Tenth U.S. National Conference on Earthquake EngineeringFrontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska 10NCEE

HYSTERETIC BEHAVIOR OF H STEEL COLUMNS WITH LARGE WIDTH-

THICKNESS RATIOS UNDER BI-AXIS MOMENTS

Y. Y. Chen1, L. Niu2, X. Cheng3

ABSTRACT It is common that H steel is used as a beam or column member in frame structures. During earthquake ground motion, the frames are actually subjected to horizontal loads in two directions simultaneously, so their columns are subjected to biaxial moments. In this paper, the hysteretic behavior of H steel columns subjected to axial compression and biaxial moments are studied. The emphasis of the study is to illustrate the post buckling performance of the relatively thin-walled steel members. The main parameters set in the test include the axial force ratio, the proportion of the horizontal loads in two directions, and the width-thickness ratios of flange and web of H steel columns. Cantilever columns as specimens were cyclically tested, and the characters of seismic performance of H steel columns under axial compression and bi-axis moments were discussed.

1Professor, State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai, China, 200092, yiyichen@tongji.edu.cn 2Graduate Student Researcher, State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai, China, 200092, firstdance@163.com 3Graduate Student Researcher, State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai, China, 200092, xcheng0309@gmail.com Chen YY, Niu L, Cheng X. Hysteretic behavior of H steel columns with large width-thickness ratios under bi-axis moments. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

Hysteretic Behavior of H Steel Columns with Large Width-Thickness Ratios Under Bi-axis Moments

Y. Y. Chen1, L. Niu2, X. Cheng3

ABSTRACT It is common that H steel is used as a beam or column member in frame structures. During

earthquake ground motion, the frames are actually subjected to horizontal loads in two directions simultaneously, so their columns are subjected to biaxial moments. In this paper, the hysteretic behavior of H steel columns subjected to axial compression and biaxial moments are studied. The emphasis of the study is to illustrate the post buckling performance of the relatively thin-walled steel members. The main parameters set in the test include the axial force ratio, the proportion of the horizontal loads in two directions, and the width-thickness ratios of flange and web of H steel columns. Cantilever columns as specimens were cyclically tested, and the characters of seismic performance of H steel columns under axial compression and bi-axis moments were discussed.

1 Introduction H-shaped steel is commonly used as beam and column members in building frames. Because of the excellent behavior of the steel frame structures, they are widely adopted in seismic zones. When the structure is arranged in a regular form, the model of structure for analysis is usually treated as a planar frame due to the merit of simplicity. During earthquake ground motion, however, the frame suffers from horizontal loads in two directions simultaneously, so the columns are actually subjected to bi-axis moments. The engineers have been aware of the issue and the researchers carried out studies on bi-axis bending behavior of H shaped steel columns [1-6]. A general review indicated that main achievements in the past were concerned with monotonic loading behavior, and the tested or analyzed members were with stocky sectional elements [7]. For the reduction of environment impact, adopting light weight steel members in structural frames is tempting, while the hysteretic behavior of such members have not been 1Professor, State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai, China, 200092, yiyichen@tongji.edu.cn 2Graduate Student Researcher, State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai, China, 200092, firstdance@163.com 3Graduate Student Researcher, State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai, China, 200092, xcheng0309@gmail.com Chen YY, Niu L, Cheng X. Hysteretic behavior of H steel columns with large width-thickness ratios under bi-axis moments. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

deeply studied. In the current research, the hysteretic behavior of built-up H steel columns subjected to axial compression and bi-axis moments are experimentally studied. The test columns are composed of relatively thin plates belonging to non-compact or slender elements, so the emphasis of the study is put on the post buckling performance of the steel members. Based on the laboratory observation, the characters of seismic performance of H steel columns under axial compression and bi-axis moments are discussed.

2 Mechanical properties of biaxial bending members The mechanical properties of steel members under biaxial bending are distinct from those under uni-axis bending. Fig. 1 schematically shows the loading and deforming of an H-section cantilever member subjected to axial force and biaxial loading. There are six internal force components, including the axial force (N), shear forces along two principle axes (Vx and Vy), bending moments about two principle axes (Mx and My) and torsional moment (Mz). Under such loading condition, despite two horizontal displacements (ux, uy), the torsional deformation (γ) is also inevitable to the member.

Figure 1. Loading and deforming of H-section beam-column under biaxial bending

(a) Resultant force and

displacement (b) force and displacement

component in x-y coordinate (c) force and displacement

component in X-Y coordinate Figure 2. Force and displacement relationships.

