Seismic behavior of specially shaped column joints with X-shaped reinforcement

Trans. Tianjin Univ. 2013, 19: 110-117 DOI 10.1007/s12209-013-1863-5

Accepted date: 2012-06-01.

*Supported by National Natural Science Foundation of China (No. 50878141); Hebei Natural Science Foundation, China (No. E2011202013)；High School of Hebei Science and Technology Research Youth Foundation, China(No. Q2012083).

Rong Xian, born in 1965, male, Dr, Prof.

Correspondence to Zhang Jianxin，E-mail:[email protected].

Seismic Behavior of Specially Shaped Column Joints with X-Shaped Reinforcement*

Rong Xian (戎贤)1, 2, Zhang Jianxin (张健新)1, 2, Li Yanyan (李艳艳)1, 2

(1. School of Civil Engineering, Hebei University of Technology, Tianjin 300401, China;

2. Civil Engineering Technology Research Center of Hebei Province, Tianjin 300401, China)

© Tianjin University and Springer-Verlag Berlin Heidelberg 2013

Abstract：To investigate the seismic behavior of specially shaped column joints with X-shaped reinforcement, twogroups of specimens with or without X-shaped reinforcement in joint core region were tested under constant axial compression load and low reversed cyclic loading, which imitated low to moderate earthquake force. The seismic be-havior of specially shaped column joints with X-shaped reinforcement in terms of bearing capacity, displacement, duc-tility, hysteretic curve, stiffness degradation and energy dissipation was studied and compared to that without X-shaped reinforcement in joint core region. With the damage estimation model, the accumulated damage was analyzed.The shearing capacity formula of specially shaped column joints reinforced by X-shaped reinforcement was proposedwith a simple form. The test results show that X-shaped reinforcement is an effective measure for improving the seis-mic behavior of specially shaped column joints including deformation behavior, ductility and hysteretic characteristic. All specimens were damaged with gradual stiffness degeneration. In addition, X-shaped reinforcement in the joint core region is an effective way to lighten the degree of cumulated damage. The good seismic performance obtained from the specially shaped column joint with X-shaped reinforcement can be used in engineering applications. The test value is higher than the calculated value, which indicates that the formula is safe for the design of specially shaped columnjoints. Keywords：specially shaped column; joint; low cyclic loading; X-shaped reinforcement; seismic behavior

The reinforcement concrete structure with specially shaped column, which possesses a series of advantages such as satisfactory architectural functions and good eco-nomic and social profit, is applied more and more widely in China. The reinforced concrete beam-column joint, which suffers from complex forces, is a weak part in earthquake-resistant engineering structure[1]. However, the joint of specially shaped column is weaker than that of rectangular column due to the small area of joint core, dense steel bar distribution and vibrating insufficiency during construction process. Therefore, the joint of spe-cially shaped column is much more likely to be damaged in earthquake. Besides, the joint of specially shaped col-umn cannot meet the seismic requirement, which limits the story height and application of the structure with specially shaped columns. Many experimental studies and theoreti-cal analyses on the joints with specially shaped columns have been performed[2-7]. However, little research has been done on the seismic behavior of specially shaped column

joint reinforced with X-shaped reinforcement, particu-larly subjected to low cyclic loading. Furthermore, owing to the lack of experimental results, none of the current X-shaped reinforcement codes or guidelines has given any recommendations on the seismic design of specially shaped column. In addition, compared to fiber, X-shaped reinforcement is more convenient in the construction process. Therefore, in this study the feasibility of X-shaped reinforcement used in specially shaped column joints was investigated under low cyclic loading. To im-prove the weak part of joints, four half-scale specimens with or without X-shaped reinforcement in joint core re-gion were studied under low cyclic loading.

1 Experimental program

1.1 Specimen design Four half-scale specially shaped column joints were

abstracted from the existing building in Kunming. The

Rong Xian et al: Seismic Behavior of Specially Shaped Column Joints with X-Shaped Reinforcement

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specimens had the same section dimension. One group was the interior joints of specially shaped columns. In the group, the specimen of J-＋X was reinforced by X-shaped reinforcement in joint core region and J-＋ was not reinforced. The other group was the exterior joints of

specially shaped columns. In the group, the specimen of J-TX was reinforced by X-shaped reinforcement in joint core region and J-T was not reinforced. Details of the specimens are shown in Fig. 1.

