 150 × 7 × 10 (mm). At the floor level,
Table 1 Material properties of steel. Steel members
fy (MPa)
fu (MPa)
δ (%)
Rebar Φ10 Rebar Φ12 Rebar Φ14 Steel column Steel strip plate
437 423 439 403 283
593 640 594 550 437
31 33 29 36 34
Note: fy = yield strength; fu = ultimate strength; δ = elongation at fracture.
elastic stiffness of MRF and EDRC-F through monotonic loading tests on the second story of the frame. Both specimens were loaded to a roof drift ratio of 1/800, and the reaction force and roof displacement were
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(a) MRF
(b) EDRC-F
Fig. 6. Instrumentation and loading systems.
0.6
3 Input record GB50011-2010
Acceleration Spectra (g)
Acceleration (g)
0.3
0.0
-0.3
-0.6
0
40
80 Time (s)
120
2
1
0
160
0
1
(a) Shifang ground motion record
2 Period (s)
3
4
(b) acceleration spectra
Fig. 7. Ground motion inputs. Table 2 List of three loading schemes. Loading schemes Test 1 Test 2 Test 3
Description
Peak acceleration (drift ratio)
Low-intensity pseudo-dynamic test High-intensity pseudo-dynamic test Quasi-static cyclic test for post-earthquake behavior
0.065 g (0.637 m/s ) 0.550 g (5.390 m/s2) Roof drift ratio amplitudes of 1/100, 1/50 and 1/30
PGA=0.065g
0 -0.04 -0.08
5
10
Time (sec)
15
20
Acceleration (g)
0.6
-0.3 5
10
3
4
5
6
-1/50
the dual columns of EDRC were pinned connected by a rigid link to transfer the lateral force and coordinate the deformation. As shown in Fig. 5(d), the column foot of EDRC was designed as a hinge support. The base plate with an H-type shear connector and the anchorage screw were embedded into the concrete base to transfer the compression and shear force from the steel column. The bottom of columns was welded with anti-pulling stiffeners, and thus the tension force in the steel
0
0
2
Fig. 9. Loading histories of quasi-static cyclic Test 3.
PGA=0.550g
0.3
1
-1/30
(a) Test 1: low-intensity pseudo-dynamic test
-0.6
1/50 1/100
-1/100
0
Fall in the frequent earthquake level Exceed the rare earthquake level 2-cycle were repeated for each amplitude
1/30
0.04
Roof drift ratio
Acceleration (g)
0.08
Remarks
2
15
Time (sec) (b) Test 2: high-intensity pseudo-dynamic test
20
Fig. 8. Acceleration time histories of pseudo-dynamic tests.
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DH2
DH2
DH1
DH1
: Displacement transducer DH0
DH0
(a) MRF
(b) EDRC-F Fig. 10. Layout of measurements.
strength (fu), and elongation at fracture (δ). The reinforcement has an average yield and ultimate strength of 433 MPa and 609 MPa, respectively. The steel column has a yield strength of 403 MPa and ultimate strength of 550 MPa. The yield and ultimate strength of steel strip plates are 283 MPa and 437 MPa, respectively. 2.3. Loading system Fig. 6 shows the instrumentation and loading system for both MRF and EDRC-F. A gravity load of 385 kN and 654 kN was imposed on the two exterior columns and one interior column, respectively, using posttension rods attached to a cap beam over the top of the columns. The rods were anchored to the strong floor using hinge supports, and thus the gravity loading device allowed free sway of the specimen frame. Two steel portal frames were constructed in each span of the frame to restrict the out of plane displacement, as shown in Fig. 6. A limit slot was placed at mid-span of the second story beam with an adequate gap from the beam, which enabled the test frame to experience in-plane displacements without any artificial restraint. The lateral loads of the frame was imposed by a computer-controlled actuator on the second story of the frame, as shown in Fig. 6. The frame beam was connected to the actuator by two pre-stressed high strength rods with a diameter of 24 mm at both sides of the beam. This beam-to-actuator connection was used to pull back the tested frame. The reason for laterally loading on the second story is explained as follows. The bottom two stories of the 6-story prototype building were physically tested in this study by using sub-structuring techniques. The seismic forces on the structure were assumed to follow an inverted triangular pattern (i.e. 6:5:4:3:2:1 from the sixth to first story). Since only the bottom two stories were tested, the seismic forces sustained by the upper four stories were added to the second story. Therefore, the seismic forces ratio between the second and first story is about 20:1, indicating that the seismic force at the first story is far less than the second story. It is thus acceptable to only exert all the seismic force at the second story without strictly satisfying the prescribed force profile, which makes the test control much simpler [29]. Finally, the single actuator loading scheme (Fig. 6) was adopted. It is noteworthy that this simplification process would not change the potential soft story collapse failure mode of the prototype structure.
