Experimental and numerical study on cyclic behaviour of...
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International Journal of Steel Structures
June 2010, Vol 10, No 2, 131-146
Experimental and Numerical Study on Cyclic Behaviour of
Steel Beam-to-Column Joints
Jun He1,2, Teruhiko Yoda2,*, Hideaki Takaku3, Yuqing Liu1, Airong Chen1, and Masashi Iura4
1Department of Bridge Engineering, Tongji University, Siping Road, Shanghai, 200092, China2Department of Civil and Environmental Engineering, Waseda University, Shinjuku-ku, Tokyo, 169-8555, Japan
3Nexco East Japan, Kisarazu-shi, Chiba, 292-0005, Japan4Department of Civil and Environmental Engineering, Tokyo Denki University, Hiki-gun, Saitama, 350-0394, Japan
Abstract
Ten specimens are tested to investigate the cyclic behavior of beam-to-column joints of steel frames with joint panels. Theperformances of the joints with respect to strength, rigidity, and hysteretic performance are examined. Three different load-carrying mechanisms can be identified. Panel resistance ratio (Rp) is presented for predicting the buckling patterns. The validityof Rp is confirmed through the present experimental results. On the basis of the experimental results of steel beam-to-columnmoment joints, 3-D nonlinear finite element models are established to analyze the mechanical properties of these connections.The load-displacement curves of the finite element analysis are in good agreement with those of the tests in terms of strengthand unloading stiffness. A shear lag phenomenon was captured in the beam flanges by not only experimental results but alsonumerical analysis. Parametric studies are conducted on the connections under monotonic loading to investigate the influencesof connection dimension, resistance ratio on the connection behavior. It was found that the failure modes are influenced by theresistance ratio, while the thickness of joint panels resulting in large effects on the strength and stiffness under shear failure mode.
Keywords: beam-to-column joints, shear panel, cyclic loading, hysteretic performance, FEA
1. Introduction
Recently, welded steel piers have been widely applied
for pier structures of urban overpasses and elevated
structures in East Asian countries due to their excellent
earthquake resistance capacity, small space requirements,
and short construction term. The behavior of weld steel
connections in frame structures is studied using experimental
investigation and numerical analysis by many researchers:
Beedle et al. (1951) proposed a stress and strength
evaluation method for an H-sectioned beam-to-column
connection by assuming that stresses are uniform in
flanges and webs. Fielding and Huang (1971) indicated
that the strength of the beam-to-column connection of H-
sectioned frame is reduced due to the axial force in the
column. Miki (1991) tested eight specimens of connections
with box beam and column up to the failure under the
condition of monotonic and cyclic loadings, test results
showed that the deformation capacity of connections was
significantly affected by the elasto-plastic deformation of
shear panels and instability caused by local buckling.
Hwang (1994a, b) presented the experimental investigations
on strength and ductility of connections with emphasis on
the influence of sectional-area ratio, width-thickness ratio
of panel zone and material properties in steel pier
structures. Shimizu (2000) made a series of numerical
analysis on the strength and behavior of the corner zones
in steel rigid frame columns with shifted beams which
has almost completely different from the one with no
shift, and the smaller shift reduces the ultimate strength.
Sasaki (2001) found that difference of stiffening methods
of shear panels affects damage modes and strength of
beam-to-column connections, and that the shear lag
phenomenon doesn’t affect the ductility of beam-to-
column. Kim (2008) investigated the design equations
and the strength behavior of the diaphragm for steel box
beams and circular column connections.
From the results of field investigations after 1995
Hyogoken-Nanbu earthquake (Watanabe, 1998), typical
damage to the steel bridge piers may be classified into:
(a) local buckling; (b) brittle crack failure; and (c) low-
cycle fatigue failure. Cracks due to fatigue are often
observed at the beam-to-column connection, which may
cause the brittle fracture of the pier in case of an
earthquake. Miki (2003, 2007) and Morikawa (2002)
Note.-Discussion open until November 1, 2010. This manuscript forthis paper was submitted for review and possible publication onApril 2, 2009; approved on April 26, 2010.