(a)J-＋ (b) J-T

Fig.1 Details of specimens (unit: mm) 1.2 Properties of materials

The strength grade of concrete is C50 and the pro-tective layer is of 15,mm. The average strengths were obtained from three cube specimens of 150 mm×150 mm× 150 mm and three cylinder specimens of 150 mm×150 mm ×300 mm. The cube compressive strength value (fcu) of concrete used in specimens is about 51.6,MPa, the axis compressive strength value (fc) of concrete used in specimens is 31.6,MPa, and the elastic module is 33.5 GPa. The grade of longitudinal bar in beams and columns is HRB400 and the grade of stirrups HPB235. The

strengths of longitudinal bars and stirrups were tested. The mechanical properties of reinforcement are shown in Tab.1.

Tab.1 Mechanical properties of reinforcement Material Yield strength fy /MPa Ultimate strength fu /MPa

8 295 449

18 445 613

22 480 623

1.3 Test setup and loading procedure The loading test setup is shown in Fig. 2. Each

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specimen was subjected to the constant vertical load and low reversed cyclic loading which imitated low to mod-erate earthquake force. The vertical load, imposed on the top of specially shaped column, remained unchanged. The force imposed on the interior joint by a vertical hy-draulic jack is 350,kN and that on the exterior joint is 250,kN. The low reversed cyclic loading was applied to the end of the beams by using tension-pressure jack.

The loading procedure was controlled by load-

displacement, which was controlled by load before the yield of specimen and by deflection after the yield of specimen[8]. At each loading level, the loading was cy-cled once under the condition of force, and then cycled three times based on integer times of yield displacement under the condition of displacement. The failure of specimen did not occur until the load value dropped by 85% of the maximum load. The loading procedure used at the end of beam is shown in Fig. 3.

(a)J-＋ (b) J-T

Fig.2 Test setup

Fig.3 Loading procedure

2 Experimental results and analysis

2.1 Damage characteristics The failure patterns are shown in Fig. 4. The oblique cracks of J-＋ X and J-TX with X-

shaped reinforcement in joint core region were relatively fewer and the crack spacing and width were smaller than those of J-＋ and J-T without X-shaped reinforcement. When the specimen failed, the concrete peeled slightly at the end of beam and in the core zone of joint in J-＋X and J-TX. The oblique crack width on the web of J-＋X was larger than that of J-TX. It can be seen from the final damage that the concrete peeled seriously at the end of beam and in the core zone of joint in J-＋and J-T. It is

indicated that X-shaped reinforcement has an important effect on confining the occurrence and extension of shear crack, confining the cracking of concrete protective coat-ing of joint core and preventing concrete from failing. The damage characteristics of joints with specially shaped columns reinforced by X-shaped reinforcement in the core region were improved significantly. 2.2 Bearing capacity, displacement and ductility

The values of cracking load, yield load, ultimate load, cracking displacement, yield displacement, ultimate displacement, failure displacement and ductility coeffi-cient of four joints are listed in Tab.2. Bearing capacity is an important indicator for struc-tural seismic performance. The averages of cracking load, yield load and ultimate load of J-＋X are about 13%, 45% and 27% higher than those of J-＋, respectively, which can be attributed to the X-shaped reinforcement in the core zone of interior joint. The displacement of J-＋X is higher than that of J-＋, especially the average ultimate displacement of J-＋X is 15.27 mm higher than that of J-＋. It is indicated that the X-shaped reinforcement in the interior joint core improves deformation property sig-nificantly. The average cracking load of J-TX is about 24% higher than that of J-T, but the averages of the yield


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(a)J-＋X (b) J-＋

(c) J-TX (d) J-T

Fig.4 Failure patterns

Tab.2 Bearing capacity, displacement and ductility coefficient of joints Load/kN Displacement/mm

