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Flexural behavior of beam to column joints with or without an overlying concrete slab
Engineering Structures 199 (2019) 109616
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Flexural behavior of beam to column joints with or without an overlying concrete slab
T
Ben Moua,b, Fei Zhaoa, Qiyun Qiaoc, , Lingling Wanga, Haitao Lib, Baojie Hea, Zhiyu Haoa ⁎
a
School of Civil Engineering, Qingdao University of Technology, Qingdao 2660332, China College of Civil Engineering, Nanjing Forestry University, Nanjing 210037, China c College of Architecture and Civil Engineering Beijing University of Technology, Beijing 100124, China b
ARTICLE INFO
ABSTRACT
Keywords: Beam column joint Composite action Flexure behavior
Composite action between a steel frame and an overlying slab plays an important role in the structure design of a beam-column joint in a steel or composite framed structure. This research investigates the seismic performance of a joint between a steel beam and a hollow square steel (HSS) or a concrete filled square tubular (CFST) column with or without an overlying concrete slab. The objective of this research is to evaluate the composite action between the steel girder and concrete slab. Four T-shaped beam to column joints are tested under cyclic loadings. The main experimental parameters are column type (HSS or CSFT) and concrete slab (with or without). Secondly, the seismic behavior of the joint is investigated in terms of failure mode, hysteretic behavior, skeleton curve, stiffness degradation, and strain distribution. Plastic deformation is concentrated at the beam end and brittle fracture is effectively avoided in the vicinity of the beam-to-column joints. All the tested specimens exhibit excellent energy dissipation capacity and ductility. The composite action between a steel girder and a concrete slab significantly enhance the capacity of the joint in terms of stiffness and yield bending moment. The plastic bending moment capacity is, however, slightly improved.
1. Introduction Earthquake is not necessarily a single event and it can have a series of active quakes (foreshock, main-shocks), such as in Kumamoto of Kyushu Island (Japan) in April 16. More than 100 steel school buildings [1] were damaged because of unexpected brittle fractures that occurred near beam-column joints, especially near the welded part between a hollow square steel column and a composite beam flange (Fig. 1). One particular observation was that overlying concrete slab markedly affected the stress distribution around the joint. When composite beams were subjected to a sagging moment, floor slab mobilized the high compressive capacity of concrete and improved the compressive resistance of the upper beam flange. However, when the composite beams were subjected to a hogging moment, only the bottom beam flange resisted the bending moment, thereby causing the brittle fracture of the bottom beam flange during the severe earthquake [2,3]. In the past three decades, a series of experimental and numerical studies were conducted to investigate the composite effect on the stiffness and strength of composite joints. The main failure modes were the steel bar fracture, brittle fracture of welded parts, local buckling of column flange, shear buckling of joint, shear buckling of panel zone,
⁎
and yield buckling of girder flange or web [4–10]. Cheng and Chen [4] experimentally studied six composite steel beam joint specimens, and found that the initial stiffness and the ultimate strength of the composite beam were increased by 67% and 27% on average, compared to those of a bare steel beam. Leon et al. [5] surveyed the seismic performance of interior steel moment-resisting beam-column joints. All specimens with concrete slab failed at the welded interface of the bottom girder flange and the column flange. The strains near the bottom flange of the specimens with concrete slab were several times larger than those near the top flange [6]. Khalid et al. [7] revealed the efficiency of carbon fiber reinforced polymer (CFRP) composite retrofit in improving the slab behavior under blast loading with different loading durations. Fan et al. [8] presented test results of 6 composite beam to CFSST (concrete-filled square steel tubular) column joints. It was found that the ultimate strength, stiffness and ductility were enhanced by the composite action. Testing on four internal joints and four external joints with concrete slab, Silva et al. [9] found that the symmetric loading and steel-reinforced concrete (SRC) column were the two main parameters that increased the bending moment and initial stiffness of a joint. Based on the experimental and analytical data, Liew et al. [10,11]
Corresponding author. E-mail address: [email protected] (Q. Qiao).
https://doi.org/10.1016/j.engstruct.2019.109616 Received 26 May 2019; Received in revised form 31 July 2019; Accepted 31 August 2019 Available online 09 September 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.
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2. Experiment 2.1. Test specimens Four T-shaped specimens were tested in terms of seismic behavior of composite beam-column joints. All specimens and details of the concrete slab are shown in Fig. 2 and Table 1. The main test parameters were joints with or without a concrete slab. As shown in Table 1, two joints with an overlying concrete slab and two joints without a concrete slab were tested. Specimen No.1 was a bare beam-column joint. The column height of No.1 was 1400 mm and was made by cold bending a square tube, which was a 200 × 200 × 9 mm hollow steel tube section and manufactured according to BCR295 [27]. The beam length of No.1 was 1500 mm, and was constructed as a built-up beam with two pieces of flange plates (300 × 6 mm) and a web plate (120 × 12 mm), which was made as SN490B [27]. The beam flanges had the same sickness as that of outer annular stiffener, which were welded to the square steel hollow column with full penetration butt weld and an additional fillet weld of 13 mm thickness. Gas metal arc welding with CO2 shielding was adopted to fabricate the welded parts of the test specimens. LB-52 [27] were selected as the welding electrodes, which was a specified minimum Charpy V-type Notch (CVN) toughness of 80 Joule at −20 degree centigrade. Specimen No.2 had the same properties as those of No.1, except for 85 mm thick reinforced concrete slab. Shear studs were set along the centerline of the beam flange at a uniform spacing of 100 mm to connect the beam with the RC slab. The details of RC slab are shown in Table 2. Furthermore, orthogonal beams were set to support the RC slab. Specimen No.3 has the same properties as No.1, except for the column was a CFST column. Moreover, specimen No.4 had the same properties as those for No.3, but with the addition of a concrete slab. According to design of connections in steel structures [28], the details of annular stiffener is shown in Fig. 2(e) and (g). Annular stiffeners play significant role in relocating the plastic hinge formation. The length of the annular stiffener, a, can be calculated by Eq. (1).
Fig. 1. Brittle fracture on the welded part between a hollow square steel column and a composite beam flange.
indicated that the Eurocode [12] overestimates the initial rotational stiffness under the hogging moment. Based on full-scale tests on composite beam to column joint, Green et al. [13] investigated the force transfer mechanism of the concrete slab. Thanoon et al. [14] investigated the structural behavior of cracked reinforced concrete oneway slab. Bui et al. [15] conducted the shear test of concrete slab under a concentrated load and quantified the shear behavior and the failure modes of slab with the influence of axial forces. Beckmann et al. [16] compared concrete specimens with and without additional fabric strengthening, and showed that substantial advantages in the resistance to the impact load and to the penetration of the impactor were seen for slabs with a strengthening layer. Fu and Lam [17] focused on the seismic behavior of semi-rigid composite joints with precast hollow core slabs. Mello et al.[18] presented an extensive parametric study of the dynamic response of composite floors, in terms of peak accelerations. Peter et al. [19] investigated the effect of confinement from the surrounding slab on the axial capacity of the columns. These studies mainly concentrated on the influence of concrete slab on stiffness, bearing capacity, ductility, and energy dissipation capacity. Qiao et al. [20] conducted the seismic behavior of innovative exposed concrete filled steel tube (CFST) column base, which takes the effect of embedded reinforcing bars into consideration. Pisano et al [21–23] researched on the flexural behavior of steel-reinforced concrete beam. Although beam-column joint with outer annular stiffener has good seismic performance [24–26], few researchers study on the seismic behavior of composite beam-column joint with outer annular stiffener. In order to investigate the seismic behavior and failure modes of a composite beam-column joint with outer annular stiffener, four specimens are fabricated and tested under cyclic loading in this paper. The composite action between the steel girder and concrete slab are discussed in detail. Moreover, six indices, affecting the seismic behavior of composite joints, are clarified, namely, stiffness, bearing capacity, ductility, energy dissipation capacity, hysteresis characteristics and damage modes. This paper aims to provide an experimental evidence for evaluating and designing the composite joints with outer annular stiffener.
a=
4h d + D 2
Bd
(1)
where hd is the depth of the annular stiffener; D is the width of column; Bd is the end width of the annular stiffener; a is the distance from surface of steel tube to edge of the annular stiffener. 2.2. Material properties of steel and concrete According to JIS Z2241 [29], the material properties of steel were obtained by performing coupon tests. For each thickness category (12.1 mm, 9.1 mm and 6.2 mm), three identical specimens were tested in a 20 ton testing machine. Table 3 shows the material properties of the steel parts used in this study, namely, thickness (t), young’s modulus (ES), yield strength (бy), tensile strength (бu), yield ratio (бy/бu), and elongation (δ). Yield strength was taken as the lower yield point as obtained from the test data. Young’s modulus was measured as the secant stiffness between points corresponding to a stress of 1/3 of yield strength to 2/3 of yield strength. The compression strength of concrete was obtained by testing concrete cubes according to JIS A1108 [30]. Three identical concrete cubes were tested in a uniaxial compressive strength testing machine. Before testing, the cube specimens were prepared by pouring properly mixed concrete mixture into cylinder standard molds and by curing the cube specimens for 28 days after demolding.
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450 450 50
250
150
Steel bar HRB335, B 10, @100
150
Beam 300×120×6×12
Beam 300×120×6×12
55
120
13
250
50
Column 200×200×9
13
110
9
Beam web Stud (d13-60 @100)
35 Outer annular stiffener (PL-12)
Slit
Outer annular stiffener (PL-12)
(a) Plan of No.1 and No.3
12 300 276
12 276
13
12
13
12
300
Beam 300×120×6×12
13
Stud (d13-60 @100) Beam 300×120×6×12
Column 200×200×9 13
85
Column 200×200×9
(b) Plan of No.2 and 4
9 9 35
35
(c) Elevation of No.1 and No.3 50
450 250
(d) Elevation of No.2 and No.4
150
Outer annular stiffener
Seam
35° Beam flange
300
120
60
150
150
60
Beam web
50
250 450
Column
Beam web
13 13
450
Weld (13mm)
(e) Details of the annular stiffener
(f) Details of the weld part
Fig. 2. Details of specimens.
