Seismic performance of high-strength steel fabricated eccentrically braced frame with vertical shear link

Journal of Constructional Steel Research 137 (2017) 262–285

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Seismic performance of high-strength steel fabricated eccentrically braced frame with vertical shear link

MARK

Ming Liana,b, Mingzhou Sua,⁎ a b

School of Civil Engineering, Xi'an University of Architecture and Technology, Xi'an 710055, China Post-doctoral Mobile Stations of Material Science and Engineering, Xi'an University of Architecture and Technology, Xi'an 710055, China

A R T I C L E I N F O

A B S T R A C T

Keywords: Eccentrically braced frame High-strength steel Seismic performance Experimental study Nonlinear finite element analysis

In high-strength steel fabricated eccentrically braced frame with vertical shear link (HSSEBF-VSL), the vertical shear links use conventional steel while beam and column use high-strength steel (HSS). Using HSS for beams and columns in HSSEBF-VSL can reduce steel weight and increased economic efficiency. In this paper, static tests for two 1:2 length scaled HSSEBF-VSL specimens with one-bay and one-story were carried out, including one static pushover test and one cyclic loading test. The failure mode, load-bearing, ductility and energy dissipation capacities of the specimens were studied through the two static tests. Shake table test of a 1:2 length scaled three-story HSSEBF-VSL specimen was used to study its dynamic responses and dynamic strain responses of the vertical shear links. In addition, the finite element models of several HSSEBF-VSL and conventional EBF with vertical shear link (EBF-VSL) buildings were established for seismic effects. Nonlinear pushover and dynamic analyses were conducted to compare their seismic performance and economy. The test results indicated that the specimen with one-bay and one story had reliable lateral stiffness, ductility and energy dissipation capacity. The three-story specimen had good lateral stiffness and there was no dangerous of collapse for the specimen during the severe earthquakes. Under the same design conditions, the seismic performance of HSSEBF-VSL was slightly lower than that of EBF-VSL if it was designed to match the member section strength of EBF-VSL, but it used less steel than that of EBF-VSL, which could reduce the usage amount of steel in HSSEBF-VSL.

1. Introduction Eccentrically braced frames (EBF) is known for its attractive combination of high elastic stiffness and superior inelastic performance characteristics. In EBF system, link dissipates the energy induced by earthquake loads through its inelastic deformation. Major contributions to the understanding of inelastic deformation of link in EBF for resisting earthquake motion were primarily made during the 1980s [1–4]. Currently, the seismic performance and design method of EBF has been wildly studied [5–10]. Moreover, improvements in the mechanical properties and weldability of high-strength steel (HSS) had made HSS an economical alternative to conventional steel in the constructions [11–14]. As HSS has a higher strength than conventional steel, the structural members made of HSS can have smaller cross-sections than those of structural members made of conventional steel under the same design conditions. This can reduce the usage amount of steel in the structure and improves economy through reduced material costs. In high-strength steel fabricated eccentrically braced frame with vertical shear link (HSSEBF-VSL), the shear link is made of conventional

⁎

steel, braces are made of conventional steel or HSS, and other structural members are made of HSS. As a point of reference, “conventional steel” is defined as steel with a specified nominal yield stress of up to 345 MPa. “HSS” is defined as steel with a specified nominal yield stress above 345 MPa. In HSSEBF-VSL, the shear links dissipate the energy through the inelastic deformation during the severe earthquakes, the columns and beams remain in elastic or experience only a slight plastification because that the HSS has higher yielding strength than that of conventional steel. In addition, considering the properties of HSS, HSSEBF-VSL will have smaller member cross-sections relative to the conventional EBF with vertical shear link (EBF-VSL), which is designed under the same conditions. Furthermore, the strength of HSS columns can have higher strength than that of the conventional steel columns of equal length and cross-section when compared on a nondimensional basis [15,16]. Using HSS columns and beams can reduce the member sections and decrease the structural total weight, which can reduce the damage of the earthquakes to structures [17]. In order to study the seismic performance of HSSEBF-VSL, static and dynamic tests were carried out. Static pushover and cyclic loading tests

Corresponding author at: School of Civil Engineering, Xi'an University of Architecture and Technology, 13 Yanta Road, Xi'an 710055, China. E-mail address: [email protected] (M. Su).

http://dx.doi.org/10.1016/j.jcsr.2017.06.022 Received 2 November 2016; Received in revised form 13 June 2017; Accepted 24 June 2017 0143-974X/ © 2017 Elsevier Ltd. All rights reserved.

Journal of Constructional Steel Research 137 (2017) 262–285

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Fig. 1. Prototype structure for static tests.

were used to observe the seismic behaviors of 1:2 length scaled HSSEBF-VSL specimens with one-bay and one-story, including the loadbearing capacity, lateral stiffness, ductility and energy dissipation capacity. Shake table test was considered to study the dynamic responses of a three-story HSSEBF-VSL specimen, including the dynamic properties, displacement responses and strain responses of shear links. Finally, the finite element models (FEMs) of several HSSEBF-VSL and EBF-VSL buildings were established for the seismic performance and steel usage amount comparison by nonlinear pushover and dynamic analyses.

link length in the specimens was 500 mm (eVp / Mp = 1.46; where e, Vp, and Mp are the link length, plastic shear capacity and plastic moment capacity, respectively). Moreover, the shear links were made of Q345 steel (the nominal yield strength is 345 MPa), while other members were made of Q460 steel (the nominal yield strength is 460 MPa), including beams, columns and braces. Table 1 shows the member sections and the mechanical properties of the steel. The connection details of the specimens are shown in Fig. 2.

2. Static test

2.2. Test setup

2.1. Test specimen

Fig. 3 shows the setup of the static tests. In this test setup, the lateral load of the actuator was applied to the load beam to have two identical lateral loads in both sides of the specimen, so the load beam had much higher stiffness than that of the beam. However, if the lateral loads were applied to the beam-end instead of the load beam, it might result in the axial compression deformation occurred at the beam, which would affect the performance of the specimen. Thus, using load beam could avoid the axial compression deformation of the beam. In order to consider the influence of the vertical load transferred from the upper layers and P-delta effects to the performance of the specimens, a constant axial load of 400 kN was applied, and using an oil jack pushing against the top of the column. The lateral loading condition was generated using an actuator that was connected to the specimen. In the tests, displacement meters and strain gauges were used to obtain the deformation and strain responses of the specimen. Fig. 4 shows the displacement meter and strain gauge distributions on the specimen.

A ten-story HSSEBF-VSL building was designed as the prototype structure for the static test specimens and it was designed through the design codes of GB50011-2010 [18] and JGJ99-98 [19]. The prototype structure is shown in Fig. 1. The prototype was characterized using the peak ground acceleration for an exceeding probability of 10% exceedance probability a in 50-year period, equal to 0.2 g, and moderately firm ground conditions. And then the HSSEBF-SLV in the eighth story of the prototype structure was selected (refer to Fig. 1) and its 1:2 scaled specimens were manufactured for the static tests. The static tests in this study included a static pushover test and a cyclic loading test. One specimen was used for the static pushover test and one specimen was used for the cyclic loading test. In order to compare the performance of these specimens under the different lateral loads, the specimens in these two tests were same. In these specimens, the story height and span were 1.8 and 3.6 m, respectively. The shear Table 1 Structural member dimensions and design properties in specimens. Structural member

Links

Braces

Beams

Columns

Steel grade designation Sectiona Link web thickness, tw Link flange thickness, tf Material nominal yield fy, MPa Material measured yield of web fyaw, MPa Material measured yield of flange fyaf Material measured strength of web fuaw, MPa Material measured strength of flange fuaf, MPa Material elongation web, % Material elongation flange, %

Q345 H225 × 125 × 6 × 10 6 10 345 427.40 383.33 571.10 554.40 26.53 31.01

Q460 H125 × 120 × 6 × 10 6 10 460 496.90 468.77 658.57 627.97 29.73 35.88

Q460 H225 × 125 × 6 × 10 6 10 460 496.90 468.77 658.57 627.97 29.73 35.88

Q460 H150 × 150 × 6 × 10 6 10 460 496.90 468.77 658.57 627.97 29.73 35.88

a

“H” refers to the welded H-shaped section, the following numbers are the section depth (h), flange width (bf), web thickness (tw), and flange thickness (tf), with unit of mm.

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Fig. 2. Details of the specimen.

Specimen for static tests

Fig. 3. Test setup.

1-Base platform; 2-Test specimen; 3-Actuator; 4-Oil jack; 5-Lateral plate; 6-Load beam; 7- Lateral supports; 8- Strong floor shows the loading history for the cyclic loading test. The test loads began with a load control stage in which the cyclic load reversals were applied until obvious stiffness degradation could be observed in the hysteretic curves of the specimen, and the corresponding displacement

2.3. Loading histories In the static pushover test, the magnitude of the loading speed used 0.05 mm/s through the actuator connected to the specimen. Fig. 5

(a) Displacement meters

(b) Strain gauges

Fig. 4. Displacement meter and strain gauge distributions.

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Table 3 Limit states (FEMA 356). Performance level

Qualitative description

Recommended drifts of EBF (%)

P-1

Immediate occupancy (IO) Life safety (LS) Collapse prevention (CP)

0.5

P-2 P-3

1.5 2.0

the link, beam-end and column base, respectively. When the flange fractured occurred at beam end, the specimen could not continue to resist the lateral loads and the test stopped. Table 2 summarizes the test phenomena during the test, in which P is the force provided by the actuator, which equals to the base shear force of the specimen, Δ is the horizontal displacement of the specimen.

