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Tests of irregular joints of lightweight aggregate concrete-filled square steel tubular column and beams with enlarged arc junctures
Mingming Guo1, *Wanzhen Wang2, Fang Zhu3, Wenwen Sun4, Shaojiang Sun5
1), 2), 3), 4) Faculty of Architectural, Civil Engineering and Environment, Ningbo University, Ningbo,
Zhejiang 315211, China 2) [email protected]
4) Jiaxing Transportation Bureau, Jiaxing, Zhejiang 314000, China
Abstract
In order to study the influence of enlarged arc junctures of through diaphragm on seismic performance of
irregular joints of lightweight aggregate concrete-filled square steel tubular column and steel H-section and box beam,
diaphragm-through irregular joints with enlarged arc junctures and traditional irregular joint were tested under
low-reversed loading. The failure modes, hysteresis loops, bearing capacity, plastic rotation and energy dissipation of
the irregular joints were obtained from the experimental results. Tests results indicate that the hysteresis curves of the
diaphragm-through irregular joints are stable without significant degradation of bearing capacity. The lightweight
aggregate concrete and diaphragm-through ribs and column walls are firmly bonded together without separated or
slip failure. The traditional irregular joint brittle fractures at the edges of butt weld of box steel beam flanges with large
rigidity and sharply changed geometry. The main failure modes of the irregular joints with enlarged arc junctures are
plastic hinge formed at the enlarged arc junctures, crack of fillet at welding holes of beam web and ductile fracture of
butt weld of beam flanges. The plastic rotation of the irregular joints with enlarged arc junctures can research
0.038~0.056rad, and the energy dissipation capacity and the bearing capacity may increase by 82%~251% and
14.2%~56.2% compared with that of the traditional irregular joint, respectively. Based on the analysis of the
experimental results, the flexural and shear calculation models of panel zones of the irregular joints are established
and formulas for calculating the flexural and shear capacity are presented for the irregular joint under compression
and bending.
Key words: irregular joints, lightweight aggregate concrete-filled square steel tubular column, steel H-section and
box beam; enlarged arc junctures; bearing capacity; plastic rotation; energy dissipation capacity, capacity calculation
1 Graduate student 2 Professor and corresponding author 3 Graduate student 4 Graduate student
Compared with ordinary concrete, lightweight aggregate concrete has an advantage of light weight.
Hence, lightweight aggregate concrete-filled square steel tubular column- steel beam frame structure have
advantages of light weight and long natural vibration period compared with those of ordinary concrete-filled
steel tubular column-steel beam frame. This is real beneficial to the seismic design of structure, foundation
design and reduction of construction cost. Lightweight aggregate concrete-filled square steel tubular column-
steel beam frame structure have wide application prospect in multistory and tall buildings.
If spans or load of frames are not equal, it is advisable to use steel beams with different cross-sectional
shapes to form the irregular joints of lightweight aggregate concrete-filled square steel tubular column and
steel H-section and box beams. The complex reinforced irregular joints of lightweight aggregate concrete-filled
square steel tubular column and steel H-section and box beams play the role of transmitting and balancing
the beam-column inner force, which is essential to structural safety.
The strength characteristics and deformation properties of lightweight aggregate concrete are quite
different from those of ordinary concrete. The failure surface of ordinary concrete intersects with the
tension side of hydrostatic stress, and opens to the compression side of hydrostatic stress. The failure
surface of lightweight aggregate concrete intersects with the tension side and compression side of the
hydrostatic stress. The failure criterion established by the strength characteristics of ordinary concrete
cannot be applied to the lightweight aggregate concrete，Wang Licheng et al.[1] and Wang Wanzhen [2]
suggested failure models intersected the tension side and compression side of hydrostatic stress for
lightweight aggregate concrete, respectively. Predictably, mechanical properties and failure modes of
irregular joints of lightweight aggregate concrete-filled square steel tubular column and steel H-section
and box beams should be quite different from those of joints of ordinary concrete-filled square steel
tubular column-steel beams.
It is difficult to ensure the quality of weld between square steel tubular column and inner partition. Weld
for joints with inner diaphragm accumulate in the connection areas, welding residual stress and welding heat
affected zone overlap. Previous tests indicate that the weld between square steel column and inner partition
prematurely crack due to poor welding quality, the bearing capacity and ductility of joints with inner diaphragm
between square concrete-filled steel tubular columns and steel beams are obviously reduced. In the
diaphragm-through joints of concrete-filled square steel tubular column and steel H-section and box beam,
square steel tubular column and diaphragm-through joints are easy to weld. The quality of weld in panel zone
is well and weld can be dispersed, which eliminates the overlapping problem between welding residual stress
and welding heat affected zone.
At present, there are many researches on ordinary concrete-filled square steel tubular column and steel
beam joints, but there is no report on the study of diaphragm-through irregular joints of lightweight aggregate
concrete-filled square steel tubular column and steel H-section and box beams.
Qin et al.[4~5] made experiments and theoretical analysis on the diaphragm-through joints of
concrete-filled steel tubular column and steel beam, and proposed a shear-resistant design method
considering the axial pressure of column; Kang et al.[6] established the analysis model of the inner diaphragm,
outer diaphragm and diaphragm-through joints of concrete-filled square steel tubular column and steel
H-section and box beams; Wang et al.[7] made a study of fracture behavior of inner diaphragm joints of
concrete-filled square steel tubular column and H-section steel beam with flange openings.
