Experimental and analytical investigation of transition steel connections in traditional-style buildings

Engineering Structures 150 (2017) 438–450

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Experimental and analytical investigation of transition steel connections in traditional-style buildings Liangjie Qi a,b, Jianyang Xue a,⇑, Roberto T. Leon b a b

Department of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg 24060, USA

a r t i c l e

i n f o

Article history: Received 19 April 2017 Revised 17 July 2017 Accepted 18 July 2017

Keywords: Traditional-style buildings Steel connections Cyclic behavior Axial compression ratio Slenderness ratio Bilinear backbone curve model

a b s t r a c t This article examines experimentally the behavior of transition steel connections between smaller rectangular and larger circular tubes in traditional-style Chinese buildings. The steel connections were subjected to combined constant axial load and lateral cyclic displacements. Tests were carried out on four 2/3 scale connections extracted from a prototype with two upper column lengths (or slenderness) and two levels of axial force. The influence of axial compression ratio and slenderness ratio on the mechanical behavior of the connections was assessed by looking at hysteretic performance, backbone curves, characteristic loads and corresponding displacements, ductility, energy dissipation capacity, and stiffness degradation. Test results showed that the primary failure modes were cracking of welds or base metal around the welds, and local buckling of the flange at the base of the rectangular steel tube column. The hysteresis loops were full and showed moderate degradation, indicating very good seismic performance for these steel connections. When failure occurred, the interstory displacement angle was between 2.2% and 2.8%, and the equivalent viscous damping coefficient was about 0.26–0.29. Based on the experimental research, an idealized bilinear backbone curve model was developed considering both stiffness degradation and second order effects. This simplified model provides both a yield and an ultimate strength and deformation capacity that can be used in design. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Ancient Chinese timber buildings reflect distinctive national characteristics, and show very high standards in artistic and structural expression as well as in construction technology [1]. Many of these buildings consist of complex wood structures (Fig. 1(a)) that require constant expensive maintenance; consequently, only a few have survived after thousands of years of natural disasters and wars. However, there is a strong desire in many regions of China to preserve ancient architectural styles, and thus wood has been replaced by modern building materials (i.e. steel, concrete) to build traditional style buildings [2]. In ancient timber buildings, columns and beams are connected by mortise-tenon joints (Fig. 1(b)). Pocket holes need to be drilled in the timber columns to insert the beams and connect the structural members. When the structure is subjected to lateral or gravity loads, the mortise-tenon joint is able to resist limited bending moments and allow significant rotations. However, in the modern steel manifestation of these ⇑ Corresponding author. E-mail addresses: [email protected] (L. Qi), [email protected] (J. Xue), [email protected] (R.T. Leon). http://dx.doi.org/10.1016/j.engstruct.2017.07.062 0141-0296/Ó 2017 Elsevier Ltd. All rights reserved.

traditional buildings, the structural components are mostly welded [3]. Modern traditional-style steel structures overcome the disadvantages of poor durability and high initial and maintenance costs associated with wood structures. In addition, they allow designers to also take advantage of the higher strength and stiffness of steel, as well as its ability to provide good seismic performance. These modern structures that mimic traditional Chinese architectural styles will be called Modern Traditional Steel (MTS) structures in this paper. Most research on steel components and connections has concentrated on traditional bolted and welded connections and beamcolumns ([5–6], for example), and only recently has the interest shifted from W shapes to tubular elements and high strength steels. For example, Shi et al. [7] carried out quasi-static test on 1.97 m long 460 MPa steel welded box columns, which showed that these columns possess excellent ductility and energy dissipation capacity. They are ideal for use in seismic steel frames, with the proviso that the width-to-thickness ratio be related to the axial compression ratio. Yang and Tan [8] presented a numerical study of steel beam-column joints using six types of connections, and showed that current design criteria for rotation capacities of web cleat, fin plate, and flush end plate connections are probably too conservative

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Nomenclature fy

ey fu Es n f F t F y ; Dy F u ; Du hey, heu Ke Kp My Mu A I

yield strength of steel yield strain of steel ultimate strength of steel elastic modulus axial compression ratio slenderness ratio of rectangular steel tube horizontal force thickness of steel tube yield load and corresponding displacement on backbone curves ultimate load and corresponding displacement on backbone curves equivalent viscous damping coefficient corresponding to the yield load and ultimate load, respectively elastic stiffness plastic stiffness yield moment ultimate moment cross-sectional area inertia moment

S Z h I1, h1, A1 I2, h2, A2 I3, h3, A3 A4 G b D t1 t2

g b d

elastic section modulus plastic section modulus height of specimen inertia moment, height, cross-sectional area of circular pipe inertia moment, height, cross-sectional area of rectangular tube inertia moment, height, cross-sectional area of the strengthen part between two tubes web cross-sectional area of rectangular tube shear modulus width of rectangular cross-section diameter of circular cross-section thickness of circular steel pipe thickness of rectangular steel tube second stiffness coefficient shape factor of cross-section web thickness of cross-section

Transition steel connections

(b) Mortise-tenon joint [4]

(a) Timber frame structure Fig. 1. The ancient wood building [4].