Fig. 11. Comparison of inter-story drift ratios in pseudo- dynamic Test 1.
Fig. 12. Comparison of hysteretic curves in pseudo-dynamic Test 1.
column can be transferred to the concrete base through the cover plates and the bolt nuts. 2.2. Material properties The compressive strength of concrete was determined through standard cubic compressive tests. The compressive cube strength (fcu) was found to be 36.99 MPa for MRF, while fcu was found to be 37.40 MPa for EDRC-F. The material properties of reinforcement, steel columns and steel strip plates in EDRC were measured by tensile coupon tests. Table 1 lists the results of yield strength (fy), ultimate
2.4. Loading scheme The continuous pseudo-dynamic testing method proposed by Molina et al. [30] was adopted in this test. The loading process was
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Table 3 Comparison of crack distribution in the interior column in Test 2. Location
Extent and distribution of cracking damage MRF
EDRC-F
No crack
Limited cracks, less than 2.0 mm
Several cross diagonal cracks in the panel zone, greater than 1.0 mm; a number of flexural cracks at the beam end, greater than 1.0 mm.
Minor diagonal cracks in the panel zone, less than 1.0 mm; several flexural cracks at the beam end, less than 1.0 mm.
Many cracks greater than 2.0 mm and minor spalling of concrete
Many flexural cracks less than 2.0 mm, no spalling of concrete
conducted by solving the general dynamic equation,
mx¨ + cx + fs (x) =
mx¨ g
components to facilitate the loading process, as illustrated in the dash block in Fig. 7(a). Two pseudo-dynamic tests with different levels of seismic intensities and one quasi-static test were conducted in this study, as listed in Table 2. The pseudo-dynamic tests include low-intensity seismic test (Test 1) and high-intensity seismic test (Test 2), which aim to investigate the linear elastic and elasto-plastic responses of the specimens. The peak acceleration value of these pseudo-dynamic tests are 0.065 g (0.637 m/s2) and 0.550 g (5.390 m/s2), respectively, which falls in the frequent earthquake level and exceeds the rare earthquake level in Chinese seismic design code [4], respectively. The acceleration time histories of low-intensity and high-intensity pseudo-dynamics tests are shown in Fig. 8. To better understand the post-earthquake behavior of the specimens, quasi-static roof drift ratio histories were imposed on the test specimens after the pseudo-dynamic tests, as shown in Fig. 9. The roof drift ratio amplitudes of 1/100, 1/50 and 1/30 were adopted, and two cycles were repeated for each amplitude.
(5)
where m is the mass matrix, c is the viscous damping matrix, fs(x) is the restoring force vector, x, x and x¨ are the nodal displacement, velocity, and acceleration, respectively. x¨ g is the input ground motion vector. To make the periods of the specimens consistent with the prototype structure, a lumped mass of 52980 kg was assigned in Eq. (5). The inherent damping was assumed to be 344.9 kN s/m, which was obtained based on the model period, 0.55 s, and 5% of equivalent damping ratio. The general dynamic equation was solved by central difference time integration, and the corresponding displacement at each time step was sent to the actuator. The Shifang ground motion record in 2008 Wenchuan Earthquake in China was adopted in the pseudo-dynamic test. As shown in Fig. 7(a), the ground motion duration exceeds 160 s. The acceleration spectra of the selected ground motion is shown in Fig. 7(b). The maximum earthquake design spectra considered in Chinese seismic design code [4] is also illustrated in the figure. Since the duration of original ground motion record is over 160 s, this experiment intercepted the 15–30 s record which contain the peak acceleration and main frequency
2.5. Layout of measurements The displacements of the test frames at the base, first and second floors were recorded during both pseudo-dynamic and quasi-static tests.
