Experimental and numerical study on cyclic behaviour of...

www.ijoss.org

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.


Figure 5. P-Δ curves of the specimens.


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.


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





02-No.1 0.815 B-C not reduced



02-No.4 0.645 B-JP; B-C slightly 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.


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).


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.


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


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.


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.


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.1 0.815 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.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


00-No.5 0.578 6 9 joint panel buckling greatly reduced






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.


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.


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.

References

Beedle, L. S., Topractsoglou, A. A., and Jonhston, B. G.

(1951). “Connection for welded continuous portal

frames.” Welding Journal, 30, pp. 354s-84s.

European Convention for Constructional Steelwork (ECCS)

(1986). Recommended testing procedure for assessing the

behaviour of structural steel elements under cyclic loads.

ECCS Publ, No. 45, Rotterdam, The Netherlands.

Fielding, D. J. and Huang, J. S. (1971). “Shear in steel beam-

to-column connections.” Welding Research, Supplement,

7, pp. 319-326.

Hwang, W. S. and Nishimura, N. (1994a). “Experimental

investigations on strength and ductility of connections in

steel frame pier structures.” Journal of Structural

Engineering, 40A, pp. 201-214 (in Japanese).

Hwang, W. S. and Nishimura, N. (1994b). “Strength and

ductility of panel zone in steel frame connections.”

Journal of Structural Engineering, 40A, pp. 215-226 (in

Japanese).

Hwang, W. S., Kim Y. P., and Park, Y. M. (2004).

“Evaluation of shear lag parameters for beam-to-column

connections in steel piers.” Structural Engineering and

Mechanics, 17(5), pp. 691-706.

Hibbit, Karlsson & Sorenson Inc. (2001). ABAQUS user’s

manual-version 6.2.4. Pawtucket, RI.

Kim, Y. P. and Hwang, W. S. (2008). “Evaluation of

diaphragm effect for steel welded box beam and circular

column connections.” International Journal of Steel

Structure, 8(3), pp. 189-198.

Kiuchi, K., Tamakoshi, T., and Ishio, M. (2007).

“Examination of analytical method using ‘the constant

shear flow panels’ for the beam-to-column connections of

steel piers.” Journal of Structural Engineering, 53A, pp.

57-66 (in Japanese).

Miki, C., Hirabayashi, Y., Tokida, H., Konishi, T., and


Yaginuma, Y. (2003). “Beam-column connection details

of steel pier and their fatigue damage mode.” Proc. the

Japan Society of Civil Engineers, 65, pp. 105-119 (in

Japanese).

Miki, C. and Hirabayashi, Y. (2007). “Fatigue damage cases

due to inappropriate fabrication in steel bridge

structures.” Proc. the Japan Society of Civil Engineers,

63(3), 518-532 (in Japanese).

Miki, T. (1991). “Experimental studies on collapse behaviors

and deformation capacity of steel beam-to-column

connections.” Journal of Structural Engineering, 37A,

pp. 121-134 (in Japanese).

Morikawa, H., Shimozato, T., Miki, C., and Ichikawa, A.

(2002). “Study on fatigue cracking in steel bridge piers

with box section and temporally repairing.” Proc. the

Japan Society of Civil Engineers, 703, pp. 177-183 (in

Japanese).

Namba, H., Tabuchi, M., and Tanaka, T. (1999). “Behavior

of joint panels in CHS column to beam connections.”

Journal of Structural and Construction Engineering, 518,

pp. 95-102 (in Japanese).

Nakai, H., Miki, T., and Hashimoto, Y. (1992). “On limit

state design method considering shear lag phenomenon of

corner parts of steel rigid frames.” Proc. the Japan

Society of Civil Engineers, 455, pp. 95-104 (in Japanese).

Okumura, T. and Ishizawa, N. (1968). “The design of knee

joints for rigid steel frames with thin walled section.”

Proc. the Japan Society of Civil Engineers, 153, pp. 1-18

(in Japanese).

Qi, W. B. and Mimura, H. (2002). “Welded beam-column

connection SCGO design and evolution.” International

Journal of Steel Structures, 2(2), pp. 87-93.

Sasaki, E., Takahashi, K., Ichikawa, A., Miki, C., and Natori,

T. (2001). “Influences of stiffening methods on elasto-

plastic behavior of beam-to-column connections of steel

rigid frame piers.” Proc. the Japan Society of Civil

Engineers, 689, pp. 201-214 (in Japanese).

Shimizu, S. and Nakano, M. (2000). “Strength and

behaviour of the corner zones in steel rigid frame

columns with shifted beams.” Journal of Constructional

Steel Research, 53, pp. 245-263.

Shimizu, S. (2008). “Strength of a corner zone of a frame

structure with a hole to prevent from the fatigue crack.”

Thin-Walled Structures, 46, pp. 792-799.

Tanabe, A., Miki, C., Ichikawa, A., Sasaki, E., and

Shimozato, T. (2004). “Fatigue strength improvement of

beam-to-column connections with box section in steel

bridge frame piers.” Proc. the Japan Society of Civil

Engineers, 733, pp. 137-148 (in Japanese).

Tanabe, A., Sasaki, E., and Miki, C. (2005). “Seismic

performance of steel bridge frame piers with fatigue

retrofitting at beam-to-column.” Journal of structure

engineering, 51A, pp. 1257-1266 (in Japanese).

Tang, J. R. (1989). Seismic resistance of joints in reinforced

concrete frames. Southeast Univ. Press Nanjing, China

(in Chinese).

Watanabe, E., Sugiura, K., Nagata, K., and Kitane, Y.

(1998). “Performances and damages to steel structures

during the 1995 Hyogoken-Nanbu earthquake.” Engineering

Structures, 20(4-6), pp. 282-290.

Yamaguchi, E., Ichikawa, A., Ikeda, M., Kubo, T., and Miki,

C. (2000). “Effect of haunch at connection of steel

moment frame subjected to cyclic loading.” Journal of

structure engineering, 46A, pp. 119-125 (in Japanese).

Zhou, T. H., He, B. K., Chen, G. J., Wei, C. W., and Shan,

Y. M. (2004). “Experimental studies on seismic behavior

of concrete-filled steel square tubular column and steel

beam joints under cyclic loading.” Journal of Building

Structures, 25(1), pp. 9-16 (in Chinese).

本文献由“学霸图书馆-文献云下载”收集自网络，仅供学习交流使用。

学霸图书馆（www.xuebalib.com）是一个“整合众多图书馆数据库资源，

提供一站式文献检索和下载服务”的24 小时在线不限IP

图书馆。

图书馆致力于便利、促进学习与科研，提供最强文献下载服务。

图书馆导航：

图书馆首页文献云下载图书馆入口外文数据库大全疑难文献辅助工具

http://www.xuebalib.com/cloud/

http://www.xuebalib.com/

http://www.xuebalib.com/cloud/


http://www.xuebalib.com/vip.html

http://www.xuebalib.com/db.php

http://www.xuebalib.com/zixun/2014-08-15/44.html


Experimental and numerical study on cyclic behaviour of...

Documents

Transcript of Experimental and numerical study on cyclic behaviour of...