Fig. 5. Loading history for cyclic loading test.

was defined as the yield displacement (Δy). The following was displacement controlled. In this stage, the specimen was tested under displacement control for three cycles with the magnitude of ± Δy, ± 2Δy, ± 3Δy, ± 4Δy, ± 5Δy, …

2.4.2. Pushover curve Three structural performance levels, i.e., immediate occupancy (IO), life safety (LS) and collapse prevention (CP) limit states were considered for the system assessment carried out in the present study. These limit states comply with seismic suggestions for EBF by FEMA 356, which is summarized in Table 3. Fig. 7 shows the pushover curve of the specimen during the test. The pushover curve shows that the load-bearing capacity of the specimen increased with the increment of the horizontal displacement and no strength degradation was observed

2.4. Test results and discussions of static pushover test 2.4.1. Test phenomena During the pushover test, the link entered the plastic stage firstly with the increment of displacement. The main deformation occurred at Table 2 Phenomena of the static pushover test. Force provided by actuator P (kN)

Horizontal displacement of specimen Δ (mm)

Description of test phenomena

− 249.95 − 273.41 − 496.79 − 694.23 − 680.16 − 683.48 − 610.03

− 4.87 − 5.55 − 24.97 − 75.78 − 99.18 − 103.38 − 109.74

Link web yielded Link flange yielded Buckling was occurred at link web and flange, as shown in Fig. 6(a) Buckling was occurred at beam end, as shown in Fig. 6(b) Flange buckling was occurred at column base, as shown in Fig. 6(c) Crack occurred at link-to-braces connection, as shown in Fig. 6(d) Weld fractured at link-to-beam connection, as shown in Fig. 6(e)

Note: “-” is the pull direction of the actuator.

(a) Buckling occurred at link

(b) Buckling occurred at beam end

(c) Buckling occurred at column base

(d) Crack occurred at link-to-braces connection

(e) Weld fractured at link-to-beam connection

(f) The specimen after testing

Fig. 6. Static pushover test phenomena.

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800

2.5. Test results and discussions of cyclic loading test

Base shear force (kN)

700

2.5.1. Test phenomena Link of the specimen was in inelastic first with the increment of the horizontal displacement. When the link entered the inelastic stage, the other members were still in elastic. During the cyclic loading test, the main deformation occurred at the link, beam-end and column base, respectively. The test was stopped till the frame could not resist the loads. Table 5 summarizes the main test phenomena observed at different loading levels.

CP

600

Peak point

LS

500

Ultimate point

IO

400 300

Yield point

200

2.5.2. Hysteretic curve The hysteretic curve of the specimen is shown in Fig. 9. The curve shows that the specimen had good plastic deformation capacity. The hysteretic curve covered a small area during the load control stage, which shows the elastic behaviors of the specimen. The hysteretic loops were large and did not have obvious degradation in the stiffness and load-carrying capacity within the three cycles of the same displacement level, which indicated that the specimen had a significant energy dissipation capacity. Fig. 10 shows the skeleton curve of the cyclic responses and the comparison of skeleton curve and static pushover curve. The skeleton curve and pushover curve had same growing trend with the increment of the horizontal displacement. The skeleton curve shows that the base shear force increased before the specimen fractured, which indicated that the specimen had good load-bearing capacity. The ultimate displacement of the skeleton curve from the cyclic loading test was smaller than that of pushover curve, which is because the effect of steel damage accumulation and fatigue to the specimen during the cyclic loads, leading the lower ultimate displacement than that of static pushover curve.

100 0

0

30

60

90

120

150

Displacement (mm) Fig. 7. Pushover curve of the specimen.

before specimen damaged. Moreover, when the displacement was larger than the limitation of CP, the specimen could continue to resist the lateral load and the load-bearing capacity increased, which indicated that the specimen had reliable load-bearing capacity.

2.4.3. Load-bearing and ductility capacities The performance of the specimen can be evaluated using the loadbearing and ductility capabilities. In this study, ductility coefficient μ was used to judge the ductility of the specimen. It is defined as μ = Δu / Δy, where Δu and Δy are the ultimate and yielding displacements, respectively. Table 4 lists the load-bearing and ductility capacities. The maximum base shear force Vm is 97% higher than the yield base force Vy and the ultimate displacement Δu is 14.6 times higher than the yield displacement Δy, which indicated that the specimen had reliable loadbearing and ductility capacities.

2.5.3. Link rotation capacity Fig. 11 shows the link rotation and the plastic rotation angles of the specimens during the cyclic loads. The two curves showed that the link rotation angles increased with the story drift increment. The maximum link rotation angle of the specimen was 30 times higher than the

Table 4 Load-bearing and ductility capacities. Yield point

Peak point

Ultimate point

Yield displacement

Yield base shear force

Displacement at peak point

Maximum base shear force

Ultimate displacement

Ultimate base shear force

Δy (mm)

Vy (kN)

Δm (mm)

Vm (kN)

Δu (mm)

Vu (kN)

8.90

346.22

91.85

682.16

130.14

546.97

Vm/Vy

Ductility coefficient (μ)

1.97

14.62

Table 5 Test phenomena of specimen. Force provided by the actuator (kN)

Horizontal displacement of the specimen (mm)

Description of the test phenomena

Loading level

− 266.01 − 365.98 + 481.97 + 564.03 − 618.98 + 585.18 + 501.15

− 6.72 − 8.13 + 16.01 + 24.07 − 32.11 + 37.52 + 36.12

No obvious phenomenon Link web and flange yield Rust dropped off at the welds of link Rust drop-off was more obvious at the welds of link Local buckling occurred at the beam end (Fig. 8(a)) Local buckling occurred at link web (Fig. 8(b)) Flange fractured at link-to-beam connection (Fig. 8(c)) Flange fractured at the beam end (Fig. 8(d))

Load control stage Δy (the 1st cycle) 2Δy (the 2nd cycle) 3Δy (the 2nd cycle) 4Δy (the 1st cycle) 4.5Δy (the 1st cycle) 5.5Δy (the 1st cycle)

Note: “+” and “-” are the push and pull direction of the actuator, respectively.

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(a) Buckling occurred at the beam end (b) Buckling occurred at the link web (c) Flange fractured at the link-to-beam connection

(d) Flange fractured at the beam end

(e) The link deformation

Fig. 8. Test phenomena during cyclic loading test.

shown in Table 6. The maximum base shear force was 54% higher than the yielding base shear force at positive direction and 58% higher than yielding base shear force at negative direction, which indicated that the load-bearing capacity of the specimen had an obvious increment after entering inelastic stage. The ratios of the maximum displacement and yielding displacement of the specimen were 3.99 at positive direction and 2.96 at negative direction, which showed that the specimen had reliable ductility capacity. The energy dissipation capacity of the specimen is shown in Fig. 13. The dissipated energy and he were increased during the test and the maximum he was 3.75 times higher than that in the load control stage, which indicated that the specimen had a steady and increasing energy dissipated capacity with the increment of plastic development in the specimen.

minimum values. When the specimen was fractured, the maximum link plastic rotation angle was 0.06 rad, which was 25% lower than the rotation angle limitation of 0.08 rad for the shear link in AISC341-10 [20]. 2.5.4. Load-bearing, ductility capacity and energy dissipation capacity The hysteretic behaviors of the specimen can be evaluated using the load-bearing, ductility and energy dissipation capabilities. The he coefficient could be judged depending on the area of the hysteretic loops. It is calculated as he = (SABC + SCDA) / (SOBE + SODF), the SABC, SCDA, SOBE, and SODF are shown in Fig. 12. The yielding base shear force, yielding displacement, maximum base shear force, maximum displacement and ductility coefficient μ are

800

800 600

400

Base shear force (kN)

Base shear force (kN)

600

200 0 -200 -400 -600 -800 -50

400 200 0 -200 -400

Static pushover curve Skeleton curve

-600 -40

-30

-20

-10

0

10

20

30

40

50

-800 -60

Displacement (mm)

-40

-20

0

20

40

60

Displacement (mm)

Fig. 9. Hysteretic curve of the test specimen.

Fig. 10. Skeleton curve.

267

80

100

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0.08

Plastic rotation angle (rad)

0.06

Rotation angle (rad)

0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0.0

0.5

1.0

1.5

2.0

0.05 0.04 0.03 0.02 0.01 0.00 0.0

2.5

0.5

1.0

1.5

2.0

2.5

Story drift (%)

Story drift (%)

(a) Link rotation angles

(b) Link plastic rotation angles Fig. 11. Link rotation capacity.

2.5.5. Failure mechanism Fig. 14 shows the strain responses of each point (as seen in Fig. 4(b)) of the specimen. The ratio ε/εy characterizes the relative strain, where ε and εy are peak strain value and yield strain, respectively. The strain values of link web were higher than those of link flange with the increment of interstory displacement, which indicated that the link exhibited shear deformation. During the test, the strain values of link web were higher than those of link flange. In addition, the strain values of link were much higher than the yield values and only few flange of column bases slightly entered plastic stage, while other structural members were still in elastic stage. It indicated that the shear link of HSSEBF-VSL entered a plastic stage and dissipated the energy via shear deformation, while the other structural members remained in an elastic stage during the seismic loads. Furthermore, when the specimen reached the ultimate state, the link entered the plastic stage completely and damaged, but the columns, beams and braces could continue resistant the seismic loads, which shows that the HSSEBF-VSL is reliable dual resistant system. Fig. 12. Calculation of energy dissipation coefficient.