*Corresponding authorTel: +81-3-5286-3399; Fax: +81-3-3200-2567E-mail: [email protected]
132 Jun He et al. / International Journal of Steel Structures, 10(2), 131-146, 2010
indicated that the fatigue cracks are developed by the
high stress intensity and the existence of the un-welded
zone in the beam-to-column connection, also weld defects
due to inappropriate fabrication such as disapproved
change of weld details to partial penetration or fillet
welds instead of full penetration welds designed. Tanabe
(2005) and Shimizu (2008) arranged a hole (named as a
“Large Core” or “LC”) at the beam-to-column connection,
which is certainly effective to prevent the development of
the fatigue cracks due to the un-welded zone and the zone
subjected to the stress intensity near the connection is
removed by the core. The effect of a haunch, which is
often utilized to reduce the stress concentration in a
connection, is investigated numerically by Yamaguchi
(2000) and the result shows that a haunch enhances
rigidity and strength, but that it does not necessarily
improve ductility. Tanabe (2004) found the rib-installation
was effective to reduce stress concentration at the corner
and could improve fatigue performance of the beam-to-
column connections by finite element analyses and
fatigue tests. Kiuchi (2007) proposed the constant shear
flow panel analysis as the practical analysis technique in
a fatigue design of beam-to-column connection of steel
pier.
Severe earthquake will, in most case, lead to inelastic
behavior in conventional civil engineering structures. In
properly design moment resisting steel frames, the
inelastic deformations usually will be concentrated at the
column around base plates and may occur in the beam
section, the beam-to-column connection and the joint
panel zone. Relevant investigations under cyclic loading
are therefore needed. For these reasons a series of cyclic
tests on ten joints were conducted. The hysteretic energy
dissipation capabilities of the joints for various levels of
ductility were determined, and the mechanisms of failure
were identified. It has been accepted that the panel zone
should not be destroyed before the collapse of beam-
column connection, and even if shear buckling occurs,
the load carrying capacity does not decrease immediately
that significantly influence on the response of the cyclic
behavior of joint panel zones in beam-to-column
connections under high shear.
Finite element analysis were carried out taking into
account geometrical and material nonlinear effects based
on the test specimens. A comparison between experimental
and numerical results was made for load-displacement
relationships, buckling modes and stress distribution. In
the case of designing moment resisting steel frame
structures, a shear lag phenomenon is an important issue
should be taken into account. The results of the tests and
numerical analysis provide reference data for the
development of design rules for such joints when applied
in moment-resisting steel frames (MRF).
2. Experimental Test Program
2.1. Specimen descriptions
The specimens were selected from steel frame of
bridge pier, as shown in Fig. 1. The dimensions of the
specimens are shown in Fig. 2 and are summarized in
Table 1. The main parameters were the height and width
of the joint panel and the thickness of the web and the
flange. For the fabrication of the specimen, the two joint
members including the end plates were welded together.
All welds were carried out as two-sided fillet welds, as is
usually done by many steel fabricators.
2.2. Material properties
All specimens were made of JIS SS400. The material
properties of the specimens have been determined by
coupon tensile tests as prescribed by the relevant
standards. The results of the tests are summarized in
Table 2, where t is the thickness of steel plate; fy is the
yield strength of steel.
2.3. Test set-up and instrumentation
It is seldom feasible to model a complete structure due
to technical and economic difficulties. In such a case,
testing of an isolated part of the structure provides an
attractive alternative. The present test specimen is modeled
as beam-to-column connection and panel zone. The
testing system is shown schematically in Fig. 3. The
Table 1. Specimen dimensions
No. Specimenb
(mm)db
(mm)dc
(mm)db/bdc/b
Lb(mm)
Lc(mm)
tf(mm)
b/tftw
(mm)db/twdc/tw
1 00-No.1 300 300 300 1.00 894.3 894.3 9 33.33 6 50.00
2 00-No.2 300 270 270 0.90 879.3 879.3 9 33.33 6 45.00
3 00-No.3 300 240 240 0.80 864.3 864.3 9 33.33 6 40.00
4 00-No.4 300 210 210 0.70 849.3 849.3 9 33.33 6 35.00
5 00-No.5 300 310 310 1.03 899.3 899.3 9 33.33 6 51.67
6 02-No.1 260 200 200 0.77 874.0 844.0 9 28.89 9 22.22
7 02-No.2 260 260 260 1.00 874.0 874.0 9 28.89 9 28.89
8 02-No.3 210 200 200 0.95 889.0 844.0 9 23.33 9 22.22
9 02-No.4 280 200 200 0.71 884.0 844.0 9 31.11 6 33.33
10 02-No.5 205 205 205 1.00 846.5 846.5 9 22.78 9 22.78
Experimental and Numerical Study on Cyclic Behaviour of Steel Beam-to-Column Joints 133
specimen was supported by pin joints at both ends. The
load was transferred from the actuator to the specimen via
a rigid member which slid on the support, and its out-of-
plane displacements were completely restricted. Frictional
forces induced at the supports were determined to be
negligible. The actuator that imposes displacements or
loads had a 500 kN capacity both in compression and
tension, and a displacement capacity of ±125 mm. The
instrumentations used in this test were the load cell, the
linear variable displacement transducers (LVDTs), and
strain gauges. The total displacement was measured
easily by displacement transducer at the point of load
application. Measurement of the relative rotation at the
joint was given with particular attention. Two LVDTs
were set diagonal on panel to measure the shear
deformation. Strain gauges were intended to capture
strains adjacent to the column web and flange, as shown
in Fig. 4.