as they only consider pure flexural resistance. Lew et al. [9] conducted an experimental study of two full-scale steel beamcolumn assemblies, each comprising three columns and two beams. These tests provided experimental data for validation of beam-tocolumn connection models to be used in assessing the robustness of structural systems. The Lew et al. [9] results indicated that the rotational capacities of connections under monotonic column displacement are about twice as large as those based on seismic testing protocols. Newell and Uang [10] performed cyclic tests of nine full-scale W14 column specimens representing a practical range of flange and web width-to-thickness ratios, which were subjected to different levels of axial force demand. These test indicated that the ASCE 41 [11] predicted plastic rotation capacities are very conservative, and the ASCE 41 criteria do not specify plastic rotation capacity at axial load ratios greater than 0.5. The specimens tested exhibited plastic rotation capacities of approximately 15–25 times the member yield rotation. The members and connections studied in the research projects briefly described above are very different from those in MTS structures. In MTS structures, circular columns are labelled as eave columns, hypostyle columns and other columns based on column

position and function in ancient wood buildings [12]. The shape of columns in MTS architecture is consistent with that of ancient wood structures, and the construction is quite complicated [13]. These columns include brackets located above the eave columns and hypostyle columns and sudden changes in cross-section as they approach the roof, as shown in the two perpendicular views in Fig. 2(a) and (b). These transitions have to be preserved for aesthetic reasons in MTS buildings; clearly more economic and structurally efficient solutions exist outside that constraint. The thicker line in these figures indicates the locations from which test specimens used in this project were extracted. There is a sudden change of strength and stiffness in the connecting section between upper columns and lower columns; the upper column is a smaller rectangular steel tube which is connected to a larger lower circular steel pipe. The rectangular tube is inserted into the circular pipe and the insertion depth is extended to the bottom beam flange. Several stiffeners and a circular ring plate are welded to ensure robust force transfer. The details are illustrated in Fig. 2(c), which shows a MTS portion of the traditional one shown in Fig. 2(b). The force flow in this section is obviously very different from that of mortise-tenon joints used in older wooden buildings. In this

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(a) Side view

(b) Front view

(c) Detailed construction

Fig. 2. Prototype of specimen.

test series, the interest is to investigate the force transfer from the heavy roof through the transition connection between the circular and rectangular tubes. The effect of the framing beams will be considered in the next phase of the study. At present, there is a lack of theoretical and experimental research on the cyclic behavior for these column transition joints, which are obviously critical to the survival of the buildings under large lateral loads. The lessons learned from these tests are applicable to many similar transition sections present in structures such as those shown in Fig. 1. To investigate the behavior of these unusual column transition joints, an eave column of a great hall building in the China’s Buddhist Academy of Mt. Putuo, one of the most beautiful temple complexes in China, was taken as a prototype. The primary aim of the experimental study was to provide insight into the structural behavior and detailing of steel copies of connections in traditional wooden structures, in order to develop design guidelines for the efficient construction of MTS. This paper describes pseudo-static reversed cyclic lateral test on four steel column transition connections. There are two different ratios of lengths of the smaller top rectangular tube to the larger bottom circular tube column (4.00 and 2.66), and each of these was tested under two axial load ratios (0.2 and 0.4 of the squash load for the upper column). The failure sequence was carefully monitored, and the load-displacement hysteresis hoops and backbone were obtained. The effects of axial compression ratio (ARC) and slenderness ratio (SSR) on the failure mode, hysteretic behavior, ductility, stiffness, bearing capacity, and energy dissipation capacity were analyzed in detail and compared to results from simple theoretical calculations for a backbone curve. The results showed that the proposed backbone curve provides a very good match to the test results, both in terms of magnitude and behavior.

2. Experimental program 2.1. Test specimen The specimens were taken out of the transition zone between the upper and lower columns and were meant to investigate the strength and ductility of the connections themselves, and not intended to fully reflect the behavior of the entire column. For practical testing reasons, the lower column is much shorter than in the prototype. The main fabrication steps consisted of welding

rectangular plates to create the upper tube column and welding stiffeners to it (Fig. 3(a)), inserting the rectangular section into the circular one and welding the stiffeners to the circular tube (Fig. 3(b), and welding a round cap plate with a rectangular hole to the top of the circular section (Fig. 3(c)). The completed specimen in the testing rig is shown in Fig. 3(d). General dimensions and other details are given in Fig. 4. In this project, the slenderness was defined as the ratio of the rectangular column length to its width (Lupper/b) and labelled as the SSR rather than using the more conventional column slenderness parameter (KL/r). The specimens were divided into two groups, namely ZLJ1 (SSR of 12.5 or KL/r of 63.3) and ZLJ2 (SSR of 8.9 or KL/r of 43.4). The rectangular tubes for ZJL1 had a b/t of 11.4 while those for ZLJ2 had a b/t of 10; current specifications for use in seismic design specify a limit of 33.0. The purpose of changing the SSR of specimens was to obtain the influence of different column slenderness on the stiffness and seismic behavior of the connection. Two axial compression ratios (ACR), or ratio of axial force to design capacity of the upper column, were used: for ZLJ1-1 and ZLJ2-1 the ACR was set at 0.2, while that of ZLJ1-2 and ZLJ2-2 was set at 0.4. In Fig. 4, the numbers inside the brackets represent the dimensions of the ZLJ2 specimen, while those outside the brackets represent the dimensions of the ZLJ1 specimens. All steel plate materials were Q345 steel (nominal fy = 345 MPa) while the circular tubes were made of Q235 steel (nominal fy = 235 MPa). A 40 mm plate was welded to the bottom of the test specimen in order to bolt it to the structural floor. The measured mechanical properties of the steel components used are shown in Table 1, and were determined from the tension tests on three coupons in each series. All the tested coupons were taken according to ‘‘Steel and Steel Products-Location and Preparation of Test Pieces for Mechanical Testing” [14]. The yield strength fy, ultimate strength fu, yield strain ey, and elastic modulus E were measured according to ‘‘Metallic Materials-Tensile Testing at Ambient Temperature” [15]. All welds are fillet welds constructed following ‘‘Code for welding of steel structures” [16]; the welds were not tested for defects. Table 2 shows the nominal and actual capacities and geometrical properties of the members. 2.2. Test setup and procedure The test rig shown in Fig. 5 was used to apply a constant axial load and slow reversed cyclic loads and displacement to the test