Zhou Peng et al. [8] carried out tests on the joints of concrete-filled rectangular steel tubular column and
steel beam. Results show that the shearing failure of the abdomen plate in panel zone and weld fracture
between the abdomen plate in panel and column flange are the typical failure modes of irregular joints; Xu
Guigen et al.[9] made researches on the diaphragm-through joints, which indicates that the weld fracture in
panel zone is serious; Chen Qingjun et al. [10] made experiments and research on seismic behavior of
discontinuous joints of concrete-filled steel tubular column and steel beam; Miao Jigui et al. [11] performed
experiments on diaphragm-through joints of concrete-filled steel tubular column and steel beam, the test
results show that the butt welding fracture problems of beam flange and diaphragm were serious. Huang
Bingsheng et al. [12] carried tests on the seismic behavior and force-transfering mechanism of outer diaphragm
joints between concrete-filled steel tubular columns and steel beams.
In this paper, five diaphragm-through irregular joints of lightweight aggregate concrete-filled square steel
tubular column and steel H-section and box beams with enlarged arc junctures and one conventional irregular
joint were tested under low-cycle reversed loading. The influence of enlarged arc junctures on failure mode,
hysteretic behavior, bearing capacity, stiffness, plastic rotation angle and energy dissipation capacity of above
irregular joints are comparatively studied, the tests provide reference for seismic design and engineering
application of this kind of irregular joints.
1. TEST PROGRAM
1.1 Specimen Design
In this test program, five diaphragm-through irregular joints of lightweight aggregate concrete-filled
square steel tubular column and steel H-section and box beam with enlarged arc junctures (hereinafter,
named as irregular joints with enlarged arc junctures) and one conventional irregular joint are designed. The
section size of the welded square steel tubular column is □250×250×8mm, the section sizes of the welded
steel box beam and H-section steel beam are □350×150×6×8mm and H200×100×6×8mm respectively. The
six specimens are produced by manual welding with Q235·B steel and E43 electrode, the beam flange is
welded by butt weld, the web and the column panel are welded by twin fillet welding seam.
According to the provisions of the GB50205-2001 Code for acceptance of construction quality of steel
structures [25] [S], the welds of the specimens were examined by ultrasonic wave after the specimens were
machined. No welding defects such as cracks were found, and the quality of welds meets the requirement of
secondary-grade quality inspection.
Fig.1 shows details of conventional irregular joint specimen BASE. In order to comparative study the
influence of enlarged arc junctures on seismic performance of diaphragm-through irregular joints of lightweight
aggregate concrete-filled square steel tubular column and steel H-section and box beams, the details of
irregular joints with enlarged arc junctures are identical to conventional irregular joint specimen BASE, except
for enlarged arc junctures connected with the top and bottom flange of beam shown in Fig.2 and tab.1.
The steel tubular columns were poured with lightweight aggregate concrete. The mix proportion was:
water: ordinary Portland cement: sand: ceramsite=1:2:2:3. After the concrete pouring is completed in the
laboratory, those will be cured for 28 days.
2 2 0 1 4 8 5 1 7 5 53 0 3 0
2 5 0 1 3 05 0
5 0 5 02 5 0
2 5 0
1700
2010
0020
015
020
3 0 3 0
26 3 5
26
6
D e ta il lo w e r le ft f lg
3 5L o w e r c o re re g io n
U p p e r co re re g io n
3 0 2 0
R 1 5
(a) Elevation drawing
150
8080
105
100
105
30 30250
(b) Planar graph Fig.1 Details of conventional irregular joint
L250 310 L1 50
220 220
100
105
150
80
105
80
R2 R1
Fig.2 Details of irregular joints with enlarged arc junctures
Tab. 1 Parameters of irregular joints with enlarged arc junctures parameters X1 X2 X3 X4 X5
L1/mm 250 300 350 300 300
R1/mm 430 600 810 600 600
L2/mm 250 250 250 200 300
R2/mm 350 350 350 240 480
1.2 Loading Scheme and Tested Arrangement
Fig.3 shows test loading device. The top and bottom ends of the column are hinged constraint, the
column base is attached to the laboratory trough with anchor bolts and the top of the column was connected
to the loading frame by two vertical steel plates (lateral restraint). An axial pressure of 1150 KN is applied to the
top of the column through hydraulic jack and the columns axial compression ratio is 0.5. Trusses with slide
way (lateral bracing) were set at the end of steel box beams and the cantilever end of H-section steel beams
to prevent lateral buckling instability of free end.
Anti-synchronous reversed cyclic load was applied to the cantilever end of steel H-section beams and
box beams by the servo load system (automatically collecting the loading displacement and load of beams
end). According to the provisions of the JGJ 101-1996 Specification for test method of seismic buildings [26],
elastic phase used force control. When the load-displacement curve has obvious inflection point, the
specimen was considered to yield (the displacement and load were defined as yield displacement and yield
load, respectively). After that, the loading was controlled by displacement and the loading rate was 6mm/min,
the loading displacement progressively increased according to the multiples of the yield displacement and the
displacement cycled 3 times in each load level until the specimen failure or the load fell below 70% of the
ultimate bearing capacity
(a) Loading schematic drawing
(b) Test drawing Fig.3 Test setup
In order to obtain the evolution of the two main directions of the panel zone with the loading process,
strain gauges are arranged in panel zone and its surroundings (Fig.4), beam flange butt weld and beam web welding positions.