2.4. Test procedure
All of the specimens were subjected to quasi-statically
applied cycles of relative end displacement. The specimen
was subjected to axial force, shearing force and bending
Figure 2. Speimen demesions.
Table 2. Material properties of steel
Typet
(mm)fy
(MPa)
Young’s modulus(MPa)
Poisson’s ratio
Flange5.6 329 203000 0.29
8.5 320 195000 0.29
Web5.7 320 194000 0.28
8.5 310 190000 0.29
Figure 3. Test setup.
Figure 4. Test instrumentations.
Figure 1. MRF and beam-to-column joint.
134 Jun He et al. / International Journal of Steel Structures, 10(2), 131-146, 2010
Figure 5. P-Δ curves of the specimens.
Experimental and Numerical Study on Cyclic Behaviour of Steel Beam-to-Column Joints 135
moment. The applied load for the test was increased
continuously until failure, with all the strain and LVDT
recorded after each load increment.
The load cycles were applied according to the provision
of ECCS(1986). If the yield displacements in the two
directions of loading are denoted as and , the cycles
were applied as following: , , 2 , 2 , 3 , 3 ...
n , n . This procedure was continued until failure of
the specimen, which was considered to be reached when
the material of the web panel tore due to low cycle
fatigue.
3. Experimental Results
3.1. P-Δ hysteretic loops
The P-Δ hysteresis loops of the specimens are shown in
Fig. 5, in which P is the load applied to the end of the
beam and Δ is the displacement at the end of the beam.
The tensile load (open direction) is defined as positive (as
shown in Fig. 6).The hysteretic curves are compared, and
observations can be made as follows:
All the hysteresis loops of the connections are in a
shuttle type, and as a result, the energy dissipated per
loop is good, and all of them are stable and plentiful
except specimens 02-No.2 and No.3, as the column of
specimen 02-No.2 buckled in the third loop and the crack
initiated at welding of connection in the fourth loop,
while the column of specimen 02-No.3 buckled and the
crack initiated at welding of connection in the second
loop. Also, they have enough strength, good ductility, and
high-energy dissipation capacity.
The skeleton curves of the P-Δ hysteresis loops are
shown in Fig. 6. The curves are compared, it was found
that the 00-specimens mostly have the same normalized
ultimate strength, and the strength softed after the peak
vulae, while the 02-specimens kept the ultimate strength
till buckling, it may be caused by different buckling
modes for specimens-00 and 02. The normaized ultimate
strength of the connection with large width-thickness
ratio (b/tf) and web thickness (tw) (02-No.1) is higher
than that of the other connections for specimens-02.
3.2. Failure process and failure mode
3.2.1. Panel resistance ratio
It is very important to predict the buckling modes in
steel frame structures. On the basis of the former reference
(Namba et al., 1999), the buckling mode can be ralated to
the panel resistance ratio Rp, whcih is difined in the
following:
; ;
; ;
;
(1)
where pMp , cMp and bMp are the full-plastic moment of
the panel zone, the column, and the beam respectively,
σyp, σyb, σyc is the yield stress of the panel zone, the beam
and the column respectively, Wb and Wc are the plastic
section modulus of beam and column, db is the distance
between centers of flange for the beam, dc is the distance
between centers of flange for the column, t, tw, tf is the
thickness of the panel zone, the web and the flange
respectively, as shown in Fig. 2.
3.2.2. Failure mode
Failure modes for the test specimens are summarized in
Table 3, and the typical fracture phenomena of the
specimens are shown in Fig. 7. In the test, loads were
applied to the end of column in two different directions:
open and closed. Three different failure modes can be
identified, which are shear buckling of the joint panel, the
buckling of column, and both shear buckling of the joint
panel and buckling of column. For the connection
specimens with smaller panel resistance ratio Rp (00-
No.1~5), the main failure modes were shear buckling of
the joint panel. As for these specimens, the thickness and
width of the flange are larger than those of the web. On
the other hand, for the connection specimens with larger
panel resistance ratio Rp (02-No.1~5), the main failure
modes were buckling of the column or both shear
buckling of the joint panel and buckling of the column. It
was found that shear buckling took place on the joint
panel when Rp is less than 0.6.
vy+
vy-
vy+
vy-
vy+
vy-
vy+
vy-
vy+
vy-
Rp
Mp p
min Mc p Mb p,[ ]---------------------------------= Mp p
16σyp
9 3
-------------dbdct=
Mc p σycWc= Mb p σybWb=
Wc b tw+( ) tf× dc×tw
2----+ dc 2 tf×–( )
2×=
Wb b tw+( ) tf× db×tw
2----+ db 2 tf×–( )
2×=
Figure 6. Comparison of P-Δ skeleton curves of thespecimens.