Table 6 Load-bearing and ductility capacity. Load direction

Positive Negative

Yielding base shear force

Yielding displacement

Maximum base shear force

Maximum displacement

Vy (kN)

Δy (mm)

Vmax (kN)

Δmax (mm)

398.8 412.9

11.09 12.66

612.3 652.6

44.24 37.42

Vmax/Vy

Ductility coefficient (μ)

1.54 1.58

3.99 2.96

Note: “positive” and “negative” are the push and pull direction of the actuator, respectively.

0.4

40

0.3

he coefficient

Dissipated energy (kJ)

50

30 20

0.2

0.1 10

0.0

0

Load control

y

2

y

3

y

4

y

4.5

y

Load control

(a) Dissipated energy

y

2

y

3

y

(b) he coefficient Fig. 13. Energy dissipation capacity.

268

4

y

4.5

y

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12

4

C1 C2 C3 C4 C5 C6 C7 C8 C9

6

3

y

y

9

2

1

3

0

C10 C11 C12 C13 C14 C15 C16 C17 C18 C19

0

5

10

15

20

25

30

35

40

0

45

0

5

10

Displacement (mm)

20

25

30

35

40

45

35

40

45

(b) Columns

(a) Link 1.0

1.0

C20 C21 C22 C23 C24 C25

y

0.6

0.8 0.6

0.4

0.4

0.2

0.2

0

5

10

C26 C27 C28 C29

y

0.8

0.0

15

Displacement (mm)

15

20

25

30

35

40

45

Displacement (mm)

0.0

0

5

10

15

20

25

30

Displacement (mm)

(d) Braces

(c) Beam

Fig. 14. The strain responses of the specimen during the cyclic loading test.

3. Shaking table test

one-bay and one-span was considered the prototype structure for this test, which is shown in Fig. 15. The plan size of the shake table using for this test is 4 m × 4 m and its maximum vertical load-bearing capacity is 300 kN. In order to fully use the shake table, considering the plan size and load-bearing capacity of the shake table, a 1:2 length scaled three-story specimen obtained from the prototype structure was used for this test. Thus, the scaling factor for length Sl equals 0.5. The material composition of the test specimen was identical to that of the prototype structure, suggesting a scaling factor for the elastic modulus SE = 1. To keep the total weight of this specimen less than the maximum vertical load-bearing capacity of the shake table without reducing the horizontal earthquake forces, the similarity ratio of acceleration Sa = 1.2 was used for the test and this factor Sa did not control the gravity acceleration. Furthermore, the other similarity ratios could be calculated based on the Sl, Sa and material properties. The similar relationships were derived for other parameters by using similar theory [21], as summarized in Table 7. The test specimen was a three-story HSSEBF-VSL with a single bay in both the x- and y-directions. Fig. 16 shows the dimensions of the specimen, in which all story height, span in both x- and y- directions were 1.8 m and 2.825 m, respectively. Reinforced concrete slabs (RC slabs) were used in the specimen and their thicknesses were 80 mm. In this specimen, links and braces used Q345 steel (steel with specified nominal yield strength of 345 MPa), columns and beams used Q460 steel (steel with specified nominal yield strength of 460 MPa). The details of the structural members in the specimen are shown in Table 8. Fig. 17 shows the links and connections in the specimen.

3.1. Test specimen The prototype structure of the shake table test specimen was designed based on GB50010-2010 and JGJ99-98 codes. The site for this prototype structure was characterized by peak ground acceleration (PGA) of 0.2 g with a 10% exceedance probability in a 50-year period and moderately firm ground conditions. A three-story HSSEBF-VSL with

Fig. 15. Prototype structure for shake table test.

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roof, live loads of 2 kN/m2 for each floor and wall loads of 4.38 kN/m2 were considered. Based on the dead and live loads, the total mass of the test specimen was 23.8 t.

Table 7 Similarity relationships and ratios of the shake table test specimen. Physical quantities

Dimensions

Similarity relation

Ratio of similarity

Strain Elastic modulus Stress Length Force Mass

– FL− 2 FL− 2 L F FT 2 L− 1

1.00 1.00 1.00 0.50 0.25 0.21

Density

FT

Time/natural period Frequency

T T− 1

Sε = 1 SE = 1 Sσ = SE Sε Sl = 0.5 SF = Sσ Sl2 = SE SεSl2 Sm = SF / Sa = (SE SεSl2) / Sa Sρ = Sm / Sl3 = (SE Sε) / (SaSl) St = ST = (Sl / Sa)− 1/2 Sf = 1/ST = (Sl / Sa)− 1/

2

L− 4

3.3. Instrument arrangement In this shake table test, the accelerometers, displacement sensors and strain gauges were used. Fig. 18 shows the sensors and strain gauge distributions. A1-A16 were the accelerometers, four were placed on each of the three RC slabs and on the base plate in the x-direction. D1D8 were the displacement sensors, two were placed on each of the three RC slabs and on the base plate. S1-S18 were the strain gauges, which were placed on the links of each story to obtain the strain responses of links.

1.67 0.65 1.55

2

Displacement acceleration

L LT− 2

Sx = Sl Sa = 1.2

0.50 1.20

3.4. Loading cases In this test, three ground motions were selected as input excitations according to the comments in GB50011-2010, including the El Centro wave (1940), Taft wave (1952) and Lanzhou artificial wave, which were used to investigate the effects of ground motions with different PGAs on the seismic performance of the specimen. Fig. 19 shows the three ground motions compressed by the time similarity ratio (refer to

3.2. Mass of the test specimen Representative values of gravity G could be computed from 1D + 0.5 L, where D and L are dead and live loads, respectively. In this test, the dead loads of 5 kN/m2 for each floor and 5.625 kN/m2 for the

Fig. 16. Dimensions of the test specimen.

Table 8 Details of structural members in the specimen. Members

Links

Braces

Beams

Columns

Steel grade designation Section Link web thickness, tw Link flange thickness, tf Material nominal yield fy, MPa Material measured yield of web fyaw, MPa Material measured yield of flange fyaf Material measured strength of web fuaw, MPa Material measured strength of flange fuaf, MPa Material elongation web, % Material elongation flange, % Link effective length, mm Link flange compactness, b/tf Link web compactness, hw/tw Link stiffener spacing, mm Vp, kN Mp, kN·m e/(Mp/Vp)

Q345 H180 × 100 × 6 × 10 6 10 345 414.68 363.82 541.18 545.81 28.29 28.74 350 10.00 26.67 2@115 192.10 63.24 1.06

Q345 H100 × 100 × 6 × 10 6 10 345 414.68 363.82 541.18 545.81 28.29 28.74 350 10.00 13.33 – – – –

Q460 H140 × 100 × 8 × 10 8 10 460 473.52 516.19 635.08 691.15 25.36 23.51 350 10.00 15.00 – – – –

Q460 H145 × 145 × 8 × 10 8 10 460 473.52 516.19 635.08 691.15 25.36 23.51 350 14.5.0 15.63 – – – –

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(d) Beam-to-column connection

(a) Link-to-frame connection

(c) Brace-to-frame connection Fig. 17. Details of connections in specimen.

Fig. 18. Layout of sensors.

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0.4

0.20

0.3

0.15

0.2

0.10

Acceleration (g)

Acceleration (g)

M. Lian, M. Su

0.1 0.0 -0.1

0.05 0.00 -0.05

-0.2 -0.3

-0.10 0

5

10

15

20

25

-0.15

30

10

15

Time (s)

(a) El Centro

(b) Taft

20

0.30

Spectral Acceleration (g)

0.02

Acceleration (g)

5

Time (s) 0.03

0.01 0.00 -0.01 -0.02 -0.03

0

0

2

4

6

8

10

12

Design spectra in GB50011-2010 [PoE: 63% in 50 years. RP:50 years] El Centro Taft Lanzhou

0.25 0.20 0.15 0.10 0.05 0.00

0

1

2

3

4

Time (s)

Period (s)

(c) Lanzhou

(d) Spectra comparison

5

Fig. 19. Ground motions and spectra comparison.

3.5. Test results and discussion

Table 7) and the comparison of acceleration response spectra and design acceleration spectrum. Moreover, in order to consider the effects of seismic excitation intensity to the seismic performance of the specimen, the acceleration of the three ground motions were scaled to the corresponding peak ground acceleration (PGA) of the seismic intensity (refer to Table 9) for each seismic excitation intensity. White noise (WN) was used to measure the dynamic behavior of the specimen before each level of PGA. The loading cases are summarized in Table 9.

3.5.1. Test phenomena When the PGAs of the ground motions were lower than 0.48 g, only oxide layer peeled off at the welds of link-to-beam connections in the first and second story. When the PGA reached 0.48 g, the residual link deformation appeared. When the PGA reached 1.0 g, no inelastic deformation was observed in the braces, beams and columns. There was no danger of collapse for the specimen. Table 10 lists the main phenomena observed during the shake table test.