2.3. Testing device and loading plan
limited specimens to move in the horizontal direction, but allowed specimens to rotate in the YZ plane. The distance between the two supports was 1800 mm. An actuator with 500 kN capacity was used to apply the vertical loads at the end of the beam. Two lateral supports were set on both sides of the beam, near the loading point in order to prevent the torsional deformation of the beam. Fig. 4 shows the loading history [31]. All the joint specimens were
Fig. 3 illustrates the overall views of the testing device. The column was arranged in the vertical direction without any axial load. The upper column was connected to the reaction frame by a vertical sliding hinge (roller pin) support, which allowed the upper column to move in the vertical direction. A pin support was set at the bottom column, which
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hd D
45o
45o
b Bd=Bf
a
b
(g) Symbols of annular stiffener
(h) Photograph of specimen No.3
(i) Photograph of specimen No.4 Fig. 2. (continued)
Table 1 Basic specimen information. Specimen
Column
Beam
Concrete slab
Column
Compressive stress (Mpa)
No.1 No.2 No.3 No.4
200 × 200 × 9
BH300 × 120 × 6 × 12
Without slab With slab Without slab With slab
HSS HSS CFT CFT
/ / 40.2 40.6
Table 2 Basic RC slab information. Specimen
Compressive strength/(Mpa)
Thickness/(mm)
Breadth/(mm)
Length/(mm)
Steel bar
Stud
No.2 No.4
34 21
85
1000
1450
B 10@100
d13-60 @100 × 11
Table 3 Material properties of steel. Member
t (mm)
ES (MPa)
бy (MPa)
бu (MPa)
бy/бu (%)
δ (%)
Outer annular stiffener, Beam flange Weld metal Beam web Square column Steel bar
12.1 13.2 6.2 9.1 –
193,000 205,000 200,000 197,000 184,000
398 406 398 408 341
529 533 546 532 442
75 76 73 77 77
21 16 22 24 21
tested under a cyclic loading and the load was applied in a displacementcontrolled mode. The test history began with two cycles repeated for story drift angle (R) amplitudes of ± 0.005, ± 0.01, ± 0.02, ± 0.03, and ± 0.04 rad. If no fracture was triggered at R = 0.04 rad, the test procedure would enter into R = 0.05 rad. It should be noted that many identical cycles were applied at R = 0.05 rad in order to investigate the low-cycle
fatigue behavior at large drift amplitude. When fracture occurred, the final cycle with R = 0.08 rad was applied in the sagging direction. The story drift angle (R) was defined as shown in Fig. 5 and can be expressed as Eq. (2),
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δU
Reaction frame
Oil jack
θb
Lc
R
Roller pin
Beam
V1 Lb
Slab
Out-of-plane movement restraint device
δL
Pin
Fig. 5. An illustration of the deformation of a specimen.
(a) Testing device and test specimen
Uu ht Ul Lt
V2
V1
(b) Photograph of a specimen placed in the testing device Fig. 3. Testing device.
Fig. 6. Set up of the displacement transducer.
Peak bending point
M Mmax 1/6
Plastic bending point
1/3
Yield bending point
θy Fig. 4. Loading history.
R=
V1 Lb
U
L
Lc
θp
θm
θu
θ
Fig. 7. Definition of characteristic points in the moment-curvature diagram.
(2)
2.4. Measurements
where V1 is vertical displacement of the loading point; Lb is the calculated beam length, which was measured from the centerline of the column to the loading point; δU is the horizontal deformation of upper column; δL is the horizontal deformation of bottom column; and Lc is the calculated column length, which was measured from the sliding hinge support to the pin support.
The beam rotation angel (θb), as shown in Fig. 5 and Fig. 6, was obtained from Eq. (3) as,
b
5
=
V1
V2 Lt
Ul
Uu ht
(3)
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(a) Photograph of specimen No.1
(b) Local buckling of the outer annular stiffener
(c) Brittle fracture of the welded part
(d) Tearing of the outer annular stiffener
(e) Photograph of specimen No.2
(f) Brittle fracture of welded part
(g) Cracking of HSS column
(h) Cracking of concrete slab
Fig. 8. Photographs showing failure phenomena.
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(i) Photograph of specimen No.3
(j) Local bucking of the upper beam flange
(k) Cracking of the upper outer annular stiffener
(l) Buckling of the beam web
(m) Photograph of specimen No.4
(n) Distance between CFT column and concrete slab
(o) Cracking of the lower outer annular stiffener
(p) Cracking of concrete slab
Fig. 8. (continued)
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400
400
200
200
M /kN•m
M /kN•m
B. Mou, et al.
0 -0.09 -0.06 -0.03 0.00 0.03 0.06 0.09
0 -0.09 -0.06 -0.03 0.00 0.03 0.06 0.09
-200
-200
-400
-400
θb/rad
θb/rad
(b) No.2
400
400
200
200
M/kN•m
M/kN•m
(a) No.1
0 -0.09 -0.06 -0.03 0.00 0.03 0.06 0.09
0 -0.09 -0.06 -0.03 0.00 0.03 0.06 0.09
-200
-200
-400
-400
θb/rad
θb/rad
(c) No.3
(d) No.4
M/kN•m
Fig. 9. Beam rotation angle and bending moment curves of specimens.
300
2.5. Deformation at key indexes in the moment–curvature diagram
200
The key indexes of the specimens, including yield bending point (My), plastic bending point (Mp), peak bending point (Mm) and ultimate bending point(Mu), could be determined in the skeleton curve, as shown in Fig. 7. The stiffness (K) is the secant modulus, which was the stiffness corresponding to the positive peak loads in the first cycle when the story drift angle was equal to 0.005 rad. The yield and plastic bending points could be obtained by the slope factor method [26], and were determined as the tangent points of lines with slopes of 1/3 K and 1/6 K, respectively. Peak bending point was the maximum bending point.
100 -0.04
-0.02
0 0.00 -100
0.02
-200 -300
θ/rad
0.04
NO.1 NO.2 NO.3 NO.4
3. Experimental results
Fig. 10. Envelope curves of four T-shaped specimens.
3.1. Failure mode Before R = 0.01 rad, all the specimens stayed in the elastic stage. Moreover, the hysteresis curves between beam rotation angle and beam bending moment were linear. When R ≥ 0.02 rad, hysteresis curves showed an obvious bending phenomenon. All the specimens entered into plastic stage. Brittle fracture occurred in all specimens
where V2 is vertical displacement of the beam end near the column; Lt is the horizontal distance between the loading point and the beam end measured point; Uu is the horizontal displacement of the upper column; Ul is the horizontal displacement of the lower column; and ht is the displacement between the two displacement transducers. Table 4 Experimental stiffness and bending moment of specimens. No
Loading direction
Ke (kN·m/rad)
My (kN·m)
θy (rad)
Mp (kN·m)
θp (rad)
Mm (kN·m)
θm (rad)
Failure mode
1
Sagging Hogging Sagging Hogging Sagging Hogging Sagging Hogging
20,000 24,000 42,000 25,000 25,000 24,000 37,000 31,000
170 159 186 167 203 196 237 191
0.012 0.010 0.006 0.010 0.012 0.011 0.009 0.010
209 212 236 216 250 244 266 248
0.023 0.019 0.013 0.018 0.020 0.019 0.016 0.017
263 262 323 268 299 301 325 292
0.045 0.046 0.044 0.047 0.047 0.046 0.036 0.037
Fracture between outer annular stiffener and lower beam flange
2 3 4
8
Fracture between outer annular stiffener and HSS column Fracture between outer annular stiffener and upper beam flange Fracture between outer annular stiffener and lower beam flange
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30
Kj/kN•rad-1
-1
Kj/kN•rad
20
10
0 0.00
0.01
0.02
0.03 R/rad
Sagging Hogging
40
Sagging Hogging
0.04
30 20 10 0 0.00
0.05
0.01
30
0.05
40 Sagging Hogging
20
10
0 0.00
0.01
0.02 0.03 R/rad
Sagging Hogging
30
Kj/kN•rad-1
-1
0.04
(b) No.2
(a) No.1
Kj/kN•rad
0.02 0.03 R/rad
0.04
20 10 0 0.00
0.05
0.01
0.02 0.03 R/rad
0.04
0.05
(d) No.4
(c) No.3 Fig. 11. K-θ curves of the test specimens.
surface of the HSS column. The lower outer annular stiffener experienced local buckling. Meanwhile, the column flange appeared concave and developed visible compressive deformation. As shown in Fig. 8(f), a brittle fracture was observed in the welded joint between the lower outer annular stiffener and the HSS column in the second cycle of R = 0.05 rad. Owing to stress concentration, the corner of the HSS column was cracked in the fourth cycle of R = 0.05 rad, as shown in Fig. 8(g). The maximum bending moment of specimen No.2 was 323 kN·m and 268 kN·m in the sagging and hogging directions, respectively. Compared to specimen No. 1, the composite effect caused by concrete slab in specimen No. 2 markedly increased the ultimate bearing moment of the specimens. Fig. 8(i) shows the final stage of specimen No.3 before failure. Response of specimen No.3 was similar to that of No.1 in the elastic stage. When R = 0.03 rad, the upper beam flange showed obvious local buckling, as shown in Fig. 8(j). The upper outer annular stiffener was torn out in the sixth cycle of R = 0.05 rad. The crack expanded diagonally at 45 degrees to the outer annular stiffener, as shown in Fig. 8(k). The web of the beam buckled in the same time, as shown in Fig. 8 (l). The maximum bending moment of specimen No.3 was 299 kN·m and 301 kN·m in the sagging and hogging directions, respectively. It showed that the bending moment of CFT column specimen was larger than that of HSS column specimen. Fig. 8(m) shows the final stage of specimen No.4. Specimen No.4 was similar to No.3 in the elastic stage. As shown in Fig. 8(n), the separated distance between CFT column and concrete slab was 18 mm when R = 0.05 rad. The lower outer annular stiffener was torn out in the sixth cycle of R = 0.05 rad, as shown in Fig. 8(o). This demonstrates that the concrete slab improved the bending moment capacity of the upper outer annular stiffener. The maximum bending moment of No.1 was 325 kN·m and 292 kN·m in the sagging and hogging directions, respectively.