136 Jun He et al. / International Journal of Steel Structures, 10(2), 131-146, 2010
During the test, fracture of the beam flange-to-column
welds occurred in some specimens, as shown in Fig. 8.
As a result, the hysteretic characteristics were influenced.
The crack initiated at the joint panel during cyclic loading
in open direction. Figure 8(b) shows the relationship
between load and displacement for the specimen whose
joint panel buckling, and it was found that the bearing
capacity reduced obviously after the crack initiated under
tensile load. Therefore, it is important to ensure the quality
of welds in connection applications, also arrangement of
a hole or reinforcement with a haunch at the beam-to-
column connection are effective to reduce stress
concentration and prevent the development of the fatigue
cracks.
3.3. Stress distributions
It is well known that shear lag phenomenon is observed
in the beam flange of steel frame structures. By recognizing
the shear lag phenomenon at box -sectioned beam-to-
column connections of the pier structure, Okumura and
Ishizawa (1968) carried out theoretical and experimental
studies using a simple beam model subjected to a
concentrated mid-span load. Instead of using a simple
beam model, Nakai et al. (1992) suggested an equation
for the shear lag stress from a study using an overhanging
beam model with additional moments due to shear
deformation occurring in the connection. Qi and Mimura
(2002) suggest design and strength evaluation method of
welded beam-column connection. Also, Hwang et al.
(2004) provide shear lag stress evaluation method for
box-sectioned welded connection using the additional
moment of cantilever beam model. Figures 9 and 10
show the surface stress distribution of the beam flange
close to the panel zone and the stress values calculated
Table 3. Summary of failure modes
Specimen Rp Failure modeMaximum resistance
reduction
00-No.1 0.564 B-JP greatly reduced
00-No.2 0.521 B-JP greatly reduced
00-No.3 0.475 B-JP greatly reduced
00-No.4 0.427 B-JP greatly reduced
00-No.5 0.578 B-JP greatly reduced
02-No.1 0.815 B-C not reduced
02-No.2 0.752 B-C not reduced
02-No.3 0.658 B-C not reduced
02-No.4 0.645 B-JP; B-C slightly reduced
02-No.5 0.638 B-C not reduced
B-JP, B-C stand for buckling of the joint panel and buckling ofcolumn respectively.
Figure 7. Typical fracture of the specimens.
Figure 8. Effect of crack on hysteretic characteristics.
Experimental and Numerical Study on Cyclic Behaviour of Steel Beam-to-Column Joints 137
from the beam thoery. Stress obtained from elementary
beam theory is as follows:
(2)
where N is the axial force; A is the area; I is the moment
of inertia; and y is the distance from the neutral axis.
Table 4 shows the principal stress results in comparsion
with beam thoery to FEA, and the relevant results of
shear lag factor (λ) for specimen 02-No.5, λ is defined as
follows:
(3)
where σpeak is the peak value of stress from FEA, σbeam is
the stress obtained from elementary beam theory.
It was obtained that under the first and second cycle of
loading, shear lag phenomenon was obvious, the value of
stress at both ends of the flange was greatly different to
that at the center. However, as the loading cycle
increased, the shear lag factor decreased, since after the
crack initiated, the stress entered inelastic state and
redistributed. And the value of shear lag factor for
specimen 02-No.5 under tensile and compressive load is
from 1.0 to 2.0.
3.4. Stiffness degradation
During the test, the stiffness decreased with the cyclic
loading for the reason of cumulative damnification. The
stiffness of specimens under cyclic loading can be
σN
A----
M
I-----y±=
λσpeak
σbeam
------------=
Table 4. Principal stress and shear lag factor
Load formElementary beam theory result:
principal stress (σbeam)/PaFEA result:
principal stress (σpeak)/PaShear lag factor
(λ)
Direction Cycle maximum minimum maximum minimum maximum minimum
Tensile load(Open)
1 1.630E+08 -1.393E+08 2.610E+08 -2.390E+08 1.60 1.72
2 1.944E+08 -1.661E+08 3.040E+08 -2.530E+08 1.56 1.52
4 2.379E+08 -2.033E+08 3.440E+08 -2.800E+08 1.45 1.38
Compressive load(Close)
1 1.860E+08 -1.589E+08 2.690E+08 -3.020E+08 1.45 1.90
2 2.198E+08 -1.878E+08 2.810E+08 -3.200E+08 1.28 1.70
4 2.415E+08 -2.064E+08 3.100E+08 -3.540E+08 1.28 1.72
Figure 9. Principle stress comparison of beam therory and FEA (open direction).