9 8
5
7
6
3
49
10
1
1
2
(a) Test point arrangement of joint region
9 1
(b) Test point arrangement of conventional irregular joint beam flange
11 9 121
(c) Test point arrangement of irregular joint beam flange with enlarged arc junctures
Fig.4 Arrangement of strain gauges
1.3 Material Properties According to the provisions of GB/T 228-2002 metallic materials-tensile testing at ambient temperature
[27], mechanical specimens of 6mm and 8mm thick steel plate and E43 weld were produced in the same batch of tested specimens, each with a total of three. Tab.2 shows tested mechanical properties of steel and weld material.
Tab.2 Tested mechanical properties of steel and weld material Mechanical fy/Mpa fu/Mpa εy εu E/×105Mpa Poisson
properties ratio
6mm plate 296.9 510 0.17% 30.4% 2.01 0.269
8mm plate 273.5 440 0.22% 22.4% 1.98 0.266
E43 weld 302.7 480 0.24% 18.7% 2.06 0.274
According to the provisions of JGJ 51-2002 Technical specification for lightweight aggregate concrete[28], six 150×150×150mm ceramsite lightweight aggregate concrete cubes cured over 28 days in standard curing condition. Fig.5 shows the failure of ceramsite lightweight aggregate concrete cubes, the cracks extend along the axial pressure direction(vertical) under uniaxial compression and did not form vertical angle conical failure surface like convertional concrete cubes. The measured poisson ratio νc≈0.19, elastic modulus Ec≈16.5×103MPa, average compressive strength fc≈40.03MPa.
Anchor bolts
Jack
Servo
actuato
Lateral
bracin
Fig.5 Failure pictures of lightweight aggregate concrete cube 2. TEST PROCESS AND FAILURE CHARACTERISTICS
At the end of the first cycle of 40 mm amplitude cyclic loads, a side crack develops at the top flange of the
BASE specimen as shown in Fig.6a and the crack initiation occurs at the lower flange when the load reaches
the second cycle of 40 mm. A crack develops in the flange of the box beam at the end of the third cycle with 50
mm amplitude loading as shown in Fig.6b and c. The crack initiation takes place in the process hole of web
plates of box girders at the end of the second cycle in the 50 mm amplitude cycle load. At this point, joints bear
more loads to stop.
(a) Flange of the box beam (b) Lower flange
(c)Top flange (d) Process hole of web plates
Fig.6 Failure pictures of specimen BASE
At the end of the first cycle of 60 mm and 70 mm amplitude cyclic loads, a side crack develops at the top and bottom flanges of the X1 specimen as shown in Fig.7a. The crack initiation occurs at the lower flange of H-section and the web plate of box girders near the flange warps when the load reaches the first cycle of 80 mm as shown in Fig.7b. A crack develops in the lower flange of the box beam at the end of the third cycle with 80 mm amplitude loading as shown in Fig.7c. At the end of the second cycle in the 90 mm amplitude cycle load as shown in Fig.7d, a crack forms in the top flange of H-section beam and the test is stopped.
A crack occurs in the lower flange of the X2 specimen at the end of the first cycle with 60 mm amplitude loading as shown in Fig.8a, the buckling develops in the top flange of the box beam when the load reaches the third cycle of 80 mm as shown in Fig.8b. At the end of the second cycle of 90 mm amplitude cyclic loads, a plastic hinge forms in the lower flange of the H-section beam as shown in Fig.8c. The web plate of box girders warps, the weld fractures in the lower flange of the box beam at the end of the second cycle with 100 mm amplitude loading. When the load reaches the third cycle of 100 mm, a crack takes place in the top flange of the box beam, a plastic hinge forms at the end of the connecting plate, meanwhile, the web plate of box girders warps and the weld fractures in the lower flange of the box beam as shown in Fig.8d. A plastic hinge occurs in the H-section beam at the end of the first cycle of 110 mm amplitude cyclic loads, the bearing capacity of box beam and H-section beam are seriously decreased and the loading is stopped.
Crack
Crack
(a) Top flange (b) Box beam
(c) Lower flange (d) H-section beam Fig.7 Failure pictures of specimen X1
(a) Box beam (b) Upper diaphragm buckling
(c) Plastic hinge of box beam (d) Crack of box beam
Fig.8 Failure pictures of specimen X2
A crack develops in the lower flange of the X3 specimen at the end of the second cycle with 50 mm amplitude loading as shown in Fig.9a. The web plate of box girders warps, the weld fractures in the lower flange of the box beam at the end of the second cycle with 60 mm amplitude loading as shown in Fig.9b. At the end of the second cycle of 70 mm amplitude cyclic loads, a crack forms in the lower flange of the box beam as shown in Fig.9c. When the load reaches the third cycle of 70 mm, a plastic hinge takes place in the end of the diaphragm connecting with H-section beam as shown in Fig.9d. A plastic hinge forms in the end of the diaphragm connecting with the box beam at the end of the third cycle of 80 mm amplitude cyclic loads, at this time, the bearing capacity of the box beam and the H-section beam are seriously decreased and the loading is stopped.
(a) Micro – crack (b) Upper diaphragm buckling
(c) Crack of box beam (d) Plastic hinge of H-section beam
Fig.9 Failure pictures of specimen X3
Buckling
When the load of the X4 specimen reaches the second cycle of 50 mm and the first cycle of 60 mm, cracks occur at the edge of the butt weld of the lower flange and top flange of the box beam as shown in Fig.10a and b. At the end of the first cycle of 70 mm amplitude cyclic loads, a plastic hinge develops at the end of the diaphragm connecting with H-section beam as shown in Fig.10c. Cracks form in the flange of the box beam and H-section beam at the end of the first cycle of 80 mm amplitude cyclic loads as shown in Fig.10d, and meanwhile, the loading is stopped.