Table 5 Kp/Ky, K0.05rad/Ky and Km/Ky. NO.
Loading direction
Kp/Ky
Km/Ky
K0.05rad/Ky
1
Sagging Hogging Sagging Hogging Sagging Hogging Sagging Hogging
0.64 0.70 0.58 0.71 0.74 0.72 0.63 0.76
0.41 0.36 0.24 0.34 0.38 0.37 0.34 0.41
0.42 0.37 0.22 0.33 0.38 0.35 0.29 0.34
2 3 4
corresponding to the R = 0.05 rad loading cycle. Fig. 8(a) shows the final stage of specimen No.1. For specimen No.1, local buckling was initiated in the upper portion of the outer annular stiffener in the first cycle of R = 0.03 rad, as shown in Fig. 8(b). Brittle fracture was observed in the welded joint between the lower outer annular stiffener and HSS column in the second cycle of R = 0.05 rad, as shown in Fig. 8(c). After another two cycles of R = 0.05 rad, cracks occurred at the welded joint between the lower beam flange and the outer annular stiffener. Meanwhile, the outer annular stiffener was torn apart, as shown in Fig. 8(d). The maximum bending moment of specimen No.1 was 263 kN·m and 262 kN·m in the sagging and hogging directions, respectively. The two value were similar to each other indicating that the loading direction had a little impact on the bending moment capacity of the specimens. Fig. 8(e) shows the final stage of specimen No.2 before failure. When R = 0.01 rad in the first loading circle, a longitudinal crack was initiated in the concrete slab around the HSS column. When R = 0.03 rad, the longitudinal crack of concrete slab extended rapidly and a transverse crack was observed approximately 35 cm from the
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Sagging Hogging
1.05
1.02
ηj
ηj
1.02 0.99
-0.04
-0.02
0.00
0.02
0.04
0.93 -0.06
0.06
-0.02
0.00
0.02
R/rad
(a) NO.1
(b) NO.2
Sagging Hogging
0.04
0.06
Sagging Hogging
1.05
1.02
1.02
ηj
ηj
-0.04
R/rad
1.05
0.99 0.96 0.93 -0.06
0.99 0.96
0.96 0.93 -0.06
Sagging Hogging
1.05
0.99 0.96
-0.04
-0.02
0.00
0.02
0.04
0.93 -0.06
0.06
-0.04
R/rad
-0.02
0.00
0.02
0.04
0.06
R/rad
(d) NO.4
(c) NO.3 Fig. 12. ηj-θ curves of specimens.
200
200 NO.1 NO.2
100 50 0 0.00
NO.3 NO.4
150
E/kN•m
E/kN•m
150
100 50 0
0.01
0.02
0.03
0.04
0.05
0.00
0.01
0.02
R/rad
0.03
0.04
0.05
0.04
0.05
R/rad Fig. 13. E-R curves of specimens.
300
300 250
150 100
150 100 50
50
0
0 0.00
NO.3 NO.4
200
Ea/kN•m
200
Ea/kN•m
250
NO.1 NO.2
0.01
0.02
0.03
0.04
0.00
0.05
R/rad
0.01
0.02
0.03
R/rad Fig. 14. Ea-R curves of specimens.
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Table 6 Equivalent viscous damping coefficient at yield, plastic and R = 0.05 rad state. Specimen
he,y
he,p
he,0.05rad
No.1 No.2 No.3 No.4
0.138 0.152 0.133 0.132
0.186 0.139 0.180 0.132
0.224 0.229 0.222 0.225
decreased with the cyclic loading. Stiffness degradation is one of the most important indices to develop computational models and to capture the seismic behavior of specimens. Stiffness degradation was calculated by the following equation:
Fig. 15. Basis to calculate the equivalent viscous damping coefficient.
2
Kj = i=1
3.2. Hysteretic performance
For a given inter-layer drift angle, the shear capacity decreased with an increase in the number of cycles. The shear capacity degradation was calculated by the following equation:
Fig. 10 shows the envelope curves of all specimens. Moreover, Table 4 shows the main performance point such as stiffness (Ke), yield bending point (θy, My), plastic bending point (θp, Mp), and maximum bending point (θm, Mm). Owing to the composite effect of concrete slab, the bearing capacities of specimen No.2 and No.4 improved generally. The My, Mp and Mm of specimen No.2 increased by 21.28%, 17.34% and 14.29%, respectively, when compared to those of No.1. Likewise, My, Mp and Mm of specimen No.4 increased by 21.25%, 13.72% and 5.20%, respectively, when compared to those of specimen No.3.
j
=
Due to the accumulated damage, the stiffness of the specimens
ξeq/kN•m
0.1
0.02
0.03
0.04
(5)
M1, j
0.2
NO.1 NO.2
0.01
M2, j
where ηj is the shear capacity degradation factor at the class j loading; M1,j is the maximum bending moment at the class j loading of the second cycle; and M2,j is the maximum bending moment at the class j loading of the second cycle. Fig. 12 shows the degradation of the shear capacity of all specimens. The trend of variation in the degradation of the shear capacity of all specimens was approximately the same. The degradation coefficient of shear capacity decreased with an increase in drift angle.
3.4. Stiffness degradation
0.0 0.00
(4)
3.5. Bending moment capacity degradation
3.3. Envelope curves of moment-curvature and the characteristic points
0.2
i, j i=1
where Mi,j is the maximum bending moment at the class j loading of the second cycle of i, and θi,j is the beam end rotation corresponding to Mi,j. Fig. 11 shows the stiffness degradation of all the four specimens. Table 5 presents the stiffness ratio between the plastic bending point and the yield bending point (Kp/Ky), the stiffness ratio between the maximum bending point and the yield point (Km/Ky) and the stiffness ratio between a point in R = 0.05 rad and the yield bending point (K0.05rad/Ky). Kp/Ky and Km/Ky of specimen No.2 and No.4 had a large difference, compared to specimen No.1 and No.3. However, K0.05rad/Ky of all specimens was in a range of 0.36–0.48. This is attributed to the fact that due to the crushing of the concrete slab, composite action was diminished.
The curves of bending moment and beam rotation angle are illustrated in Fig. 9. The black solid circles represent the maximum bending moment of tested specimens. All the curves of the T-shaped specimens are plump and similar to each other. When R ≤ 0.01 rad, the curves were linear. All the four T-shaped specimens stayed in the elastic stage. When R exceed 0.01 rad, the hysteretic curve was bent and the specimens entered into the plastic stage. Bearing capacity began to degrade when R = 0.05 rad and brittle fracture occurred in all specimens at this loading level. During the whole test process, all specimens showed excellent ductility as evidenced by the stable hysteretic curves. In addition, according to the composite effect of the floor slab, the sagging bending moment of specimens No.2 and No.4 decreased by 20.52% and 11.70% respectively, when compared to the hogging bending moment.
ξeq/kN•m
2
Mi, j /
0.1
0.0 0.00
0.05
NO.3 NO.4
R/rad
0.01
0.02
0.03
R/rad Fig. 16. ξeq–R curves of specimens.
11
0.04
0.05
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Rigid plate Column
1
1
0
0 0
z
ux uy uz
1
θx θy θ z
x
y
1：restrain 0：free
Weld Slab
Concrete layer Steel layer
1
1
1
0
0
0
Beam Rigid plate
Loading point
(b) Shell element of concrete slab
(a) Finite element models
40
700
Stress (N/mm )
600 500 400 0.0
30
2
2
True stress(N/mm )
800
Outer annular stiffener, beam flange Fillet weld metal Beam web Column
0.1 0.2 Plastic strain
20 10 0
0.3
0.1fc
-10
(c) True stress-plastic strain curves for steelpart
0.2fc
0.002 0.004 Strain
0.006
(d) Stress-strain relation for concrete slab
Fig. 17. Finite element models.
3.6. Energy dissipation capacity
indices to evaluate the energy dissipating capacity of the test specimens. Fig. 15 illustrates the calculation diagram for one hysteresis loop. The equivalent viscous damping coefficient was obtained by Eq. (6) as:
The area of hysteresis loops represents the dissipated energy in each cycle for all specimens. Fig. 13 and Fig. 14 show the dissipated energy for each cycle (E), and the cumulative energy consumption (Ea), respectively. When R was less than 0.01 rad, all specimens were in the elastic range; no plastic deformation was observed and the dissipated energy was almost zero. When R reached 0.01 rad, E and Ea increased slowly. After R reached 0.04 rad, obvious differences were obtained among the specimens. The energy dissipation capacity of specimens with CFST column was higher than that of specimens with HSS column. Moreover, the energy dissipation capacity of specimens with a concrete slab was smaller than that of specimens without a concrete slab. The total energy consumption was mainly related to the deformation capacity of the specimens. Equivalent viscous damping ratio (ξ) was one of the important
=
1 SABC + SCDA · 2 SOBE + SODF
(6)
where, SABC + SCDA indicates the area of hysteresis loop in one cycle; and SOBE + SODE indicates the area of the corresponding triangle. Fig. 16 shows the relationship between the equivalent viscous damping coefficients (he) of each specimen and the story drift angle. The coefficient he increased gradually with an increase in the rotation angle of specimens but at a decreasing rate. Table 6 lists the equivalent viscous damping corresponding to R = 0.05 rad (he,0.05rad) for all specimens. It is observed that the equivalent viscous damping coefficients of specimens without concrete slab were almost equal to each other at the three characteristic points. Similarly, he,0.05rad of all specimens were similar because composite girder lost its composite action at
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400
200
200
M/kN·m
M/kN·m
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0 -0.09 -0.06 -0.03 0.00 0.03 0.06 0.09 -200
0 -0.09 -0.06 -0.03 0.00 0.03 0.06 0.09 -200
Experiment Analysis
-400 θ /rad
-400 θ /rad
(a) No.1
(b) No.2 400
200
200
M/kN·m
M/kN·m
400
0 -0.09 -0.06 -0.03 0.00 0.03 0.06 0.09 -200
Experiment Analysis
Experiment Analysis
-0.09
-0.06
-0.03
0 0.00
0.03
-200
-400 θ /rad
-400
0.06
0.09
Experiment Analysis
θ /rad
(c) No.3
(d) No.4
Fig. 18. Comparison of hysteretic curves from the finite element analysis and the test.