L. Qi et al. / Engineering Structures 150 (2017) 438–450

(a) Welding tubes and stiffeners

(b) Welding in the circular tubes

(c) Top plate

(d) Complete specimen

441

Fig. 3. Fabrication procedure.

specimens. The vertical load was applied by a hydraulic jack on the top of the specimens; axial forces of 352 kN, 704 kN, 223 kN and 446 kN were used for ZLJ1-1, ZLJ1-2, ZLJ2-1 and ZLJ2-2, respectively. These corresponded to 0.2 and 0.4 of the design axial capacity of the upper columns. The values of vertical load were held constant during the loading process. Several rollers were employed between the reaction upper girder and the axial force hydraulic jack, allowing the jack to displace laterally with very low friction. The lateral cyclic loads and displacements were applied to the top of the column through a MTS973 electro-hydraulic servosystem following the ‘‘Specification of Testing Methods for Earthquake Resistant Building” [17] protocol. In this protocol, a load/displacement hybrid control program is used, utilizing force-control until specimens started to yield and then switching to displacementcontrol for the rest of the loading history. The loading procedure is illustrated in Fig. 6. For the initial elastic loading stage, the load is increased by 5 kN and cycled once. When the specimen starts to yield, each displacement-loading cycle was repeated three times at 20 mm increments. Table 3 shows the inelastic cycles and each inelastic level cycles three times.

2.3. Measurement and data acquisition devices The arrangement of strain measurement and the displacement transducers are shown in Fig. 7. Strain gauges (Fig. 7(a)) and strain rosettes (Fig. 7(b)) were attached at different locations to determine strain changes during the loading process. The numbers inside the brackets represent the dimensions of the ZLJ2 specimen, while those outside the brackets represent the dimensions of the ZLJ1 specimens. Displacements were monitored by the linear variable differential transducers (Fig. 7(c)). Test data was acquired by a Tokyo Sokki TDS-602 data automatic acquisition system.

3. Results and discussion 3.1. Damage evolution and failure modes For all the specimens, the initial elastic behavior was followed by yielding at the bottom of the upper column and weld cracking as the specimens entered the plastic stage. After cycling at this level, buckling occurred on both sides of the rectangular column base flange, leading to the failure of specimen. Fig. 8 compares the axial force (N) – total moment (M) path at the transition section obtained from test with the limits provided by the Chineses seismic code (essentially an elastic beam-column interaction equation) and an ultimate strength envelope from FEA analyses. Fig. 8 indicates that the specimens reached moment strengths close to the predicted ultimate capacity but that the axial load effects were small because of the low axial load ratios. For ZLJ1-1, there was no yielding phenomenon until the load reached about 60 kN, when the bottom end of rectangular tube reached the yield strain. At this point the testing control was switched from load- to displacement-controlled. There were no obvious fractures but only minor cracks at the bottom corners of the square column beginning at the first loading cycle of 50 mm (Fig. 9(a)). The damage progression for ZLJ1-2 was similar to that of ZLJ1-1, but the specimen entered the plastic stage when the loads went up to 50 kN. Cracks appeared in the joint area of rectangular and circular tube at the second loading cycle of 30 mm. The cracking and local buckling phenomena (Fig. 9(b)) in the ZLJ2 series were more obvious than in the ZLJ1 series. During the loading of ZLJ2-1, the south and north webs of the rectangular tube cracked when the load reached 70 kN. At the 3rd circle of 30 mm loads, half-wave local buckling appeared in the east and west flanges of rectangular tube bottom, and the crack of west flange extended to the whole section at that time. When the test ended,

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(b) ZLJ2

(a) ZLJ1

(c) Structural details

Fig. 4. Dimensions and details of specimens.

Table 1 Mechanical properties of steel. Materials

t (mm)

fy (MPa)

ey (10
6)

fu (MPa)

E (MPa)

Plates

12 14

390.1 395.4

1885 1929

557.7 530.5

2.07  105 2.05  105

Pipes

8 12

308.5 289.3

1566 1418

442.8 425.3

1.97  105 2.04  105

Table 2 Section properties. Specimen

A (mm2)

I (107 mm4)

S (105 mm3)

Z (105 mm3)

My,n* (kNm)

Mp,n* (kNm)

My,a* (kNm)

Mp,a* (kNm)

ZLJ1

Rectangular column Circular column

8132 13753

2.93 22.9

2.99 9.42

4.49 16.0

103 221

155 376

118 273

178 463

ZLJ2

Rectangular column Circular column

5184 7963

1.02 10.0

1.41 4.73

2.11 8.04

48.6 111

72.8 189

55 146

82.3 248

Note: A, I, S, Z and M* are the area, moment of inertia, elastic section modulus, plastic section modulus and bending moment of the cross-section, respectively. Subscripts n and a represent capacities using nominal and actual material properties, respectively.

the cracks in the north flange propagated through the entire flange while no such phenomenon occurred at the south flange. For ZLJ22, the damage phenomenon was similar to ZLJ2-1, but the cracking and local buckling began earlier than those of ZLJ2-1. The specimens were able to reach large deformations as shown in Fig. 9(c). Thus, the behavior of all the specimens can be summarized by two phases (elastic and inelastic):

(1) When the specimens were in the elastic range, there was no significant stiffness degradation and almost no residual deformation. (2) When the specimens entered the inelastic range, fine cracks could be observed in the heat affected zone of the weld between the cap plate and the rectangular tubular column. For the ZLJ1 series, cracks usually started from a corner of

L. Qi et al. / Engineering Structures 150 (2017) 438–450

(a) General view

443

(b) Detailed construction Fig. 5. Test setup.

line in the Figure represent the yield Fy and ultimate load Fu based on the actual material properties, respectively. The following observations can be drawn based on Fig. 10:

Fig. 6. Loading procedure.