(a) Lower flange of box beam (b) Top flange of box beam
(c) Plastic hinge (d) Butt weld of box beam
Fig.10 Failure pictures of specimen X4
At the end of the first cycle of 70 mm amplitude cyclic loads of the X5 specimen, a plastic hinge occurs at the end of the diaphragm connecting with H-section beam as shown in Fig.11a. The butt welds of the lower flange and top flange crack at the end of the third cycle of 70 mm and the first cycle of 80 mm amplitude cyclic loads as shown in Fig.11b. The plastic hinge forms at the end of the diaphragm connecting with H-section beam when the load reaches the third cycle of 80 mm as shown in Fig.11c. Cracks develop in the lower flange of the box beam and the H-section beam at the end of the third cycle of 90 mm amplitude cyclic loads as shown in Fig.11d, the loading is stopped.
(a) Plastic hinge (b) Crack of the flange
(c) H-section beam (d) Box beam
Fig.11 Failure pictures of specimen X5
Fig.12 records the test hysteresis curves of the specimen BASE. The bearing capacity of box beams and H-section beams are 87.82kN and 39.08kN, and the corresponding ultimate moments are 0.95 1pM and
1.06 2pM ( 1pM and 2pM are the full-section plastic moments of the box beam and the H-section beam
respectively), the plastic rotation of the box beam and the H-section beam are 0.031rad and 0.023rad. In this paper, the plastic angle of beams is defined as follows: the plastic rotation angle p is equal to the
total rotation of beam subtracting the elastic angle e of beam. The length bL refers to the length of
beam, K denotes the initial rotational stiffness of beam (gets from the elastic regression of the M hysteretic curve), P represents the loading when the loading displacement at the beam end is ,
and meanwhile, the corresponding moment is equal to the loading multiplying the length, bLPM .Where
the plastic rotation follows, K
M
Lbp -
-90-60-30
0306090
-90 -60 -30 0 30 60 90Δ (mm)
P(k
N)
-0.9-0.6-0.3
00.30.60.9
-0.03 -0.01 0.01 0.03 0.05θ p (rad)
M/M
p
(a) Box beam, P-∆ (b) Box beam, ppMM /
-40-30-20-10
010203040
-90 -60 -30 0 30 60 90Δ (mm)
P(k
N)
-1.2-0.9-0.6-0.3
00.30.60.91.2
-0.03 -0.02 -0.01 0 0.01 0.02 0.03θ p (rad)
M/M
p
(c) H-section beam, P-∆ (d) H-section beam, ppMM /
Fig.12 Hysteresis loops of specimen BASE
Fig13~Fig17 show the hysteresis loops of specimen X1~X5 respectively, the bearing capacity of the box
beam are 128.22kN, 137.17kN, 119.58kN, 107.98kN and 122.64kN respectively, which are approximately
equal to 1.17 1pM , 1.25 1pM , 1.09 1pM , 0.99 1pM and 1.12 1pM respectively, the bearing capacity of the
H-section beam are 47.5kN, 47.66kN, 48.06kN, 44.64kN and 47.95kN, which are approximately equal to
1.29 2pM , 1.30 2pM , 1.31 2pM , 1.22 2pM and 1.31 2pM respectively. The plastic angle of the box beam
are 0.040rad, 0.051rad, 0.045rad, 0.044rad and 0.045rad respectively, and the plastic angle of the H-section
beam are 0.038rad, 0.056rad, 0.045rad, 0.045rad and 0.044rad respectively.
-150-120-90-60-30
0306090
120
-120 -90 -60 -30 0 30 60 90 120Δ (mm)
P(k
N)
-1.2-0.9-0.6-0.3
00.30.60.91.2
-0.05 -0.03 -0.01 0.01 0.03 0.05θ p (rad)
M/M
p
(a) Box beam, P-∆ (b) Box beam, ppMM /
-50-40-30-20-10
01020304050
-120 -90 -60 -30 0 30 60 90 120Δ (mm)
P(k
N)
-1.5-1.2-0.9-0.6-0.3
00.30.60.91.2
-0.05 -0.03 -0.01 0.01 0.03 0.05θ p (rad)
M/M
p
(c) H-section beam，P-∆ (d) H-section beam, ppMM /
Fig.13 Hysteresis loops of specimen X1
-150-120-90-60-30
0306090
120150
-120 -90 -60 -30 0 30 60 90 120Δ (mm)
P(k
N)
-1.2-0.9-0.6-0.3
00.30.60.91.2
-0.06 -0.04 -0.02 0 0.02 0.04 0.06θ p (rad)
M/M
p
(a) Box beam, P-∆ (b) Box beam, ppMM /
-50-40-30-20-10
01020304050
-120 -90 -60 -30 0 30 60 90 120Δ (mm)
P(k
N)
-1.5-1.2-0.9-0.6-0.3
00.30.60.91.2
-0.06 -0.04 -0.02 0 0.02 0.04 0.06θ p (rad)
M/M
p
(c) H-section beam, P-∆ (d) H-section beam, ppMM /
Fig.14 Hysteresis loops of specimen X2
-120-90-60-30
0306090
120
-90 -60 -30 0 30 60 90Δ (mm)
P(k
N)
-1.2-0.9-0.6-0.3
00.30.60.91.2
-0.05 -0.03 -0.01 0.01 0.03 0.05θ p (rad)
M/M
p
(a) Box beam，P-∆ (b) Box beam， ppMM /
-50-40-30-20-10
01020304050
-90 -60 -30 0 30 60 90Δ (mm)
P (
kN)
-1.5-1.2-0.9-0.6-0.3
00.30.60.91.2
-0.05 -0.03 -0.01 0.01 0.03 0.05θ p (rad)
M/M
p
(c) H-section beam，P-∆ (d) H-section beam， ppMM /
Fig.15 Hysteresis loops of specimen X3
-120-90-60-30
0306090
120
-90 -60 -30 0 30 60 90Δ (mm)