R = 0.05 rad. During the tested process, he,y, he,p and he,0.05rad ranged from 0.132 to 0.38, 0.132 to 0.186, and 0.222 to 0.229, respectively.
issue, and therefore accommodating these cracks dominates the development of this material model. Cracking model was chosen as damage effects [32]. Buyukozturk model was chosen as the yield criterion of concrete [36]. In order to accurately simulate the experimental loading process, rigid plates were placed at both ends of the column in the finite element model, and boundary conditions were imposed on the column through the rigid plate as shown in Fig. 17(a). The rigid plate at the bottom of the column was used to simulate the fixed hinge support in the loading device. Boundary conditions were given to limit the translational displacement in the three directions of ux, uy and uz and the rotation in the θx and θz directions, while allowing the rotation in the θy direction. The rigid plate on the top of the column was used to simulate the sliding hinge support of the loading device. Boundary conditions were given to restrain the translational displacement in the ux and uy directions and the rotation in the θx and θz directions, while allowing the column to undergo vertical deformation in the direction of uz and to rotate in the θy direction. The vertical loading applied on the loading point are controlled with the same loading history as experimental tests in order to simulate the story drift angle caused by lateral loading, as shown in Fig. 17(a).
4. Finite element analysis 4.1. Finite element models Based on the tested specimens, finite element models were established by using the software MSC. Marc 2012 [32]. The analytical model was composed of a rigid plate, an H-beam, an octagonal outer annular stiffener, fillet weld, a square steel tube column and a concrete slab. In order to improve the calculation efficiency, symmetry of the test specimen was used to establish a half-side model along the beam center line, as shown in Fig. 17(a). All parts were meshed by Element type 7, which is 8-node, isoparametric, arbitrary hexahedral solid element. In order to improve the calculation effect, concrete slab were meshed by shell elements. According to the principle of volume equivalent substitution, the concrete slab was divided into 19 layers, as shown in Fig. 17(b). The middle layer is steel bar with the thickness of 1.2 mm. Moreover, one layer with the thickness of 1.9 mm and 8 layers with the thickness of 5 mm are set from the inside to outside on both sides. Steel is modelled by elasto-plastic material, which behave as nonlinear isotropic model. True stress-logarithmic strain curves from coupon tests are used to specify the nonlinear parts [33]. Yield criterion is based on the von Mises yield criterion, and kinematic hardening rule is adopted in the analysis [34]. True stress-logarithmic plastic strain curves for all parts are shown in Fig. 17(c). Poisson’s ratio of concrete and Young’s modulus were assumed as 0.2 was 30 GPa, respectively. Stress-strain relationship of concrete are shown in Fig. 17(d). In addition, a linear ending of 0.2 fc residual strength was assumed [35]. Cracking was considered to be an important
4.2. Results of numerical analysis 4.2.1. Comparison of hysteretic curves Fig. 18 compares the hysteresis curves from the finite element analysis and the experiment. The finite element analysis curve agreed well with the test data. While, the peak moment obtained by the finite element model was slightly larger than that obtained from the experiment. Moreover, the hysteretic curves of the finite element model were smoother and fuller when compared to the test. This is attributed to the
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Fig. 19. Comparison of failure modes of specimens from the finite element analysis and the test.
fact that the finite element model did not consider the initial defects of the specimens and the stress concentration factor during the welding process. In general, the hysteresis curve of finite element analysis agreed well to the experimental results. Therefore, the finite element method could be used as an effective tool to study the performance of this joint.
and numerical analyses were performed. The following conclusions were drawn: (1) The composite action of the floor slab and the steel beam was particularly significant under the sagging moment. (2) The beam-to-column connection with outer annular stiffener was helpful to make the plastic hinge away from the connection and to effectively avoid the occurrence of the fracture in the vicinity of the weld. However, owing to the effect of a concrete slab, there is a possibility of fracture near the connection for this type of connection. (3) The hysteresis curves were stable for all specimens. In the plastic stage, the equivalent viscous damping coefficients of the specimens without slab were slightly larger when compared to the specimens with a concrete slab. Before that, the coefficients were almost equal for all specimens when the story drift angle reached 0.05 rad. (4) Results from finite element analysis were in good agreement with the experimental results. Finite element models as proposed in this study will be utilized to perform parametric studies in future.
4.2.2. Comparison of failure modes Fig. 19 compares the failure modes as obtained by the finite element analysis and the test results of the specimens. The yield stress of column and beam was 408 and 398 MPa, respectively. The joint failure mode obtained from finite element analysis was basically similar to that observed in the experiment. Plastic deformation was mainly concentrated at the joint between the outer annular stiffener and the beam, and at the welded part of the column ring. The stress concentration region obtained in the finite element analysis was the fracture location in the experiment, thus confirming the accuracy of the finite element model. 5. Conclusions This paper investigated the flexure behavior of a beam to column joint in a steel frame with an overlying concrete slab. Both experimental
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Fig. 19. (continued)
Declaration of Competing Interest
1998;20(4-6):249–60. [4] Cheng Chin-Tung, Chen Cheng-Chih. Seismic behavior of steel beam and reinforced concrete column connections. J Constr Steel Res 2005;61:587–606. [5] Leon Roberto T, Hajjar Jerome F, Michael A, et al. Seismic response of composite moment-resisting connections. I: Performance. J Struct Eng ASCE 1998;124(8):868–76. [6] Hajjar Jerome F, Leon Roberto T, Members Z, et al. Seismic response of composite moment-resisting connections. II: Behavior. J Struct Eng, ASCE 1998;124(8):877–85. [7] Mosalam Khalid M, Mosallam Ayman S. Nonlinear transient analysis of reinforced concrete slabs subjected to blast loading and retrofitted with CFRP composites. Compos: Plan B 2001;32:623–36. [8] Fan JS, Li QW, Nie JG, Zhou H. Experimental study on the seismic performance of 3D joints between concrete-filled square steel tubular columns and composite beams. J Struct Eng, ASCE 2014;140(12):04014094. [9] Silva LS, Simoes RD, Cruz PJS. Experimental behaviour of end-plate beam-tocolumn composite joints under monotonical loading. Eng Struct 2001;23(11):1383–409. [10] Richard Liew JY, Teo TH, Shanmugam NE. Composite joints subject to reversal of loading—Part 1: experimental study. J Constr Steel Res 2004;60(2):221–46. [11] Richard Liew JY, Teo TH, Shanmugam NE. Composite joints subject to reversal of loading— Part 2: analytical assessments. J Constr Steel Res 2004;60(2):274–1268. [12] DD ENV 1994-1-1: 1992 Eurocode 4. Design of composite steel and concrete structures, part 1.1 general rules and rules for building. London: British Standard Institution; 1994. [13] Green Travis P, Leon Roberto T, Rassati Gian A. Bidirectional tests on partially restrained, composite beam-to-column connections. J Struct Eng, ASCE 2004;130(2):3320–7. [14] Thanoon Waleed A, Jaafar MS, Razali M, Kadir A, Noorzaei J. Repair and structural performance of initially cracked reinforced concrete slabs. Constr Build Mater 2005;19(8):595–603. [15] Bui TT, Nana WSA, Abouri S. Influence of uniaxial tension and compression on shear strength of concrete slabs without shear reinforcement under concentrated loads. Constr Build Mater 2017;146:86–101. [16] Beckmann, Hummeltenberg, Weber. Strain behaviour of concrete slabs under
The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. Acknowledgements Professor Akihiko Kawano, Prof. Shintaro Matsuo, former graduate students Mr. Ikeda Ryusuke and Mr. Takeuchi Takuya from Kyushu University are greatly appreciated for their valuable helps and advices on this study. Mou Ben was supported by the First-class Discipline Project Funded by the Education Department of Shandong Province. Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.engstruct.2019.109616. References [1] Iyama J, Matsuo S, Kishiki S, Ishida T, Azuma K, Kido M, et al. Outline of reconnaissance of damaged steel school buildings due to the 2016 Kumamoto earthquake. AIJ J Technol Des 2018;24(56):183–8. [2] Nakashima M, Bruneu M. English edition of preliminary reconnaissance report of the 1995 Hyogoken Nanbu Earthquake. Tokyo: The Arch Inst, of Japan (AIJ); 1995. [3] Miller Duane K. Lessons learned from the northridge earthquake. Eng Struct
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B. Mou, et al. impact load. Structural Eng Int 2012;22:562–8. [17] Fu F, Lam D. Experimental study on semi-rigid composite joints with steel beams and precast hollow core slabs. J Constr Steel Res 2006;62:771–82. [18] Mello AVA, da Silva JGS, Vellasco PCG da S, et al. Dynamic analysis of composite systems made of concrete slabs and steel beams. J Constr Steel Res 2008;64:1142–51. [19] McHung Peter J, Cook William D, Mitchell Denis, et al. Improved transmission of high-strength concrete column loads through normal strength concrete slabs. ACI Struct J 2000;97:157–65. [20] Qiao Q, Zhang W, Mou B, Cao W. Seismic behavior of exposed concrete filled steel tube column bases with embedded reinforcing bars: Experimental investigation. Thin-walled Struct 2019;136(03):367–81. [21] Pisano ⇑ AA, Fuschi P, De Domenico D. Peak loads and failure modes of steel-reinforced concrete beams: Predictions by limit analysis. Eng Struct 2013;56:477–88. [22] De Domenico D, Fuschi P, Pardo S, Pisano AA. Strengthening of steel-reinforced concrete structural elements by externally bonded FRP sheets and evaluation of their load carrying capacity. Compos Struct 2014;118(1):377–84. [23] Fuschi P, Pisano AA, Pucinotti R. Plastic collapse load numerical evaluation of welded beam-to-column steel joints. J Constr Steel Res 2017;139:457–65. [24] Mou Ben, Bai Yongtao. Experimental investigation on shear behavior of H-shaped beam-to-CFST column connections with irregular panel zone. Eng Struct 2018;168(08):487–504. [25] Mou Ben, Li Xi, Qiao Qiyun, He Baojie, Menglong Wu. Seismic Behavior of frame corner joints under bidirectional cyclic loading test. Eng Struct 2019;196(10):109316.