Figure 10. Principle stress comparison of beam therory and FEA (closed direction).
138 Jun He et al. / International Journal of Steel Structures, 10(2), 131-146, 2010
evaluated by the index-cyclic stiffness (Tang 1989),
which can be calculated as follows:
(4)
where Kl is the cyclic stiffness; is the peak load of the
i-th cycle when the deformation is controlled as Δj, as
shown in Fig. 11; is the peak displacement of the i-th
cycle when the deformation is controlled as Δj; and n is
the number of cycles when the deformation is controlled
as Δj.
The Kl-Δ curves of the specimens are shown in Fig. 12.
These cyclic stiffness degradation curves are compared,
and observations can be made as follows:
(1) The cyclic stiffness of the specimens degraded
steadily during the entire test process.
(2) The stiffness of the connection with thick and wide
web plate is higher than that of the other connections.
(3) The positive stiffness value is almost the same as
the negative one, only at the beginning cycle the
negative stiffness is a little larger than the positive
one.
3.5. Ductility and energy dissipation capacity
The En-nc curves, he-nc curves, and normalized En-he
curves of the specimens are shown in Figs. 13~15,
respectively, where En is the energy dissipated per cycle
of the hysteresis loops, nc is the number of cycles, and he
is the equivalent damping ratio of the specimens. These
curves are compared, and observations can be made as
follows:
(1) The energy dissipation capacities of the specimens
increased with the increase in cycles of the
hysteresis loops. After the connections reached
their ultimate capacities, the strength of some
connections went down, but the energy dissipation
capacities still grew.
(2) The average final equivalent damping ratios of the
connections of 00-No.1~5 and 02-No.1~5 are
shown in Table 5. Comparing this data with the
results of the concrete connections (Zhou et al.,
2004), it can be concluded that the energy
dissipation capacity is much higher than that of the
concrete connections.
(3) The normalized dissipation capacities En/E1
increased with the equivalent damping ratio,
especially at the end of the loop, En/E1 growed
rapidly while he increased slowly even kept
invariant in some specimens.
4. Finite Element Analysis
4.1. Finite element model
On the basis of the experimental results of steel beam-
column moment joint, 3-D nonlinear finite element models
are established using genearal finite element program
ABAQUS (2001) to analyze the mechanical properties of
these connections. The effects of both geometrical and
material nonlinerities are taken into account. Two kinds
of elements were adopted in the finite element models:
• S4R element. This is a four-node doubly curved
general-purpose shell with six degrees of freedom at each
node, namely translations in the x, y, and z directions, and
rotations about the x, y, and z axes. And reduced
integration with hourglass control is adopted, it was used
to model the steel plate.
• B31 element. This is a two-node linear beam element.
The element has six degrees of freedom at each node,
namely translation in the nodal x, y, and z directions and
rotations about the nodal x, y, and z axes. It was used to
model the rigid part connecting the specimen to the
support.
Kl Pj
i
i 1=
n
∑ Δj
i
i 1=
n
∑⁄=
Pj
i
Δj
i
Figure 11. Definition of cyclic stiffness.
Figure 12. Comparison of Kl-Δ curves.
Experimental and Numerical Study on Cyclic Behaviour of Steel Beam-to-Column Joints 139
4.2. Material properties
The von Mises yield criterion with kinematic hardening
rule was adopted to model the steel material in the finite
element analysis. The bilinear stress-strain relationship,
as shown in Fig. 16, was used to model the steel plate.
Based on the material test of steel for the specimen, for
simplification, Et=0.01Es, σs is the stress, εs is the strain,
fy is the yield strength, εy is the yield strain, Es is the
Young’s modulus, and Et is the hardening modulus of
steel, respectively. For the steel material in the finite
element model, the elastic modulus Es and Poisson’s ratio
νs were assumed to be 1.95×105 MPa and 0.3, respectively.
4.3. Finite element mesh and boundary conditions
Three-dimensional numerical models were established
to represent the test specimens. The finite element meshes
of the connections are shown in Fig. 17.