P(k
N)
-0.9-0.6-0.3
00.30.60.9
-0.05 -0.03 -0.01 0.01 0.03 0.05θ p (rad)
M/M
p
(a) Box beam, P-∆ (b) Box beam, ppMM /
-50-40-30-20-10
01020304050
-120 -90 -60 -30 0 30 60 90 120Δ (mm)
P (
kN)
-1.2-0.9-0.6-0.3
00.30.60.91.2
-0.05 -0.03 -0.01 0.01 0.03 0.05θ p (rad)
M/M
p
(c) H-section beam, P-∆ (d) H-section beam, ppMM /
Fig.16 Hysteresis loops of specimen X4
-150-120-90-60-30
0306090
120
-120 -90 -60 -30 0 30 60 90 120Δ (mm)
P(k
N)
-1.2-0.9-0.6-0.3
00.30.60.91.2
-0.05 -0.03 -0.01 0.01 0.03 0.05θ p (rad)
M/M
p
(a) box beam，P-∆ (b) box beam， ppMM /
-50-40-30-20-10
01020304050
-120 -90 -60 -30 0 30 60 90 120Δ (mm)
P(k
N)
-1.5-1.2-0.9-0.6-0.3
00.30.60.91.2
-0.05 -0.03 -0.01 0.01 0.03 0.05θ p (rad)
M/M
p
(c) H-section beam，P-∆ (d) H-section beam， ppMM /
Fig.17 Hysteresis loops of specimen X5 3. TEST RESULT ANALYSIS
3.1 Failure Mode Analysis
The brittle fracture prematurely develops in the side of the box beam flange butt weld of the traditional
irregular joint specimen BASE. This is because the narrower beam flange is welded directly to the wide
diaphragm, which results in geometric catastrophe and stress concentration form in the side of the box beam
flange butt weld, the wide diaphragm generates strong constraints on the narrower beam flange and limits the
plastic development of the butt weld and its surrounding steel, in addition, the side of the box beam flange butt
weld is up-arc or down-arc point and welding defects are more. Under the same loading displacement, the
stress amplitude of butt welds of box beam with larger stiffness is larger than that of H-section beam with
smaller stiffness, leading to the box beam flange butt weld cracks before the H-section beam.
The structural parameters of the five irregular joints with enlarged arc junctures are different. The plastic
hinge forms at the end of enlarged arc junctures of the five irregular joints, and the plastic rotation is all
substantially increased than that of the traditional irregular joints, all of which reach the FEMA[29] requirements
of 0.03rad. The structure of enlarged arc junctures through diaphragm slows down the geometric catastrophe
and stress concentration of the beam flange butt weld, and reduces the stress amplitude of butt welds and the
constraint of the diaphragm on the beam flange. This structure also prompts the formation of plastic hinge at
the end of enlarged arc junctures through diaphragm, to avoid the premature brittle fracture of beam flange
butt weld.
The main failure models of irregular joints with enlarged arc junctures are cracking of butt welds of beam
flange, plastic hinge of enlarged arc junctures and cracking of the process hole of web plates. Under the cyclic
loading, the end of the enlarged arc junctures through diaphragm is repeatedly buckled and stretched, the
stress state of beam flange butt weld is deteriorated, and the damage accumulation of beam flange butt weld
leads to continuous pull-off. In the welding process hole of web plates, the geometric changes are severe, the
stress concentration is serious, the amplitude of bending normal stress and shearing stress are high, and all
above the situation lead to the welding process hole of web plates at the greater risk of tearing.
The experiment results show that there are no cracks in the welds between diaphragm and column
panel of irregular joints of lightweight aggregate concrete-filled square steel tubular column and steel H-section
and box beams with enlarged arc junctures. The welding quality is easy to be ensured because the welds
between diaphragm and column panel are conventional to apply welding. The decentralized distribution of
welds in panel zone can help to alleviate the problem of the overlapping of welding residual stress and
welding heat affected zone.
When cutting open the square steel tubular column after test (Fig.18), the lightweight aggregate
concrete in panel zone and the column section of point zone are not crushed or cracked, the lightweight
aggregate concrete is well bonded with throughout diaphragm and steel tubular column, and no peeling or
sliding failure occurs. It can be seen that the lightweight aggregate concrete and steel tubular column can
work well together, reduce the stress amplitude of point zone and increase the strength and stiffness of the
joints.