Table 3 Inelastic loading. Specimen

ZLJ1-1

ZLJ1-2

ZLJ2-1

ZLJ2-2

Inelastic loading level D at Fy (mm) Dy (mm) Dy + D (mm) Dy + 2D (mm)

2 30.79 50 70 /

3 20.34 30 50 70

2 13.63 20 30 /

2 12.05 20 40 /

the rectangular column and propagated along the weld when this side of the column was in tension, leading to final failure. In the ZLJ2 series the initial cracking was followed local buckling of the rectangular tube walls. These two fairly simple behavior modes were translated into a simple bi-linear backbone curve as described later in this paper.

(1) All the hysteresis loops are relatively full and spindleshaped. This indicates that these transition connections between rectangular and circular tubes have great toughness and energy dissipation capacity. (2) The variation in maximum positive and negative loads, or vertical asymmetry of the hysteresis loops, is due primarily to cracking of the weld around the flange of the rectangular steel column base. When the cracked weld was pulled open, only the steel webs sustained the tensile load, while both the web and flange bore loads when the welds were in compression. (3) The influence of the SSR is obvious. A decrease of load appears in the last cycle of the hysteresis loops for ZLJ22 due to the propagating crack and local buckling, while no apparent decline is shown on the hysteresis loops for ZLJ1. (4) With the increasing magnitude of the axial compression ratio, the load applied to the specimens decreases to some extent and the deformation capacity decreases substantially. This finding indicates that an appropriate axial compression ratio can improve the seismic behavior of steel connections in traditional-style buildings. 3.3. Characteristic loads The horizontal loads and displacements at each characteristic point measured by the electronic equipment are shown in Table 4. The yield point (Fy, Dy) is defined when the inflection point appeared on the backbone curve and its slope changed, while the ultimate point (Fu, Du) is determined as the end point of the test. From Table 4, the following observations can be made:

3.2. Hysteretic behavior Fig. 10 shows the hysteresis behavior observed in the experiment, as shown by the relation between the lateral loads and displacements at the top of the columns. The dotted line and dashed

(1) When compared yield points, the yield loads decrease with increasing ACR. When compared with the ultimate loads of ZLJ1-1 and ZLJ2-1, the ultimate loads of ZLJ1-2 and ZLJ2-2 are lower by 9% and 4%, respectively

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LVDT-1

16 17

1 2 3 10 1112 4 5 6

18

LVDT-2

LVDT-3

78 9 13 14 15

19

(b) North elevation

(a) East elevation

(c) Displacement measurement device

4800 Cross-section strength Chinese seismic code ZLJ 1-1 ZLJ 1-2

3200 Cross-section strength Chinese seismic code ZLJ 2-1 ZLJ 2-2

3600

-125

2400

2400

1600

1200

800

0 -250

N /kN

N /kN

Fig. 7. Arrangement of measuring points.

0 0

125

250

-150

M /kNm

-75

0

75

150

M /kNm

(a) ZLJ1 series

(b) ZLJ2 series Fig. 8. N-M interaction diagram.

(2) From the backbone curves, it can be seen that the negative values of load are larger than that of the positive values, which may be due to testing error and/or the existence of a gap between the actuator and specimens. As the test continues, the difference between the two directions becomes larger, which may result from the asymmetric crack distribution.

(3) The SSR obviously influences the ultimate loads of connections. The ultimate load of ZLJ1-1 is 72.97 kN (average value of two directions), while that of ZLJ2-1 is 81.44 kN, which shows a 12% increase. All of the data indicate that the strength of the steel connections increases with decreasing of the SSR.

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Local buckling

Crack

(a) Crack at the bottom of rectangular tube

(b) Buckling of rectangular tube

(c) Ultimate deformation Fig. 9. Failure modes.

100

Fy

Load /kN

50

0

0

-50

-50

ZLJ1-2

ZLJ1-1 -100 -100

Fu

Cracks at bottom corners of square column (2nd 30 mm cycle)

Fy

50

Load /kN

100

Fu

Cracks at bottom corners of square column (1st 50 mm cycle)

-50

0

50

100

-100

-59

0

59

Displacement/mm

Displacement/mm 100

100

Fu

0

Fu

Fy

South and north webs of rectangular tube crack (70 kN cycle)

Fy

50

Local buckling at rectangular tube bottom flanges (3rd 30mm cycles)

Load /kN

Load /kN

50

0

Local buckling at transition zone (1rd 20mm cycles)

-50

-50

ZLJ2-1 -100 -50

-25

0

25

ZLJ2-2 50

-100 -50

-25

0

25

50

Displacement/mm

Displacement/mm Fig. 10. Hysteretic loops.