Specimen Loading

direction Cracking Yield Ultimate Cracking Yield Ultimate Failure

Ductility

coefficient

Positive 40.50 78.50 87.00 6.97 15.82 44.76 61.60 3.89

Negative 39.50 70.00 81.00 7.93 18.12 51.03 60.17 3.32 J-＋X

Average 40.00 74.25 84.00 7.45 16.97 47.89 60.88 3.61

Positive 37.50 45.40 58.00 7.32 10.63 28.76 38.35 3.61

Negative 33.00 56.85 74.50 7.01 16.30 36.47 63.01 3.87 J-＋

Average 35.25 51.13 66.25 7.17 13.47 32.62 50.66 3.74

Positive 39.00 75.00 85.00 5.89 14.45 24.90 － 3.51

Negative 40.00 74.00 84.00 7.85 15.22 42.26 － 3.34 J-TX

Average 39.50 74.50 84.50 6.87 14.84 33.58 － 3.43

Positive 30.00 80.00 86.00 4.17 17.61 46.78 51.22 2.91

Negative 30.00 79.00 92.00 3.85 16.83 33.83 48.79 2.90 J-T

Average 30.00 79.50 89.00 4.01 17.22 40.31 50.01 2.91

load and the ultimate load are hardly improved. The duc-tility is very important for ensuring ductile response and assessing deformation capacity. In Tab.2, ductility coeffi-cient is a ratio of yield displacement to failure displace-ment. The yield displacement is determined by area method. The failure displacement is the displacement when the load in load-displacement curve falls off to 85% of the ultimate load. The research shows that the value of structural displacement ductility coefficient is within the range of 3—5 to ensure enough curvature ductility of structural components for the anti-seismic structure [9]. The average displacement ductility coefficient of J-T is

smaller than 3, which indicates that the ductility of exte-rior joint with X-shaped reinforcement is 15% higher than that without X-shaped reinforcement. The displacement ductility coefficient of interior joint with specially shaped columns is within the range of 3.32—3.89, which is very good. 2.3 Hysteretic characteristics

The hysteretic curves of load-displacement can re-flect seismic behavior. The gathered hysteretic curves of reversed cyclic loading versus displacement at the end of beam for four specimens are shown in Fig.5.


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(a)J-＋X

(b) J-＋

(c) J-TX

(d) J-T

Fig.5 Hysteretic curves of load-displacement

It can be seen from Fig.5 that at the beginning the hysteretic curve is in the form of spindle shape, then gradually develops into bow shape and a flex point turns up. After the yield of steel, the total displacement in-creases continuously while the force does not change much with the increase of times of cyclic loading. The slope of loading curve becomes lower and lower in each

loading process. The unloading curve is relatively abrupt at the beginning and then slowly becomes flat with the increase of unloading. There is residual defor-mation in specimens after unloading to zero. With the increase of times of cyclic loading and unloading, the residual deformation increases continuously. With the increase of time, the slopes of hysteretic curves in the same direction controlled by the same level of dis-placement decrease. It is shown that the specimens ex-perienced stiffness degenerations under the cyclic load-ing. However, the joint of specially shaped column without X-shaped reinforcement in the core region shows good hysteretic performance at the early stage, but the force descends fast at the later stage. In the whole process, the degradation of hysteretic curve of specimens with X-shaped reinforcement becomes slower, the area of hysteretic loop gradually becomes fuller, the deformation capacity is larger and the hyster-etic performance has greater improvement than those without X-shaped reinforcement.

2.4 Stiffness degeneration Stiffness is also an important indicator for structural

seismic performance. The stiffness degeneration of speci-mens under low reversed cyclic loading can be estimated by loop-cyclic stiffness [8], which is a ratio of load to dis-placement of loading cycle. The curves of stiffness de-generation are shown in Fig. 6.

Fig.6 Curves of stiffness degeneration

Comparison of the curves of stiffness degeneration of four joints with specially shaped columns shows that the rule of stiffness degeneration and the speed of stiff-ness degeneration of the four specimens are basically the same. Stiffness degeneration is fast at first, and then gradually becomes slow. In the whole process, stiffness degenerates gradually and equally. The joints of specially shaped columns with X-shaped reinforcement in the core zone achieve a greater improvement of stiffness degen-eration. Moreover, the stiffness degeneration of interior


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joints is much slower than that of exterior joints. 2.5 Energy dissipation capacity

The more the energy of specimen dissipates through plastic deformation, the better the specimen duc-tility will be. The total area in load-displacement hyster-

etic curve shows the energy dissipation capacity of speci-men, which can be expressed by equivalent viscous damping coefficient he

[10]. The equivalent viscous damp-ing coefficients at each stage are listed in Tab.3.