[26] Mou Ben, Li Xi, Bai Yongtao, Wang Lisa. Shear behavior of panel zones in steel beam-to-column connections with unequal depth of outer annular stiffener. J Struct Eng, ASCE 2019;145(2):04018247. [27] JIS G3136. Rolled steels for building structure. Tokyo: Japanese Industrial Standards Committee; 2005. [28] Architectural Institute of Japan. Recommendation for design of connections in steel structures. [29] Metallic materials – Tensile testing – Method of test at room temperature. Tokyo: Japanese Industrial Standards Committee, 2011. [30] Method of test for compressive strength of concrete. Tokyo: Japanese Industrial Standards Committee, 2006. [31] Kuwahara S, Kumano T, Inoue K. The elasto-plastic behaviour of joint panels at the connection of rectangular steel column and two H-shaped beams with different depth. J Struct Constr, AIJ 2000;533:175–81. [In Japanese]. [32] MSC, Software Corporation, MSC.Marc user's manual (Marc 2012, volume A, theory and user information), 2012 [Santa Ana, CA 92707, USA]. [33] Mou B, Li X, Bai YY, Patel VI. Numerical investigation on shear behavior of steel beam to CFST column connections with unequal panel zone. J Construct Steel Res 2018;148(09):422–35. [34] Kim YJ, Shin KJ, Kim WJ. Effect of stiffener details on behavior of CFT column-tobeam connections. Int J Steel Struct 2008;8(2):119–33. [35] Elnashai AS, Di Sarno L. Fundamentals of earthquake engineering. UK: Wiley; 2008. [36] Buyukozturk O. Nonlinear analysis of reinforced concrete structures. Comput Struct 1977;7(1):149–56.
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Flexural behavior of beam to column joints with or without an overlying concrete slab
T
Ben Moua,b, Fei Zhaoa, Qiyun Qiaoc, , Lingling Wanga, Haitao Lib, Baojie Hea, Zhiyu Haoa ⁎
a
School of Civil Engineering, Qingdao University of Technology, Qingdao 2660332, China College of Civil Engineering, Nanjing Forestry University, Nanjing 210037, China c College of Architecture and Civil Engineering Beijing University of Technology, Beijing 100124, China b
ARTICLE INFO
ABSTRACT
Keywords: Beam column joint Composite action Flexure behavior
Composite action between a steel frame and an overlying slab plays an important role in the structure design of a beam-column joint in a steel or composite framed structure. This research investigates the seismic performance of a joint between a steel beam and a hollow square steel (HSS) or a concrete filled square tubular (CFST) column with or without an overlying concrete slab. The objective of this research is to evaluate the composite action between the steel girder and concrete slab. Four T-shaped beam to column joints are tested under cyclic loadings. The main experimental parameters are column type (HSS or CSFT) and concrete slab (with or without). Secondly, the seismic behavior of the joint is investigated in terms of failure mode, hysteretic behavior, skeleton curve, stiffness degradation, and strain distribution. Plastic deformation is concentrated at the beam end and brittle fracture is effectively avoided in the vicinity of the beam-to-column joints. All the tested specimens exhibit excellent energy dissipation capacity and ductility. The composite action between a steel girder and a concrete slab significantly enhance the capacity of the joint in terms of stiffness and yield bending moment. The plastic bending moment capacity is, however, slightly improved.
1. Introduction Earthquake is not necessarily a single event and it can have a series of active quakes (foreshock, main-shocks), such as in Kumamoto of Kyushu Island (Japan) in April 16. More than 100 steel school buildings [1] were damaged because of unexpected brittle fractures that occurred near beam-column joints, especially near the welded part between a hollow square steel column and a composite beam flange (Fig. 1). One particular observation was that overlying concrete slab markedly affected the stress distribution around the joint. When composite beams were subjected to a sagging moment, floor slab mobilized the high compressive capacity of concrete and improved the compressive resistance of the upper beam flange. However, when the composite beams were subjected to a hogging moment, only the bottom beam flange resisted the bending moment, thereby causing the brittle fracture of the bottom beam flange during the severe earthquake [2,3]. In the past three decades, a series of experimental and numerical studies were conducted to investigate the composite effect on the stiffness and strength of composite joints. The main failure modes were the steel bar fracture, brittle fracture of welded parts, local buckling of column flange, shear buckling of joint, shear buckling of panel zone,
⁎
and yield buckling of girder flange or web [4–10]. Cheng and Chen [4] experimentally studied six composite steel beam joint specimens, and found that the initial stiffness and the ultimate strength of the composite beam were increased by 67% and 27% on average, compared to those of a bare steel beam. Leon et al. [5] surveyed the seismic performance of interior steel moment-resisting beam-column joints. All specimens with concrete slab failed at the welded interface of the bottom girder flange and the column flange. The strains near the bottom flange of the specimens with concrete slab were several times larger than those near the top flange [6]. Khalid et al. [7] revealed the efficiency of carbon fiber reinforced polymer (CFRP) composite retrofit in improving the slab behavior under blast loading with different loading durations. Fan et al. [8] presented test results of 6 composite beam to CFSST (concrete-filled square steel tubular) column joints. It was found that the ultimate strength, stiffness and ductility were enhanced by the composite action. Testing on four internal joints and four external joints with concrete slab, Silva et al. [9] found that the symmetric loading and steel-reinforced concrete (SRC) column were the two main parameters that increased the bending moment and initial stiffness of a joint. Based on the experimental and analytical data, Liew et al. [10,11]
Corresponding author. E-mail address: [email protected] (Q. Qiao).
https://doi.org/10.1016/j.engstruct.2019.109616 Received 26 May 2019; Received in revised form 31 July 2019; Accepted 31 August 2019 Available online 09 September 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.
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2. Experiment 2.1. Test specimens Four T-shaped specimens were tested in terms of seismic behavior of composite beam-column joints. All specimens and details of the concrete slab are shown in Fig. 2 and Table 1. The main test parameters were joints with or without a concrete slab. As shown in Table 1, two joints with an overlying concrete slab and two joints without a concrete slab were tested. Specimen No.1 was a bare beam-column joint. The column height of No.1 was 1400 mm and was made by cold bending a square tube, which was a 200 × 200 × 9 mm hollow steel tube section and manufactured according to BCR295 [27]. The beam length of No.1 was 1500 mm, and was constructed as a built-up beam with two pieces of flange plates (300 × 6 mm) and a web plate (120 × 12 mm), which was made as SN490B [27]. The beam flanges had the same sickness as that of outer annular stiffener, which were welded to the square steel hollow column with full penetration butt weld and an additional fillet weld of 13 mm thickness. Gas metal arc welding with CO2 shielding was adopted to fabricate the welded parts of the test specimens. LB-52 [27] were selected as the welding electrodes, which was a specified minimum Charpy V-type Notch (CVN) toughness of 80 Joule at −20 degree centigrade. Specimen No.2 had the same properties as those of No.1, except for 85 mm thick reinforced concrete slab. Shear studs were set along the centerline of the beam flange at a uniform spacing of 100 mm to connect the beam with the RC slab. The details of RC slab are shown in Table 2. Furthermore, orthogonal beams were set to support the RC slab. Specimen No.3 has the same properties as No.1, except for the column was a CFST column. Moreover, specimen No.4 had the same properties as those for No.3, but with the addition of a concrete slab. According to design of connections in steel structures [28], the details of annular stiffener is shown in Fig. 2(e) and (g). Annular stiffeners play significant role in relocating the plastic hinge formation. The length of the annular stiffener, a, can be calculated by Eq. (1).