3.4. Characteristic displacements and ductility factors Table 4 lists the displacements corresponding to the characteristic loads, namely yield displacement and ultimate displacement. Based on the data in Table 4, the maximum ultimate displacements of ZLJ1 and ZLJ2 are 70 mm and 40 mm, respectively. The experimental yield displacements show a large effect of axial compres-

sion, and to a lesser extent that of the slenderness ratio. Both ZLJ1-2 and ZLJ2-2 specimens meet the ductility specification requirement of steel structures, as the ductility factor is larger than 3 [18], while the other two don’t possess great ductility. In addition, Table 4 also demonstrates the ultimate displacement angles of four specimens, all ranging between 1/35 and 1/45. The value shows that they can meet the required interstory

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Table 4 Characteristic values. Specimen

Loading direction

Yield point

Ultimate point

Fy/kN

Dy/mm

hy

Fu/kN

Du/mm

hu

ZLJ1-1

Positive Negative

60.16
64.86

27.59
33.99

1/87 1/71

70.33
75.60

70.01
70.01

1/35 1/35

ZLJ1-2

Positive Negative

55.22
56.5

19.59
21.08

1/123 1/114

66.70
65.50

70.02
70.00

1/35 1/35

ZLJ2-1

Positive Negative

69.67
69.24

12.58
14.67

1/108 1/93

75.57
87.30

30.00
30.02

1/45 1/45

ZLJ2-2

Positive Negative

58.3
55.4

12.50
11.60

1/109 1/118

74.19
81.70

40.00
40.01

1/35 1/35

drift ratios of steel structures, namely 1/50 for the plastic stage. All the description indicates that steel connections between rectangular tube and circular pipe have great deformability and collapse resistance.

dissipation ability of the specimens. The values of the equivalent viscous damping coefficient he at each stage are listed in Table 5. The equivalent viscous damping coefficients hey and heu correspond to the yield point and the ultimate point, respectively.

he ¼ SðABCþCDAÞ =ð2p  SðOBEþODFÞ Þ

3.5. Stiffness degradation The stiffness of specimens under low cyclic reversed loading can be defined by the secant stiffness, which will tend to decrease due to cumulative damage of components. In order to describe the cumulative damage effect, the stiffness degradation rules of connections in traditional-style buildings can be obtained from the test data. Fig. 11 shows the diagram of secant stiffness (Ki) versus the ratio of lateral displacements to the absolute value of yield displacement (D/|Dy|). It can be seen from Fig. 11 that the stiffness degradation law of the four specimens is similar, with the stiffness decreasing rapidly in the initial loading stages. When the specimens completely enter the plastic stage, the stiffness degradation tends to be more stable. It can also be concluded that the initial stiffness of the connections with the low slenderness ratio are greater than those of the high SSR, and that lower SSR specimen shows more obvious stiffness degradation. By comparison, high axial load means high initial stiffness, and the rate of stiffness degradation in high axial compression ratio specimens is quicker than that in specimens of low axial compression ratio.

ð1Þ

where SðABCþCDAÞ is the area of the shadow and SðOBEþODFÞ is represented by the sum of the area of the triangle OBE and triangle ODF as shown in Fig. 12. Fig. 13 demonstrates the influence of some design parameters on he of connection specimens. The following observations can be drawn from Table 5 and Fig. 13. (1) Compared with ZLJ1-1, whose axial compression ratio is 0.2, the heu of ZLJ1-2 was 11% higher, and the same trend is observed when comparing ZLJ2-1 with ZLJ2-2. The ARC doesn’t play an important role in the damping coefficient hey at the yield point. These results suggest that the axial compression ratio has a moderate influence on the energy dissipation capacity of the connections. (2) Compared with ZLJ1-1, with a SSR of 12.5, the equivalent viscous damping coefficient hey and heu of ZLJ2-1, with an SSR of 8.9, were 12% and 5% higher, respectively. Thus, the equivalent viscous damping coefficients increase as the SSR decreases. The calculation results show that SSR plays a vital

3.6. Energy dissipation capacity The energy dissipation capacity of a structure or structural component reflects its seismic energy absorption ability [19], and is usually quantified by the equivalent viscous damping coefficient he. It is calculated using Eq. (1) to evaluate the accurate energy

Table 5 Equivalent viscous damping coefficients. Specimen

hey

heu

ZLJ1-1 ZLJ1-2 ZLJ2-1 ZLJ2-2

0.059 0.040 0.066 0.078

0.262 0.291 0.274 0.294

Ki /kN·mm-1

6 ZL1-1 ZL1-2 ZL2-1 ZL2-2

4

P B

2

0 -4

F A

-2

0

Δ ⏐Δy⏐ Fig. 11. Stiffness degradation.

2

4

O

C E

D Fig. 12. Calculation of energy dissipation capacity.

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0.3

0.3 ZLJ1-1 ZLJ1-2

ZLJ1-1 ZLJ2-1

0.2

he

he

0.2

0.1

0.1

0.0

Yield load

0.0

Ultimate load

(a) The influence of axial compression ratio

Yield load

Ultimate load

(b) The influence of slenderness ratio

Fig. 13. The influence of different design parameters on equivalent viscous damping coefficients.

45

45

P/kN

90

P/kN

90

0

0

-45

-45

-90 -25000 -20000 -15000 -10000 -5000

0

5000

-90 -500

0

500

(a) Point 16 and 17

1000

1500

2000

2500

με

με

(b) Maxmium principle strain of points 1-3

Fig. 14. Load – average strain curves.