Tab.3 Equivalent viscous damping coefficients J-＋X J-＋ J-TX J-T

Load/kN he Load/kN he Load/kN he Load/kN he

15.75 0.186,3 — — 21.00 0.071,9 — —

36.25 0.097,7 37.75 0.059,2 41.00 0.073,8 40.50 0.081,9

50.50 0.079,7 46.00 0.071,0 48.50 0.053,7 69.00 0.070,8

81.00 0.132,9 61.50 0.143,2 76.50 0.102,4 84.00 0.165,9

84.00 0.170,5 65.50 0.166,8 82.00 0.131,5 88.00 0.191,2

67.75 0.295,2 61.25 0.156,2 81.50 0.137,6 84.00 0.199,9

— — 35.00 0.261,7 84.00 0.158,1 30.00 0.217,6

The larger the equivalent viscous damping coeffi-cient is, the better the energy dissipation capacity will be. From the equivalent viscous damping coefficients of two interior joints with specially shaped columns, it can be seen that the total amount of dissipated energy with X-shaped reinforcement in the core zone of interior joints is higher than that without X-shaped reinforcement, which indicates that the interior joints of specially shaped col-umns with X-shaped reinforcement in the core zone achieve a greater improvement of energy dissipation. However, the energy dissipation of exterior joints of spe-cially shaped columns with X-shaped reinforcement is hardly improved.

3 Accumulated damage

The damage estimation model can reflect the accu-mulated damage characteristics of energy dissipation, stiffness degeneration and intensity degradation of con-crete structure in deformation process under low cyclic loading. According to the principle of energy dissipation

and the load-displacement hysteretic curves of rein-forcement concrete structure, the damage estimation model was set up under low cyclic loading, with the power worked by external force as initial scalar under the ideal state without injuries. The accumulated damage degree of structure was expressed by the accumulated damage index Dcy under any cycle [11]. The actual damage degree of joints can be divided into five injury stages according to the accumulated dam-age index. When the accumulated damage index is within the range of 0—0.2, the joint is basically intact. When the index is within the range of 0.2—0.4, the joint is slightly injured and the crack width is no more than 0.2 mm. When the index is within the range of 0.4—0.6, the joint is mediumly injured and the crack width is 0.2 mm to the yield of specimen. When the index is within the range of 0.6—0.9, the load is from yield to failure and the joint is damaged seriously. When the accumulated damage index is over 0.9, the joint collapses[11]. The accumulated dam-age indexes of joints at the five stages are listed in Tab.4.

Tab.4 Accumulated damage indexes of joints at five stages Beginning cracking 0.2 mm cracking Yield state Limited state Failure state

Specimen Fcr /kN Dcr F0.2 /kN D0.2 Fy /kN Dy Fmax /kN Dmax Fu /kN Du

J-＋X 40.00 0.01 78.30 0.58 74.25 0.42 84.00 0.69 67.80 0.87

J-＋ 35.25 0.02 46.00 0.38 51.13 0.53 66.25 0.73 56.60 0.93

J-TX 39.50 0.08 77.00 0.57 74.50 0.46 84.50 0.67 — —

J-T 30.00 0.06 51.00 0.39 79.50 0.51 89.00 0.79 66.50 0.95

It can be seen from Tab.4 that the accumulated dam-

age index at the main loading stage of specimens basi-cally conforms to the five injury stages. However, the accumulated damage index at the stage of 0.2 mm crack-

ing of specimens with X-shaped reinforcement in the core zone is bigger than those in yield state. It is shown that X-shaped reinforcement can delay the cracking of concrete and the development of crack width. After the


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yield of specimen, the crack width of joint core will ex-tend to 0.2 mm. After the yield of joint with specially shaped columns, the accumulated damage of specimen with X-shaped reinforcement in the core region is smaller than that without X-shaped reinforcement. It is demon-strated that X-shaped reinforcement in the core region of joint can lighten the degree of accumulated damage of joints with specially shaped columns and be good for structural seismic performance.

4 Shearing capacity

The shearing capacity formula of joint can be ex-pressed as j c sV V V (1)

where Vj is the shearing capacity of specially shaped col-umn joint; Vc is the shearing capacity of concrete; Vs is the shearing capacity of stirrup.