Fig. 1. Brittle fracture on the welded part between a hollow square steel column and a composite beam flange.
indicated that the Eurocode [12] overestimates the initial rotational stiffness under the hogging moment. Based on full-scale tests on composite beam to column joint, Green et al. [13] investigated the force transfer mechanism of the concrete slab. Thanoon et al. [14] investigated the structural behavior of cracked reinforced concrete oneway slab. Bui et al. [15] conducted the shear test of concrete slab under a concentrated load and quantified the shear behavior and the failure modes of slab with the influence of axial forces. Beckmann et al. [16] compared concrete specimens with and without additional fabric strengthening, and showed that substantial advantages in the resistance to the impact load and to the penetration of the impactor were seen for slabs with a strengthening layer. Fu and Lam [17] focused on the seismic behavior of semi-rigid composite joints with precast hollow core slabs. Mello et al.[18] presented an extensive parametric study of the dynamic response of composite floors, in terms of peak accelerations. Peter et al. [19] investigated the effect of confinement from the surrounding slab on the axial capacity of the columns. These studies mainly concentrated on the influence of concrete slab on stiffness, bearing capacity, ductility, and energy dissipation capacity. Qiao et al. [20] conducted the seismic behavior of innovative exposed concrete filled steel tube (CFST) column base, which takes the effect of embedded reinforcing bars into consideration. Pisano et al [21–23] researched on the flexural behavior of steel-reinforced concrete beam. Although beam-column joint with outer annular stiffener has good seismic performance [24–26], few researchers study on the seismic behavior of composite beam-column joint with outer annular stiffener. In order to investigate the seismic behavior and failure modes of a composite beam-column joint with outer annular stiffener, four specimens are fabricated and tested under cyclic loading in this paper. The composite action between the steel girder and concrete slab are discussed in detail. Moreover, six indices, affecting the seismic behavior of composite joints, are clarified, namely, stiffness, bearing capacity, ductility, energy dissipation capacity, hysteresis characteristics and damage modes. This paper aims to provide an experimental evidence for evaluating and designing the composite joints with outer annular stiffener.
a=
4h d + D 2
Bd
(1)
where hd is the depth of the annular stiffener; D is the width of column; Bd is the end width of the annular stiffener; a is the distance from surface of steel tube to edge of the annular stiffener. 2.2. Material properties of steel and concrete According to JIS Z2241 [29], the material properties of steel were obtained by performing coupon tests. For each thickness category (12.1 mm, 9.1 mm and 6.2 mm), three identical specimens were tested in a 20 ton testing machine. Table 3 shows the material properties of the steel parts used in this study, namely, thickness (t), young’s modulus (ES), yield strength (бy), tensile strength (бu), yield ratio (бy/бu), and elongation (δ). Yield strength was taken as the lower yield point as obtained from the test data. Young’s modulus was measured as the secant stiffness between points corresponding to a stress of 1/3 of yield strength to 2/3 of yield strength. The compression strength of concrete was obtained by testing concrete cubes according to JIS A1108 [30]. Three identical concrete cubes were tested in a uniaxial compressive strength testing machine. Before testing, the cube specimens were prepared by pouring properly mixed concrete mixture into cylinder standard molds and by curing the cube specimens for 28 days after demolding.
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450 450 50
250
150
Steel bar HRB335, B 10, @100
150
Beam 300×120×6×12
Beam 300×120×6×12
55
120
13
250
50
Column 200×200×9
13
110
9
Beam web Stud (d13-60 @100)
35 Outer annular stiffener (PL-12)
Slit
Outer annular stiffener (PL-12)
(a) Plan of No.1 and No.3
12 300 276
12 276
13
12
13
12
300
Beam 300×120×6×12
13
Stud (d13-60 @100) Beam 300×120×6×12
Column 200×200×9 13
85
Column 200×200×9
(b) Plan of No.2 and 4
9 9 35
35
(c) Elevation of No.1 and No.3 50
450 250
(d) Elevation of No.2 and No.4
150
Outer annular stiffener
Seam
35° Beam flange
300
120
60
150
150
60
Beam web
50
250 450
Column
Beam web
13 13
450
Weld (13mm)
(e) Details of the annular stiffener
(f) Details of the weld part
Fig. 2. Details of specimens.
2.3. Testing device and loading plan
limited specimens to move in the horizontal direction, but allowed specimens to rotate in the YZ plane. The distance between the two supports was 1800 mm. An actuator with 500 kN capacity was used to apply the vertical loads at the end of the beam. Two lateral supports were set on both sides of the beam, near the loading point in order to prevent the torsional deformation of the beam. Fig. 4 shows the loading history [31]. All the joint specimens were
Fig. 3 illustrates the overall views of the testing device. The column was arranged in the vertical direction without any axial load. The upper column was connected to the reaction frame by a vertical sliding hinge (roller pin) support, which allowed the upper column to move in the vertical direction. A pin support was set at the bottom column, which
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hd D
45o
45o
b Bd=Bf
a
b
(g) Symbols of annular stiffener
(h) Photograph of specimen No.3
(i) Photograph of specimen No.4 Fig. 2. (continued)
Table 1 Basic specimen information. Specimen
Column
Beam
Concrete slab
Column
Compressive stress (Mpa)
No.1 No.2 No.3 No.4
200 × 200 × 9
BH300 × 120 × 6 × 12
Without slab With slab Without slab With slab
HSS HSS CFT CFT
/ / 40.2 40.6
Table 2 Basic RC slab information. Specimen
Compressive strength/(Mpa)
Thickness/(mm)
Breadth/(mm)
Length/(mm)
Steel bar
Stud
No.2 No.4
34 21
85
1000
1450
B 10@100
d13-60 @100 × 11
Table 3 Material properties of steel. Member
t (mm)
ES (MPa)
бy (MPa)
бu (MPa)
бy/бu (%)
δ (%)
Outer annular stiffener, Beam flange Weld metal Beam web Square column Steel bar
12.1 13.2 6.2 9.1 –
193,000 205,000 200,000 197,000 184,000
398 406 398 408 341
529 533 546 532 442
75 76 73 77 77
21 16 22 24 21
tested under a cyclic loading and the load was applied in a displacementcontrolled mode. The test history began with two cycles repeated for story drift angle (R) amplitudes of ± 0.005, ± 0.01, ± 0.02, ± 0.03, and ± 0.04 rad. If no fracture was triggered at R = 0.04 rad, the test procedure would enter into R = 0.05 rad. It should be noted that many identical cycles were applied at R = 0.05 rad in order to investigate the low-cycle
fatigue behavior at large drift amplitude. When fracture occurred, the final cycle with R = 0.08 rad was applied in the sagging direction. The story drift angle (R) was defined as shown in Fig. 5 and can be expressed as Eq. (2),
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δU
Reaction frame
Oil jack
θb
Lc
R
Roller pin
Beam
V1 Lb
Slab
Out-of-plane movement restraint device
δL
Pin
Fig. 5. An illustration of the deformation of a specimen.
(a) Testing device and test specimen
Uu ht Ul Lt
V2
V1
(b) Photograph of a specimen placed in the testing device Fig. 3. Testing device.
Fig. 6. Set up of the displacement transducer.
Peak bending point
M Mmax 1/6
Plastic bending point
1/3
Yield bending point
θy Fig. 4. Loading history.
R=
V1 Lb
U
L
Lc
θp
θm
θu
θ
Fig. 7. Definition of characteristic points in the moment-curvature diagram.
(2)
2.4. Measurements
where V1 is vertical displacement of the loading point; Lb is the calculated beam length, which was measured from the centerline of the column to the loading point; δU is the horizontal deformation of upper column; δL is the horizontal deformation of bottom column; and Lc is the calculated column length, which was measured from the sliding hinge support to the pin support.
The beam rotation angel (θb), as shown in Fig. 5 and Fig. 6, was obtained from Eq. (3) as,
b
5
=
V1
V2 Lt
Ul
Uu ht
(3)
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(a) Photograph of specimen No.1
(b) Local buckling of the outer annular stiffener
(c) Brittle fracture of the welded part
(d) Tearing of the outer annular stiffener
(e) Photograph of specimen No.2
(f) Brittle fracture of welded part
(g) Cracking of HSS column
(h) Cracking of concrete slab
Fig. 8. Photographs showing failure phenomena.
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(i) Photograph of specimen No.3
(j) Local bucking of the upper beam flange
(k) Cracking of the upper outer annular stiffener
(l) Buckling of the beam web
(m) Photograph of specimen No.4
(n) Distance between CFT column and concrete slab
(o) Cracking of the lower outer annular stiffener
(p) Cracking of concrete slab
Fig. 8. (continued)
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400
400
200
200
M /kN•m
M /kN•m
B. Mou, et al.
0 -0.09 -0.06 -0.03 0.00 0.03 0.06 0.09
0 -0.09 -0.06 -0.03 0.00 0.03 0.06 0.09
-200
-200
-400
-400
θb/rad
θb/rad
(b) No.2
400
400
200
200
M/kN•m
M/kN•m
(a) No.1
0 -0.09 -0.06 -0.03 0.00 0.03 0.06 0.09
0 -0.09 -0.06 -0.03 0.00 0.03 0.06 0.09
-200
-200
-400
-400
θb/rad
θb/rad
(c) No.3
(d) No.4
M/kN•m
Fig. 9. Beam rotation angle and bending moment curves of specimens.
300
2.5. Deformation at key indexes in the moment–curvature diagram
200
The key indexes of the specimens, including yield bending point (My), plastic bending point (Mp), peak bending point (Mm) and ultimate bending point(Mu), could be determined in the skeleton curve, as shown in Fig. 7. The stiffness (K) is the secant modulus, which was the stiffness corresponding to the positive peak loads in the first cycle when the story drift angle was equal to 0.005 rad. The yield and plastic bending points could be obtained by the slope factor method [26], and were determined as the tangent points of lines with slopes of 1/3 K and 1/6 K, respectively. Peak bending point was the maximum bending point.
100 -0.04
-0.02
0 0.00 -100
0.02
-200 -300
θ/rad
0.04
NO.1 NO.2 NO.3 NO.4
3. Experimental results
Fig. 10. Envelope curves of four T-shaped specimens.