(a) Concrete in upper core (b) Concrete in lower core
area of panel zones area of panel zones
(c) Concrete in upper columns (d) Concrete in lower columns
Fig.18 Pictures of lightweight aggregate concrete in panel zones and columns
3.2 Strain analysis
Fig.19 records the strain distribution of beam flange butt weld with loading process (frequency of 10
seconds / times). It can be seen from the figure that the strain of conventional box beam and H-section beam
flange butt welds of irregular joints is equivalent to those of the irregular joints with enlarged arc junctures at
the initial stage of loading. During the large displacement loading stage, the strain of box beam and H-section
beam flange butt welds of conventional irregular joints increase rapidly, and which is much larger than that of
the irregular points with enlarged arc junctures. The stress concentration of the butt welds of the conventional
beam flange is serious , the stress and strain amplitude are high, leading to the premature brittle fracture of the
traditional irregular joints in the butt welds of beam flange. The butt weld of the beam flange of irregular joints
with enlarged arc junctures is moved to the end of enlarged arc junctures away from the panel zone, which
leads to the great decrease of the burden of stress and strain.
At the same loading displacement, the strain of butt welds of box beam flange is larger than that of
H-section beam, which is because the stiffness of the box beam is greater than that of the H-section beam,
the burden of the bending normal stress and the normal strain of the box beam flange butt weld are greater
under the same loading displacement.
(a) Box beam flange butt weld (b) H-section beam flange butt weld
Fig.19 Strain evolution at butt weld of beam flanges
The lateral (beam length direction) and vertical (column height direction) strain evolution of panel zone
shown in Fig.20 shows that the lateral and vertical strains of the upper core region on the panel zone are
larger than those of the lower core region. The upper core region of the panel zone not only bears the axial
pressure from the top of the column, but also bears the horizontal shear force from the box beam and
H-section beam (from the decomposition of moment at beam end) and the vertical shear force from beam
ends. The lower core region only undertakes the axial pressure from the column, the horizontal shear force
from the box beam and a part of the vertical shear force from the web plates of box girders.
(a) Top core zones vertical strain (b) Lower core zones vertical strain
(c) Top core zones lateral strain (d) Lower core zones lateral strain
Fig.20 Strain evolution of core zones
3.3 Hysteretic behavior and ductility
Fig. 12 ~ Fig. 17 show that the hysteresis curves of the box beams are not significantly degraded and
the hysteresis curves of the H-section beams are almost coincident with each other at the same loading
displacement, indicating that the hysteretic behavior of diaphragm-through irregular joints of lightweight
aggregate concrete-filled square steel tubular column and steel H-section and box beam with enlarged arc
junctures are steady and the seismic performance is well.
The hysteresis curve of the H-section beam is full fusiform and the hysteresis curve of the box beam is
pinching. This is because the butt weld of the box beam flange cracks first and the damage of the beam
flange butt weld accumulates under cyclic loading, resulting in a gradual decline in the bearing capacity of box
beam and the hysteresis curve begins to scatter.
The experimental results listed in tab.2 and tab.3 show that the bearing capacity of the box beam and
the H-section beam with enlarged arc junctures improve 23.0% ~ 56.2% and 14.2% ~ 23.0% than that of
basic type respectively, and the plastic rotations of the box beam and the H-section beam also increase by
29.0% ~ 64.5% and 65.2% ~ 143.5%, respectively.
Tab. 2 Bearing capacity and plastic rotation of steel box beams
Properties BASE X1 X2 X3 X4 X5
BC/kN 87.8 128.2 137.1 119.5 107.9 122.6
RD — 46% 56.2% 36.2% 23.0% 39.6%
PR/rad 0.031 0.04 0.051 0.045 0.044 0.045
RD — 29.0% 64.5% 45.2% 41.9% 45.2%
(BC: Bearing capacity, PR: Plastic rotation, RD: Relative difference)
Tab. 3 Bearing capacity and plastic rotation of steel H-section beams Properties BASE X1 X2 X3 X4 X5
BC/kN 39.1 47.5 47.6 48.1 44.6 47.9
RD — 21.5% 22.0% 23.0% 14.2% 22.7%
PR/rad 0.023 0.038 0.056 0.045 0.045 0.044
RD — 65.2% 143.5% 95.7% 95.7% 91.3%
(BC: Bearing capacity, PR: Plastic rotation, RD: Relative difference)
3.4 Skeleton curves
The skeleton curves of the specimens shown in Fig. 21 show that the skeleton curves of the irregular
joints with enlarged arc junctures and the traditional irregular joints are almost coincident during the small
displacement loading stage (point is elastic). In the stage of large displacement loading (point is plastic), the
skeleton curve of the traditional joint of box beam obviously descends, and the bearing capacity of the
H-section beam increases slowly and even tends to be flat, the skeleton curves of the irregular joints of box
beam and H-section beam are obviously increased. When loading to the failure, the ductility and bearing
capacity of the box beam and the H-section beam of joints with enlarged arc junctures are significantly higher
than those of the traditional points.
The skeleton curve of box beam of conventional irregular joints develops obvious inflection point at the
stage of large displacement loading, then the bearing capacity sharply drops and the loading displacement is
smaller when the failure occurs. The conventional irregular joints show brittle failure pattern. The lower stage of
skeleton curve of irregular joints with enlarged arc junctures is gentle and the load displacement is larger than
that of conventional points when failure develops, the irregular points with enlarged arc junctures show ductile
failure mode.
The descent segment of skeleton curve of H-section beam is not as obvious as box beam because the
butt weld of the box beam flange with the larger stiffness cracks first and the damage accumulation effect of
the box beam flange butt weld is bigger than that of the H-section beam.