3.7. Strain distribution The force at the transition region is complex. Fig. 14 presents the strain gage measurements for specimen ZLJ2-1 for the transition region between the upper rectangular steel tube and the lower circular steel pipe column. Data from measuring locations 1, 2, 3 and 16 in Fig. 7 are reported in Fig. 14. 3.7.1. Flange of rectangular tube It can be seen from Fig. 14(a) that after an initial elastic stage with some residual strains, the material entered the plastic stage at a lateral load of about 75 kN. As the load increased, the strain of this region increased rapidly, leading to weld cracking in the column flange. After that, the strain in the rectangular tube flange is unsymmetrical, because the strain increased only when the gap closed. 3.7.2. Web of rectangular tube Data from the rosette (measuring points 1–3) from the web portions of the tube are shown in Fig. 14(b). No yielding was observed when cracks occured on the surface of the web. When the horizon-

tal load reached 75 kN, the maximum principal strain increased sharply.

4. Calculation of backbone curve model 4.1. Backbone curve The backbone curve is obtained by connecting the peak points of each cycle of the hysteretic loops [20]. It reflects the mutual relationship between the peak load and corresponding displacement. From the trends shown, as discussed before, the behavior can be easily divided into two parts, i.e. elastic and plastic stages. The measured backbone curves of the specimens are shown in Fig. 15. 100

50

Load /kN

role in the energy dissipation capacity, and the slenderness ratio should be controlled strictly in actual engineering applications. (3) The average value of equivalent viscous damping coefficients at the yield load is 0.061 and 0.214 at the ultimate load, which indicate steel connections between rectangular tube and circular pipe in traditional-style buildings have great energy dissipating capacity.

ZL1-1 ZL1-2 ZL2-1 ZL2-2

0

-50

-100 -80

-40

0

40

Displacement /mm Fig. 15. Backbone curves of specimen.

80

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L. Qi et al. / Engineering Structures 150 (2017) 438–450

(1) Before reaching the elastic limit point, the backbone curves are close to a straight line, indicating the specimen remains in the elastic state. After the weld cracking, the backbone curve gradually leans to the horizontal x-direction. This phenomenon indicates that the bearing capacity and lateral stiffness of the connections degrade under lateral cyclic loads. (2) The axial compression ratio presents an obvious impact on the backbone curves. For specimens with an axial compression ratio of 0.2, the yield load and ultimate load of the specimen are higher than that of axial compression of 0.4. Therefore, an appropriate axial compression ratio is extremely important for seismic performance of connections in traditional-style buildings. (3) As shown in Fig. 15 and Table 4, the slenderness ratio of columns also affects the seismic behavior of the connections. The reason is that the P-D, or second-order, effect for the higher SSR specimens is more significant. The backbone curves flatten out earlier and show a lower post-elastic stiffness.

Based on the conclusions above, an idealized bilinear backbone curve model can be derived from the simplified load-displacement curves, as shown in Fig. 16. In this backbone curve, Pt. Y represents the yield load and deflection, point U represents the ultimate load and deflection, Ke and Kp are the elastic and plastic stiffness, respectively. The backbone curve model is determined by the following method. 4.2. Elastic stage The initial yield moment My of the upper column is determined by the following:

My ¼

2I f b y

ð2Þ

where I = moment of inertia (unit: mm4), b = width of cross-section, and fy = yield strength of steel. The horizontal deformation can be calculated by adding the elastic deformation contributions of the three specimen components: the bottom round column, the transition zone, and the upper rectangular column as shown in Fig. 17. The elastic deformation is given by: 3

U

Fu Y

3

3

2

2

2

2

!

From Eq. (3), the elastic stiffness Ke of the connections in traditional-style buildings can be obtained. Ke ¼

Ke

O

2

ð3Þ

Kp

Load

Fy

2

h2 3h3 h2 þ 3h3 h2 þ h3 h1 þ 3h1 h2 þ 3h1 h3 þ 3h2 h1 þ 3h1 h3 þ 6h1 h2 h3 þ þ 3EI2 3EI3 3EI1

DM ¼ F

1 3

2

2

3

3

2

2

2

2

h2 3h3 h2 þ 3h3 h2 þ h3 h1 þ 3h1 h2 þ 3h1 h3 þ 3h2 h1 þ 3h1 h3 þ 6h1 h2 h3 þ þ 3EI2 3EI3 3EI1

ð4Þ y

Displacement

The deflection of the specimens is mainly caused by bending deformation; the shear deformation is relative small, so it can be neglected. To facilitate the calculation of the lateral stiffness, the contribution of the stiffeners in the circular tube is ignored.

u

Fig. 16. Simplified load-displacement curves.

(a) Symbolic representation Fig. 17. Calculation diagram.

(b) Force analysis model

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L. Qi et al. / Engineering Structures 150 (2017) 438–450

By thorough analysis, the stresses at cross-section 1–1 and anchoring terminal 2–2 can be drawn using Eq. (2). The stress at section 1–1 is always larger than that of section 2–2, so the calculation results of the yield moment at cross-section 1–1 is the controlling bending moment. Considering the P-D effect as well, the bending moment of this test is caused by horizontal force F and axial force N. At the same time, the yield stress f y is composed of axial stress rN and bending stress rM . Combining Eq. (2) with basic elastic mechanics yields the following relationships:

8 M y ¼ Fh2 þ NDy ¼ 2Ib rM > > > > < f y ¼ rM þ rN

ð5Þ

N > rN ¼ b2
ðb
2t 2 > > 2Þ > : F y ¼ K e Dy

where t2 = thickness of rectangular steel tube. Solving these equations, the yield displacement and can be obtained as:

Z Mu ¼ 2f y

m=2

ð8Þ

yZðyÞdy 0

where y is the coordinates along the loading direction, Z(y) is the thickness of steel plate vertical to the loading direction, and m represents the length of cross-section (rectangular cross-section) or diameter (circular cross-section). When any section of the connection is fully yielded, a plastic hinge is formed at the location, and the load cannot continue to increase. Section 1–1 and 2–2 are comparatively considered to go into the plastic stage. Making the assumption that the external force loading direction is consistent with the y-axis in Fig. 18, the distance from center of the tensile part (the shaded part in Fig. 18 (a)) or compression part to the neutral axis is as follows: 2

y1
1 ¼

2

2

2

b  b
ðb
2t2 Þ  ðb
2t2 Þ b ðb
2t2 Þ =ð
Þ 8 2 2 2

Dy ¼

2I2 ðf y
rN Þ bðK e h2 þ NÞ

ð6Þ

¼

Fy ¼

2K e I2 ðf y
rN Þ bðK e h2 þ NÞ

ð7Þ

y2
2 ¼

3b
6bt 2 þ 4t22 8b
8t2

ð9Þ

3D2
6Dt 1 þ 4t21 6pðD
t1 Þ

ð10Þ

The integration can be obtained by Eq. (8) as follows: 4.3. Plastic stage When the specimen entered into the plastic stage totally, the moment is taken as:

8  2  2 2 3b
6bt2 þ4t22 > 2 2Þ > ¼ f y t2 ð3b
6bt 2 þ 4t 22 Þ=2 for rectangular section < Mu ¼ 2f y b
ðb
2t 2 8b
8t 2  2  2  > 2 3D
6Dt1 þ4t 21 > : Mu ¼ 2f y pD
pðD
2t1 Þ ¼ f y t1 ð3D2
6Dt1 þ 4t 21 Þ=6 for circular section 8 6pðD
t1 Þ

ð11Þ

Comparing the bending moment of these two sections, it can be found that the stress of section 2–2 is always larger than that of the section 1–1, that is to say, the ultimate bearing capacity is controlled by rectangular cross section. The plastic stiffness is shown as following:

K p ¼ gK e ¼

(a) Rectangular-section

(b) Circular-section

Fu
Fy Du
Dy

ð12Þ

where g is second stiffness coefficient. According to Ref. [21], the ultimate displacement value is taken as the displacement when the specimen entered into the plastic stage completely, and the plastic stiffness K p and second stiffness factor g where

K p ¼ gK e

Fig. 18. Calculation diagram of steel tubes.

ð13Þ

Table 6 Comparison of characteristic parameters between calculation and test results. Specimen

f

n

Characteristic parameters

Test

Calculation

Calculation/test

ZLJ1-1

12.5

0.2

Fy/kN Dy/mm Fu/kN Du/mm

62.51 30.79 72.97 70.01

63.72 27.79 81.67 69.53

1.019 0.903 1.119 0.993

ZLJ1-2

12.5

0.4

Fy/kN Dy/mm Fu/kN Du/mm

55.86 20.34 66.10 70.01

52.15 22.75 70.41 65.20

0.934 1.118 1.065 0.931

ZLJ2-1

8.9

0.2

Fy/kN Dy/mm Fu/kN Du/mm

69.46 13.63 81.44 30.01

65.74 11.27 85.85 29.57

0.946 0.827 1.054 0.985

ZLJ2-2

8.9

0.4

Fy/kN Dy/mm Fu/kN Du/mm

56.85 12.05 77.95 40.00

56.29 9.65 77.63 30.57

0.990 0.801 0.996 0.764

450

g¼

L. Qi et al. / Engineering Structures 150 (2017) 438–450

1 b2

b
1   qffiffiffiffiffiffiffiffiffiffiffiqffiffiffiffi þ p1ffiffi3 2 þ 1b h 1
1b bSd
1

ð14Þ

where b = shape factor of cross-section, S = elastic section modulus, and d = web thickness of cross-section. The bending moment of the controlling section can be described as Eq. (15)where 2

2

M u ¼ F u h2 þ NDu ¼ f y =2ð3b t 2
6bt2 þ 4t 32 Þ

ð15Þ

The calculation formulation of ultimate load and corresponding ultimate displacement on the basis of Eqs. (12)(15) is shown as below. 2