To simulate the experiments, the same loading conditions
and constraints as the experiments were used in the finite
element analysis. The numerical models were loaded as
the experiment did, the rollers of the test setup were
modeled and the cyclic load was applied to the bottom
roller. The displacements in the x, y, and z directions and
the rotations about the x and z axes of the upper roller
were constrained. While, rotation about the y axis of the
model and displacement in the z direction of the bottom
support are free. The end of the beam and the surface of
the shell connected by the methods of multi-point
constraints. The Newton-Raphson equilibrium iteration
method was used to solve the nonlinear problems.
Figure 13. Comparison of En-n
c curves of the specimens.
Figure 14. Comparison of he-n
c curves of the specimens.
Figure 15. Comparison of normalized En-h
e curves of the specimens.
Table 5. Equivalent damping ratios of the connections
Series No.1 No.2 No.3 No.4 No.5 Ave.
00 0.392 0.372 0.379 0.407 0.361 0.382
02 0.238 0.259 0.122 0.376 0.269 0.253
140 Jun He et al. / International Journal of Steel Structures, 10(2), 131-146, 2010
4.4. Numerical results
Numerical P-Δ curves under cyclic loading are compared
with the experimental curves, as shown in Fig. 18. In
which typical specimen with different failure modes are
chosen to investigate the cyclic behavior. The finite
element analysis results showed fairly good agreement
with the experimental ones in terms of strength, deformation,
and unloading stiffness.
The comparisons of the yield strength and ultimate
strength of the connections are given in Table 6. Based on
the comparison of Table 6 and Fig. 18, it is found that the
strengths calculated from numerical models under cyclic
loading are approximate to the test results. Figure 19
shows the comparison of numerical and experimental
failure deformation under ultimate loading for specimen
02-No.4, the buckling occurs at the joint panel and
column flange near connection from the FE analysis, that
is the same as the experimental result. Only the comparison
result of specimen 02-No.4 was presented due to the
limited space. Comparison of experimental results and
numerical ones for En-n
c curves, h
e-n
c curves, and
nomalized En-h
e are shown in Figs. 20, 21 and 22
respectively. The results of average energy dissipated per
cycle and equivalent damping ratios calculated by the FE
models and obtained from tests are summarized in Table
7. The dissipated energy and equivalent damping ratios
from the finite element analysis agreed well with those of
the tests, and the trends are almost the same for the
numerical results and experimental ones. Therefore, the
finite element models can be used to provide some
guidance in the design of the MRF connections.
5. Parametric Analyses
In order to investigate the effects of different parameters
on the behavior of the connections, parametric analysis
Figure 16. Bilinear stress–strain relation model used for steel.
Figure 17. Finite element model.
Table 6. Comparison of experimental and numerical results under cyclic loading
SpecimenLoadingdirection
Yield strength (kN) Ultimate strength (kN)
Pyc,FEA Pyc,E Pyc,FEA/Pyc,E Puc,FEA Puc,E Puc,FEA/Puc,E
00-No.5+ 216 207 1.04 250 279 0.90
- -215 -239 0.90 -268 -280 0.96
02-N0.4+ 122 86 1.42 166 152 1.09
- -120 -110 1.09 -155 -158 0.98
02-No.5+ 149 131 1.14 188 195 0.96
- -145 -159 0.91 -176 -200 0.88
Average 1.08 0.96
Standard deviation 0.19 0.08
Pyc,FEA, Pyc,E and Puc,FEA, Puc, E are the yield strength and ultimate strength under cyclic loading from finite element analysis predictionand experimental results, respectively.
Experimental and Numerical Study on Cyclic Behaviour of Steel Beam-to-Column Joints 141
Figure 18. Comparison of experimental and numerical P-Δ curves under cyclic loading.
Figure 19. Typical numerical and experimental strain distribution and deformation of the connections (02-No.4).
Figure 20. Comparison of experimental and numerical results for En-n
c curves.
Figure 21. Comparison of experimental results and numerical ones for he-nc curves.
142 Jun He et al. / International Journal of Steel Structures, 10(2), 131-146, 2010
were conducted based on the numerical model of the
connections under monotonic loading. The panel resistance
ratio, and dimensions of the web and flange were varied
in the finite element models, and their effects were
observed and are summarized below.
5.1. Panel resistance ratio
On the basis of the test specimen 02-No.1 to No.5, the
thickness of web and flange was changed to obtain
different panel resistance ratio Rp, the dimension and Rp
of the modified models and test specimen are shown in
Figure 22. Comparison of experimental results and numerical ones for normalized En-he curves.