3.1. Failure mode Before R = 0.01 rad, all the specimens stayed in the elastic stage. Moreover, the hysteresis curves between beam rotation angle and beam bending moment were linear. When R ≥ 0.02 rad, hysteresis curves showed an obvious bending phenomenon. All the specimens entered into plastic stage. Brittle fracture occurred in all specimens
where V2 is vertical displacement of the beam end near the column; Lt is the horizontal distance between the loading point and the beam end measured point; Uu is the horizontal displacement of the upper column; Ul is the horizontal displacement of the lower column; and ht is the displacement between the two displacement transducers. Table 4 Experimental stiffness and bending moment of specimens. No
Loading direction
Ke (kN·m/rad)
My (kN·m)
θy (rad)
Mp (kN·m)
θp (rad)
Mm (kN·m)
θm (rad)
Failure mode
1
Sagging Hogging Sagging Hogging Sagging Hogging Sagging Hogging
20,000 24,000 42,000 25,000 25,000 24,000 37,000 31,000
170 159 186 167 203 196 237 191
0.012 0.010 0.006 0.010 0.012 0.011 0.009 0.010
209 212 236 216 250 244 266 248
0.023 0.019 0.013 0.018 0.020 0.019 0.016 0.017
263 262 323 268 299 301 325 292
0.045 0.046 0.044 0.047 0.047 0.046 0.036 0.037
Fracture between outer annular stiffener and lower beam flange
2 3 4
8
Fracture between outer annular stiffener and HSS column Fracture between outer annular stiffener and upper beam flange Fracture between outer annular stiffener and lower beam flange
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30
Kj/kN•rad-1
-1
Kj/kN•rad
20
10
0 0.00
0.01
0.02
0.03 R/rad
Sagging Hogging
40
Sagging Hogging
0.04
30 20 10 0 0.00
0.05
0.01
30
0.05
40 Sagging Hogging
20
10
0 0.00
0.01
0.02 0.03 R/rad
Sagging Hogging
30
Kj/kN•rad-1
-1
0.04
(b) No.2
(a) No.1
Kj/kN•rad
0.02 0.03 R/rad
0.04
20 10 0 0.00
0.05
0.01
0.02 0.03 R/rad
0.04
0.05
(d) No.4
(c) No.3 Fig. 11. K-θ curves of the test specimens.
surface of the HSS column. The lower outer annular stiffener experienced local buckling. Meanwhile, the column flange appeared concave and developed visible compressive deformation. As shown in Fig. 8(f), a brittle fracture was observed in the welded joint between the lower outer annular stiffener and the HSS column in the second cycle of R = 0.05 rad. Owing to stress concentration, the corner of the HSS column was cracked in the fourth cycle of R = 0.05 rad, as shown in Fig. 8(g). The maximum bending moment of specimen No.2 was 323 kN·m and 268 kN·m in the sagging and hogging directions, respectively. Compared to specimen No. 1, the composite effect caused by concrete slab in specimen No. 2 markedly increased the ultimate bearing moment of the specimens. Fig. 8(i) shows the final stage of specimen No.3 before failure. Response of specimen No.3 was similar to that of No.1 in the elastic stage. When R = 0.03 rad, the upper beam flange showed obvious local buckling, as shown in Fig. 8(j). The upper outer annular stiffener was torn out in the sixth cycle of R = 0.05 rad. The crack expanded diagonally at 45 degrees to the outer annular stiffener, as shown in Fig. 8(k). The web of the beam buckled in the same time, as shown in Fig. 8 (l). The maximum bending moment of specimen No.3 was 299 kN·m and 301 kN·m in the sagging and hogging directions, respectively. It showed that the bending moment of CFT column specimen was larger than that of HSS column specimen. Fig. 8(m) shows the final stage of specimen No.4. Specimen No.4 was similar to No.3 in the elastic stage. As shown in Fig. 8(n), the separated distance between CFT column and concrete slab was 18 mm when R = 0.05 rad. The lower outer annular stiffener was torn out in the sixth cycle of R = 0.05 rad, as shown in Fig. 8(o). This demonstrates that the concrete slab improved the bending moment capacity of the upper outer annular stiffener. The maximum bending moment of No.1 was 325 kN·m and 292 kN·m in the sagging and hogging directions, respectively.
Table 5 Kp/Ky, K0.05rad/Ky and Km/Ky. NO.
Loading direction
Kp/Ky
Km/Ky
K0.05rad/Ky
1
Sagging Hogging Sagging Hogging Sagging Hogging Sagging Hogging
0.64 0.70 0.58 0.71 0.74 0.72 0.63 0.76
0.41 0.36 0.24 0.34 0.38 0.37 0.34 0.41
0.42 0.37 0.22 0.33 0.38 0.35 0.29 0.34
2 3 4
corresponding to the R = 0.05 rad loading cycle. Fig. 8(a) shows the final stage of specimen No.1. For specimen No.1, local buckling was initiated in the upper portion of the outer annular stiffener in the first cycle of R = 0.03 rad, as shown in Fig. 8(b). Brittle fracture was observed in the welded joint between the lower outer annular stiffener and HSS column in the second cycle of R = 0.05 rad, as shown in Fig. 8(c). After another two cycles of R = 0.05 rad, cracks occurred at the welded joint between the lower beam flange and the outer annular stiffener. Meanwhile, the outer annular stiffener was torn apart, as shown in Fig. 8(d). The maximum bending moment of specimen No.1 was 263 kN·m and 262 kN·m in the sagging and hogging directions, respectively. The two value were similar to each other indicating that the loading direction had a little impact on the bending moment capacity of the specimens. Fig. 8(e) shows the final stage of specimen No.2 before failure. When R = 0.01 rad in the first loading circle, a longitudinal crack was initiated in the concrete slab around the HSS column. When R = 0.03 rad, the longitudinal crack of concrete slab extended rapidly and a transverse crack was observed approximately 35 cm from the
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Sagging Hogging
1.05
1.02
ηj
ηj
1.02 0.99
-0.04
-0.02
0.00
0.02
0.04
0.93 -0.06
0.06
-0.02
0.00
0.02
R/rad
(a) NO.1
(b) NO.2
Sagging Hogging
0.04
0.06
Sagging Hogging
1.05
1.02
1.02
ηj
ηj
-0.04
R/rad
1.05
0.99 0.96 0.93 -0.06
0.99 0.96
0.96 0.93 -0.06
Sagging Hogging
1.05
0.99 0.96
-0.04
-0.02
0.00
0.02
0.04
0.93 -0.06
0.06
-0.04
R/rad
-0.02
0.00
0.02
0.04
0.06
R/rad
(d) NO.4
(c) NO.3 Fig. 12. ηj-θ curves of specimens.
200
200 NO.1 NO.2
100 50 0 0.00
NO.3 NO.4
150
E/kN•m
E/kN•m
150
100 50 0
0.01
0.02
0.03
0.04
0.05
0.00
0.01
0.02
R/rad
0.03
0.04
0.05
0.04
0.05
R/rad Fig. 13. E-R curves of specimens.
300
300 250
150 100
150 100 50
50
0
0 0.00
NO.3 NO.4
200
Ea/kN•m
200
Ea/kN•m
250
NO.1 NO.2
0.01
0.02
0.03
0.04
0.00
0.05
R/rad
0.01
0.02
0.03
R/rad Fig. 14. Ea-R curves of specimens.
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Table 6 Equivalent viscous damping coefficient at yield, plastic and R = 0.05 rad state. Specimen
he,y
he,p
he,0.05rad
No.1 No.2 No.3 No.4
0.138 0.152 0.133 0.132
0.186 0.139 0.180 0.132
0.224 0.229 0.222 0.225
decreased with the cyclic loading. Stiffness degradation is one of the most important indices to develop computational models and to capture the seismic behavior of specimens. Stiffness degradation was calculated by the following equation:
Fig. 15. Basis to calculate the equivalent viscous damping coefficient.
2
Kj = i=1
3.2. Hysteretic performance
For a given inter-layer drift angle, the shear capacity decreased with an increase in the number of cycles. The shear capacity degradation was calculated by the following equation:
Fig. 10 shows the envelope curves of all specimens. Moreover, Table 4 shows the main performance point such as stiffness (Ke), yield bending point (θy, My), plastic bending point (θp, Mp), and maximum bending point (θm, Mm). Owing to the composite effect of concrete slab, the bearing capacities of specimen No.2 and No.4 improved generally. The My, Mp and Mm of specimen No.2 increased by 21.28%, 17.34% and 14.29%, respectively, when compared to those of No.1. Likewise, My, Mp and Mm of specimen No.4 increased by 21.25%, 13.72% and 5.20%, respectively, when compared to those of specimen No.3.
j
=
Due to the accumulated damage, the stiffness of the specimens
ξeq/kN•m
0.1
0.02
0.03
0.04
(5)
M1, j
0.2
NO.1 NO.2
0.01
M2, j
where ηj is the shear capacity degradation factor at the class j loading; M1,j is the maximum bending moment at the class j loading of the second cycle; and M2,j is the maximum bending moment at the class j loading of the second cycle. Fig. 12 shows the degradation of the shear capacity of all specimens. The trend of variation in the degradation of the shear capacity of all specimens was approximately the same. The degradation coefficient of shear capacity decreased with an increase in drift angle.
3.4. Stiffness degradation
0.0 0.00
(4)
3.5. Bending moment capacity degradation
3.3. Envelope curves of moment-curvature and the characteristic points
0.2
i, j i=1
where Mi,j is the maximum bending moment at the class j loading of the second cycle of i, and θi,j is the beam end rotation corresponding to Mi,j. Fig. 11 shows the stiffness degradation of all the four specimens. Table 5 presents the stiffness ratio between the plastic bending point and the yield bending point (Kp/Ky), the stiffness ratio between the maximum bending point and the yield point (Km/Ky) and the stiffness ratio between a point in R = 0.05 rad and the yield bending point (K0.05rad/Ky). Kp/Ky and Km/Ky of specimen No.2 and No.4 had a large difference, compared to specimen No.1 and No.3. However, K0.05rad/Ky of all specimens was in a range of 0.36–0.48. This is attributed to the fact that due to the crushing of the concrete slab, composite action was diminished.