Table 9 List of test cases. Case

Ground motions

PGA (g)

Case

Ground motions

PGA (g)

WN1 1 2 3 WN2 4 5 6 WN3 7 8 9 WN4 10 11 12 WN5 13 14 15

WN El Centro Taft Lanzhou WN El Centro Taft Lanzhou WN El Centro Taft Lanzhou WN El Centro Taft Lanzhou WN El Centro Taft Lanzhou

0.05 0.042

WN6 16 17 18 WN7 19 20 21 WN8 22 23 24 WN9 25 26 27 WN10

WN El Centro Taft Lanzhou WN El Centro Taft Lanzhou WN El Centro Taft Lanzhou WN El Centro Taft Lanzhou WN

0.05 0.264

0.05 0.084

0.05 0.12

0.05 0.168

0.05 0.24

Table 10 Test phenomena. Case

PGA (g)

Description of test phenomena

1–3 4–6 7–9 10–12 13–15

0.042 0.084 0.12 0.168 0.24

Case 16–18 Case 19–21

0.264 0.48

Case 22–24

0.744

Case 25–27

1.0

No obvious phenomenon in the elastic region No obvious phenomenon in the elastic region No obvious phenomenon in the elastic region No obvious phenomenon in the elastic region The oxide layer peeled off at the link and brace-to-frame connection, as shown in Fig. 20(a) and (b) The oxide layer peeled off at links was more obviously The oxide layer peeled off at the weld of link-to-braces connection in first and second story, as shown in Fig. 20(c) The slight residual link deformation appeared, as shown in Fig. 20(d) The peeling of the oxide layer was more obvious at link web and the link-to-braces connection The residual link deformation was more obvious

Case Case Case Case Case

0.05 0.48

0.05 0.744

0.05 1.0

0.05

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(a) The oxide layer peeled (b) The oxide layer peeled off at off at the weld brace-to-frame connection

(c) The oxide layer peeled off

(d) The residual link deformation appeared

Fig. 20. The phenomena of shake table test.

3.5.2. Natural vibration properties Table 11 shows the natural frequency and damping ratio of the specimen, which were obtained by the WN used to obtain the dynamic properties of the specimen in the x-direction. The initial frequency and damping ratio were 6.557 Hz and 3.21%, respectively. When the seismic load increased, the natural frequency decreased, while the damping ratio increased, which indicated that the lateral stiffness of the specimen decreased with the increment of the dynamic load.

Table 11 Scanning frequency and damping ratios of the model. Serial number of the white noise wave

Natural frequency (Hz)

Damping ratio (%)

WN1 WN 2 WN 3 WN 4 WN 5 WN 6 WN 7 WN 8 WN 9 WN 10

6.56 6.55 6.55 6.53 6.50 6.47 6.46 6.40 6.33 6.24

3.21 3.27 3.37 3.49 3.59 3.72 3.76 3.95 4.08 4.44

10 0 -10 -20 -30 -2

-1

0

1

2

90 60 30 0 -30 -60 -90 -120 -10

3

Base shear force (kN)

20

-40 -3

250

120

30

Base shear force (kN)

Base shear force (kN)

40

3.5.3. Hysteretic curves Fig. 21 shows the hysteretic curves of interstory displacement-story shear force relation for second story at the states of IO, LS and CP during the El Centro wave. Fig. 22 shows the hysteretic curves of top displacement-base shear force relation of the specimen at the states of IO, LS and CP during the El Centro wave. The story shear force and base shear force were calculated by the peak acceleration response of the specimen under seismic intensity. The displacement responses were

200 150 100 50 0 -50 -100 -150 -200

-8

-6

-4

-2

0

2

4

6

8

-250 -15

10

-12

-9

-6

-3

0

3

6

9

Top displacement (mm)

Top displacement (mm)

Top displacement (mm)

(a) PGA=0.084g (IO)

(b) PGA=0.24g (LS)

(c) PGA=0.48g (CP)

12

15

9

12

Fig. 21. Base shear force-top displacement hysteretic curves of the specimen.

100

20 10 0 -10 -20

200

80

Story shear force (kN)

Story shear force (kN)

Story shear force (kN)

30

60 40 20 0 -20 -40 -60 -80 -100

-30 -2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

-120 -5

-4

-3

-2

-1

0

1

2

3

Interstory displacement (mm)

Interstory displacement (mm)

(a) PGA=0.084g (IO)

(b) PGA=0.24g (LS)

4

150 100 50 0 -50 -100 -150 -200 -12

Fig. 22. Base shear force-top displacement hysteretic curves of the specimen.

273

-9

-6

-3

0

3

6

Interstory displacement (mm)

(c) PGA=0.48g (CP)

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Table 12 Maximum roof drifts of the specimen. Ground motions

Maximum roof drifts (D/H, %)

El Centro wave Taft wave Lanzhou wave

0.042 g

0.084 g

0.12 g

0.168 g

0.24 g

0.264 g

0.48 g

0.744 g

1.0 g

0.03 0.02 0.01

0.04 0.03 0.02

0.07 0.05 0.03

0.08 0.08 0.04

0.12 0.12 0.06

0.16 0.13 0.08

0.26 0.27 0.20

0.38 0.39 0.29

0.62 0.50 0.45

lower than 0.48 g. The maximum roof drifts obviously increased when the PGAs reached 0.48 g, 0.744 g, and 1.0 g, respectively. Table 13 shows the maximum interstory drifts of the specimen during each seismic load, respectively. The maximum interstory drifts were 0.09%, 0.21% and 0.49% when the PGA reached the corresponding values for IO, LS and CP in Table 3, respectively, these interstory values of the specimen were lower than the limitation for the EBF in FEMA 356. Table 14 shows the maximum link rotations of the specimen during the seismic loads.

Table 13 Maximum interstory drifts of the specimen. PGA (g)

0.042

0.084

0.12

0.168

0.24

0.264

0.48

0.744

1.0

Maximum interstory drifts (d/ h)

0.04

0.09

0.14

0.14

0.21

0.33

0.49

0.88

1.37

3.5.5. Dynamic strain response of links The strain responses of shear links were obtained by the strain gauges located on the specimen. Figs. 23–25 show the dynamic strain curves of each point at links during the El Centro, Taft and Lanzhou earthquakes with different intensity, respectively, in which the ratio ε/ εy characterizes the relative strain, where ε and εy are the peak strain value and yield strain, respectively. The curves show that the strain responses of shear links increased with the increment of the seismic loads. The strain responses of link webs were higher than those of link flanges, which indicated that the deformation of the links had obvious shear deformation properties. Moreover, when the strain of link webs were higher than the yielding values, the strains of link flanges were lower than the yielding ones, which indicated that the links dissipated the energy via the deformation of the web.

measured by the displacement sensors. When the PGAs increased, the top displacement and interstory displacement increased. The hysteretic curves show that the hysteretic loops were stable and did not have obvious degradation in the stiffness and load-carrying capacity, which indicated that the specimen had a reliable energy dissipation capacity. 3.5.4. Displacement responses Three deformational quantities are monitored herein, namely interstory drifts (d/h, where d and h are interstory displacements and story height, respectively), roof drifts (D/H, where D and H are the top displacements and total height of the specimen, respectively) and maximum link rotations. Table 12 shows the maximum roof drifts of the specimen during each seismic load in x-direction. The maximum roof drifts of the specimen were nearly proportional when the PGAs were Table 14 Maximum link rotations of the specimen. PGAs (g)

0.042

0.084

0.12

0.168

0.24

0.264

0.48

0.744

1.0

Link rotations (rad)

0.003

0.005

0.008

0.009

0.011

0.016

0.025

0.045

0.070

1.4

0.8

1.0 0.8

1.4

S7 S8 S9 S10 S11 S12

1.2 1.0 y

y

1.0

1.2

y

1.2

1.4

S1 S2 S3 S4 S5 S6

0.8

0.6

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

0.0 0.0

0.0 0.0

0.2

0.4

0.6

PGA (g)

(a) First story

0.8

1.0

0.2

0.4

0.6

0.8

1.0

0.0 0.0

S13 S14 S15 S16 S17 S18

0.2

0.4

0.6

PGA (g)

PGA (g)

(b) Second story

(c) Third story

Fig. 23. Variation of strain under the El Centro wave.

274

0.8

1.0

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1.4

0.8

1.2 1.0 0.8

1.4

S7 S8 S9 S10 S11 S12

1.2 1.0 y

y

1.0

1.4

S1 S2 S3 S4 S5 S6

y

1.2

0.8

0.6

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

0.0 0.0

0.0 0.0

0.2

0.4

0.6

0.8

1.0

0.2

0.4

0.6

0.8

0.0 0.0

1.0

S13 S14 S15 S16 S17 S18

0.2

0.4

0.6

PGA (g)

PGA (g)

PGA (g)

(a) First story

(b) Second story

(c) Third story

0.8

1.0

0.8

1.0

Fig. 24. Variation of strain under the Taft wave.

1.4

0.8

1.0 0.8

0.6

0.6

0.4

0.4

0.2

0.2

0.0 0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.0

1.2

S7 S8 S9 S10 S11 S12

1.0 0.8 y

y

1.0

1.2

y

1.2

1.4

S1 S2 S3 S4 S5 S6

0.6

S13 S14 S15 S16 S17 S18

0.4 0.2

0.2

0.4

0.6

0.8

1.0

0.0 0.0

0.2

0.4

0.6

PGA (g)

PGA (g)

PGA (g)

(a) First story

(b) Second story

(c) Third story

Fig. 25. Variation of strain under the Lanzhou wave.

probability in a 50-year period and moderately firm ground conditions. Fig. 26 shows the designed buildings. In all buildings, the story heights were 3 m and there were five bays in x-direction and three bays in ydirection. The span in both x-direction and that in y-direction were 6 m. The shear link lengths were 700 mm in all designs. The dead load for the floors and roofs were 4.8 kN/m2. The floor live load, roof live load and snow load used 2, 0.5 and 0.25 kN/m2 respectively. Additionally, the HSSEBF-VSL buildings were designed to match the member section strengths of the conventional EBF-VSL who had the same building heights to the corresponding HSS-VSL buildings rather than to use the equivalent lateral force procedure. The designations of all buildings are summarized in Table 15. Table 16 shows the fundamental natural periods of four HSSEBF-VSL

4. Seismic performance comparison of HSSEBF-VSL and conventional EBF-VSL 4.1. Designs and finite element models Four HSSEBF-VSL buildings with different building heights (5-story, 10-story, 15-story and 20-story) and four conventional EBF-VSL buildings with different building heights (5-story, 10-story, 15-story and 20story) were designed based on GB50010-2010 and JGJ99-98 codes. In the HSSEBF-VSL buildings, links and braces used Q345 steel and other structural members used Q460 steel. In the conventional EBF-VSL buildings, all structural members used Q345 steel. The site for these designs was characterized by PGA of 0.2 g with a 10% exceedance

Fig. 26. Building plan and elevation views.