It is noticed that, the flexural stiffnesses of H-section members about two principle axes are significantly different from each other. As a result the directions of resultant force vector (V) and resultant displacement vector (u) would not coincide with each other, as shown in Fig. 2 (a).

z

x

y

N

VyVx

My

Mz

Mx

L

x

y

ux

u y

γN

Vy

Vx

Y

xαwh

bf

b

h

tf

tw

y

X

u

V

x

y

u

V

Vx

Vy

ux

uy

α

X

Y

x

y

u

V

αVY VX

X

Y

With the development of plastic deformation of the member, V and u would demonstrate a complicated relation. Generally, the inelastic features of biaxial loading can be investigated through the relationships of shear forces and horizontal displacement components along the corresponding principle axes, i.e. Vx~ux and Vy~uy, as shown in Fig. 2 (b). However, it is difficult in the experimental study to apply displacements along two directions simultaneously while obtain accurate reaction forces. Thus, instead of applying displacements along x and y axes respectively, in this study a testing system, considered to be more feasible to realize, was to apply displacement along X-axis (target resultant displacement direction) and measure reaction forces along X and Y axes (VX and VY), as shown in Fig. 2 (c). Then the relationships of Vx~ux and Vy~uy can be easily derived through simple calculations. The angle between resultant displacement u and strong axis of the H-section (x-axis) is denoted as loading angle (α) in this paper, representing the initial proportion of the horizontal loads in two directions. For the biaxial scenario, α is one of the main characters that affect the member’s inelastic behavior.

3 Test Program 3.1 Test facilities The loading condition of the specimens, as shown in Fig. 3, was cantilever beam-columns subjected to constant vertical load (N) and cyclic horizontal displacement (u). The top of the specimen connected to two horizontal actuators and a vertical oil jack (Fig. 4). With the help of a universal hinge connection, on the top, the specimen could rotate freely and only the shear forces and the axial force could be transferred to the specimen, thereby the free end boundary condition could be realized. All the three loading devices were settled perpendicular to each other, applying 3D forces to the specimen. Oil jack 1 applied the constant vertical load; Actuator 2 generated the cyclic horizontal displacement u and therefore the load VX; meanwhile the displacement in the direction of Actuator 3 was kept as zero during the whole loading process to generate load VY. All the loading devices were connected to the hinge connection on one end and on the other end to the sliding devices, where only linear movement along the given direction was possible. As a result, the horizontal loads and the constant vertical load could act on the specimen along the horizontal and vertical directions respectively during the entire test. To ensure a fixed restraint on the bottom, the specimen was bolted to a reaction frame through a rigid foot.

(a) Plane view in X-z plane (b) Spatial view (c) Top view

Figure 3. Loading condition.

(a) Designed program (b) Photo of testing system Figure 4. Testing system.

3.2 Specimen design With the combinations of different flange and web width-thickness ratios, axial force ratios and loading angles, 15 built-up H-section cantilever specimens were designed in this study to investigate the influence of these parameters on the cyclic biaxial bending behavior. The nominal length L (Fig. 3 b) was taken as 1500 mm for all the specimens. The descriptions of the geometric dimensions are shown in Fig. 2 (a). All the specimens were fabricated from low alloy

w

L

u

X

z

N

z

L

NVY

VX X

Y

x

y

u

αVY VX

X

Y

x

y

structural steel plates (nominal yield stress fy=345MPa) with the nominal thickness of 4mm, 6mm and 8mm, of which the measured mechanical properties are listed in Table 1.

Table 1. Measured mechanical properties of steel plates Nominal Plate thickness (mm)

Actual thickness (mm) fy (MPa) fu (MPa) E (MPa) δ (elongation factor)

4 3.8 392 507 2.01E+5 35.1％ 6 6.0 350 499 2.03E+5 30.2％ 8 7.9 361 546 1.98E+5 31.3％

Table 2 summarizes the basic parameters of the test specimens, where the values of rw, rf, λy, λx and axial force ratio n were calculated from the measured sizes and yield stress. Different cross-section combinations were achieved through various steel plate combinations for the specimens, such that the interactive effects of the flange/web width-thickness ratios could be fully investigated. The effect of axial force ratio can be investigated considering two levels of axial force ratio (expressed by n=N/Ny), namely 0.2 and 0.4, where Ny is the nominal yield axial load. Moreover, loading angles α for specimens were taken as 15° and 30° to investigate the effect of loading directions.