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Table 4 Comparison of crack distribution in the exterior column in Test 2. Location
Extent and distribution of cracking damage MRF
EDRC-F
No crack
Minor flexural cracks, less than 1.0 mm
A number of flexural cracks less than 2.0 mm, a wide crack about 4.0 mm formed at the beam end
Minor flexural cracks at the beam end, less than 2.0 mm
Many flexural cracks greater than 2.0 mm and minor spalling of concrete
Many flexural cracks less than 2.0 mm, no spalling of concrete
Fig. 14. Comparison of hysteretic curves in pseudo-dynamic Test 2. Fig. 13. Comparison of inter-story drift ratios between MRF and EDRC-F in pseudo-dynamic Test 2.
3. Test results 3.1. Results of pseudo-dynamic Test 1
As shown in Fig. 10, three displacement transducers were arranged at each floor level to measure the floor displacement of the specimens. The inter-story drift ratio was obtained as the ratio of displacement difference between top and bottom of current story to the story height.
Fig. 11 shows a comparison of inter-story drift ratios (IDRs) on the first and second story of MRF and EDRC-F in pseudo-dynamic Test 1, respectively. In general, the IDRs response was quite similar for the two specimens. Although the maximum inter-story drift ratios (IDRmax) of both specimens were quite small, the IDRmax value in the first story of MRF was much higher than that of EDRC-F. It is noteworthy that no crack was observed on the MRF or EDRC-F specimen after test 1. Fig. 12 414
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no spalling of concrete appeared for EDRC-F. Significant cracks were observed in the first-story beam-to-column joint of MRF, and particularly a wide crack through the whole section was found in the beam end. While only minor cracks were observed in the first-story beam-tocolumn joint of EDRC-F. For both specimens, no significant crack was observed at the second-story beam-to-column joint where connected to the actuator. The natural periods of specimens were calculated with free vibration method, using the 15–20 sec drift time history record. After Test 2, the natural periods of MRF and EDRC-F are 0.987 sec and 0.830 sec, respectively. It indicates that both specimens experienced significant stiffness degradation in Test 2. Specifically, the stiffness degradation of MRF is more severe than that of EDRC-F. Fig. 13 shows a comparison of inter-story drift ratios (IDRs) on the first and second story of MRF and EDRC-F, respectively. In general, the IDRs and residual drift ratio of MRF were significantly larger than those of EDRC-F. Fig. 14 shows the story shear v.s. inter-story drift ratio response for MRF and EDRC-F in Test 2, respectively. The hysteretic curves indicted that the two specimens experienced significant elastoplastic deformation, and this phenomenon is consistent with the direct observation. Fig. 15 and Table 5 show the maximum and residual interstory drift ratio distribution of MRF and EDRC-F. For the conventional MRF, the maximum inter-story drift ratio (IDRmax) and residual drift ratio (Res) at the first story were 2.21% and 0.35%, respectively. While the IDRmax and Res values at the second story were 1.60% and 0.24%, respectively. For the EDRC-F, the IDRmax and Res values at the first story were 1.56% and 0.01%, respectively, while the IDRmax and Res values at the second story were 1.62% and 0.06%, respectively. It indicates that the maximum inter-story drift ratio tended to concentrate in the first story for MRF, while EDRC-F was capable of achieving relatively more uniform inter-story drift ratios and much smaller residual inter-story drift ratios. To quantify the efficiency of EDRC, a reduction rate was defined as the ratio of difference in response values between MRF and EDRC-F to the response values of MRF, given as
Fig. 15. Comparison of maximum and residual inter-story drift ratios in pseudo-dynamic Test 2. Table 5 Comparison of maximum and residual inter-story drift ratios between MRF and EDRC-F in Test 2. Parameter
MRF
EDRC-F
Reduction rate (%)
Maximum drift ratio at first story (%) Maximum drift ratio at second story (%) Maximum drift ratio (%) Inhomogeneous coefficient Residual drift ratio at first story (%) Residual drift ratio at second story (%) Maximum residual drift ratio (%)
2.21 1.60 2.21 1.38 0.35 0.24 0.35
1.56 1.62 1.62 1.04 0.01 0.06 0.06
29.17 −1.38 26.59 24.64 97.15 73.97 82.05
shows the story shear v.s. inter-story drift ratio response for MRF and EDRC-F in Test 1, respectively. The hysteretic curves indicated that the two specimens only experienced elastic deformation. The natural periods of specimens were calculated with free vibration method, using the 15–20 sec drift time history record. After Test 1, the natural periods of MRF and EDRC-F are 0.560 sec and 0.559 sec, respectively. It indicates that both specimens had no significant stiffness degradation in Test 1.