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Table 15 Designation of the all buildings. Frames

Designation

HSSEBF-VSL

EBF-VSL

5-story

10-story

15-story

20-story

5-story

10-story

15-story

20-story

HEV1

HEV2

HEV3

HEV4

EV1

EV2

EV3

EV4

interstory drifts of the buildings reached the limitation of the performance levels for EBF in FEMA 356. Table 19 lists the yield strength Vy, the maximum load-bearing capacity Vm and the strength at different performance levels. The elastic lateral stiffnesses of HEV1, HEV2, HEV3 and HEV4 were slightly lower than those of EV1, EV2, EV3 and EV4, respectively. The Vy of HEV1 was 7% lower than that of EV1. For HEV2, HEV3 and HEV4 compared with EV2, EV3 and EV4, the differences were 9%, 8% and 8%, respectively. The Vmax of HEV1 was 9% lower than that of EV1. For HEV2, HEV3 and HEV4 compared with EV2, EV3 and EV4, the differences were 7%, 12% and 4%, respectively. It indicated that the load-bearing capacity of HSSEBF-VSL was slightly lower than that of conventional EBF-VSL if they had similar member section strengths, which is because HSS was used in the beams and columns of HEV1-HEV4 and smaller HSS beam and column sections were selected to match the member section strengths of EV1-EV4. The smaller beam and column sections reduced the lateral stiffness of HEV1HEV4, which leading the lower load-bearing capacity.

Table 16 Fundamental natural periods of all buildings. Frames

HEV1 HEV2 HEV3 HEV4 EV1 EV2 EV3 EV4

Periods (s) T1

T2

T3

0.61 0.93 1.11 1.57 0.54 0.88 1.02 1.45

0.56 0.89 1.07 1.52 0.52 0.82 0.96 1.36

0.51 0.82 0.97 1.36 0.47 0.78 0.93 1.28

buildings and four conventional EBF-VSL buildings. The structural member sections of HSSEBF-VSL buildings and conventional EBF-VSL buildings all are summarized in Tables 17 and 18, respectively. The FEMs of the analytical frame in all designs (refer to Fig. 26) were established by SAP2000. In the FEMs, beam elements were used for all structural members. Nominal yield strength was adopted for the steel. The elastic modulus and Poisson's ratio are assumed to be 206,000 MPa and 0.3, respectively. The influence of initial imperfections and residual stress is not considered and P-delta effects were included in the nonlinear analyses. Nonlinear hinges were defined at the links, beams, columns and braces. Moreover, the analysis was conducted using life safety structural performance level as well as the nonlinear behavior of shear link by FEMA-356. For shear link, the model presented in Tables 5–6 of FEMA-356 was considered for the nonlinear behaviors.

4.3. Nonlinear dynamic analysis

4.2. Nonlinear pushover analysis

4.3.1. Ground motions All buildings were subjected to nonlinear dynamic analysis with various ground motions to study the performance of HSSEBF-VSL compared with that of conventional EBF-VSL during the dynamic loads. The dynamic analysis was performed using a set of ground motions. The seismological properties of the ground motions are summarized in Table 20, which also shows that three levels of seismic hazard were employed: 50%, 10% and 2% probability of exceedance in a 50-year period. The acceleration response spectra of the ensemble of accelerograms, along with the design acceleration spectrum are shown in Fig. 31.

Pushover (static) analysis was performed through inverted triangular displacement-controlled patterns. In the pushover analysis, target drift selected 3% of the total height (D/H = 3%, D and H are the top displacement and total height of structure) of the frame. The lateral resistance capacities of all buildings were investigated through the nonlinear pushover analysis. Figs. 27–29 show the plastic hinges distributions of all buildings when the D/H reached 1%, 2% and 3%, respectively. When D/H reached 1%, the plastic hinges distributions of HEV1 and HEV2 were similar to those of EV1 and EV2, respectively. EV3 and EV4 had more plastic hinges on beams than HEV3 and HEV4, respectively. When D/H reached 2% and 3%, respectively, compared with the plastic hinges distributions of HEV1-HEV4, there were more plastic hinges on beams and column bases in the EV1-EV4. It because the HSS beams and columns of HEV1-HEV4 had higher yielding strength compared with the conventional steel members of EV1-EV4, leading the less plastic hinges in HEV1-HEV4. Fig. 30 shows the pushover curves of all buildings by considering displacement-controlled horizontal patterns (triangular distribution), in which the points of “IO”, “LS” and “CP” on the curves refer that the

4.3.2. Dynamic analysis results The mean maximum interstory drifts (d/h) for the HSSEBF-VSL and conventional EBF-VSL buildings were found for the ground motions with probability exceedance of 50% in a 50-year period as displayed in Fig. 32. For the serviceability check, the interstory drifts of HEV1-HEV4 were larger than those of EV1-EV4, indicating that the HSSEBF-VSL buildings had lower lateral stiffness caused by the smaller member sections than those of conventional EBF-VSL buildings. However, the interstory drifts of all buildings were less than the limitation of IO for EBF in FEMA356, though the drifts of HSSEBF-VSL buildings were larger than those of conventional EBF-VSL buildings, indicating that both of HSSEBF-VSL and conventional EBF-VSL buildings had good capacity in controlling story drifts. The maximum interstory drift of HEV1 was 8.7% lower than that of EV1. For HEV2, HEV3 and HEV4 compared with EV2, EV3 and EV4, the differences were 7.9%, 9.6% and 6.2%, respectively. It indicated that though the beam and column sections of HEV1-HEV4 were smaller than those of EV1-EV4, the maximum interstory drifts of HEV1-HEV4 were slightly higher (less than 10%) than those of EV1-EV4 during the earthquakes with probability exceedance of 50% in a 50-year period.

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Table 17 Structural member sections of HSSEBF-VSL buildings. HEV1

HEV2

HEV3

HEV4

Story

Links (e/(Mp/Vp))

Beams

Columns

Braces

1

H320 × 150 × 10 × 20 (1.19)

H330 × 200 × 10 × 15

H500 × 500 × 20 × 30

H300 × 200 × 15 × 20

2

H300 × 150 × 10 × 20 (1.20)

H320 × 200 × 10 × 15

H490 × 490 × 20 × 30

H300 × 200 × 15 × 20

3

H320 × 150 × 8 × 20 (1.19)

H310 × 200 × 10 × 15

H470 × 470 × 20 × 25

H300 × 200 × 15 × 20

4

H330 × 150 × 6 × 20 (1.17)

H280 × 180 × 8 × 15

H450 × 450 × 20 × 25

H300 × 200 × 15 × 20

5

H320 × 100 × 4 × 20 (1.18)

H200 × 180 × 8 × 15

H420 × 420 × 20 × 25

H300 × 200 × 15 × 20

Story 1 2 3 4 5 6 7 8 9 10 Story 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Story 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Links (e/(Mp/Vp)) H370 × 200 × 12 × 20 (1.06) H350 × 200 × 12 × 20 (1.07) H340 × 200 × 12 × 20 (1.07) H320 × 200 × 12 × 20 (1.08 H350 × 150 × 10 × 20 (1.18) H320 × 150 × 10 × 20 (1.19) H330 × 150 × 8 × 20 (0.97) H300 × 150 × 8 × 20 (0.98) H250 × 150 × 6 × 15 (0.99) H200 × 100 × 4 × 15 (1.01) Links (e/(Mp/Vp)) H400 × 200 × 13 × 20 (1.12) H390 × 200 × 13 × 20 (1.12) H390 × 200 × 13 × 20 (1.12) H390 × 200 × 13 × 20 (1.12) H380 × 200 × 13 × 20 (1.13) H370 × 200 × 13 × 20 (1.13) H380 × 200 × 12 × 20 (1.05) H420 × 200 × 12 × 20 (1.04) H400 × 200 × 12 × 20 (1.05) H380 × 200 × 12 × 20 (1.05) H350 × 200 × 12 × 20 (1.07) H320 × 200 × 12 × 20 (1.08) H320 × 150 × 7 × 15 (1.11) H320 × 150 × 7 × 15 (1.1) H250 × 100 × 4 × 15 (0.99) Links (e/(Mp/Vp)) H420 × 250 × 16 × 20 (1.10) H420 × 250 × 16 × 20 (1.10) H410 × 250 × 16 × 20 (1.10) H410 × 250 × 16 × 20 (1.10) H400 × 250 × 16 × 20 (1.11) H400 × 250 × 16 × 20 (1.11) H390 × 250 × 16 × 20 (1.11) H380 × 250 × 16 × 20 (1.11) H380 × 250 × 16 × 20 (1.11) H360 × 250 × 16 × 20 (1.12) H350 × 250 × 16 × 20 (1.13) H340 × 250 × 16 × 20 (1.13) H320 × 250 × 16 × 20 (1.14) H320 × 250 × 14 × 20 (1.02) H310 × 200 × 12 × 20 (1.09) H330 × 200 × 10 × 15 (1.17) H300 × 200 × 10 × 15 (1.19) H300 × 200 × 9 × 15 (1.08) H270 × 150 × 5 × 10 (1.20) H250 × 150 × 5 × 10 (1.21)