(a) Skeleton curve of box beam
(b) Skeleton curve of H-section beam Fig.21 Envelope curves of irregular joints
3.5 Stiffness degradation
Fig.22 records the stiffness degradation curves of the tested specimens. The stiffness of the traditional
irregular joints is equal to that of the irregular joints with enlarged arc junctures at the initial stage of loading, but
the stiffness degradation rate of the traditional joint is larger than that of the irregular joints with enlarged arc
junctures. When loading to 4 y , the stiffness of conventional joints decreases dramatically. At the same time,
the butt welds of the beam flange of the conventional irregular joints begin to crack, and the crack propagation
leads to the substantial reduction of the rotational stiffness of the box beam with enlarged arc junctures. The
diaphragm-through enlarged arc junctures structure increases the rotational stiffness of the beam and delays
the cracking process of the beam flange butt weld.
The residual stiffness of the irregular joints of the H-section beam with enlarged arc junctures is much
less than that of the conventional irregular joints, and the irregular joints of the H-section beam with enlarged
arc junctures show ductile failure mode, the stiffness degradation of the H-section beam is sufficient. The box
beam cracks first, its stiffness degradation is not as sufficient as H-section beam.
When the irregular joints with enlarged arc junctures are loaded to 4 y , the stiffness degradation of the
beam accelerates, and when the beam is loaded to 5 y , the stiffness degradation rate of the beam slows
down. When loading to 6 y ~7 y , the stiffness degradation of the beam accelerates again. This is because
the tangent modulus of the steel is much smaller than the elastic modulus when the irregular joints with
enlarged arc junctures is loaded to the yield point, which results in the decrease of the rotational stiffness of
beam. After the steel in yield zone enters into hardening stage, the strengthening effect counteracts the
degradation effect of beam rotation stiffness. When loading to the joints cracking, the crack propagation and
the damage accumulation at the cyclic loading accelerate the degradation of the rotation stiffness of beam
again.
0500
1000150020002500300035004000
0 2 4 6 8 10 12Δ /Δ y
Ki (k
N/m
)
BASE X1X2 X3X4 X5
(a) Stiffness degradation of the box beam
200
400
600
800
1000
1200
1400
0 2 4 6 8 10 12Δ /Δ y
Ki (k
N/m
)
BASE X1X2 X3X4 X5
(b) Stiffness degradation of the H-section beam Fig.22 Rigidity degradation of irregular joints
4. BEARING CAPACITY OF IRREGULAR JOINTS
4.1 Flexural bearing capacity of irregular joints
The experimental results show that the typical failure mode of diaphragm-through irregular joints of
lightweight aggregate concrete-filled square steel tubular column and steel H-section and box beam is that the
butt weld of the beam flange is broken and the plastic hinge is formed at the end of the enlarged arc junctures.
Therefore, the flexural bearing capacity uM of diaphragm-through irregular joints of lightweight aggregate
concrete-filled square steel tubular column and steel H-section and box beam takes the minimum between
the ultimate moment fwM of the cracks of beam flange butt welds and the ultimate moment pdM of the
plastic hinge at the end of enlarged arc junctures of through-diaphragm. As shown in following：
min{ , }u pd fwM M M (1)
Wherein：
( )fw bf bf b bf fwM b t h t f (2)
( )pd pd d f d b d ydM W f b t h t f 2( ) / 4b d w ydh t t f
(3)
bfb , bft , bh , bwt and dt are the width of beam flange, the thickness of beam flange, the height of beam
section, the sum of beam web thickness and the thickness of through diaphragm, respectively,
fwf and ydf are the tensile strength of beam flange butt weld and the yield strength of the diaphragm-through
steel, respectively.
The width of the end of enlarged arc junctures of through-diaphragm (plastic-hinge area) is slightly larger
than the width of the beam flange. In the calculation formula of the bending moment of through-diaphragm
plastic hinge, the width of the through-diaphragm plastic hinge zone is slightly conservative and is taken as the
beam flange width.
4.2 Shear bearing capacity
The upper, middle and lower diaphragms divide the panel zone into the upper and lower panel zones,
the upper panel zone should bear the shear force from the box beam and H-section beam flanges on both
sides of the panel zone, the lower panel zone only needs to bear the shearing force from the flange of the box
beam with large section in the unilateral panel zone. Obviously, the shearing load of the upper panel zone is
larger than that of the lower panel zone. The experimental results show that (Fig.20), the shear stress and
shear strain of the upper panel zone are significantly larger than that of the lower panel zone. Therefore, the
shear strength of the irregular panel zone depends on the upper panel zone. If the shear strength of the upper
panel zone satisfies the requirements, the lower panel zone automatically satisfies the shear strength
requirements.
In the upper panel zone, the upper diaphragm, the middle diaphragm, the left and right column flange
plates and the front and behind column webs make up the similar steel frame-shear wall structure (Fig.24).
The "diagonal compression strut" effect forms in the lightweight aggregate concrete of the upper panel zone,
and that is equivalent to the support of the framework.