Table 2. Basic parameters of the specimens

Specimen No. h×b×tw×tf rw* rf* λx* λx* N(kN) Actual n (nominal n) α

B1-0.2-15 300×200×6×4 59.5 34.0 25.6 76.0 231 0.2(0.19) 15° B2-0.2-15 350×150×4×6 114.9 15.3 20.8 91.2 217 0.2(0.19) 15° B3-0.2-15

350×175×4×4 116.4 29.7 21.3 84.0 191 0.2(0.19) 15°

B3-0.2-30 30° B4-0.2-15

350×200×4×6 114.9 20.3 20.1 64.3 259 0.2(0.19)

15° B4-0.2-30 30° B4-0.4-15 114.9 20.3 20.0 64.1 518 0.4(0.39) 15° B5-0.2-15

300×175×4×4 97.9 20.3 23.2 63.2 245 0.2(0.19)

15° B5-0.2-30 30° B5-0.4-15 97.9 20.3 23.6 62.4 490 0.4(0.39) 15° B6-0.2-15 300×150×4×6 97.9 15.3 24.0 88.1 204 0.2(0.19) 15° B7-0.2-15

375×175×6×8

52.7 13.7 26.1 73.5 300 0.2(0.19) 15°

B7-0.2-30 30° B7-0.4-15

52.7 13.7 26.4 74.1 600 0.4(0.39) 15°

B7-0.4-30 30°

*Note: f f f yf( / ) / 235r b t f= ; w w w yw( / ) / 235r h t f= ; fyf, yield stress of the flange; fyw, yield stress

of the web; λx, member slenderness about x-x axis; λy, member slenderness about y-y axis; n, axial force ratio.

3.3 Loading condition and protocol During the test, the axial force was applied to the specimen firstly and then maintained constant. Cyclic horizontal displacement u in terms of increasing displacement amplitudes towards 10ue was subsequently applied (Fig. 5) with the cooperation work of two horizontal actuators. ue is the nominal yield displacement, which was roughly taken as 8mm for all the specimens with n=0.2 and α=15° and 6mm for the rest specimens according to the calculation. Notable deterioration of strength and stiffness of members with large width-thickness ratios under repeated loading cycles has been pointed out by references [8-10]. In order to investigate such effect, three cycles were repeated for every displacement amplitude. Beyond that, the structure was pushed up to complete failure, till the specimen completely lost its resistance against the lateral load.

-100

-80

-60

-40

-20

0

20

40

60

80

100

u/u e

Cycle Figure 5. Loading protocol.

4 Cyclic bending test on steel column

4.1 Test on specimens subjected to uni-axis bending

W-H4-0.2(α=0°) S-H4-0.2(α=90°)

Hysteretic curves

-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06

-40

-20

0

20

40

My (

kN.m

)

θy (rad)

W-H4-0.2

-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03-150

-100

-50

0

50

100

150

Mx (k

N.m

)

θ x(rad)

S-H4-0.2

Failure pictures

Figure 6. Test results typical specimens under uni-axis bending.

Cheng et. al [9, 10] conducted two series of cyclic tests with the same dimension and axial force ratios as those in this study but bent about uni-axis, including both the strong axis and weak axis. Fig. 6 takes the hysteretic curves and failure pictures of the typical specimen H4-0.2 (H350×200×4×6, n=0.2) bent about both principle axes for example, where W-H4-0.2 presenting the specimen bent about the weak axis (α=0°) while S-H4-0.2 presenting the specimen bent about the strong axis (α=90°). In Fig. 6, Mx=Vy·L+N·uy, θx=uy/L; My=Vx·L+N·ux, θy=ux/L. Local buckling was found to be the dominating failure mechanism for all the specimens and obvious deterioration of both the strength and stiffness was observed. For the specimens with the same section and axial force level but bent about different principle axes, significant difference of the hysteric behavior were noted due to different stress distribution modes, highlighting the importance of investigating their biaxial behavior. In addition, the interactive effects of the width-thickness ratio of flange and web of H-sectional beam-columns under uni-axis bending were proved. 4.2 Test on specimens subjected to bi-axis bending

B4-0.2-15 (α=15°) B4-0.2-30 (α=30°)

Mx~θx

-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03-150

-100

-50

0

50

100

150

Mx (k

N.m

)

θ x(rad)

B4-0.2-15

-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03-150

-100

-50

0

50

100

150

Mx (k

N.m

)

θ x(rad)

B4-0.2-30

My~θy

-0.111 -0.074 -0.037 0.000 0.037 0.074 0.111

-40

-20

0

20

40

My (

kN.m

)

θy (rad)

B4-0.2-15

-0.054 -0.036 -0.018 0.000 0.018 0.036 0.054

-40

-20

0

20

40

My (

kN.m

)

θy (rad)

B4-0.2-30

Failure picture

s

Figure 7. Test results typical specimens under bi-axis bending.