Beams H460 × 250 × 15 × 20 H440 × 250 × 15 × 20 H420 × 250 × 15 × 20 H400 × 250 × 15 × 20 H430 × 200 × 14 × 20 H390 × 200 × 14 × 20 H360 × 200 × 12 × 20 H360 × 150 × 12 × 20 H340 × 150 × 10 × 15 H280 × 100 × 8 × 15 Beams H500 × 200 × 14 × 20 H490 × 200 × 14 × 20 H480 × 200 × 14 × 20 H470 × 200 × 14 × 20 H500 × 200 × 10 × 15 H490 × 200 × 10 × 15 H480 × 200 × 10 × 15 H460 × 200 × 10 × 15 H480 × 200 × 8 × 12 H460 × 200 × 8 × 12 H460 × 200 × 8 × 12 H460 × 200 × 6 × 10 H440 × 200 × 6 × 10 H400 × 200 × 4 × 10 H380 × 200 × × 10 Beams H500 × 300 × 14 × 25 H490 × 300 × 14 × 25 H480 × 300 × 14 × 25 H470 × 300 × 14 × 25 H480 × 250 × 14 × 25 H470 × 250 × 14 × 25 H460 × 250 × 14 × 20 H450 × 250 × 14 × 0 H440 × 250 × 14 × 20 H460 × 200 × 12 × 20 H450 × 200 × 12 × 20 H430 × 200 × 12 × 20 H490 × 150 × 12 × 20 H480 × 150 × 12 × 20 H470 × 150 × 12 × 20 H460 × 200 × 12 × 5 H450 × 200 × 10 × 15 H440 × 200 × 10 × 15 H430 × 200 × 10 × 15 H380 × 200 × 8 × 15

Columns H640 × 640 × 20 × 35 H640 × 640 × 20 × 35 H630 × 630 × 20 × 35 H600 × 600 × 20 × 35 H580 × 580 × 20 × 30 H550 × 550 × 20 × 30 H520 × 520 × 20 × 30 H500 × 500 × 20 × 30 H450 × 450 × 20 × 25 H380 × 380 × 15 × 20 Columns H800 × 800 × 40 × 50 H800 × 800 × 40 × 50 H800 × 800 × 40 × 50 H750 × 750 × 40 × 50 H750 × 750 × 40 × 50 H750 × 750 × 40 × 50 H700 × 700 × 30 × 40 H700 × 700 × 30 × 40 H700 × 700 × 30 × 40 H650 × 650 × 20 × 30 H650 × 650 × 20 × 30 H650 × 650 × 20 × 30 H600 × 600 × 20 × 30 H600 × 600 × 20 × 30 H600 × 600 × 20 × 30 Columns H1000 × 1000 × 50 × 60 H1000 × 1000 × 50 × 60 H1000 × 1000 × 50 × 60 H900 × 900 × 50 × 60 H900 × 900 × 50 × 60 H900 × 900 × 50 × 60 H800 × 800 × 40 × 50 H800 × 800 × 40 × 50 H800 × 800 × 40 × 50 H700 × 700 × 30 × 40 H700 × 700 × 30 × 40 H700 × 700 × 30 × 40 H600 × 600 × 25 × 30 H600 × 600 × 25 × 30 H600 × 600 × 25 × 30 H500 × 500 × 25 × 30 H500 × 500 × 25 × 30 H500 × 500 × 25 × 30 H400 × 400 × 15 × 25 H400 × 400 × 15 × 25

Braces H300 × 200 × 12 × 16 H300 × 200 × 12 × 16 H300 × 200 × 12 × 16 H300 × 200 × 12 × 16 H300 × 200 × 12 × 16 H250 × 200 × 12 × 16 H250 × 200 × 12 × 16 H250 × 200 × 12 × 16 H250 × 200 × 12 × 16 H250 × 200 × 12 × 16 Braces H400 × 200 × 12 × 20 H400 × 200 × 12 × 20 H400 × 200 × 12 × 20 H400 × 200 × 12 × 20 H400 × 200 × 12 × 20 H350 × 200 × 12 × 20 H350 × 200 × 12 × 20 H350 × 200 × 12 × 20 H350 × 200 × 12 × 20 H350 × 200 × 12 × 20 H300 × 200 × 12 × 20 H300 × 200 × 12 × 20 H300 × 200 × 12 × 20 H300 × 200 × 12 × 20 H300 × 200 × 12 × 20 Braces H500 × 300 × 20 × 25 H500 × 300 × 20 × 25 H500 × 300 × 20 × 25 H500 × 300 × 20 × 25 H500 × 300 × 20 × 25 H450 × 200 × 15 × 20 H450 × 200 × 15 × 20 H450 × 200 × 15 × 20 H450 × 200 × 15 × 20 H450 × 200 × 15 × 20 H400 × 200 × 15 × 25 H400 × 200 × 15 × 25 H400 × 200 × 15 × 25 H400 × 200 × 15 × 25 H400 × 200 × 15 × 25 H350 × 200 × 15 × 20 H350 × 200 × 15 × 20 H350 × 200 × 15 × 20 H350 × 200 × 15 × 20 H350 × 200 × 15 × 20

respectively. It is found that the HSSEBF-VSL buildings exhibited larger interstory drifts than those of conventional EBF-VSL buildings during the earthquakes with probability exceedance of 10% in a 50-year period, but the difference was less than 12%. The mean maximum interstory drifts (d/h) of all buildings during the earthquakes with probability exceedance of 2% in a 50-year period are shown in Fig. 34, which shows that the interstory drifts of all

For earthquakes with probability exceedance of 10% in a 50-year period, the mean maximum interstory drifts (d/h) for the HEV1-HEV4 and EV1-EV4 are shown in Fig. 33. Most of the mean maximum interstory drifts of all buildings were between the limitation of IO and LS for EBF in FEMA356. The maximum interstory drift of HEV1 was 10.8% lower than that of EV1. For HEV2, HEV3 and HEV4 compared with EV2, EV3 and EV4, the differences were 9.3%, 11.7% and 9.9%,

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Table 18 Structural member sections of conventional EBF-VSL buildings. EV1

EV2

EV3

EV4

Story

Links (e/(Mp/Vp))

Beams

Columns

Braces

1

H350 × 150 × 12 × 20 (1.07)

H400 × 200 × 12 × 20

H500 × 500 × 20 × 30

H300 × 200 × 15 × 20

2

H320 × 150 × 12 × 20 (1.08)

H380 × 200 × 12 × 20

H490 × 490 × 20 × 30

H300 × 200 × 15 × 20

3

H330 × 150 × 10 × 20 (1.18)

H350 × 200 × 12 × 20

H470 × 470 × 20 × 25

H300 × 200 × 15 × 20

4

H330 × 150 × 8 × 20 (0.97)

H340 × 150 × 12 × 20

H450 × 450 × 20 × 25

H300 × 200 × 15 × 20

5

H320 × 100 × 6 × 20 (1.08)

H290 × 150 × 10 × 20

H420 × 420 × 20 × 25

H300 × 200 × 15 × 20

Story 1 2 3 4 5 6 7 8 9 10 Story 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Story 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Links (e/(Mp/Vp)) H370 × 200 × 12 × 20 (1.06) H350 × 200 × 12 × 20 (1.07) H340 × 200 × 12 × 20 (1.07) H320 × 200 × 12 × 20 (1.08 H350 × 150 × 10 × 20 (1.18) H320 × 150 × 10 × 20 (1.19) H330 × 150 × 8 × 20 (0.97) H300 × 150 × 8 × 20 (0.98) H250 × 150 × 6 × 15 (0.99) H200 × 100 × 4 × 15 (1.01) Links (e/(Mp/Vp)) H390 × 200 × 15 × 20 (1.27) H380 × 200 × 15 × 20 (1.28) H410 × 200 × 14 × 20 (1.19) H400 × 200 × 14 × 20 (1.19) H390 × 200 × 14 × 20 (1.20) H380 × 200 × 14 × 20 (1.20) H370 × 200 × 14 × 20 (1.21) H360 × 200 × 14 × 20 (1.22) H390 × 200 × 12 × 20 (1.05) H370 × 200 × 12 × 20 (1.06) H340 × 200 × 12 × 20 (1.07) H350 × 200 × 10 × 20 (0.91) H300 × 200 × 10 × 15 (1.19) H280 × 200 × 8 × 15 (0.98) H250 × 150 × 6 × 15 (0.99) Links (e/(Mp/Vp)) H420 × 300 × 18 × 20 (1.04) H420 × 300 × 18 × 20 (1.04) H410 × 300 × 18 × 20 (1.04) H410 × 300 × 18 × 20 (1.04) H400 × 300 × 18 × 20 (1.05) H400 × 300 × 18 × 20 (1.05) H390 × 300 × 18 × 20 (1.05) H380 × 300 × 18 × 20 (1.05) H380 × 300 × 18 × 20 (1.05) H360 × 300 × 18 × 20 (1.06) H350 × 300 × 18 × 20 (1.07) H340 × 300 × 18 × 20 (1.07) H320 × 300 × 18 × 20 (1.08) H320 × 250 × 16 × 20 (1.14) H310 × 200 × 12 × 20 (1.09) H330 × 150 × 10 × 20 (1.18) H300 × 150 × 10 × 20 (1.20) H300 × 150 × 7 × 15 (1.12) H270 × 150 × 7 × 15 (1.13) H250 × 150 × 7 × 15 (1.14)