reduction
rate =
MRF
EDRC - F
× 100%
(6)
MRF
An inhomogeneous coefficient is defined as the ratio of the larger response value in the two stories to the smaller response value in the two stories for MRF and EDRC-F, respectively, as given
3.2. Results of pseudo-dynamic Test 2
Inhomogeneous
A comparison of damage distribution in the interior column of MRF and EDRC-F is shown in Table 3. It shows that there were cracks appeared at the column bottom of both MRF and EDRC-F. However, there was no spalling of concrete at the column bottom of EDRC-F, compared to minor concrete spalling for MRF. Several cross diagonal cracks, greater than 1.0 mm in width, were observed in the beam-to-column panel zone of the first story of MRF. A number of flexural cracks, greater than 1.0 mm in width, were observed at the beam end, outside of the panel zone. In contrast, only minor diagonal cracks, less than 1.0 mm in width, were observed in the beam-to-column panel zone of of the first story of EDRC-F. Several flexural cracks, less than 1.0 mm in width, were observed at the beam end, outside of the panel zone of EDRC-F. For the second-story beam-to-column joint, there was no crack for MRF, while some medium cracks were observed in the column of EDRC-F. This indicates that the inter-story drift ratio of MRF was concentrated at the first story, while the inter-story drift ratio concentration was not significant in EDRC-F. Table 4 shows the crack distribution of one exterior column of MRF and EDRC-F. A large number of cracks were observed at the column base of both MRF and EDRC-F. Similarly,
coefficient =
Larger Smaller
× 100%
(7)
By using EDRC, under rare earthquakes, the inhomogeneous coefficient of inter-story drift ratios reduced by 24.64%, the maximum inter-story drift ratio reduced by 26.59% and the residual drift ratio reduced by 82.05%. It indicates that the application of EDRC can effectively mitigate the soft story failure of reinforced concrete buildings. 3.3. Results of quasi-static cyclic Test 3 Table 6 shows the distribution of cracks in the interior column of MRF and EDRC-F after Test 3. A large number of cracks appeared at the column base of both MRF and EDRC-F. Also, many crossed diagonal cracks were observed in the beam-to-column joint at the first story of MRF, while only a small amount of diagonal cracks was observed in the same location of EDRC-F. Specifically, many cross diagonal cracks greater than 3.0 mm, as well as a certain amount of concrete spalling, were observed in the beam-to-column panel zone of the first story of MRF. A number of flexural cracks greater than 1.0 mm appeared at the beam end, outside of the panel zone. However, only minor diagonal
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Table 6 Comparison of crack distribution in the interior column in Test 3. Location
Extent and distribution of cracking damage MRF
EDRC-F
No crack
A number of cracks less than 2.0 mm, minor spalling of concrete
Many cross diagonal cracks in the panel zone, greater than 3.0 mm; a certain amount of concrete spalling; a number of flexural cracks at the beam end, greater than 1.0 mm.
Minor diagonal cracks in the panel zone, less than 2.0 mm; several flexural cracks at the beam end, less than 1.0 mm.