Table 7. Comparison of experimental and numerical results of dissipated energy and equivalent damping ratios undercyclic loading
Specimen EFEA/kN·mm Ee/kN·mm EFEA/Ee hcFEA hce hcFEA/hce
00-No.5 10282 10401 0.99 0.35 0.36 0.98
02-N0.4 7353 7815 0.94 0.33 0.38 0.87
02-No.5 4997 6312 0.79 0.23 0.27 0.85
Average 0.91 0.90
Standard deviation 0.10 0.07
EFEA is the average energy dissipated per cycle from finite element prediction, and Ee is the average energy dissipated per cycle fromtests.
Table 8. Summary of failure modes of different Rp
Specimen Rp
Web thickness/mm
Flange thickness/mm
Failure modeMaximum resistance
reduction
02-No.4w9 1.156 9 6 column buckling greatly greatly reduced
02-No.1w6 0.898 6(panel 9) 9 column buckling greatly greatly reduced
02-No.4w6f6 0.878 6 6 column buckling greatly greatly reduced
02-No.4w9f9 0.877 9 9 column buckling greatly greatly reduced
02-No.1w6f6 0.815 6 6 column buckling greatly greatly reduced
02-No.1 0.815 9 9 column buckling not reduced
02-No.2w6f6 0.753 6 6 column buckling greatly greatly reduced
02-No.2 0.752 9 9 column buckling not reduced
02-No.3w6 0.726 6(panel 9) 9 column buckling greatly greatly reduced
02-No.3w6f6 0.658 6 6 column buckling greatly slightly reduced
02-No.3 0.658 9 9 column buckling not reduced
02-No.4 0.645 6 9 both joint panel and column buckling slightly reduced
02-No.5w6f6 0.638 6 6 both joint panel and column buckling not reduced
02-No.5 0.638 9 9 column buckling not reduced
00-No.5 0.578 6 9 joint panel buckling greatly reduced
00-No.1 0.564 6 9 joint panel buckling greatly reduced
00-No.2 0.521 6 9 joint panel buckling greatly reduced
00-No.3 0.475 6 9 joint panel buckling greatly reduced
00-No.4 0.427 6 9 joint panel buckling greatly reduced
Experimental and Numerical Study on Cyclic Behaviour of Steel Beam-to-Column Joints 143
Table 8. It can be seen that the failure modes are
influenced by the resistance ratio, the shear buckling
occurs at the joint panel when Rp is less than 0.6, and the
bending buckling take place at the column when Rp is
more than 0.7, however, the failure mode is very
complicated when Rp is between 0.6 to 0.7, both shearing
and bending bucklings appear at the joint panel and the
column respectively.
5.2. Web thickness
Based on the specimen 02-No.1, the thickness of web
changes from 9 mm to 6 mm, the thickness of joint panel
keeps invariant. The displacement under monotonic
compressive load in closed direction is shown in Fig. 23.
And the failure mode is shown in Fig. 24. It can be seen
that the strength drops obviously at the displacement of
26 mm (D/Dy=3.7) for 02-No.1w6 model due to bending
buckling occured at the column near connection, but the
stength increases until the displacement reaches to
108 mm (D/Dy=14.8) for 02-No.1 model. The failure
modes for two different web thickness model are the
same except the deformation degree and post-buckling
behavior, since the parameter Rp of both models is more
than 0.7.
5.3. Beam and column length
Based on the specimen 02-No.3, the length of beam and
column changes to 2 times of specimen 02-No.3, the other
parameters keep invariant. The displacement under
monotonic compressive load in closed direction is shown
in Fig. 25. And the failure mode is shown in Fig. 26. It can
be seen that the strength drops obviously at the displacement
of 72 mm (D/Dy=9.3) for 02-No.3w6 model comparing to
02-No.3 due to bending buckling occured at the column
near the joint panel. As the length of column and beam
increases, the ultimate strength reduces, but the normalized
Figure 23. P-Δ curve for different web thickness.
Figure 24. Failure mode comparison.
Figure 25. P-Δ curve for different beam and column length.
Figure 26. Failure mode comparison.
144 Jun He et al. / International Journal of Steel Structures, 10(2), 131-146, 2010
strength F/Fy increases with the length of the column and
the beam. The failure modes for different beam and
column length models are the same except the deformation
degree and post-buckling behavior, since the parameter Rp
of the models is in the same buckling mode region.