Beams H460 × 250 × 15 × 20 H440 × 250 × 15 × 20 H420 × 250 × 15 × 20 H400 × 250 × 15 × 20 H430 × 200 × 14 × 20 H390 × 200 × 14 × 20 H360 × 200 × 12 × 20 H360 × 150 × 12 × 20 H340 × 150 × 10 × 15 H280 × 100 × 8 × 15 Beams H490 × 250 × 15 × 25 H480 × 250 × 14 × 25 H470 × 250 × 14 × 25 H460 × 250 × 14 × 25 H450 × 250 × 14 × 25 H440 × 250 × 14 × 25 H430 × 250 × 14 × 25 H420 × 250 × 14 × 25 H400 × 250 × 14 × 25 H440 × 200 × 12 × 25 H420 × 200 × 12 × 25 H390 × 200 × 12 × 25 H370 × 200 × 12 × 20 H370 × 150 × 10 × 20 H330 × 150 × 8 × 12 Beams H530 × 300 × 16 × 30 H520 × 300 × 16 × 30 H510 × 300 × 16 × 30 H500 × 300 × 16 × 30 H510 × 250 × 16 × 30 H500 × 250 × 16 × 30 H490 × 250 × 16 × 25 H480 × 250 × 16 × 25 H470 × 250 × 16 × 25 H490 × 200 × 14 × 25 H480 × 200 × 14 × 25 H460 × 200 × 14 × 25 H520 × 150 × 14 × 25 H510 × 150 × 14 × 25 H500 × 150 × 14 × 25 H490 × 200 × 14 × 20 H480 × 200 × 12 × 20 H470 × 200 × 12 × 20 H460 × 200 × 12 × 20 H410 × 200 × 10 × 20

Columns H640 × 640 × 20 × 35 H640 × 640 × 20 × 35 H630 × 630 × 20 × 35 H600 × 600 × 20 × 35 H580 × 580 × 20 × 30 H550 × 550 × 20 × 30 H520 × 520 × 20 × 30 H500 × 500 × 20 × 30 H450 × 450 × 20 × 25 H380 × 380 × 15 × 20 Columns H800 × 800 × 40 × 50 H800 × 800 × 40 × 50 H800 × 800 × 40 × 50 H750 × 750 × 40 × 50 H750 × 750 × 40 × 50 H750 × 750 × 40 × 50 H700 × 700 × 30 × 40 H700 × 700 × 30 × 40 H700 × 700 × 30 × 40 H650 × 650 × 20 × 30 H650 × 650 × 20 × 30 H650 × 650 × 20 × 30 H600 × 600 × 20 × 30 H600 × 600 × 20 × 30 H600 × 600 × 20 × 30 Columns H1000 × 1000 × 50 × 60 H1000 × 1000 × 50 × 60 H1000 × 1000 × 50 × 60 H900 × 900 × 50 × 60 H900 × 900 × 50 × 60 H900 × 900 × 50 × 60 H800 × 800 × 40 × 50 H800 × 800 × 40 × 50 H800 × 800 × 40 × 50 H700 × 700 × 30 × 40 H700 × 700 × 30 × 40 H700 × 700 × 30 × 40 H600 × 600 × 25 × 30 H600 × 600 × 25 × 30 H600 × 600 × 25 × 30 H500 × 500 × 25 × 30 H500 × 500 × 25 × 30 H500 × 500 × 25 × 30 H400 × 400 × 15 × 25 H400 × 400 × 15 × 25

Braces H300 × 200 × 12 × 16 H300 × 200 × 12 × 16 H300 × 200 × 12 × 16 H300 × 200 × 12 × 16 H300 × 200 × 12 × 16 H250 × 200 × 12 × 16 H250 × 200 × 12 × 16 H250 × 200 × 12 × 16 H250 × 200 × 12 × 16 H250 × 200 × 12 × 16 Braces H400 × 200 × 12 × 20 H400 × 200 × 12 × 20 H400 × 200 × 12 × 20 H400 × 200 × 12 × 20 H400 × 200 × 12 × 20 H350 × 200 × 12 × 20 H350 × 200 × 12 × 20 H350 × 200 × 12 × 20 H350 × 200 × 12 × 20 H350 × 200 × 12 × 20 H300 × 200 × 12 × 20 H300 × 200 × 12 × 20 H300 × 200 × 12 × 20 H300 × 200 × 12 × 20 H300 × 200 × 12 × 20 Braces H500 × 300 × 20 × 25 H500 × 300 × 20 × 25 H500 × 300 × 20 × 25 H500 × 300 × 20 × 25 H500 × 300 × 20 × 25 H450 × 200 × 15 × 25 H450 × 200 × 15 × 25 H450 × 200 × 15 × 25 H450 × 200 × 15 × 25 H450 × 200 × 15 × 25 H400 × 200 × 15 × 25 H400 × 200 × 15 × 25 H400 × 200 × 15 × 25 H400 × 200 × 15 × 25 H400 × 200 × 15 × 25 H350 × 200 × 15 × 20 H350 × 200 × 15 × 20 H350 × 200 × 15 × 20 H350 × 200 × 15 × 20 H350 × 200 × 15 × 20

probability exceedance of 2% in a 50-year period, though the member sections of HSSEBF-VSL buildings were smaller than those of conventional EBF-VSL buildings.

buildings were below the limitation of CP for EBF in FEMA356 in all cases. Both of HSSEBFVSL and conventional EBF-VSL buildings were effective for high-magnitude earthquakes and hence in inelastic. The maximum interstory drift of HEV1 was 14.1% lower than that of EV1. For HEV2, HEV3 and HEV4 compared with EV2, EV3 and EV4, the differences were 11.2%, 12.3% and 10.8%, respectively. It indicated that the deformation capacities of HSSEBF-VSL buildings were close to those of conventional EBF-VSL buildings during the earthquakes with

4.4. Steel weight comparison The total steel weights of four HSSEBF-VSL buildings and four conventional EBF-VSL building are listed in Table 21. The total weights

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HEV1

EV1

HEV2

(a) 5-story buildings

HEV3

EV2

(b) 10-story buildings

EV3

HEV4

EV4

(d) 20-story buildings

(c) 15-story buildings Fig. 27. Plastic hinges distributions at D/H = 1%.

the member section strengths of conventional EBF-VSL buildings, the higher yielding strength of HSS led to the smaller member sections than those of the conventional EBF-VSL using conventional steel. However, as the structural height increases, the lateral stiffness requirements are more considerable for design, which reduces the advantage of saving steel of HSSEBF-VSL.

of HSSEBF-VSL buildings were less than those of EBF-VSL buildings, which indicated that the HSSEBF-VSL had advantages of saving steel usage and improving economy. The total weight of HEV1 was 14% less than that of EV1. For HEV2, HEV3 and HEV4 compared with EV2, EV3 and EV4, the differences were 12%, 11% and 10%, respectively. It is because that HSSEBF-VSL buildings were designed using HSS to match

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M. Lian, M. Su

HEV1

EV1

HEV2

HEV3

EV2

(b) 10-story buildings

(a) 5-story buildings

EV3

HEV4

EV4

(d) 20-story buildings

(c) 15-story buildings Fig. 28. Plastic hinges distributions at D/H = 2%.

Thus, based on the nonlinear finite elament analysis results above, the seismic performance of HSSEBF-VSL was slightly lower than that of conventional EBF-VSL if the HSSEBF-VSL was designed to match the member section strengths of conventional EBF-VSL under the same design conditions, but the performance of HSSEBF-VSL could meet the limitation requirements in the design codes. Moreover, HSS beams and

columns using in HSSEBF-VSL led to the smaller member sections than those of conventional EBF-VSL, which could reduce the total steel weight and improved economy. Based on the analyses described in this paper, HSSEBF-VSL performed best when building heights do not exceed fifteen stories.

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HEV1

EV1

HEV2

(b) 10-story buildings

(a) 5-story buildings

HEV3

EV2

EV3

HEV4

(c) 15-story buildings

EV4

(d) 20-story buildings

Fig. 29. Plastic hinges distributions at D/H = 3%.

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5000

5000

4000

4000

Base shear force (kN)

Base shear force (kN)

M. Lian, M. Su

3000 2000

HEV1 EV1 IO LS CP

1000 0 0.0

0.5

1.0

1.5

2.0

2.5

3000 2000

HEV2 EV2 IO LS CP

1000 0 0.0

3.0

0.5

1.0

D/H (%)

(a) 5-story buildings

2.0

2.5

3.0

(b) 10-story buildings 9000

7000

8000

Base shear force (kN)

6000

Base shear force (kN)

1.5

D/H (%)

5000 4000 3000 HEV3 EV3 IO LS CP

2000 1000 0 0.0

0.5

1.0

1.5

2.0

7000 6000 5000 4000 HEV4 EV4 IO LS CP

3000 2000 1000

2.5

0 0.0

3.0

0.5

1.0

1.5

2.0

2.5

D/H (%)

D/H (%)

(c) 15-story buildings

(d) 20-story buildings

3.0

Fig. 30. Pushovers curves.