Complete spalling of cover concrete
Large cracks greater than 3.0 mm, no spalling of cover concrete
cracks less than 2.0 mm were observed in the beam-to-column panel zone of EDRC-F. Several flexural cracks less than 1.0 mm in width were observed at the beam end, outside of the panel zone. There was no crack at the second-story beam-to-column joint of MRF, while some medium cracks were observed in the second-story column of EDRC-F. This is again because that the inter-story drift ratio of MRF was concentrated on the first story, while the inter-story drift ratio concentration was not significant for EDRC-F. Table 7 shows the crack distribution of one exterior column of MRF and EDRC-F at failure. In general, the damage degree of the edge column was slighter than that of the middle column, since the axial load ratio of the edge column is much smaller than that of the middle column. A large number of cracks were observed at the column base of both MRF and EDRC-F. Significant cracks were found in the first-story joint of MRF, while minor cracks were observed in the first-story joint of EDRC-F. The hysteretic curves and skeleton curves of MRF and EDRC-F under static loading phase are shown in Figs. 16 and 17, respectively. As shown in Fig. 16, the inter-story drift ratio amplitude in first story of MRF was significantly larger than that of EDRC-F, so the hysteretic loop of MRF seemed even fuller than that of EDRC-F. However, this is at the cost of serious damage of concrete column end region for the MRF in the first story. In fact, under the same inter-story drift ratio amplitude,
the bearing capacity and hysteretic loop area of EDRC-F were significantly larger than that of MRF. The quantified results are listed in Table 8. For the conventional MRF, the inter-story drift ratio (IDR) at the first story ranged from −3.60% to 4.16%, while the IDR value at the second story ranged from −3.30% to 2.00%. For EDRC-F, the IDR values at the first and second story varied in a range of −2.80% to 3.14% and −3.53% to 2.80%, respectively. It indicates that the interstory drift ratio tended to concentrate in the first story for MRF, while EDRC-F was still capable of achieving relatively uniform inter-story drift ratios. Due to the presence of EDRC, the inhomogeneous coefficient of inter-story drift ratios reduced by 11.11% and the maximum inter-story drift ratio reduced by 15.14%. As shown in Fig. 17 and Table 8, the difference in stiffness between the MRF and EDRC-F was not significant at the loading amplitude of 1/ 100 roof drift ratio. While with the increment of loading amplitude, the stiffness of MRF degraded rapidly, compared to a low stiffness degradation of EDRC-F. The ultimate capacity of MRF and EDRC-F were 139.7 kN and 177.3 kN, respectively, resulting in an increment of ultimate capacity of 26.91% for EDRC-F. Fig. 18 and Table 9 show the comparison of energy dissipation between MRF and EDRC-F in static Test 3. As listed in Table 9, for the conventional MRF, seismic energy dissipated in the first story is
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Table 7 Comparison of crack distribution in the exterior column in Test 3. Location
Extent and distribution of cracking damage MRF
EDRC-F
No crack
Minor flexural cracks, less than 1.0 mm
Many flexural cracks less than 2.0 mm, a wide crack about 4.0 mm through the section, the middle bottom longitudinal rebar was fractured
A number of cracks at the beam-to-column joint, less than 2.0 mm
Many flexural cracks greater than 2.0 mm, some spalling of concrete
Many flexural cracks less than 2.0 mm, minor spalling of concrete
Fig. 17. Skeleton curves of the specimens in static cyclic Test 3.
Fig. 16. Hysteretic curves of the specimens in quasi-static Test 3.
Table 8 Comparison of inter-story drift ratios in static Test 3.
5112 kN·m , while this value in the second story is 2517 kN·m . For the EDRC-F, the seismic energy dissipated in the first and second story are 4877 kN·m and 3922 kN·m , respectively. The total energy dissipation of MRF and EDRC-F are 7629 kN·m and 8799 kN·m , respectively. Similar to the inter-story drift response, seismic energy dissipation is tending to concentrate in the first story for the MRF, while the EDRC-F is still capable of achieving relatively uniform seismic energy dissipation distribution. By adopting the EDRC, the total energy dissipation increased by 15.34%. the inhomogeneous coefficient of story seismic energy dissipation reduced by 38.92%.