5.4. Section constitution type
Based on the specimen 02-No.4, the thickness of the
web, flange and joint panel is changed to form four
different section constitution type, as follows: Type1-02-
No.4; Type2-thickness of the joint panel changed to 12
mm; Type3-thickness of the web changed to 9 mm;
Type4- thickness of the web changed to 9 mm and
thickness of the flange changed to 6 mm, with reference
to Fig. 27. The displacement under monotonic compressive
load in closed direction is shown in Fig. 28. It can be seen
that the ultimate strengths for type 2, 3 are more than type
1, 4. The thicker joint panel improves the ultimate
strength from the comparison of type 2 to type 1. And
aslo the increase of the thickness of flange (tf) and web
(tw) would improve the ultimate strngth from comparsion
of type 3 to type 1, 4.
The load carrying capacity decreases rapidly after
ultimate strength, which means the energy absorption
capacity is lower, this behavior should be avoided in the
design. And for the sake of convenient maintenance, the
same thickness of web and flange are chosen.
5.5. Disscussion
On the basis of the test results in this research and
previous studies (Miki, 1991; Hwang, 1994a), the
Figure 27. Section constitution type (Bule: 6 mm; Red:9 mm-except for joint panel is 12 mm in type 2).
Figure 28. P-Δ curve for different section constitution type.
Figure 29. Relationship between buckling mode and Rp.
Figure 30. Effect of Rp on strength Pu/Py.
Figure 31. Relationship between section-area ratio S andRp.
Experimental and Numerical Study on Cyclic Behaviour of Steel Beam-to-Column Joints 145
relationship between the bucking modes and resistance
ratio Rp is shown in Fig. 29, it was found that the shear
buckling or shear hinge occured at the joint panel when
Rp is less than 0.6, and the bending buckling takes place
at the column or beam when Rp is more than 0.7,
however, the failure mode is very complicated when Rp is
between 0.6 to 0.7, both shearing and bending buckling
appears at the joint panel and column respectively. The
effect of Rp on the strength (Pu/Py: Pu-ultimate load, Py-
yiled load) is shown in Fig. 30, the harden strength
decreased with Rp when its value less than 0.6, due to the
ultimate strength reduced greatly after joint panel backling.
There were no obvious trends between the strength (Pu/
Py) and Rp when its value more than 0.6, it may caused
by different bucking modes. The relation between
sectional-area ratio S (Hwang, 1994a) and Rp is shown in
Fig. 31, the Rp increased almost linearly with S, some
deviations occured as Rp not only included the influence
of the section parameters but aslo the material properties.
Therefore, Rp can be used to predict the buckling mode of
the beam to column connection in preliminary design
stage.
6. Conclusions
The experimental and numerical studies are performed
to investigate the cyclic behavior of beam-to-column
joints of steel frames. The performance of the joints with
respect to strength, rigidity, and hysteretic performance
are examined. Three different load-carrying mechanisms
including shear bucking of the joint panel, the buckling of
column, and both shear bucking of the joint panel and
buckling of column are identified. Panel resistance ratio
is presented for predicting the buckling patterns. The
validity of the present parameter is confirmed through the
present experimental results.
3-D nonlinear finite element models are established to
analyze the mechanical properties of these connections.
The load-displacement curves of the finite element analyses
are in good agreement with those of the tests in terms of
strength and unloading stiffness. And the failure modes
caculated form FEA is the same as those of the tests. The
bearing capacity reduces obviously after the crack
initiates under tensile load. And the crack initiation is
very difficult to simulate by the use of FEA. Therefore, it
is important to ensure the quality of welds in connection
applications. The dissipated energy and equivalent
damping ratios from the finite element analysis agreed
well with that of the tests, and the trends are almost the
same for the numerical results and experimental ones.
Therefore, the finite element models can be used to
provide some guidance in the design of the MRF
connections. A shear lag phenomenon was captured in
the beam flanges by not only experimental results but
also numerical analysis that should be taken into account
for the design of the MRF connections. Parametric studies
are conducted on the connections under monotonic loading
to investigate the influences of connection dimension,
panel resistance ratio on the connection behavior. It was
found that the failure modes are influenced by the
resistance ratio, the shear buckling occurs at the joint
panel when Rp is less than 0.6, and the bending buckling
takes place at the column when Rp is more than 0.7,
however, the failure mode is very complicated when Rp is
between 0.6 to 0.7, both shearing and bending buckling
appears at the joint panel and column respectively. The
vaule of Rp is recommended to predict the buckling mode
of the beam to column connection in preliminary design
stage.
Acknowledgments
Assistances for experimental studies from Prof. IURA
inTokyo Denki University, Engineer TAKAKU in NEXCO
EAST JAPAN are appreciated. This paper was written
when the first author visited Prof. YODA’s Lab in
Department of Civil and Environmental Engineering,
Waseda University, Japan supported by China Scholarship
Council. The support is gratefully acknowledged.
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