5. Conclusions Table 19 Strength at different stages of all buildings. Frames

HEV1 HEV2 HEV3 HEV4 EV1 EV2 EV3 EV4

Yielding strength

Maximum loadbearing capacity

Strength of IO

Strength of LS

Strength of CP

Vy (kN)

Vm (kN)

VIO (kN)

VLS (kN)

VCP (kN)

1040 1664 1966 2583 1117 1811 2126 2784

4386 4491 5922 7798 4359 4799 6610 8141

1326 1797 2301 2967 1739 2199 2807 3476

2469 3478 4406 5640 3349 4012 5346 6282

3044 4059 4961 6470 3862 4375 5818 6816

Static tests and shake table test were used to study the seismic performance of the HSSEBF-VSL specimens. Four HSSEBF-VSL buildings and four EBF-VSL buildings were designed and their FEMs were established by SAP2000. The FEMs of all buildings were analyzed using nonlinear pushover and dynamic analyses. Their seismic performance and total steel weight were verified by comparisons. The following conclusions can be drawn within the limitations of the research: (1) The HSSEBF-VSL with one-bay and one-story specimen had reliable load-bearing and ductility capacities under the static lateral pushover loads. The HSS frame could still resist the lateral loads when the shear links damaged, which indicated that the HSSEBF-VSL was a safe and dual system. (2) During the cyclic loading test, the hysteretic loops of HSSEBF-

Table 20 Characteristics of ground motions. Earthquake

Record

Pr. of exc. (% in 50 yrs)

Magnitude

Source distance (km)

PGA (g)

PGV (cm/s)

Scale factors

Imperial Valley Loma Prieta Cape Mendocino Landers Landers Kobe, Japan Kobe, Japan Kocaeli, Turkey Duzce, Turkey Manjil, Iran

IMPVALL/H-DLT352 LOMAP/G03000 CAPEMEND/RIO360 LANDERS/CLW-LN LANDERS/YER360 KOBE/NIS090 KOBE/SHI090 KOCAELI/ARC000 DUZCE/BOL090 MANJIL/ABBAR–L

50/10/2 50/10/2 50/10/2 50/10/2 50/10/2 50/10/2 50/10/2 50/10/2 50/10/2 50/10/2

6.53 6.93 7.01 7.28 7.28 6.9 6.9 7.51 7.14 7.37

12.45 12.82 14.33 19.74 23.62 7.08 19.15 13.49 12.04 12.56

0.24 0.56 0.39 0.28 0.24 0.51 0.24 0.22 0.73 0.51

26.0 35.6 44.1 25.6 51.4 37.3 37.8 17.7 56.4 42.8

0.29/0.83/1.67 0.13/0.36/0.71 0.18/0.51/1.03 0.25/0.71/1.43 0.29/0.83/1.67 0.14/0.39/0.78 0.29/0.83/1.67 0.32/0.91/1.82 0.10/0.27/0.55 0.14/0.39/0.78

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VSL with one-bay and one-story specimen were very plump. The specimen possessed stable and expanding hysteretic loops with no deterioration in the stiffness and load-bearing capacity. It indicated that the specimen had good plastic deformation and energy dissipation capacities. (3) The three-story specimen in the shake table test could resist the loads by severe earthquakes and there was no danger of the structure collapse. In the test specimen, the shear links dissipated the earthquake energy through the inelastic shear deformation. (4) The seismic performance of HSSEBF-VSL was slightly lower than that of conventional EBF-VSL if the HSSEBF-VSL was designed to match the member section strengths of conventional EBF-VSL under the same design conditions, but the HSS beams and columns using in HSSEBFVSL could reduce the total steel weight and improved economy. Moreover, HSSEBF-VSL performs best when structure height does not exceed fifteen stories.

0.30 Response spectrum of scaled ground motions Average spectra Design spectra in GB50011-2010 [PoE: 63% in 50 years. RP:50 years]

0.25 0.20 0.15 0.10 0.05

0

1

2

3

4

5

6

Period T (s) Fig. 31. Design spectra and scaled earthquake spectra.

10

5

9 8

4

3

Story

7

Story

IO

6

IO

5 4

2

3 HEV1 EV1

1 0.0

0.1

0.2

0.3

0.4

HEV2 EV2

2 0.5

1 0.0

0.6

0.1

Interstoty drifts (%)

IO

HEV3 EV3

0.1

0.2

0.3

0.3

0.4

0.5

0.6

(b) 10-story buildings

(a) 5-story buildings 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0.0

0.2

Interstoty drifts (%)

Story

0.00

Story

Acceleration response spectra Sa (g)

M. Lian, M. Su

0.4

0.5

0.6

20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0.0

IO

HEV4 EV4

0.1

0.2

0.3

0.4

Interstoty drifts (%)

Interstoty drifts (%)

(c) 15-story buildings

(d) 20-story buildings

Fig. 32. Mean maximum interstory drifts of frames during the earthquakes with pro. exc. of 50% in a 50-year period.

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0.5

0.6

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10

5

9 8

4

Story

Story

7

3

6

IO

LS

5 4

2

3 HEV1 EV1

IO 1 0.0

0.3

0.6

0.9

1.2

1.5

HEV2 EV2

2

LS

1 0.0

1.8

0.3

0.6

Story

Story

IO

LS

HEV3 EV3

0.3

0.6

0.9

1.2

1.5

1.8

(b) 10-story buildings

(a) 5-story buildings 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0.0

0.9

Interstoty drifts (%)

Interstoty drifts (%)

1.2

1.5

1.8

20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0.0

IO

LS

HY-20 Y-20

0.3

0.6

0.9

1.2

Interstoty drifts (%)

Interstoty drifts (%)

(c) 15-story buildings

(d) 20-story buildings

Fig. 33. Mean maximum interstory drifts of frames during the earthquakes with pro. exc. 10% in a 50-year period.

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1.5

1.8

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10

5 HEV1 EV1

9

HEV2 EV2

8

4

LS

3

Story

Story

7

CP

6

LS

5

CP

4 2

3 2

1 0.0

0.5

1.0

1.5

2.0

1 0.0

2.5

0.5

CP

LS

1.0

Story

Story

HEV3 EV3

0.5

1.5

2.0

2.5

(b) 10-story buildings

(a) 5-story buildings 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0.0

1.0

Interstoty drifts (%)

Interstoty drifts (%)

1.5

2.0

2.5

20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0.0

HEV4 EV4

CP

LS

0.5

1.0

1.5

2.0

2.5

Interstoty drifts (%)

Interstoty drifts (%)

(c) 15-story buildings

(d) 20-story buildings

Fig. 34. Mean maximum interstory drifts of frames during the earthquakes with pro. exc. of 2% in a 50-year period.

[6] M. Bosco, P.P. Rossi, Seismic behaviour of eccentrically braced frames, Eng. Struct. 31 (3) (2009) 664–674. [7] L. Mastrandrea, V. Piluso, Plastic design of eccentrically braced frames, I: moment–shear interaction, J. Constr. Steel Res. 65 (5) (2009) 1007–1014. [8] K.C. Lin, et al., Seismic reliability of steel framed buildings, Struct. Saf. 32 (3) (2010) 174–182. [9] M. Bosco, P.P. Rossi, A design procedure for dual eccentrically braced systems: analytical formulation, J. Constr. Steel Res. 80 (1) (2013) 440–452. [10] R. Montuori, E. Nastri, V. Piluso, Theory of plastic mechanism control for eccentrically braced frames with inverted y-scheme, J. Constr. Steel Res. 92 (2014) 122–135. [11] D.M. Yang, G.J. Hancock, Compression tests of high strength steel channel columns with interaction between local and distortional buckling, J. Struct. Eng. 130 (12) (2004) 1954–1963. [12] G. Shi, et al., Experimental study on column buckling of 420MPa high strength steel welded circular tubes, J. Constr. Steel Res. 100 (2014) 71–81. [13] B.W. Wang, et al., Seismic behavior of high strength steel welded beam–column members, J. Constr. Steel Res. 102 (11) (2014) 245–255. [14] G. Shi, et al., Local buckling behavior of welded stub columns with normal and high strength steels, J. Constr. Steel Res. 119 (2016) 144–153. [15] K.J. Rasmussen, G.J. Hancock, Plate slenderness limits for high strength steel sections, J. Constr. Steel Res. 23 (1) (1992) 73–96. [16] K.J. Rasmussen, G.J. Hancock, Tests of high strength steel columns, J. Constr. Steel Res. 34 (1) (1995) 27–52. [17] G. Pocock, High strength steel use in Australia, Japan and the US, Struct. Eng. 84 (21) (2006) 27–30. [18] GB50011-2010, Code for Seismic Design of Buildings, China Architecture & Building Press, Beijing (China), 2010 (in Chinese). [19] JGJ 99-98, Technical Specification for Steel Structure of Tall Buildings, China Architecture & Building Press, Beijing (China), 1998 (in Chinese). [20] AISC 341-10, Seismic Provisions for Structural Steel Buildings, (2010) (Chicago (USA)). [21] L.I. ZX, Theory and Technique of Engineering Structure Experiments, (2014) (Tianjin).

Table 21 Total steel weight comparison. Frames

Steel weight m1 (t)

Frames

Steel weight m2 (t)

(m2 − m1) / m2

HEV1 HEV2 HEV3 HEV4

179 445 990 1580

EV1 EV2 EV3 EV4

207 508 1111 1766

14% 12% 11% 10%

1. Acknowledgements The authors are grateful for the partial financial support from the National Natural Science Foundation of China (Grant No. 51178382). References [1] C.W. Roeder, E.P. Popov, Eccentrically braced steel frames for earthquake, J. Struct. Div. 104 (3) (1978) 391–412. [2] K.D. Hjelmstad, E.P. Popov, Characteristics of eccentrically braced frames, J. Struct. Eng. 110 (2) (1982) 340–353. [3] K.D. Hjelmstad, E.P. Popov, Cyclic behavior and design of link beams, J. Struct. Eng. 109 (10) (1983) 2387–2403. [4] K. Kasai, E.P. Popov, Cyclic web buckling control for shear link beams, J. Struct. Eng. 112 (3) (1986) 505–523. [5] D. Dubina, A. Stratan, F. Dinu, Dual high-strength steel eccentrically braced frames with removable links, Earthq. Eng. Struct. Dyn. 37 (7) (2008) 1703–1720.

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