Similar to uni-axis bending test, for all the biaxial bending specimens in this study, evident local buckling of both the flanges and webs were noted concentrating near the bottom part while the remaining part of the member remained elastic. The hysteretic curves and failure pictures of the typical specimen B4-0.2 (H350×200×4×6, n=0.2) with different loading angels α=15° and 30° are listed in Fig. 7, where the hysteretic curves are expressed by moment components about the principle axes. It is observed that, before onset of local buckling, the non-linear behavior in terms of increased moment resistance but decreased stiffness is exhibited for the hysteretic curves of both Mx-θx and My-θy. The maximum moment strength of My is then reached with occurrence of local buckling. As the lateral displacement continues to increase with more cycles, significant reductions in both stiffness and resistance of My-θy curves are noted, mainly due to severe accumulation of local plate deformations. In addition, Mx-θx curves are found to significantly different with different loading angles. 4.3 Comparison of the behavior of H steel column subjected to uni-axis and bi-axis bending From Fig. 6 and Fig. 7, the spatial inelastic behavior of a typical thin-plate H-section steel member (H350×200×4×6) under axial force ratio n=0.2, can be fully investigated through different loading angles, including α=0°, 15°, 30° and 90°. Due to their relatively large width-thickness ratio, the dominant failure modes for all the specimens were local buckling. It is also observed that, the magnitudes of buckling deformation were increased with increasing α, and bending about the strong-axis (α=90°) makes the most unfavorable deterioration after ultimate.

0 10 20 30 40 500

50

100

150

200

Test

Chen[11]

Mpcy

Mpcx

B4-0.2-30(α=300)

B4-0.2-15(α=150)

W-H4-0.2(α=00)

Muy

(kN.m)

Mux

(kN

.m)

S-H4-0.2(α=900)

Figure 8. Interaction curve of ultimate strengths of specimen H4-0.2.

The ultimate strength for strong and weak axes, denoted as Mux and Muy respectively, are the maximum moments, representing resistance of the member. The biaxial interaction curve of specimen H4-0.2 can be extracted from hysteretic curves from Fig. 6 and Fig. 7, as shown in Fig. 8. It is indicated that, for steel members with small and medium overall slenderness ratio, the interaction curve is convex, suggesting that linear interaction curve for design purpose is conservative for such members. Furthermore, the test results are compared with the interaction curve for H-section attaining its full plastic moment considering the effect of axial force derived by Chen[11] (Fig. 8.), where Mpcx and Mpcy is the uni-axis full plastic moment. Thus from the test results, it can be demonstrated that for H-section dominated by local buckling, the shape of its interaction curve is similar to that of a section without considering the effect of local buckling. The torsion moments (Mz) at ultimate stage for B4-0.2-15 and B4-0.2-30 are 1.7 kN.m and 2.22 kN.m, respectively, indicating that the effect of torsion is increased with increasing loading angle. Moreover, compared with ultimate strength (Mux and Muy), Mz is relatively small; in view of this the effect of torsion is insignificant before the ultimate stage.

5 Summary The cyclic behavior of H-sectional columns with large width-thickness ratios under combined axial compression and bi-axial bending is studied via experimental investigations. By the test results of 15 specimens, the following important conclusions are obtained.

Local buckling of both the flange and web was the dominating failure mechanism for all the specimens.

Despite observation of deteriorations of the strength and stiffness after occurrence of local buckling, plastic deformability capacity as well as energy dissipation capacity was exhibited.

With the help of corresponding uni-axis bending test completed beforehand, the effect of loading angle was illustrated.

For steel members with small and medium overall slenderness ratio, the biaxial moment capacity interaction curve of members dominated by local buckling is convex upward.

Acknowledgement The research was sponsored by The National Natural Science Foundation of China key project (No.51038008). The authors would also like to thank the students in the Steel and Lightweight Steel Structure Research Group of Tongji University for their assistance of the laboratory work.

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