2

Fu ¼

f y =2gK e ð3b t 2
6bt2 þ 4t 32 Þ þ F y N
K e Dy gN N þ h2 gK e

Du ¼

f y =2ð3b t 2
6bt2 þ 4t 32 Þ þ h2 gK e Dy
h2 F y N þ h2 gK e

2

ð16Þ

2

ð17Þ

4.4. Verification of calculation results The calculated parameters Ke, Fy, Dy , Kp, Fu and Du are compared with the test results in Table 6. The test ultimate displacements agree well with the calculated ultimate displacements. It can be found from Table 6 that the average ratio of the calculated values to experimental values is 0.965, the standard deviation is 0.104 and the coefficient of variation is 0.108. The calculation coincides with the experimental results, which reflects the robustness of the calculation method. 5. Conclusions Based on the quasi-static test and theoretical analysis of four steel connections between rectangular tube and circular pipe columns in traditional-style buildings, the following conclusions can be drawn: 1. The hysteresis loops of the four specimens are plump and spindle-shape with great deformability, which shows excellent collapse-resistant capacity and good seismic performance. A sharp decrease of the load appears on the last cycle of the hysteresis loops for ZLJ2-2 while no apparent decline is shown on the hysteresis loops for ZLJ1; this due to the more significant crack and local buckling phenomenon in ZLJ2-2. 2. The yield load and ultimate load are influenced by axial compression. An increase of the axial compression results in a gradual decrease of the lateral resistance. However, axial compression doesn’t affect the characteristic displacements significantly for the axial rations shown. The bearing capacity of steel connections increases with the decreasing of the slenderness ratio. 3. The initial stiffness of the connections with the low slenderness ratio is greater than that of the high slenderness ratios. By comparison, a high axial load means high initial stiffness, and the rate of stiffness degradation in high axial compression ratio specimens is more obvious than that in specimens of low axial compression ratio. 4. The equivalent viscous damping coefficients decrease considerably as the slenderness ratio increases, but do not seem to vary appreciably with axial compression ratio. The average value of the equivalent viscous damping coefficient is 0.061 at the yield

load and 0.214 at the ultimate load, which indicate steel connections in traditional-style buildings have the great energy dissipating capacity. 5. Based on the cyclic loading test results, a bilinear backbone curve model considering stiffness degradation is provided. The model matches the tests well and can be used in design.

Acknowledgements The authors would like to thank the support provided by the National Natural Science Foundation of China (Grant no. 51678478), National Science and Technology Support Program of the 12th Five-Year (Grant no. 2014BAL06B03) and Scientific Research Foundation of Outstanding Doctoral Dissertation of XAUAT (6040317006). In addition, financial support from the China Scholarship Council for Liangjie Qi’s work at Virginia Tech, as a visiting scholar, is highly appreciated. References [1] Zhang XC, Xue JY, Zhao HT, Sui Y. Experimental study on Chinese ancient timber-frame building by shaking table test. Struct Eng Mech 2011;40 (4):453–69. [2] Xue JY, Qi LJ. Experimental studies on steel frame structures of traditional-style buildings. Steel Compos Struct 2016;22(2):235–55. [3] Yao K, Zhao HT, Ge HP. Experimental studies on the characteristic of mortisetenon joint in historic timber buildings. Eng Mech 2006;23(10):168–73 [in Chinese]. [4] Fang DP, Iwasaki S, Yu MH, Shen QP, Miyamoto Y, Hikosaka H. Ancient Chinese timber architecture. I: experimental study. J Struct Eng 2001;127 (11):1348–57. [5] Qin Y, Chen ZH, Yang QY, Shang KJ. Experimental seismic behavior of throughdiaphragm connections to concrete-filled rectangular steel tubular columns. J Constr Steel Res 2014;93:32–43. [6] Elkady A, Lignos DG. Modeling of the composite action in fully restrained beam-to-column connections: implications in the seismic design and collapse capacity of steel special moment frames. Earthquake Eng Struct Dynam 2014;43(13):1935–54. [7] Shi G, Deng CC, Ban HY, Chen YY, Wang YQ, Shi YJ. Experimental study on hysteretic behavior of high strength steel box-section columns. J Build Struct 2012;33(3):1–7 [in Chinese]. [8] Yang B, Tan KH. Numerical analyses of steel beam-column joints subjected to catenary action. J Constr Steel Res 2012;70:1–11. [9] Lew HS, Main JA, Robert SD, Sadek F. Performance of steel moment connections under a column removal scenario. I: experiments. J Struct Eng 2012;139 (1):98–107. [10] Newell JD, Uang CM. Cyclic behavior of steel wide-flange columns subjected to large drift. J Struct Eng 2008;134(8):1334–42. [11] ASCE 41. Seismic rehabilitation of existing buildings. Reston, USA: ASCE; 2007. [12] Yin WD, Yamamoto H, Yin MF, Gao J, Trifkovic S. Estimating the volume of large-size wood parts in historical timber-frame buildings of China: case study of imperial palaces of the Qing Dynasty in Shenyang. J Asian Archit Build Eng 2012;11(2):321–6. [13] Zhao HT, Xue JY, Sui Y, Xie QF. Chinese ancient buildings and corresponding seismic method. Beijing, China: Science Press; 2011 [in Chinese]. [14] GB/T 2975. Steel and steel products-location and preparation of test pieces for mechanical testing. Beijing, China: State Bureau of Quality Technical Supervision; 1998 [in Chinese]. [15] GB/T 228. Metallic materials-tensile testing at ambient temperature. Beijing, China: Chinese Standard Press; 2002 [in Chinese]. [16] GB 50661–2011. Code for welding of steel structures. Beijing, China: Chinese Standard Press; 2012 [in Chinese]. [17] JGJ 101–2015. Specification of testing methods for earthquake resistant building. Beijing, China: China Building Industry Press; 2015 [in Chinese]. [18] GB 50011–2010. Code for seismic design of buildings. Beijing, China: China Architecture & Building Press; 2010 [in Chinese]. [19] Ma H, Xue JY, Zhang XC, Luo DM. Seismic performance of steel-reinforced recycled concrete columns under low cyclic loads. Constr Build Mater 2013;48:229–37. [20] Ma H, Xue JY, Liu YH, Zhang XC. Cyclic loading tests and shear strength of steel reinforced recycled concrete short columns. Eng Struct 2015;92:55–68. [21] Ou JP, Niu DT, Wang GY. Fuzzy dynamical reliability analysis and design of multi-storey nonlinear a seismic steel structures. Earthquake Eng Eng Vibr 1990;10(4):27–37 [in Chinese].