417
Parameter
MRF
EDRC-F
Reduction rate (%)
Maximum drift ratio at first story (%) Maximum drift ratio at second story (%) Maximum drift ratio (%) Inhomogeneous coefficient Ultimate capacity (kN)
4.16 3.30 4.16 1.26 139.7
3.14 3.53 3.53 1.12 177.3
32.48 −6.97 15.14 11.11 −26.91
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Test 2. Corresponding uplift of the column branch flange is about 8 mm, as shown in Fig. 19(b). After Test 2, significant residual deformation of the cover plate was observed which indicated it was yield during the test, as shown in Fig. 19(c). In practical, the cover plate can be replaced after strong earthquakes due to the bolt connection. However, to test the reliability of this configuration, the cover plate was not replaced in this study. In static cyclic Test 3, the maximum inter-story drift ratio of EDRC-F is 3.53%. Corresponding uplift of the cover plate was about 14 mm, as shown in Fig. 20(a). After Test 3, a gap about 4 mm in width was observed between the cover plate and the stiffener of column flange, due to the plastic deformation of cover plate and elongation of the anchorage screw. This connection can be easy repaired after earthquakes. During the tests, two strain gauges were used to monitor the strain of steel strip dampers. One strain gauge was set on the steel strip at the top of the first story, the other strain gauge was set on the steel strip at the top of the second story. The strain of one edge of each steel strip is shown Fig. 21. According to the material test, the steel strips yield in tension at strain about 1400 µ , as illustrated in Fig. 21. Though the steel strips sustained both moment and shear forces, the tension yield strain can be adopted as a reference index. Obviously, the edge of each steel strip experienced yielding during the pseudo-dynamic Test 2. However, the strain gauges were failure during static cyclic Test 3, and the strain data was not recorded.
Fig. 18. Comparison of energy dissipation in static Test 3. Table 9 Comparison of energy dissipation in static Test 3. Parameter
MRF
EDRC-F
Reduction rate (%)
Energy dissipation 1F (kN·m ) Energy dissipation 2F (kN·m ) Inhomogeneous coefficient Total energy dissipation (kN·m )
5112 2517 2.03 7629
4877 3922 1.24 8799
4.60 −55.82 38.92 −15.34
(a)
Maximum column foot uplift
(b)
4. Conclusions
column foot after Test 2
This paper experimentally investigated the effect of steel EnergyDissipative Rocking Column (EDRC) system on the seismic behavior of reinforced concrete frames. A comparison of seismic responses of pure reinforced concrete moment resisting frame (MRF) and combined MRFEDRC system was made by conducting pseudo-dynamic tests. The postearthquake behavior of these two systems was also compared by conducting quasi-static cyclic tests. The following conclusions can be drawn based on the experimental results:
(c)
(1) The EDRC can effectively mitigate the inter-story drift ratio concentration and prevent soft story failure of conventional MRF under earthquakes. Compared to a conventional MRF, the presence of EDRC led to a reduction in the inter-story drift ratio inhomogeneous index of 25.0% and 11.0%, respectively, as found in the pseudodynamic and quasi-static test. (2) The combined MRF-EDRC system had stable lateral load resisting capacity and energy dissipation capacity. The results from the pseudo-dynamic tests showed that the maximum and residual interstory drift ratio of EDRC-F system was reduced by 26.0% and 82.0%, respectively, comparing to MRF. The quasi-static test results also showed that the ultimate capacity was increased by 27.0% comparing to MRF.
Maximum drift in Test 2
Fig. 19. Behavior of EDRC in Test 2.
3.4. Response of the Energy-Dissipative Rocking Column Acknowledgments
No significant response of the Energy-Dissipative Rocking Column (EDRC) was observed in low intensity pseudo-dynamic Test 1. However, the EDRC experienced rocking and yielding in the high intensity pseudo-dynamic Test 2 as well as in the static cyclic Test 3. Specifically, the bottom of steel column branches uplifted and triggered the rocking behavior of EDRC system, as shown in Figs. 19 and 20. The maximum inter-story drift ratio of EDRC-F is 1.62% in pseudo-dynamic
The work presented in this paper was supported by the National Key Research and Development Program of China (Project No. 2017YFC0703607). Ground motion for this study is provided by China Strong Motion Network Centre at Institute of Engineering Mechanics, China Earthquake Administration.
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Maximum column foot uplift in Test 3
column foot after Test 3
(a)
(b) Fig. 20. Behavior of EDRC column foot in Test 3.
y , strip
y , strip
(a) strip at the top of story 1
(b) strip at the top of story 2
Fig. 21. Strain of steel strips in Test 2.
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