The curves of bending moment and beam rotation angle are illustrated in Fig. 9. The black solid circles represent the maximum bending moment of tested specimens. All the curves of the T-shaped specimens are plump and similar to each other. When R ≤ 0.01 rad, the curves were linear. All the four T-shaped specimens stayed in the elastic stage. When R exceed 0.01 rad, the hysteretic curve was bent and the specimens entered into the plastic stage. Bearing capacity began to degrade when R = 0.05 rad and brittle fracture occurred in all specimens at this loading level. During the whole test process, all specimens showed excellent ductility as evidenced by the stable hysteretic curves. In addition, according to the composite effect of the floor slab, the sagging bending moment of specimens No.2 and No.4 decreased by 20.52% and 11.70% respectively, when compared to the hogging bending moment.
ξeq/kN•m
2
Mi, j /
0.1
0.0 0.00
0.05
NO.3 NO.4
R/rad
0.01
0.02
0.03
R/rad Fig. 16. ξeq–R curves of specimens.
11
0.04
0.05
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Rigid plate Column
1
1
0
0 0
z
ux uy uz
1
θx θy θ z
x
y
1：restrain 0：free
Weld Slab
Concrete layer Steel layer
1
1
1
0
0
0
Beam Rigid plate
Loading point
(b) Shell element of concrete slab
(a) Finite element models
40
700
Stress (N/mm )
600 500 400 0.0
30
2
2
True stress(N/mm )
800
Outer annular stiffener, beam flange Fillet weld metal Beam web Column
0.1 0.2 Plastic strain
20 10 0
0.3
0.1fc
-10
(c) True stress-plastic strain curves for steelpart
0.2fc
0.002 0.004 Strain
0.006
(d) Stress-strain relation for concrete slab
Fig. 17. Finite element models.
3.6. Energy dissipation capacity
indices to evaluate the energy dissipating capacity of the test specimens. Fig. 15 illustrates the calculation diagram for one hysteresis loop. The equivalent viscous damping coefficient was obtained by Eq. (6) as:
The area of hysteresis loops represents the dissipated energy in each cycle for all specimens. Fig. 13 and Fig. 14 show the dissipated energy for each cycle (E), and the cumulative energy consumption (Ea), respectively. When R was less than 0.01 rad, all specimens were in the elastic range; no plastic deformation was observed and the dissipated energy was almost zero. When R reached 0.01 rad, E and Ea increased slowly. After R reached 0.04 rad, obvious differences were obtained among the specimens. The energy dissipation capacity of specimens with CFST column was higher than that of specimens with HSS column. Moreover, the energy dissipation capacity of specimens with a concrete slab was smaller than that of specimens without a concrete slab. The total energy consumption was mainly related to the deformation capacity of the specimens. Equivalent viscous damping ratio (ξ) was one of the important
=
1 SABC + SCDA · 2 SOBE + SODF
(6)
where, SABC + SCDA indicates the area of hysteresis loop in one cycle; and SOBE + SODE indicates the area of the corresponding triangle. Fig. 16 shows the relationship between the equivalent viscous damping coefficients (he) of each specimen and the story drift angle. The coefficient he increased gradually with an increase in the rotation angle of specimens but at a decreasing rate. Table 6 lists the equivalent viscous damping corresponding to R = 0.05 rad (he,0.05rad) for all specimens. It is observed that the equivalent viscous damping coefficients of specimens without concrete slab were almost equal to each other at the three characteristic points. Similarly, he,0.05rad of all specimens were similar because composite girder lost its composite action at
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400
200
200
M/kN·m
M/kN·m
B. Mou, et al.
0 -0.09 -0.06 -0.03 0.00 0.03 0.06 0.09 -200
0 -0.09 -0.06 -0.03 0.00 0.03 0.06 0.09 -200
Experiment Analysis
-400 θ /rad
-400 θ /rad
(a) No.1
(b) No.2 400
200
200
M/kN·m
M/kN·m
400
0 -0.09 -0.06 -0.03 0.00 0.03 0.06 0.09 -200
Experiment Analysis
Experiment Analysis
-0.09
-0.06
-0.03
0 0.00
0.03
-200
-400 θ /rad
-400
0.06
0.09
Experiment Analysis
θ /rad
(c) No.3
(d) No.4
Fig. 18. Comparison of hysteretic curves from the finite element analysis and the test.
R = 0.05 rad. During the tested process, he,y, he,p and he,0.05rad ranged from 0.132 to 0.38, 0.132 to 0.186, and 0.222 to 0.229, respectively.
issue, and therefore accommodating these cracks dominates the development of this material model. Cracking model was chosen as damage effects [32]. Buyukozturk model was chosen as the yield criterion of concrete [36]. In order to accurately simulate the experimental loading process, rigid plates were placed at both ends of the column in the finite element model, and boundary conditions were imposed on the column through the rigid plate as shown in Fig. 17(a). The rigid plate at the bottom of the column was used to simulate the fixed hinge support in the loading device. Boundary conditions were given to limit the translational displacement in the three directions of ux, uy and uz and the rotation in the θx and θz directions, while allowing the rotation in the θy direction. The rigid plate on the top of the column was used to simulate the sliding hinge support of the loading device. Boundary conditions were given to restrain the translational displacement in the ux and uy directions and the rotation in the θx and θz directions, while allowing the column to undergo vertical deformation in the direction of uz and to rotate in the θy direction. The vertical loading applied on the loading point are controlled with the same loading history as experimental tests in order to simulate the story drift angle caused by lateral loading, as shown in Fig. 17(a).
4. Finite element analysis 4.1. Finite element models Based on the tested specimens, finite element models were established by using the software MSC. Marc 2012 [32]. The analytical model was composed of a rigid plate, an H-beam, an octagonal outer annular stiffener, fillet weld, a square steel tube column and a concrete slab. In order to improve the calculation efficiency, symmetry of the test specimen was used to establish a half-side model along the beam center line, as shown in Fig. 17(a). All parts were meshed by Element type 7, which is 8-node, isoparametric, arbitrary hexahedral solid element. In order to improve the calculation effect, concrete slab were meshed by shell elements. According to the principle of volume equivalent substitution, the concrete slab was divided into 19 layers, as shown in Fig. 17(b). The middle layer is steel bar with the thickness of 1.2 mm. Moreover, one layer with the thickness of 1.9 mm and 8 layers with the thickness of 5 mm are set from the inside to outside on both sides. Steel is modelled by elasto-plastic material, which behave as nonlinear isotropic model. True stress-logarithmic strain curves from coupon tests are used to specify the nonlinear parts [33]. Yield criterion is based on the von Mises yield criterion, and kinematic hardening rule is adopted in the analysis [34]. True stress-logarithmic plastic strain curves for all parts are shown in Fig. 17(c). Poisson’s ratio of concrete and Young’s modulus were assumed as 0.2 was 30 GPa, respectively. Stress-strain relationship of concrete are shown in Fig. 17(d). In addition, a linear ending of 0.2 fc residual strength was assumed [35]. Cracking was considered to be an important
4.2. Results of numerical analysis 4.2.1. Comparison of hysteretic curves Fig. 18 compares the hysteresis curves from the finite element analysis and the experiment. The finite element analysis curve agreed well with the test data. While, the peak moment obtained by the finite element model was slightly larger than that obtained from the experiment. Moreover, the hysteretic curves of the finite element model were smoother and fuller when compared to the test. This is attributed to the
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Fig. 19. Comparison of failure modes of specimens from the finite element analysis and the test.
fact that the finite element model did not consider the initial defects of the specimens and the stress concentration factor during the welding process. In general, the hysteresis curve of finite element analysis agreed well to the experimental results. Therefore, the finite element method could be used as an effective tool to study the performance of this joint.
and numerical analyses were performed. The following conclusions were drawn: (1) The composite action of the floor slab and the steel beam was particularly significant under the sagging moment. (2) The beam-to-column connection with outer annular stiffener was helpful to make the plastic hinge away from the connection and to effectively avoid the occurrence of the fracture in the vicinity of the weld. However, owing to the effect of a concrete slab, there is a possibility of fracture near the connection for this type of connection. (3) The hysteresis curves were stable for all specimens. In the plastic stage, the equivalent viscous damping coefficients of the specimens without slab were slightly larger when compared to the specimens with a concrete slab. Before that, the coefficients were almost equal for all specimens when the story drift angle reached 0.05 rad. (4) Results from finite element analysis were in good agreement with the experimental results. Finite element models as proposed in this study will be utilized to perform parametric studies in future.
4.2.2. Comparison of failure modes Fig. 19 compares the failure modes as obtained by the finite element analysis and the test results of the specimens. The yield stress of column and beam was 408 and 398 MPa, respectively. The joint failure mode obtained from finite element analysis was basically similar to that observed in the experiment. Plastic deformation was mainly concentrated at the joint between the outer annular stiffener and the beam, and at the welded part of the column ring. The stress concentration region obtained in the finite element analysis was the fracture location in the experiment, thus confirming the accuracy of the finite element model. 5. Conclusions This paper investigated the flexure behavior of a beam to column joint in a steel frame with an overlying concrete slab. Both experimental
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Fig. 19. (continued)
Declaration of Competing Interest
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The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. Acknowledgements Professor Akihiko Kawano, Prof. Shintaro Matsuo, former graduate students Mr. Ikeda Ryusuke and Mr. Takeuchi Takuya from Kyushu University are greatly appreciated for their valuable helps and advices on this study. Mou Ben was supported by the First-class Discipline Project Funded by the Education Department of Shandong Province. Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.engstruct.2019.109616. References [1] Iyama J, Matsuo S, Kishiki S, Ishida T, Azuma K, Kido M, et al. Outline of reconnaissance of damaged steel school buildings due to the 2016 Kumamoto earthquake. AIJ J Technol Des 2018;24(56):183–8. [2] Nakashima M, Bruneu M. English edition of preliminary reconnaissance report of the 1995 Hyogoken Nanbu Earthquake. Tokyo: The Arch Inst, of Japan (AIJ); 1995. [3] Miller Duane K. Lessons learned from the northridge earthquake. Eng Struct
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