According to the technical specification for concrete structures with specially shaped columns (JGJ149—2006)[12], the resistance of shearing capacity in the joint region can be expressed as

c N f h t j jc

0.31.1 (1 )

NV f b h

f A (2)

yv svj

s 0( )b s

f AV h - a

s (3)

where N is the design value of axial force; A is the sec-tional area of specimen; fc is the design value of axial tensile strength of concrete; ft is the design value of ten-sile strength of concrete; bj and hj are effective thickness and height in joint core section; N is axial compression

ratio influence coefficient; f is flange influence coeffi-cient; h is sectional height influence coefficient; fyv is the design value of shearing strength of stirrup; Asvj is the sectional area of stirrup; s is stirrup space; 0bh is effective section height; sa is the resultant force of longitudinal steel in tension to the near section.

The resistance consists of concrete, stirrup and X-shaped reinforcement[13] for joint reinforced by X-shaped reinforcement, namely

j c s xV V V V (4)

x x yx2 sinV A f θ (5)

where Vx , Ax and fyx are the shearing capacity, sectional area and tensile strength of X-shaped reinforcement, re-spectively; θ is the angle between X-shaped reinforce-ment and horizontal surface.

The enhancement of specially shaped column joints with X-shaped reinforcement can approximate to the half of increment of shearing capacity of joint for stirrup in-teracting with X-shaped reinforcement. The proposed formula of specially shaped column joints with X-shaped reinforcement is put forward.

j N f h t j jRE c

1 0.3[1.1 (1 )

NV f b h

r f A ≤

yv svj0 x yx( ) 2 sin ]b s

f Ah - a A f θ

s (6)

where REr is the seismic adjustment coefficient of shear-ing capacity.

The measured value of mechanical properties is brought into Eq.(6) and the test value can be obtained according to the experimental data of load and displace-ment. Therefore, the values of calculation and test, Vcal and Vtest , can be obtained as shown in Tab.5.

Tab.5 Test values and calculated values of shearing capacity of joint Specimen Vc /kN Vs /kN Vx /kN Vcal /kN Vtest /kN Vtest / Vcal

J-＋ 128.75 229.43 — 358.18 525.41 1.47

J-＋X 128.75 229.43 42.90 401.08 669.43 1.67

J-T 128.75 93.32 — 222.07 294.00 1.32

J-TX 128.75 93.32 42.90 264.97 279.62 1.06

The ratios of test value to calculated value of interior joint J-＋and J-＋X are 1.47 and 1.67, and those of exte-rior joint J-T and J-TX are 1.32 and 1.06, respectively. The proposed formula is safe for the design of specially shaped column joints. Especially, the safety margin of interior joint is higher than that of exterior joint.

5 Conclusions

From the analysis of test on joints of specially shaped columns reinforced by X-shaped reinforcement under low reversed cyclic loading, the following conclu-


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sions can be drawn. (1) The joints of specially shaped columns with X-shaped reinforcement in the core region show a tremen-dous increase in ductility. The ductility of exterior joint with X-shaped reinforcement is 15% higher than that without X-shaped reinforcement. Moreover, X-shaped reinforcement contributes much more to the improvement the bearing capacity and deformation behavior of interior joints. (2) It can be seen from the curve of stiffness de-generation that stiffness degeneration is delayed for the effect of X-shaped reinforcement in joint core region of specially shaped columns. Moreover, the stiffness degen-eration of interior joints is much slower than that of exte-rior joints.

(3) The results of equivalent viscous damping coef-ficient indicate that the interior joints of specially shaped columns with X-shaped reinforcement in the core region achieve a greater improvement of energy dissipation, while the energy dissipation of exterior joints of specially shaped columns with X-shaped reinforcement is hardly improved.

(4) The analysis of accumulated damage by the damage estimation model demonstrates that the accumu-lated damage of specimen with X-shaped reinforcement in joint core region is smaller than that without X-shaped reinforcement after the yield of specially shaped column joints. Therefore, X-shaped reinforcement in joint core region can lighten the degree of accumulated damage of specially shaped column joints.

(5) According to the resistance of concrete, stirrup and X-shaped reinforcement, the shearing capacity for-mula of specially shaped column joints reinforced by X-shaped reinforcement is proposed based on the technical specification for concrete structures with specially shaped columns(JGJ149—2006). The formula form is simple and can be used to calculate the shearing capacity of spe-cially shaped column joints reinforced by X-shaped rein-forcement.

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(Editor: Zhao Yang)

Seismic behavior of specially shaped column joints with X-shaped reinforcement

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