Nc
Nc
tdtd
htp
FRMR
HRb
HR
bH
Lb
td
MR
ML
Plastic hingeYield zone
FLML
HLbFR
MR
HRb
Fig.24 Model of braced frame with shear walls of top panel zone
The plastic hinge mechanism takes place in the frame-shear wall structure shown in Fig.24 under the
action of horizontal shear forceV and column axial pressure cN . The shear capacity tpV of the upper panel
zone consists of the ultimate shear capacity scfV of the plastic hinges formed by the left and right column
flange plates, the ultimate shear capacity scwV of the front and behind web plates subjected to shear yielding,
and the ultimate shear capacity lwcV of the "diagonal compression strut" failure formed in the lightweight
aggregate concrete. As follows:
tp scf scw lwcV V V V (4)
①Ultimate shear capacity of column flange plates scfV
The ultimate shear capacity scfV can be obtained from the moment equilibrium (Fig.25) at the plastic
hinge, as shown below:
214
4scf tp sc sc yscV h w t f (5)
2 /scf sc sc ysc tpV w t f h (6)
Wherein, scw , sct and yscf are the width of column section, the thickness of column panel and the
strength of steel yield, respectively.
Wc
Mscf Mscf
Mscf Mscf =
Vscf
14 Wctcf ysc
2
Vscf
htp
Fig.25 Plastic hinges of column walls
②Ultimate shear capacity of column web plates scwV
The column axial pressure cN is assumed by the square steel tubular column and the column
lightweight aggregate concrete. According to the deformation coordination of square steel column and
lightweight aggregate concrete under axial compression, the axial pressure of the square steel column and
lightweight aggregate concrete are respectively:
sc scsc c
sc sc lwc lwc
E AN N
E A E A
(7)
lwc lwclwc c
sc sc lwc lwc
E AN N
E A E A
(8)
Wherein, scE and lwcE are elastic modulus of column steel and elastic modulus of lightweight
aggregate concrete respectively, scA and lwcA are section area of the square tubular column and section area
of lightweight aggregate concrete, respectively.
Axial compressive stress of column webs:
/scw sc scN A (9)
Shear stress of column webs：
2(w 2 t ) tscw
scwsc sc sc
V
(10)
Plug Mises yielding model into:
2 2 23scw scw yscf (11)
Get：
2 2 2
2 (w 2 t )3
ss ysc sc
scw sc sc sc
sc
A f NV t
A
(12)
③Ultimate shear capacity of lightweight aggregate concrete lwcV
The "diagonal compression strut" effect is formed by the shearing force of the lightweight aggregate
concrete in the upper panel zone. According to the literature [30], the angle between the baroclinic principal
stress trace of the lightweight aggregate concrete and the horizontal plane is shown below:
tan2( 2 )
tp
c c
h
w t
The lightweight aggregate concrete in the upper joints is in the state of biaxial compressive stress
(Fig.26) between the baroclinic pressure along the angle and vertical axial compression. When calculating
the ultimate tensile strength lwcV of lightweight aggregate concrete in the upper panel zone, it is conservative
to take the two-way compressive strength equal to uniaxial compressive strength, that is to say, the
compressive strength elevation effect of lightweight aggregate concrete under biaxial compressive stress is
not considered.
According to the virtual work principle,
( 2 ) cos2lwc c c tp cV w t h f (13)
Ultimate shear strength of lightweight aggregate concrete in the upper panel zone:
2 2
( 2 ) cos ( 2 )
2 2 4( 2 )
c c tp c c c tp clwc
tp c c
w t h f w t h fV
h w t
(14)
Shear strength of irregular panel zone:
tp scf scw lwcV V V V 2
sc sc ysc
tp
w t f
h
2 2 2
2 (w 2 t )3
ss ysc sc
sc sc sc
sc
A f Nt
A
2 2
( 2 )
2 4( 2 )
c c tp c
tp c c
w t h f
h w t
(15)
┍
NLwc
NLwc┙ ┙
VLwc
VLwc
htp
Wc - 2
t c
(Wc - 2tc)htpf c
Fig.26 Failure mechanism of lightweight aggregate concrete in top panel zone 5. CONCLUSIONS
Cyclic loading tests were carried out on five diaphragm-through irregular joints of lightweight aggregate
concrete-filled square steel tubular column and steel H-section and box beam with enlarged arc junctures and
one conventional irregular joint. Comparatively studying the influence of enlarged arc junctures on the failure
mode, node strain, bearing capacity, plastic rotation angle, stiffness degradation and energy dissipation
capacity of above irregular joints. The present study supports the following conclusions:
(1) The traditional irregular joint brittle fractures at the edges of butt weld of steel box beam flanges with
large rigidity and sharply changed geometry. The plastic rotation of steel H-section beam and steel box beam
of the traditional irregular joint are about 0.023rad and 0.031rad, respectively.
(2) The plastic rotation of the irregular joints with enlarged arc junctures can reach 0.038-0.056rad, the
bearing capacity of box beam and H-section beam may increase by 23.0%~56.2% and 14.2%~23.0%
compared with that of the conventional joints respectively, and the energy dissipation capacity can increase by
82%~251% and 106%~190% than those of the conventional joints, respectively.
(3) The diaphragm-through enlarged arc junctures moves beam flange butt weld to the end of the
enlarged area of the arc away from panel zone, which slows down the geometric catastrophe and stress
concentration of beam flange butt weld, reduces the stress amplitude and avoid the premature brittle fracture
in joints.
(4) The main failure modes of the irregular joints with enlarged arc junctures are plastic hinge formed at
the enlarged arc junctures, crack of fillet at welding holes of beam web and ductile fracture of butt weld of
beam flanges.
(5) There are no tearing failures of welding between through-diaphragm and column walls until joints
failure. The lightweight aggregate concrete and through- diaphragm and column walls are firmly bonded
together without separated or slip failure.
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